diff --git a/.gitignore b/.gitignore index 5169bee31..5a89396d1 100644 --- a/.gitignore +++ b/.gitignore @@ -11,6 +11,12 @@ *.o *.obj +# Thingi10K dataset +extras/Thingi10K/* + +# Output file +*/output_log_fin.txt + # Precompiled Headers *.gch *.pch diff --git a/.vscode/settings.json b/.vscode/settings.json index 378812de1..f405b86b0 100644 --- a/.vscode/settings.json +++ b/.vscode/settings.json @@ -113,7 +113,12 @@ "format": "cpp", "numbers": "cpp", "ranges": "cpp", - "stop_token": "cpp" + "stop_token": "cpp", + "csetjmp": "cpp", + "cuchar": "cpp", + "propagate_const": "cpp", + "scoped_allocator": "cpp", + "filesystem": "cpp" }, "C_Cpp.clang_format_fallbackStyle": "google", "editor.formatOnSave": true, @@ -150,4 +155,4 @@ }, "python.formatting.provider": "none", "clang-format.executable": "clang-format", -} \ No newline at end of file +} diff --git a/extras/.gitignore b/extras/.gitignore new file mode 100644 index 000000000..63400aa2d --- /dev/null +++ b/extras/.gitignore @@ -0,0 +1,2 @@ +*.csv +*.txt \ No newline at end of file diff --git a/extras/CMakeLists.txt b/extras/CMakeLists.txt index 27824f270..8489bcb11 100644 --- a/extras/CMakeLists.txt +++ b/extras/CMakeLists.txt @@ -39,7 +39,12 @@ if(MANIFOLD_EXPORT) endif() if(BUILD_TEST_CGAL) - add_executable(perfTestCGAL perf_test_cgal.cpp) + add_executable(perfTestCGAL perf_test_cgal.cpp ${PROJECT_SOURCE_DIR}/../samples/src/menger_sponge.cpp) + target_include_directories(perfTestCGAL + PUBLIC ${PROJECT_SOURCE_DIR}/../samples/include + ) + target_link_libraries(perfTestCGAL manifold) + target_link_libraries(perfTestCGAL meshIO) find_package(CGAL REQUIRED COMPONENTS Core) find_package(Boost REQUIRED COMPONENTS thread) target_compile_definitions(perfTestCGAL PRIVATE CGAL_USE_GMPXX) diff --git a/extras/GLB_Files/1750623.glb b/extras/GLB_Files/1750623.glb new file mode 100644 index 000000000..029b53b8b Binary files /dev/null and b/extras/GLB_Files/1750623.glb differ diff --git a/extras/GLB_Files/1750623.stl b/extras/GLB_Files/1750623.stl new file mode 100644 index 000000000..c898df139 Binary files /dev/null and b/extras/GLB_Files/1750623.stl differ diff --git a/extras/GLB_Files/1750623_hull1.glb b/extras/GLB_Files/1750623_hull1.glb new file mode 100644 index 000000000..d7ae75c6f Binary files /dev/null and b/extras/GLB_Files/1750623_hull1.glb differ diff --git a/extras/GLB_Files/1750623_hull1_hull2.glb b/extras/GLB_Files/1750623_hull1_hull2.glb new file mode 100644 index 000000000..e7b82dc7d Binary files /dev/null and b/extras/GLB_Files/1750623_hull1_hull2.glb differ diff --git a/extras/GLB_Files/1750623_hull2.glb b/extras/GLB_Files/1750623_hull2.glb new file mode 100644 index 000000000..ffe08d462 Binary files /dev/null and b/extras/GLB_Files/1750623_hull2.glb differ diff --git a/extras/GLB_Files/18points.bin b/extras/GLB_Files/18points.bin new file mode 100644 index 000000000..a69510972 Binary files /dev/null and b/extras/GLB_Files/18points.bin differ diff --git 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time_column = f'Time{algorithm}' + # print(row) + if type(row[time_column]) is str: + time_value = float(row[time_column].split()[0]) + else: + time_value=float(row[time_column]) + # Checking if the time value is not empty and less than the current fastest time + if time_value and time_value < fastest_time: + fastest_algorithm = algorithm + fastest_time = time_value + if fastest_algorithm: + algorithm_counts[fastest_algorithm] += 1 + +for algorithm, count in algorithm_counts.items(): + print(f'Algorithm {algorithm}: {count} times fastest') + diff --git a/extras/diff.py b/extras/diff.py new file mode 100644 index 000000000..96b6511a3 --- /dev/null +++ b/extras/diff.py @@ -0,0 +1,36 @@ +import pandas as pd + +file_path = 'normalized_output.csv' +df = pd.read_csv(file_path) + +# List of base columns to check against +columns_to_check = ['VolHull', 'AreaHull'] +# List of suffixes to check +suffixes = ['_hull2', '_CGAL'] + +# Dictionary to hold filenames and implementations with significant differences for each base column +files_with_diff = {col: [] for col in columns_to_check} + +for base in columns_to_check: + for suffix in suffixes: + col_name = f"{base}{suffix}" + if col_name in df.columns: + # Check for 1% difference + difference = (df[col_name] - 1.0).abs() > 0.01 + if difference.any(): + for index in df[difference].index: + filename = df.loc[index, 'Filename'] + files_with_diff[base].append((filename, col_name)) + print(filename) + print(f"{base} : {df.loc[index,base]}") + print(f"{col_name} : {df.loc[index,col_name]}") + +# Saving output to separate files based on the base being compared +for base in columns_to_check: + output_filename = f'files_with_differences_{base}.txt' + with open(output_filename, 'w') as file: + for filename, implementation in files_with_diff[base]: + file.write(f"{filename},{implementation}\n") + print(f"Filenames with more than 1% difference in {base} saved to '{output_filename}'.") + +print("Check complete.") diff --git a/extras/merge.py b/extras/merge.py new file mode 100644 index 000000000..1bac73b35 --- /dev/null +++ b/extras/merge.py @@ -0,0 +1,138 @@ +import pandas as pd + +filenames=[] +# merged_data = {} +def parse_csv_and_merge(csv_files, output_file='merged_data.csv'): + """ + Merges CSV files, handling multiline entries and various error conditions. + + Args: + csv_files (list): List of tuples containing (filename, implementation_name). + output_file (str, optional): Name of the output CSV file. Defaults to 'merged_data.csv'. + """ + + # merged_data = pd.DataFrame(columns=['Filename']) + merged_data={} + is_multiline = False + multiline_data = [] + curr_file="" + for file, implementation in csv_files: + print(f"Starting File : {file}") + try: + df = pd.read_csv(file) + except FileNotFoundError: + print(f"Error: File '{file}' not found. Skipping...") + continue + + for i, row in df.iterrows(): + if is_multiline: + # Handling multiline entries (Before standard algorithm call) + if 'After standard algorithm call' in row.values[0]: + is_multiline = True + continue + elif row.values[1] == "Error": + row.fillna(0, inplace=True) + row['Status'] = 'Error' + row.values[0]= curr_file + row.values[1] = 0 + is_multiline=False + filename = row['Filename'] + if filename not in merged_data: + merged_data[filename] = row.to_dict() + else: + for col in df.columns: + if col != 'Filename' and not pd.isna(row[col]): + merged_data[filename][col+"_"+implementation] = row[col] + elif row.values[0] == "Invalid Output by algorithm": + is_multiline = True + continue + else: + is_multiline = False + prev_item=curr_file + filenames.append(curr_file) + temp_item=row.values[0] + temp_len=row.values.size + for i in range(1,temp_len): + # print(temp_item) + temp_item=row.values[i-1] + row.values[i-1]=prev_item + prev_item=temp_item + # print(row) + filename = row['Filename'] + if filename not in merged_data: + merged_data[filename] = row.to_dict() + else: + for col in df.columns: + if col != 'Filename' and not pd.isna(row[col]): + merged_data[filename][col+"_"+implementation] = row[col] + else: + # Handling single-line entries or first line of multiline entries + # Checking for timeout or error + if pd.isna(row['VolManifold']): + if (row['VolHull']=="Timeout"): + # if 'Timeout' in row['Status']: + row['VolHull']=0 + row['VolManifold'] = 0 + row.fillna(0, inplace=True) + row['Status'] = 'Timeout' + elif 'Error' in row['Status']: + row.fillna(0, inplace=True) + row['Status'] = 'Error' + elif (row['VolHull'] == "Error"): + row.fillna(0, inplace=True) + row['Status'] = 'Error' + pass + filename = row['Filename'] + if filename not in merged_data: + merged_data[filename] = row.to_dict() + else: + for col in df.columns: + if col != 'Filename' and not pd.isna(row[col]): + merged_data[filename][col+"_"+implementation] = row[col] + continue + # Converting Series to df for renaming columns + if 'Before standard algorithm call' in row.values[1]: + if row.values[2] == "Timeout": + row.fillna(0, inplace=True) + row['Status'] = 'Timeout' + row['VolHull']=0 + row['VolManifold'] = 0 + filename = row['Filename'] + if filename not in merged_data: + merged_data[filename] = row.to_dict() + else: + for col in df.columns: + if col != 'Filename' and not pd.isna(row[col]): + merged_data[filename][col+"_"+implementation] = row[col] + continue + is_multiline = True + curr_file=row.values[0] + else: + if (row['VolManifold']=="timeout: the monitored command dumped core"): + row.fillna(0, inplace=True) + row['VolManifold']=0 + row['VolHull'] = 0 + row['Status'] = 'Error' + filename = row['Filename'] + if filename not in merged_data: + merged_data[filename] = row.to_dict() + else: + # print(merged_data[filename]) + for col in df.columns: + if col != 'Filename' and not pd.isna(row[col]): + merged_data[filename][col+"_"+implementation] = row[col] + + # multiline_data.append(row.tolist()) + # print(merged_data) + + if not merged_data: + print("Warning: No valid data found in any CSV files.") + return + + # Creating df from the dictionary to store the merged data + merged_data = pd.DataFrame.from_dict(merged_data, orient='index') + + merged_data.to_csv(output_file, index=False) + +csv_files = [('Hull1.csv','hull1'),('Hull2.csv', 'hull2'),('Hull3.csv', 'hull3'),('Hull4.csv', 'hull4'),('Hull5.csv', 'hull5'), ('CGAL.csv', 'CGAL')] +parse_csv_and_merge(csv_files) diff --git a/extras/normalize.py b/extras/normalize.py new file mode 100644 index 000000000..d9e64e28c --- /dev/null +++ b/extras/normalize.py @@ -0,0 +1,43 @@ +import pandas as pd + +file_path = 'merged_data.csv' +df = pd.read_csv(file_path) + +time_columns = [col for col in df.columns if 'Time' in col] +for col in time_columns: + df[col] = df[col].str.replace(' sec', '').astype(float) + +# List of base columns to normalize against +base_columns = ['VolManifold', 'VolHull', 'AreaManifold', 'AreaHull', 'ManifoldTri', 'HullTri', 'Time'] +# List of suffixes to normalize +suffixes = ['_hull2', '_hull3', '_hull4', '_hull5','_CGAL'] +# for suffix in suffixes : +# For time metric avoiding cases with time less than 0.001 seconds +df = df[(df['Time'] > 0.001)] +# Normalize the columns and check for zero base values +stl_files_with_diff = [] + +for base in base_columns: + base_col = base + if base_col in df.columns: + for suffix in suffixes: + col_name = f"{base}{suffix}" + if col_name in df.columns: + # Checking if base column is zero and suffix column is not zero + zero_base_nonzero_suffix = (df[base_col] == 0) & (df[col_name] != 0) + if zero_base_nonzero_suffix.any(): + raise ValueError(f"Error: {base_col} is zero while {col_name} is not zero in row(s): {df[zero_base_nonzero_suffix].index.tolist()}") + + # Setting col_name column in df to 1 if both are zero + both_zero = (df[base_col] == 0) & (df[col_name] == 0) + df.loc[both_zero, col_name] = 1 + + # Normalizing the column while handling division by zero + df[col_name] = df[col_name] / df[base_col].replace({0: 1}) + + df[base_col] = 1.0 + + +df.to_csv('normalized_output.csv', index=False) + + diff --git a/extras/perf_test_cgal.cpp b/extras/perf_test_cgal.cpp index 562511425..709e811d1 100644 --- a/extras/perf_test_cgal.cpp +++ b/extras/perf_test_cgal.cpp @@ -15,14 +15,26 @@ #include #include #include +#include #include +#include #include +#include #include #include +#include +#include + #include "manifold.h" +#include "meshIO.h" +#include "samples.h" +#include +#include // For string manipulation +using namespace std; +using namespace glm; using namespace manifold; // Epick = Exact predicates Inexact constructions. Seems fair to use to compare @@ -54,7 +66,13 @@ void manifoldToCGALSurfaceMesh(Manifold &manifold, TriangleMesh &cgalMesh) { } } -int main(int argc, char **argv) { +void computeCGALConvexHull(const std::vector &points, + TriangleMesh &hullMesh) { + CGAL::convex_hull_3(points.begin(), points.end(), hullMesh); +} + +// Performance test for CGAL (original main function) +void perfTestCGAL() { for (int i = 0; i < 8; ++i) { Manifold sphere = Manifold::Sphere(1, (8 << i) * 4); Manifold sphere2 = sphere.Translate(glm::vec3(0.5)); @@ -76,3 +94,365 @@ int main(int argc, char **argv) { << " sec" << std::endl; } } + +// Prints the volume and area of the manifold, the convex hull of the manifold, +// and the CGAL implementations. +void PrintVolArea(Manifold &manfiold_obj, TriangleMesh &manifoldMesh, + TriangleMesh &hullMesh, Manifold &hullManifold) { + // std::cout << CGAL::Polygon_mesh_processing::volume(manifoldMesh) << ","; + // std::cout << CGAL::Polygon_mesh_processing::volume(hullMesh) << ","; + // std::cout << CGAL::Polygon_mesh_processing::area(manifoldMesh) << ","; + // std::cout << CGAL::Polygon_mesh_processing::area(hullMesh) << ","; + // std::cout << std::distance(manifoldMesh.faces_begin(),manifoldMesh.faces_end()) + // << ","; + // std::cout << std::distance(hullMesh.faces_begin(), hullMesh.faces_end()) + // << ","; + std::cout << manfiold_obj.GetProperties().volume + << ","; + std::cout << hullManifold.GetProperties().volume + << ","; + std::cout << manfiold_obj.GetProperties().surfaceArea + << ","; + std::cout << hullManifold.GetProperties().surfaceArea + << ","; + std::cout << manfiold_obj.NumTri() << ","; + std::cout << hullManifold.NumTri() << ","; +} + +void PrintManifold(Manifold input, Manifold (Manifold::*hull_func)() const) { + TriangleMesh cgalInput; + // manifoldToCGALSurfaceMesh(input, cgalInput); + // std::vector points; + // for (const auto &vert : cgalInput.vertices()) { + // points.push_back(cgalInput.point(vert)); + // } + + // Convex Hull + TriangleMesh hullMesh; + auto start = std::chrono::high_resolution_clock::now(); + // computeCGALConvexHull(points, hullMesh); + Manifold hullManifold = (input.*hull_func)(); + auto end = std::chrono::high_resolution_clock::now(); + // Manifold hullManifold; + // Manifold hullManifold2 = hullManifold.Hull2(); + PrintVolArea(input, cgalInput, hullMesh, hullManifold); + // PrintVolArea(input, cgalInput, hullMesh, hullManifold2); + // Manifold Fin21 = hullManifold2 - hullManifold; + // Manifold Fin12 = hullManifold - hullManifold2; + std::chrono::duration elapsed = end - start; + // ExportMesh("1750623.glb", Fin.GetMesh(), {}); + // ExportMesh("39202_hull2_hull1.glb", Fin21.GetMesh(), {}); + // ExportMesh("39202_hull1_hull2.glb", Fin12.GetMesh(), {}); + // ExportMesh("39202_hull1.glb", hullManifold.GetMesh(), {}); + // ExportMesh("39202_hull2.glb", hullManifold2.GetMesh(), {}); + std::cout << elapsed.count() << " sec" ; +} + +// Constructs a Menger Sponge, and tests the convex hull implementation on it +// (you can pass the specific hull implementation to be tested). Comparing the +// volume and surface area with CGAL implementation, for various values of +// rotation +void MengerTestHull(Manifold (Manifold::*hull_func)() const, float rx, float ry, + float rz) { + Manifold sponge = MengerSponge(4); + sponge = sponge.Rotate(rx, ry, rz); + PrintManifold(sponge, hull_func); +} + +// Constructs a high quality sphere, and tests the convex hull implementation on +// it (you can pass the specific hull implementation to be tested). Comparing +// the volume and surface area with CGAL implementation +void SphereTestHull(Manifold (Manifold::*hull_func)() const) { + Manifold sphere = Manifold::Sphere(1, 6000); + sphere = sphere.Translate(glm::vec3(0.5)); + PrintManifold(sphere, hull_func); +} + +void RunThingi10K(Manifold (Manifold::*hull_func)() const) { + std::string folderPath = "../extras/Thingi10K/raw_meshes"; + std::string logFilePath = "../extras/output_log.txt"; + + // Create an ofstream object to write to a temporary file + std::ofstream logFile(logFilePath); + if (!logFile) { + std::cerr << "Error opening log file: " << logFilePath << std::endl; + return; + } + + // Redirect std::cout to the log file + std::streambuf *originalCoutBuffer = std::cout.rdbuf(); + std::streambuf *originalCerrBuffer = std::cerr.rdbuf(); + std::cout.rdbuf(logFile.rdbuf()); + std::cerr.rdbuf(logFile.rdbuf()); + // Iterate through the directory + for (const auto &entry : std::filesystem::directory_iterator(folderPath)) { + if (entry.is_regular_file() && (entry.path().filename() == "74463.stl" || + entry.path().filename() == "286163.stl" || + entry.path().filename() == "49911.stl" || + entry.path().filename() == "81313.obj" || + entry.path().filename() == "77942.stl")) { + } else if (entry.is_regular_file()) { + std::cout << entry.path().filename() << std::endl; + auto inputMesh = ImportMesh(entry.path(), 1); + Manifold inputManifold = Manifold(inputMesh); + PrintManifold(inputManifold, hull_func); + } + } + std::cout.rdbuf(originalCoutBuffer); + std::cerr.rdbuf(originalCerrBuffer); + + // Close the log file + logFile.close(); +} + +bool runHullAlgorithm(std::vector& pts) { + + std::ostringstream errBuffer; + std::streambuf* originalCerr = std::cerr.rdbuf(errBuffer.rdbuf()); + + bool hasError = false; + + try { + Manifold output = Manifold::Hull(pts); + } catch (...) { + hasError = true; + } + + // Restore the original std::cerr + std::cerr.rdbuf(originalCerr); + + if (!errBuffer.str().empty()) { + std::cerr << "Captured error: " << errBuffer.str() << std::endl; + hasError = true; + } + + return hasError; +} + +bool runHullAlgorithm2(std::vector& pts) { + + + try { + Manifold output = Manifold::Hull(pts); + Manifold output2 = Manifold::Hull2(pts); + if (output.GetProperties().volume - output2.GetProperties().volume > 200 || output.GetProperties().volume - output2.GetProperties().volume < -200) { + std::cout << "Volume difference: " << output.GetProperties().volume - output2.GetProperties().volume << std::endl; + return true; + } + else + { + return false; + } + } catch (...) { + return false; + } + +} + +void savePointsToFile( const std::vector& points,const string& filename) { + ofstream outfile(filename); + + if (outfile.is_open()) { + outfile << points.size() << endl; + outfile << fixed << setprecision(10); // Set precision to 15 decimal places + for (const glm::vec3& point : points) { + outfile << point.x << " " << point.y << " " << point.z << endl; + } + + outfile.close(); + cout << "Points saved to file: " << filename << endl; + } else { + cerr << "Error opening file for writing: " << filename << endl; + } +} + + +void saveBinaryData(const std::vector& data, const std::string& filename) { + std::ofstream outFile(filename, std::ios::binary); + if (!outFile) { + std::cerr << "Error opening file for writing!" << std::endl; + return; + } + for (const glm::vec3& vec : data) { + outFile.write(reinterpret_cast(&vec), sizeof(glm::vec3)); + } + outFile.close(); +} + +std::vector readBinaryData(const std::string& filename) { + std::ifstream inFile(filename, std::ios::binary); + if (!inFile) { + std::cerr << "Error opening file for reading!" << std::endl; + return {}; + } + std::vector data; + glm::vec3 vec; + while (inFile.read(reinterpret_cast(&vec), sizeof(glm::vec3))) { + data.push_back(vec); + } + inFile.close(); + return data; +} + +std::vector loadPointsFromFile(const string& filename) { + ifstream infile(filename); + vector points; + + if (infile.is_open()) { + int numPoints; + infile >> numPoints; + + for (int i = 0; i < numPoints; ++i) { + string line; + getline(infile, line); // Read entire line + + stringstream ss(line); + float x, y, z; + + ss >> x >> y >> z; + + points.push_back(glm::vec3(x, y, z)); + } + + infile.close(); + cout << "Points loaded from file: " << filename << endl; + } else { + cerr << "Error opening file for reading: " << filename << endl; + } + + return points; +} + + +std::vector getRandomSubset(const std::vector& pts, int size) { + std::vector subset; + + std::random_device rd; + std::mt19937 gen(rd()); + + std::vector shuffled_points = pts; + std::shuffle(shuffled_points.begin(), shuffled_points.end(), gen); + + subset.assign(shuffled_points.begin(), shuffled_points.begin() + size); + + return subset; +} + +std::vector getRandomSubset2(const std::vector& pts, const std::vector& required_pts, int size) { + std::vector subset; + + // Ensure the required points are part of the subset + subset.insert(subset.end(), required_pts.begin(), required_pts.end()); + + // Calculate the number of remaining points needed + int remaining_size = size - required_pts.size(); + if (remaining_size <= 0) { + return std::vector(subset.begin(), subset.begin() + size); + } + + // Initialize random number generator + std::random_device rd; + std::mt19937 gen(rd()); + + // Create a list of points excluding the required points + std::vector remaining_points; + for (const auto& pt : pts) { + if (std::find(required_pts.begin(), required_pts.end(), pt) == required_pts.end()) { + remaining_points.push_back(pt); + } + } + + // Shuffle the remaining points + std::shuffle(remaining_points.begin(), remaining_points.end(), gen); + + // Add the required number of points from the shuffled list to the subset + subset.insert(subset.end(), remaining_points.begin(), remaining_points.begin() + remaining_size); + + return subset; +} + +std::vector narrowDownPoints(const std::vector& points, int initialSize) { + std::vector prev_subset = points; + Manifold Hull1 = Manifold::Hull(points); + Manifold Hull2 = Manifold::Hull2(points); + // std::vector saved_points = (Hull1-Hull2).GetMesh().vertPos; + // std::cout << "Saved Size" << saved_points.size() << std::endl; + std::vector subset = getRandomSubset(points, initialSize); + // std::vector subset = getRandomSubset2(points,saved_points, initialSize); + + int step = 0; + while (subset.size() > 5) { + + if (runHullAlgorithm2(subset)) { + // If errors occur, narrow down further + // savePointsToFile(subset, "points_step_" + std::to_string(step) + ".txt"); + saveBinaryData(subset, "points_step_" + std::to_string(step) + ".bin"); + // Manifold temp = Manifold::Hull(subset); + // ExportMesh("Horizon_hull_" + std::to_string(step) + ".glb", temp.GetMesh(), {}); + std::cout << "Step " << step << ": " << subset.size() << " points\n"; + prev_subset = subset; + subset = getRandomSubset(subset, subset.size() / 2); // Halve the subset size + // subset = getRandomSubset2(subset,saved_points, subset.size() / 2); // Halve the subset size + } + else + { + subset=getRandomSubset(prev_subset,prev_subset.size() / 2); + // subset=getRandomSubset2(prev_subset, saved_points,prev_subset.size() / 2); + } + step++; + } + + return subset; +} + + +int main(int argc, char **argv) { + // perfTestCGAL(); + // SphereTestHull(Manifold::Hull); + // MengerTestHull(Manifold::Hull, 1, 2, 3); + + // std::cout << argv[1] << std::endl; + + // Narrowing down points + // auto inputMesh = ImportMesh(argv[1], 1); + // Manfiold inputManifold = Manifold(inputMesh); + // inputMesh = inputManifold.GetMesh(); + // std::vector problematicPoints = narrowDownPoints(inputMesh.vertPos, inputMesh.vertPos.size()); + + // M2 + // std::vector narrowed_points = readBinaryData("points_step_265052.bin"); + // std::vector problematicPoints = narrowDownPoints(narrowed_points, narrowed_points.size()); + + + // // Print the problematic points (if any) + // std::cout << "Problematic points causing errors:\n"; + // for (const auto& p : problematicPoints) { + // std::cout << "(" << p.x << ", " << p.y << ", " << p.z << ")\n"; + // } + + // Rendering the points + + std::vector narrowed_points = readBinaryData("points_step_108368.bin"); + Manifold HorizonMesh = Manifold::Hull(narrowed_points); + Manifold HorizonMesh2 = Manifold::Hull2(narrowed_points); + for (auto pts : HorizonMesh.GetMesh().vertPos) + { + std::cout << pts.x << "," << pts.y << "," << pts.z << std::endl; + } + std::cout << std::endl; + for (auto pts : HorizonMesh2.GetMesh().vertPos) + { + std::cout << pts.x << "," << pts.y << "," << pts.z << std::endl; + } + ExportMesh("HorizonMeshhope1.glb", HorizonMesh.GetMesh(), {}); + ExportMesh("HorizonMeshhope2.glb", HorizonMesh2.GetMesh(), {}); + std::cout << "HorizonMeshhope1 volume: " << HorizonMesh.GetProperties().volume << std::endl; + std::cout << "HorizonMeshhope2 volume: " << HorizonMesh2.GetProperties().volume << std::endl; + // auto inputMesh = ImportMesh(argv[1], 1); + // Manifold temp = Manifold::Hull(inputMesh.vertPos); + // Manifold inputManifold = Manifold(inputMesh); + // PrintManifold(inputManifold, &Manifold::Hull6); + + + // RunThingi10K(&Manifold::Hull4); +} diff --git a/extras/plot.py b/extras/plot.py new file mode 100644 index 000000000..78d6cb973 --- /dev/null +++ b/extras/plot.py @@ -0,0 +1,69 @@ +import pandas as pd +import matplotlib.pyplot as plt + +file_path = 'normalized_output.csv' +df = pd.read_csv(file_path) + +# Filtering out rows where VolHull_hull2 is 0 (Timeout cases) +df = df[df['VolHull_hull2'] != 0] + +# Exclude rows where the absolute difference between any two columns is greater than 0.01% Used to look at the minute trends +df = df[((df['VolHull_CGAL'] - df['VolHull']).abs() < 0.0001) & ((df['VolHull_CGAL'] - df['VolHull_hull2']).abs() < 0.0001) & ((df['VolHull'] - df['VolHull_hull2']).abs() < 0.0001)] +print(df) + +# Plotting +plt.plot(df.index, df['VolHull_CGAL'], label='VolHull_CGAL',marker='o') +plt.plot(df.index, df['VolHull_hull2'], label='VolHull_hull2',marker='o') +plt.plot(df.index, df['VolHull'], label='VolHull',marker='o') +plt.xlabel('Index') +plt.ylabel('Volume') +plt.title('Volume Comparison') +plt.legend() +plt.show() + +#Scatter Plot + +plt.scatter(df['AreaHull_CGAL'], df['VolHull_CGAL'], label='VolHull_CGAL', marker='o') +plt.scatter(df['AreaHull_hull2'], df['VolHull_hull2'], label='VolHull_hull2', marker='o') +plt.scatter(df['AreaHull'], df['VolHull'], label='VolHull', marker='o') + +plt.xlabel('AreaHull') +plt.ylabel('Volume') +plt.title('Volume vs AreaHull Comparison') +plt.legend() +plt.show() + + +file_path = 'normalized_output.csv' +df = pd.read_csv(file_path) + +# Filtering out rows where AreaHull_hull2 is 0 (Timeout cases) +df = df[df['VolHull_hull2'] != 0] + +# Exclude rows where the absolute difference between any two columns is less than 0.01% Used to look at the outlier trends +df = df[((df['VolHull_CGAL'] - df['VolHull']).abs() > 0.0001) | ((df['VolHull_CGAL'] - df['VolHull_hull2']).abs() > 0.0001) | ((df['VolHull'] - df['VolHull_hull2']).abs() > 0.0001)] +print(df) + +# Plotting +plt.plot(df.index, df['VolHull_CGAL'], label='VolHull_CGAL',marker='o') +plt.plot(df.index, df['VolHull_hull2'], label='VolHull_hull2',marker='o') +plt.plot(df.index, df['VolHull'], label='VolHull',marker='o') +plt.xlabel('Index') +plt.ylabel('Volume') +plt.title('Volume Comparison') +plt.legend() +plt.show() + +#ScatterPlot +plt.scatter(df['AreaHull_CGAL'], df['VolHull_CGAL'], label='VolHull_CGAL', marker='o') +plt.scatter(df['AreaHull_hull2'], df['VolHull_hull2'], label='VolHull_hull2', marker='o') +plt.scatter(df['AreaHull'], df['VolHull'], label='VolHull', marker='o') + +plt.xlabel('AreaHull') +plt.ylabel('Volume') +plt.title('Volume vs AreaHull Comparison') +plt.legend() +plt.show() + +#Storing the output to the csv +df.to_csv('diff.csv', index=False) \ No newline at end of file diff --git a/extras/run.sh b/extras/run.sh new file mode 100755 index 000000000..45caf75eb --- /dev/null +++ b/extras/run.sh @@ -0,0 +1,40 @@ +#!/bin/bash + +# Go to manifold/extras directory and run the command as `./run.sh ../build/extras/perfTestCGAL {path_to_dataset_folder} {name_of_csv}` +# example ./run.sh ../build/extras/perfTestCGAL ./Thingi10K/raw_meshes/ Hull4.csv + +# Checking if the correct number of arguments is provided +if [ "$#" -ne 3 ]; then + echo "Usage: $0 " + exit 1 +fi + +EXECUTABLE=$1 +INPUT_FOLDER=$2 +OUTPUT_CSV=$3 +TIME_LIMIT=10m # time limit in minutes +RAM_LIMIT=6000 # Memory limit in MB + +# Initializing the headers +echo "Filename,VolManifold,VolHull,AreaManifold,AreaHull,ManifoldTri,HullTri,Time,Status," > $OUTPUT_CSV + +# Iterate over all files in the input folder +for INPUT_FILE in "$INPUT_FOLDER"/*; do + FILE_NAME=$(basename "$INPUT_FILE") + + # Run the EXECUTABLE with the specified argument, time limit, and used to capture the output + OUTPUT=$(ulimit -v $((RAM_LIMIT * 1024)); timeout $TIME_LIMIT "$EXECUTABLE" "$INPUT_FILE" 2>&1) + STATUS=$? + + # Checking if the EXECUTABLE timed out + if [ $STATUS -eq 124 ]; then + STATUS="Timeout" + elif [ $STATUS -ne 0 ]; then + STATUS="Error" + else + STATUS="Success" + fi + + # Adding the result to the output file + echo "\"$FILE_NAME\",$OUTPUT,\"$STATUS\"" >> $OUTPUT_CSV +done diff --git a/extras/stats.py b/extras/stats.py new file mode 100644 index 000000000..768602873 --- /dev/null +++ b/extras/stats.py @@ -0,0 +1,51 @@ +import pandas as pd + +file_path = 'normalized_output.csv' +df = pd.read_csv(file_path) + +# Columns for statistics calculation +columns = ['VolHull', 'AreaHull', 'HullTri', 'Time'] +# Columns suffixes to use +suffixes = ['', '_hull2', '_hull3', '_hull4','_hull5', '_CGAL'] + +# Function to calculate statistics for each base and implementation +def calculate_stats(column, status,suffix): + filtered_df = df[(df['Status'+suffix] == status) & ~df[column].isnull()] + # filtered_df = df[(df['Status'+suffix] == status) & ~df[column].isnull() & (df['Time'+suffix] > 0.001) & (df['Time'] > 0.001)] + success_count = filtered_df.shape[0] + + if success_count > 0: + mean_val = filtered_df[column].mean() + median_val = filtered_df[column].median() + mode_val = filtered_df[column].mode().iloc[0] if not filtered_df[column].mode().empty else None + max_val = filtered_df[column].max() + min_val = filtered_df[column].min() + else: + mean_val = median_val = mode_val = max_val = min_val = None + + return mean_val, median_val, mode_val, max_val, min_val, success_count + +stats_dict = {} + +# Calculating stats for each column and their suffixes +for base in columns: + for suffix in suffixes: + col_name = f"{base}{suffix}" + if col_name in df.columns: + mean_val, median_val, mode_val, max_val, min_val, success_count = calculate_stats(col_name, 'Success',suffix) + stats_dict[col_name] = { + 'mean': mean_val, + 'median': median_val, + 'mode': mode_val, + 'max': max_val, + 'min': min_val, + 'Success_Count': success_count + } + +# Converting the stats dictionary to a df for better visualization +stats_df = pd.DataFrame(stats_dict).T + +stats_df.to_csv('statistics_output.csv') + +print("Statistics calculation complete. Output saved to 'statistics_output.csv'.") +print(stats_df) diff --git a/src/manifold/CMakeLists.txt b/src/manifold/CMakeLists.txt index 109aa3cc5..66069005b 100644 --- a/src/manifold/CMakeLists.txt +++ b/src/manifold/CMakeLists.txt @@ -13,7 +13,18 @@ # limitations under the License. project (manifold) +# Include FetchContent module to fetch external projects. +include(FetchContent) +# Declare the Fast-Quick-Hull library. +FetchContent_Declare( + qhull_lib + GIT_REPOSITORY https://github.com/andreacasalino/Fast-Quick-hull.git + GIT_TAG master +) + +# Fetch the declared library. +FetchContent_MakeAvailable(qhull_lib) file(GLOB_RECURSE SOURCE_FILES CONFIGURE_DEPENDS *.cpp) add_library(${PROJECT_NAME} ${SOURCE_FILES}) @@ -22,9 +33,9 @@ target_include_directories(${PROJECT_NAME} PUBLIC $) target_link_libraries(${PROJECT_NAME} PUBLIC utilities cross_section sdf - PRIVATE collider polygon ${MANIFOLD_INCLUDE} quickhull + PRIVATE collider polygon ${MANIFOLD_INCLUDE} quickhull Fast-Quick-Hull ) - +# target_link_libraries(${PROJECT_NAME} Fast-Quick-Hull) target_compile_options(${PROJECT_NAME} PRIVATE ${MANIFOLD_FLAGS}) target_compile_features(${PROJECT_NAME} diff --git a/src/manifold/include/manifold.h b/src/manifold/include/manifold.h index fa9a0a45a..3300580ee 100644 --- a/src/manifold/include/manifold.h +++ b/src/manifold/include/manifold.h @@ -287,8 +287,23 @@ class Manifold { */ ///@{ Manifold Hull() const; + Manifold Hull2() const; static Manifold Hull(const std::vector& manifolds); static Manifold Hull(const std::vector& pts); + static Manifold Hull2(const std::vector& manifolds); + static Manifold Hull2(const std::vector& pts); + Manifold Hull3() const; + static Manifold Hull3(const std::vector& manifolds); + static Manifold Hull3(const std::vector& pts); + Manifold Hull4() const; + static Manifold Hull4(const std::vector& manifolds); + static Manifold Hull4(const std::vector& pts); + Manifold Hull5() const; + static Manifold Hull5(const std::vector& manifolds); + static Manifold Hull5(const std::vector& pts); + Manifold Hull6() const; + static Manifold Hull6(const std::vector& manifolds); + static Manifold Hull6(const std::vector& pts); ///@} /** @name Testing hooks diff --git a/src/manifold/src/manifold.cpp b/src/manifold/src/manifold.cpp index 4b9c46a2f..e6d9ea85f 100644 --- a/src/manifold/src/manifold.cpp +++ b/src/manifold/src/manifold.cpp @@ -15,14 +15,26 @@ #include #include #include +#include #include "QuickHull.hpp" #include "boolean3.h" #include "csg_tree.h" #include "impl.h" #include "par.h" + +#define ENABLE_VHACD_IMPLEMENTATION 1 +#include "VHACD.h" +#define QUICKHULL_IMPLEMENTATION +#include "quickhull2.h" #include "tri_dist.h" +#define CONVHULL_3D_USE_SINGLE_PRECISION +#define CONVHULL_3D_ENABLE +#include "convhull_3d.h" + +#include "quickhull.hpp" + namespace { using namespace manifold; using namespace thrust::placeholders; @@ -292,7 +304,8 @@ MeshGL Manifold::GetMeshGL(glm::ivec3 normalIdx) const { // Duplicate verts with different props std::vector vert2idx(impl.NumVert(), -1); std::vector> vertPropPair(impl.NumVert()); - out.vertProperties.reserve(numVert * static_cast(out.numProp)); + out.vertProperties.reserve(static_cast(numVert) * + static_cast(out.numProp)); for (int run = 0; run < out.runOriginalID.size(); ++run) { for (int tri = out.runIndex[run] / 3; tri < out.runIndex[run + 1] / 3; @@ -937,11 +950,466 @@ Manifold Manifold::Hull(const std::vector& pts) { return Manifold(mesh); } +/** + * Compute the convex hull of a set of points using VHACD's Convex Hull + * Implementation. If the given points are fewer than 4, or they are all + * coplanar, an empty Manifold will be returned. + * + * @param pts A vector of 3-dimensional points over which to compute a convex + * hull. + */ +Manifold Manifold::Hull2(const std::vector& pts) { + ZoneScoped; + const int numVert = pts.size(); + if (numVert < 4) return Manifold(); + + std::vector vertices(numVert); + for (int i = 0; i < numVert; i++) { + vertices[i].mX = pts[i].x; + vertices[i].mY = pts[i].y; + vertices[i].mZ = pts[i].z; + } + + // Compute the Convex Hull + VHACD::ConvexHull hull(vertices, double(0.0000001)); + + Mesh mesh; + + auto& vlist = hull.GetVertexPool(); + if (!vlist.empty()) { + mesh.vertPos.resize(vlist.size()); + for (int i = 0; i < vlist.size(); i++) { + mesh.vertPos[i] = {vlist[i].GetX(), vlist[i].GetY(), vlist[i].GetZ()}; + } + } + + auto outputVertices = hull.GetList(); + mesh.triVerts.reserve(outputVertices.size()); + for (std::list::const_iterator node = + outputVertices.begin(); + node != outputVertices.end(); ++node) { + const VHACD::ConvexHullFace& face = *node; + mesh.triVerts.push_back( + {face.m_index[0], face.m_index[1], face.m_index[2]}); + } + + return Manifold(mesh); +} + +/** + * Compute the convex hull of a set of points using Karimnaaji's Quick Hull + * Implementation. If the given points are fewer than 4, or they are all + * coplanar, an empty Manifold will be returned. + * + * @param pts A vector of 3-dimensional points over which to compute a convex + * hull. + */ +Manifold Manifold::Hull3(const std::vector& pts) { + ZoneScoped; + const int numVert = pts.size(); + if (numVert < 4) return Manifold(); + qh_vertex_t* input_pts = new qh_vertex_t[numVert]; + // std::vector input_pts(numVert); + // Let's assume for now pts[i].x is float too + // pts.size() ideally returns unsigned int + for (int i = 0; i < numVert; i++) { + input_pts[i].x = static_cast(pts[i].x); + input_pts[i].y = static_cast(pts[i].y); + input_pts[i].z = static_cast(pts[i].z); + } + // Generic Hash Function, can try to find the optimum hash function to + // improve effeciency + + // struct qh_vertex_hash { + // std::size_t operator()(const qh_vertex_t& vertex) const { + // // Custom hash function for qh_vertex_t + // return std::hash()(vertex.x) ^ + // std::hash()(vertex.y) ^ + // std::hash()(vertex.z); + // } + // }; + + // struct qh_vertex_equal { + // bool operator()(const qh_vertex_t& lhs, const qh_vertex_t& rhs) const { + // // Custom equality function for qh_vertex_t + // return std::tie(lhs.x, lhs.y, lhs.z) == std::tie(rhs.x, + // rhs.y,rhs.z); + // } + // }; + + struct qh_vertex_compare { + bool operator()(const qh_vertex_t& lhs, const qh_vertex_t& rhs) const { + if (lhs.x != rhs.x) return lhs.x < rhs.x; + if (lhs.y != rhs.y) return lhs.y < rhs.y; + return lhs.z < rhs.z; + } + }; + + // We can also use unordered_map with custom hash and equality functions + // std::unordered_map + // vertexIndexMap; + + std::map vertexIndexMap; + + // Converting input pts to a format that the algorithm accepts + std::vector uniqueVertices; + + // std::cout << pts.size() << std::endl; + + // Standard Algorithm Call + float epsilon; + qh_context_t context; + std::cout << "Before standard algorithm call" << std::endl; + epsilon = qh__compute_epsilon(input_pts, pts.size()); + qh__init_context(&context, input_pts, pts.size()); + qh__remove_vertex_duplicates(&context, epsilon); + + // The function just below gives the segfault error for larger cases, and we + // need to look into how we can fix it. + qh__build_tetrahedron(&context, epsilon); + + unsigned int failurestep = 0; + qh__build_hull(&context, epsilon); + int valid = qh__test_hull(&context, epsilon, 0); + + // I tried running this function directly without the valid check to see if + // itworks, but even this segfaults, so I included the valid check as it helps + // identify where the issue might be + qh__free_context(&context); + std::cout << "After standard algorithm call" << std::endl; + if (!valid) { + std::cout << "Invalid Output by algorithm" << std::endl; + return Manifold(); + } + qh_mesh_t mesh_quick = qh_quickhull3d(input_pts, pts.size()); + delete[] input_pts; + // Iterating through the vertices array to create a map of the vertices, since + // the vertices array has the vertices not indices, and the indices array in + // the algorithm isn't correct, I looked into the code the indices array is + // essentially just assigning indices[i]=i always + for (int i = 0; i < mesh_quick.nvertices; i++) { + qh_vertex_t vertex = mesh_quick.vertices[i]; + if (vertexIndexMap.find(vertex) == vertexIndexMap.end()) { + vertexIndexMap[vertex] = uniqueVertices.size(); + uniqueVertices.push_back(vertex); + } + } + + // Standard checks to prevent segfaults + + // If no unique vertices were present + if (uniqueVertices.empty()) { + // std::cerr << "Error: No unique vertices found." << std::endl; + qh_free_mesh(mesh_quick); + return Manifold(); + } + + // In case the indices or number of indices was empty + if (mesh_quick.indices == nullptr || mesh_quick.nindices <= 0) { + qh_free_mesh(mesh_quick); + return Manifold(); + } + + // Inputting the output in the format expected by our Mesh Function + const unsigned int numTris = mesh_quick.nindices / 3; + Mesh mesh; + mesh.vertPos.reserve(uniqueVertices.size()); + mesh.triVerts.reserve(numTris); + + for (const auto& vertex : uniqueVertices) { + mesh.vertPos.push_back({vertex.x, vertex.y, vertex.z}); + } + + for (unsigned int i = 0; i < mesh_quick.nindices; i += 3) { + unsigned int idx1 = vertexIndexMap[mesh_quick.vertices[i]]; + unsigned int idx2 = vertexIndexMap[mesh_quick.vertices[i + 1]]; + unsigned int idx3 = vertexIndexMap[mesh_quick.vertices[i + 2]]; + mesh.triVerts.push_back({idx1, idx2, idx3}); + } + qh_free_mesh(mesh_quick); + return Manifold(mesh); + // return Manifold(); +} + +/** + * Compute the convex hull of a set of points using VHACD's Convex Hull + * Implementation. If the given points are fewer than 4, or they are all + * coplanar, an empty Manifold will be returned. + * + * @param pts A vector of 3-dimensional points over which to compute a convex + * hull. + */ +Manifold Manifold::Hull4(const std::vector& pts) { + ZoneScoped; + const int numVert = pts.size(); + if (numVert < 4) return Manifold(); + + ch_vertex* vertices; + vertices = (ch_vertex*)malloc(numVert * sizeof(ch_vertex)); + for (int i = 0; i < numVert; i++) { + vertices[i].x = pts[i].x; + vertices[i].y = pts[i].y; + vertices[i].z = pts[i].z; + } + + int* faceIndices = NULL; + int nFaces; + convhull_3d_build(vertices, numVert, &faceIndices, &nFaces); + free(vertices); + + Mesh mesh; + mesh.vertPos = pts; + // std::cout << nFaces << std::endl; + mesh.triVerts.reserve(nFaces); + // int index=0; + for (int i = 0; i < nFaces; i++) { + const int j = i * 3; + // std::cout << "ok" << std::endl; + // std::cout << faceIndices[j] << " " << faceIndices[j+1] << " " << + // faceIndices[j+2] << std::endl; index++; + mesh.triVerts.push_back( + {faceIndices[j], faceIndices[j + 1], faceIndices[j + 2]}); + } + // std::cout << index << std::endl; + free(faceIndices); + + return Manifold(mesh); +} + +/** + * Compute the convex hull of a set of points using VHACD's Convex Hull + * Implementation. If the given points are fewer than 4, or they are all + * coplanar, an empty Manifold will be returned. + * + * @param pts A vector of 3-dimensional points over which to compute a convex + * hull. + */ +Manifold Manifold::Hull5(const std::vector& pts) { + ZoneScoped; + const int numVert = pts.size(); + + if (numVert < 4) return Manifold(); + + using F = float; + constexpr std::size_t dim = 3; + using Points = std::vector>; + Points points; // input + for (int i = 0; i < numVert; i++) { + points.push_back({pts[i].x, pts[i].y, pts[i].z}); + } + // Generic Hash Function, can try to find the optimum hash function to + // improve effeciency + + // struct qh_vertex_hash { + // std::size_t operator()(const qh_vertex_t& vertex) const { + // // Custom hash function for qh_vertex_t + // return std::hash()(vertex.x) ^ + // std::hash()(vertex.y) ^ + // std::hash()(vertex.z); + // } + // }; + + // struct qh_vertex_equal { + // bool operator()(const qh_vertex_t& lhs, const qh_vertex_t& rhs) const { + // // Custom equality function for qh_vertex_t + // return std::tie(lhs.x, lhs.y, lhs.z) == std::tie(rhs.x, + // rhs.y,rhs.z); + // } + // }; + + struct qh_vertex_compare { + bool operator()(const glm::vec3& lhs, const glm::vec3& rhs) const { + if (lhs[0] != rhs[0]) return lhs[0] < rhs[0]; + if (lhs[1] != rhs[1]) return lhs[1] < rhs[1]; + return lhs[2] < rhs[2]; + } + }; + + // We can also use unordered_map with custom hash and equality functions + // std::unordered_map + // vertexIndexMap; + + std::map vertexIndexMap; + + // Converting input pts to a format that the algorithm accepts + std::vector uniqueVertices; + + // std::cout << pts.size() << std::endl; + const auto eps = std::numeric_limits::epsilon(); + quick_hull qh{dim, eps}; + qh.add_points(std::cbegin(points), std::cend(points)); + auto initial_simplex = qh.get_affine_basis(); + if (initial_simplex.size() < dim + 1) { + std::cout << "Degenerated input set" << std::endl; + return Manifold(); // degenerated input set + } + qh.create_initial_simplex(std::cbegin(initial_simplex), std::prev(std::cend(initial_simplex))); + qh.create_convex_hull(); + // if (!qh.check()) { + // std::cout << "Resulted structure is not convex" << std::endl; + // return Manifold(); // resulted structure is not convex (generally due to precision errors) + // } + // qh.facets_; // use as result + + int nFacesVert = qh.facets_.size(); + Mesh mesh; + mesh.vertPos = pts; + // // std::cout << nFaces << std::endl; + mesh.triVerts.reserve(nFacesVert); + for (int i = 0; i < pts.size(); i++) { + if (vertexIndexMap.find(pts[i]) == vertexIndexMap.end()) { + vertexIndexMap[pts[i]] = uniqueVertices.size(); + uniqueVertices.push_back(pts[i]); + } + } + if (uniqueVertices.empty()) { + // std::cerr << "Error: No unique vertices found." << std::endl; + std::cout << "No unique vertices found" << std::endl; + return Manifold(); + } + + // Inputting the output in the format expected by our Mesh Function + + for (auto const & facet_ : qh.facets_) { + auto const & vertices_ = facet_.vertices_; + glm::vec3 pts_temp[3]; + int temp_index=0; + int temp_index2=0; + for (auto const & vertex_ : vertices_) { + for (float const & coordinate_ : *vertex_) { + pts_temp[temp_index][temp_index2] = coordinate_; + temp_index2++; + } + temp_index2=0; + temp_index++; + } + + unsigned int idx1 = vertexIndexMap[pts_temp[0]]; + unsigned int idx2 = vertexIndexMap[pts_temp[1]]; + unsigned int idx3 = vertexIndexMap[pts_temp[2]]; + mesh.triVerts.push_back({idx1, idx2, idx3}); + } + return Manifold(mesh); + // } + + // // int index=0; + // for (int i = 0; i < nFaces; i++) { + // const int j = i * 3; + // // std::cout << "ok" << std::endl; + // // std::cout << faceIndices[j] << " " << faceIndices[j+1] << " " << + // // faceIndices[j+2] << std::endl; index++; + // mesh.triVerts.push_back( + // {faceIndices[j], faceIndices[j + 1], faceIndices[j + 2]}); + // } + // // std::cout << index << std::endl; + + // return Manifold(mesh); +} + +/** + * Compute the convex hull of a set of points. If the given points are fewer + * than 4, or they are all coplanar, an empty Manifold will be returned. + * + * @param pts A vector of 3-dimensional points over which to compute a convex + * hull. + */ + +hull::Coordinate convert_function(const glm::vec3 &vector) { + return hull::Coordinate{vector.x, vector.y, + vector.z}; +}; + +Manifold Manifold::Hull6(const std::vector& pts) { + ZoneScoped; + const int numVert = pts.size(); + if (numVert < 4) return Manifold(); + + // compute the incidences (index of the vertices in the passed points cloud, + // which delimits each facet), of the facets constituting the convex hull of + // the points + qh::ConvexHullContext context; + context.thread_pool_size = 0; + std::vector normals; + std::vector + incidences; + try{ + incidences= // qh::FacetIncidences is an array of incidences: + // std::array + qh::convex_hull(pts.begin(), pts.end(), convert_function,normals,context); + } + catch(const std::exception &e) + { + std::cerr << e.what() << std::endl; + } + Mesh mesh; + mesh.vertPos = pts; + + int numTris=incidences.size(); + mesh.triVerts.reserve(numTris); + for (int i=0;i& manifolds) { return Compose(manifolds).Hull(); } +/** + + * Compute the convex hull enveloping a set of manifolds. + * + * @param manifolds A vector of manifolds over which to compute a convex hull. + */ +Manifold Manifold::Hull2(const std::vector& manifolds) { + return Compose(manifolds).Hull2(); +} + +/** + * Compute the convex hull enveloping a set of manifolds. + * + * @param manifolds A vector of manifolds over which to compute a convex hull. + */ +Manifold Manifold::Hull3(const std::vector& manifolds) { + return Compose(manifolds).Hull3(); +} + +/** + * Compute the convex hull enveloping a set of manifolds. + * + * @param manifolds A vector of manifolds over which to compute a convex hull. + */ +Manifold Manifold::Hull4(const std::vector& manifolds) { + return Compose(manifolds).Hull4(); +} + +/** + * Compute the convex hull enveloping a set of manifolds. + * + * @param manifolds A vector of manifolds over which to compute a convex hull. + */ +Manifold Manifold::Hull5(const std::vector& manifolds) { + return Compose(manifolds).Hull5(); +} + +/** + * Compute the convex hull enveloping a set of manifolds. + * + * @param manifolds A vector of manifolds over which to compute a convex hull. + */ +Manifold Manifold::Hull6(const std::vector& manifolds) { + return Compose(manifolds).Hull6(); +} + /** * Returns the minimum gap between two manifolds. Returns a float between * 0 and searchLength. diff --git a/src/utilities/include/VHACD.h b/src/utilities/include/VHACD.h new file mode 100644 index 000000000..bcb411f63 --- /dev/null +++ b/src/utilities/include/VHACD.h @@ -0,0 +1,7010 @@ +/* Copyright (c) 2011 Khaled Mamou (kmamou at gmail dot com) + All rights reserved. + + Redistribution and use in source and binary forms, with or without + modification, are permitted provided that the following conditions are met: + + 1. Redistributions of source code must retain the above copyright notice, this + list of conditions and the following disclaimer. + + 2. Redistributions in binary form must reproduce the above copyright notice, + this list of conditions and the following disclaimer in the documentation + and/or other materials provided with the distribution. + + 3. The names of the contributors may not be used to endorse or promote products + derived from this software without specific prior written permission. + + THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND + ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED + WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE + DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE + FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR + SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER + CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, + OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE + OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + */ +#pragma once +#ifndef VHACD_H +#define VHACD_H + +// Please view this slide deck which describes usage and how the algorithm +// works. +// https://docs.google.com/presentation/d/1OZ4mtZYrGEC8qffqb8F7Le2xzufiqvaPpRbLHKKgTIM/edit?usp=sharing + +// VHACD is now a header only library. +// In just *one* of your CPP files *before* you include 'VHACD.h' you must +// declare #define ENABLE_VHACD_IMPLEMENTATION 1 This will compile the +// implementation code into your project. If you don't have this define, you +// will get link errors since the implementation code will not be present. If +// you define it more than once in your code base, you will get link errors due +// to a duplicate implementation. This is the same pattern used by ImGui and +// StbLib and other popular open source libraries. + +#define VHACD_VERSION_MAJOR 4 +#define VHACD_VERSION_MINOR 1 + +// Changes for version 4.1 +// +// Various minor tweaks mostly to the test application and some default values. + +// Changes for version 4.0 +// +// * The code has been significantly refactored to be cleaner and easier to +// maintain +// * All OpenCL related code removed +// * All Bullet code removed +// * All SIMD code removed +// * Old plane splitting code removed +// +// * The code is now delivered as a single header file 'VHACD.h' which has both +// the API +// * declaration as well as the implementation. Simply add '#define +// ENABLE_VHACD_IMPLEMENTATION 1' +// * to any CPP in your application prior to including 'VHACD.h'. Only do this +// in one CPP though. +// * If you do not have this define once, you will get link errors since the +// implementation code +// * will not be compiled in. If you have this define more than once, you are +// likely to get +// * duplicate symbol link errors. +// +// * Since the library is now delivered as a single header file, we do not +// provide binaries +// * or build scripts as these are not needed. +// +// * The old DebugView and test code has all been removed and replaced with a +// much smaller and +// * simpler test console application with some test meshes to work with. +// +// * The convex hull generation code has changed. The previous version came from +// Bullet. +// * However, the new version is courtesy of Julio Jerez, the author of the +// Newton +// * physics engine. His new version is faster and more numerically stable. +// +// * The code can now detect if the input mesh is, itself, already a convex +// object and +// * can early out. +// +// * Significant performance improvements have been made to the code and it is +// now much +// * faster, stable, and is easier to tune than previous versions. +// +// * A bug was fixed with the shrink wrapping code (project hull vertices) that +// could +// * sometime produce artifacts in the results. The new version uses a 'closest +// point' +// * algorithm that is more reliable. +// +// * You can now select which 'fill mode' to use. For perfectly closed meshes, +// the default +// * behavior using a flood fill generally works fine. However, some meshes have +// small +// * holes in them and therefore the flood fill will fail, treating the mesh as +// being +// * hollow. In these cases, you can use the 'raycast' fill option to determine +// which +// * parts of the voxelized mesh are 'inside' versus being 'outside'. Finally, +// there +// * are some rare instances where a user might actually want the mesh to be +// treated as +// * hollow, in which case you can pass in 'surface' only. +// * +// * A new optional virtual interface called 'IUserProfiler' was provided. +// * This allows the user to provide an optional profiling callback interface to +// assist in +// * diagnosing performance issues. This change was made by Danny Couture at +// Epic for the UE4 integration. +// * Some profiling macros were also declared in support of this feature. +// * +// * Another new optional virtual interface called 'IUserTaskRunner' was +// provided. +// * This interface is used to run logical 'tasks' in a background thread. If +// none is provided +// * then a default implementation using std::thread will be executed. +// * This change was made by Danny Couture at Epic to speed up the voxelization +// step. +// * + +// The history of V-HACD: +// +// The initial version was written by John W. Ratcliff and was called 'ACD' +// This version did not perform CSG operations on the source mesh, so if you +// recursed too deeply it would produce hollow results. +// +// The next version was written by Khaled Mamou and was called 'HACD' +// In this version Khaled tried to perform a CSG operation on the source +// mesh to produce more robust results. However, Khaled learned that the +// CSG library he was using had licensing issues so he started work on the +// next version. +// +// The next version was called 'V-HACD' because Khaled made the observation +// that plane splitting would be far easier to implement working in voxel space. +// +// V-HACD has been integrated into UE4, Blender, and a number of other projects. +// This new release, version4, is a significant refactor of the code to fix +// some bugs, improve performance, and to make the codebase easier to maintain +// going forward. + +#include + +#include +#include +#include +#include +#include + +namespace VHACD { + +struct Vertex { + double mX; + double mY; + double mZ; + + Vertex() = default; + Vertex(double x, double y, double z) : mX(x), mY(y), mZ(z) {} + + const double& operator[](size_t idx) const { + switch (idx) { + case 0: + return mX; + case 1: + return mY; + case 2: + return mZ; + }; + return mX; + } +}; + +struct Triangle { + uint32_t mI0; + uint32_t mI1; + uint32_t mI2; + + Triangle() = default; + Triangle(uint32_t i0, uint32_t i1, uint32_t i2) : mI0(i0), mI1(i1), mI2(i2) {} +}; + +template +class Vector3 { + public: + /* + * Getters + */ + T& operator[](size_t i); + const T& operator[](size_t i) const; + T& GetX(); + T& GetY(); + T& GetZ(); + const T& GetX() const; + const T& GetY() const; + const T& GetZ() const; + + /* + * Normalize and norming + */ + T Normalize(); + Vector3 Normalized(); + T GetNorm() const; + T GetNormSquared() const; + int LongestAxis() const; + + /* + * Vector-vector operations + */ + Vector3& operator=(const Vector3& rhs); + Vector3& operator+=(const Vector3& rhs); + Vector3& operator-=(const Vector3& rhs); + + Vector3 CWiseMul(const Vector3& rhs) const; + Vector3 Cross(const Vector3& rhs) const; + T Dot(const Vector3& rhs) const; + Vector3 operator+(const Vector3& rhs) const; + Vector3 operator-(const Vector3& rhs) const; + + /* + * Vector-scalar operations + */ + Vector3& operator-=(T a); + Vector3& operator+=(T a); + Vector3& operator/=(T a); + Vector3& operator*=(T a); + + Vector3 operator*(T rhs) const; + Vector3 operator/(T rhs) const; + + /* + * Unary operations + */ + Vector3 operator-() const; + + /* + * Comparison operators + */ + bool operator<(const Vector3& rhs) const; + bool operator>(const Vector3& rhs) const; + + /* + * Returns true if all elements of *this are greater than or equal to all + * elements of rhs, coefficient wise LE is less than or equal + */ + bool CWiseAllGE(const Vector3& rhs) const; + bool CWiseAllLE(const Vector3& rhs) const; + + Vector3 CWiseMin(const Vector3& rhs) const; + Vector3 CWiseMax(const Vector3& rhs) const; + T MinCoeff() const; + T MaxCoeff() const; + + T MinCoeff(uint32_t& idx) const; + T MaxCoeff(uint32_t& idx) const; + + /* + * Constructors + */ + Vector3() = default; + Vector3(T a); + Vector3(T x, T y, T z); + Vector3(const Vector3& rhs); + ~Vector3() = default; + + template + Vector3(const Vector3& rhs); + + Vector3(const VHACD::Vertex&); + Vector3(const VHACD::Triangle&); + + operator VHACD::Vertex() const; + + private: + std::array m_data{T(0.0)}; +}; + +typedef VHACD::Vector3 Vect3; + +struct BoundsAABB { + BoundsAABB() = default; + BoundsAABB(const std::vector& points); + BoundsAABB(const Vect3& min, const Vect3& max); + + BoundsAABB Union(const BoundsAABB& b); + + bool Intersects(const BoundsAABB& b) const; + + double SurfaceArea() const; + double Volume() const; + + BoundsAABB Inflate(double ratio) const; + + VHACD::Vect3 ClosestPoint(const VHACD::Vect3& p) const; + + VHACD::Vect3& GetMin(); + VHACD::Vect3& GetMax(); + const VHACD::Vect3& GetMin() const; + const VHACD::Vect3& GetMax() const; + + VHACD::Vect3 GetSize() const; + VHACD::Vect3 GetCenter() const; + + VHACD::Vect3 m_min{double(0.0)}; + VHACD::Vect3 m_max{double(0.0)}; +}; + +/** + * This enumeration determines how the voxels as filled to create a solid + * object. The default should be 'FLOOD_FILL' which generally works fine + * for closed meshes. However, if the mesh is not watertight, then using + * RAYCAST_FILL may be preferable as it will determine if a voxel is part + * of the interior of the source mesh by raycasting around it. + * + * Finally, there are some cases where you might actually want a convex + * decomposition to treat the source mesh as being hollow. If that is the + * case you can pass in 'SURFACE_ONLY' and then the convex decomposition + * will converge only onto the 'skin' of the surface mesh. + */ +enum class FillMode { + FLOOD_FILL, // This is the default behavior, after the voxelization step it + // uses a flood fill to determine 'inside' from 'outside'. + // However, meshes with holes can fail and create hollow results. + SURFACE_ONLY, // Only consider the 'surface', will create 'skins' with hollow + // centers. + RAYCAST_FILL, // Uses raycasting to determine inside from outside. +}; + +class IVHACD { + public: + /** + * This optional pure virtual interface is used to notify the caller of the + * progress of convex decomposition as well as a signal when it is complete + * when running in a background thread + */ + class IUserCallback { + public: + virtual ~IUserCallback(){}; + + /** + * Notifies the application of the current state of the convex decomposition + * operation + * + * @param overallProgress : Total progress from 0-100% + * @param stageProgress : Progress of the current stage 0-100% + * @param stage : A text description of the current stage we are in + * @param operation : A text description of what operation is currently + * being performed. + */ + virtual void Update(const double overallProgress, + const double stageProgress, const char* const stage, + const char* operation) = 0; + + // This is an optional user callback which is only called when running + // V-HACD asynchronously. This is a callback performed to notify the user + // that the convex decomposition background process is completed. This call + // back will occur from a different thread so the user should take that into + // account. + virtual void NotifyVHACDComplete() {} + }; + + /** + * Optional user provided pure virtual interface to be notified of warning or + * informational messages + */ + class IUserLogger { + public: + virtual ~IUserLogger(){}; + virtual void Log(const char* const msg) = 0; + }; + + /** + * An optional user provided pure virtual interface to perform a background + * task. This was added by Danny Couture at Epic as they wanted to use their + * own threading system instead of the standard library version which is the + * default. + */ + class IUserTaskRunner { + public: + virtual ~IUserTaskRunner(){}; + virtual void* StartTask(std::function func) = 0; + virtual void JoinTask(void* Task) = 0; + }; + + /** + * A simple class that represents a convex hull as a triangle mesh with + * double precision vertices. Polygons are not currently provided. + */ + class ConvexHull { + public: + std::vector m_points; + std::vector m_triangles; + + double m_volume{0}; // The volume of the convex hull + VHACD::Vect3 m_center{0, 0, 0}; // The centroid of the convex hull + uint32_t m_meshId{0}; // A unique id for this convex hull + VHACD::Vect3 mBmin; // Bounding box minimum of the AABB + VHACD::Vect3 mBmax; // Bounding box maximum of the AABB + }; + + /** + * This class provides the parameters controlling the convex decomposition + * operation + */ + class Parameters { + public: + IUserCallback* m_callback{ + nullptr}; // Optional user provided callback interface for progress + IUserLogger* m_logger{ + nullptr}; // Optional user provided callback interface for log messages + IUserTaskRunner* m_taskRunner{ + nullptr}; // Optional user provided interface for creating tasks + uint32_t m_maxConvexHulls{ + 64}; // The maximum number of convex hulls to produce + uint32_t m_resolution{400000}; // The voxel resolution to use + double m_minimumVolumePercentErrorAllowed{ + 1}; // if the voxels are within 1% of the volume of the hull, we + // consider this a close enough approximation + uint32_t m_maxRecursionDepth{10}; // The maximum recursion depth + bool m_shrinkWrap{true}; // Whether or not to shrinkwrap the voxel + // positions to the source mesh on output + FillMode m_fillMode{FillMode::FLOOD_FILL}; // How to fill the interior of + // the voxelized mesh + uint32_t m_maxNumVerticesPerCH{64}; // The maximum number of vertices + // allowed in any output convex hull + bool m_asyncACD{true}; // Whether or not to run asynchronously, taking + // advantage of additional cores + uint32_t m_minEdgeLength{ + 2}; // Once a voxel patch has an edge length of less than 4 on all 3 + // sides, we don't keep recursing + bool m_findBestPlane{ + false}; // Whether or not to attempt to split planes along the best + // location. Experimental feature. False by default. + }; + + /** + * Will cause the convex decomposition operation to be canceled early. No + * results will be produced but the background operation will end as soon as + * it can. + */ + virtual void Cancel() = 0; + + /** + * Compute a convex decomposition of a triangle mesh using float vertices and + * the provided user parameters. + * + * @param points : The vertices of the source mesh as floats in the form of + * X1,Y1,Z1, X2,Y2,Z2,.. etc. + * @param countPoints : The number of vertices in the source mesh. + * @param triangles : The indices of triangles in the source mesh in the form + * of I1,I2,I3, .... + * @param countTriangles : The number of triangles in the source mesh + * @param params : The convex decomposition parameters to apply + * @return : Returns true if the convex decomposition operation can be started + */ + virtual bool Compute(const float* const points, const uint32_t countPoints, + const uint32_t* const triangles, + const uint32_t countTriangles, + const Parameters& params) = 0; + + /** + * Compute a convex decomposition of a triangle mesh using double vertices and + * the provided user parameters. + * + * @param points : The vertices of the source mesh as floats in the form of + * X1,Y1,Z1, X2,Y2,Z2,.. etc. + * @param countPoints : The number of vertices in the source mesh. + * @param triangles : The indices of triangles in the source mesh in the form + * of I1,I2,I3, .... + * @param countTriangles : The number of triangles in the source mesh + * @param params : The convex decomposition parameters to apply + * @return : Returns true if the convex decomposition operation can be started + */ + virtual bool Compute(const double* const points, const uint32_t countPoints, + const uint32_t* const triangles, + const uint32_t countTriangles, + const Parameters& params) = 0; + + /** + * Returns the number of convex hulls that were produced. + * + * @return : Returns the number of convex hulls produced, or zero if it failed + * or was canceled + */ + virtual uint32_t GetNConvexHulls() const = 0; + + /** + * Retrieves one of the convex hulls in the solution set + * + * @param index : Which convex hull to retrieve + * @param ch : The convex hull descriptor to return + * @return : Returns true if the convex hull exists and could be retrieved + */ + virtual bool GetConvexHull(const uint32_t index, ConvexHull& ch) const = 0; + + /** + * Releases any memory allocated by the V-HACD class + */ + virtual void Clean() = 0; // release internally allocated memory + + /** + * Releases this instance of the V-HACD class + */ + virtual void Release() = 0; // release IVHACD + + // Will compute the center of mass of the convex hull decomposition results + // and return it in 'centerOfMass'. Returns false if the center of mass could + // not be computed. + virtual bool ComputeCenterOfMass(double centerOfMass[3]) const = 0; + + // In synchronous mode (non-multi-threaded) the state is always 'ready' + // In asynchronous mode, this returns true if the background thread is not + // still actively computing a new solution. In an asynchronous config the + // 'IsReady' call will report any update or log messages in the caller's + // current thread. + virtual bool IsReady() const { return true; } + + /** + * At the request of LegionFu : out_look@foxmail.com + * This method will return which convex hull is closest to the source + * position. You can use this method to figure out, for example, which + * vertices in the original source mesh are best associated with which convex + * hull. + * + * @param pos : The input 3d position to test against + * + * @return : Returns which convex hull this position is closest to. + */ + virtual uint32_t findNearestConvexHull(const double pos[3], + double& distanceToHull) = 0; + + protected: + virtual ~IVHACD() {} +}; +/* + * Out of line definitions + */ + +template +T clamp(const T& v, const T& lo, const T& hi) { + if (v < lo) { + return lo; + } + if (v > hi) { + return hi; + } + return v; +} + +/* + * Getters + */ +template +inline T& Vector3::operator[](size_t i) { + return m_data[i]; +} + +template +inline const T& Vector3::operator[](size_t i) const { + return m_data[i]; +} + +template +inline T& Vector3::GetX() { + return m_data[0]; +} + +template +inline T& Vector3::GetY() { + return m_data[1]; +} + +template +inline T& Vector3::GetZ() { + return m_data[2]; +} + +template +inline const T& Vector3::GetX() const { + return m_data[0]; +} + +template +inline const T& Vector3::GetY() const { + return m_data[1]; +} + +template +inline const T& Vector3::GetZ() const { + return m_data[2]; +} + +/* + * Normalize and norming + */ +template +inline T Vector3::Normalize() { + T n = GetNorm(); + if (n != T(0.0)) (*this) /= n; + return n; +} + +template +inline Vector3 Vector3::Normalized() { + Vector3 ret = *this; + T n = GetNorm(); + if (n != T(0.0)) ret /= n; + return ret; +} + +template +inline T Vector3::GetNorm() const { + return std::sqrt(GetNormSquared()); +} + +template +inline T Vector3::GetNormSquared() const { + return this->Dot(*this); +} + +template +inline int Vector3::LongestAxis() const { + auto it = std::max_element(m_data.begin(), m_data.end()); + return int(std::distance(m_data.begin(), it)); +} + +/* + * Vector-vector operations + */ +template +inline Vector3& Vector3::operator=(const Vector3& rhs) { + GetX() = rhs.GetX(); + GetY() = rhs.GetY(); + GetZ() = rhs.GetZ(); + return *this; +} + +template +inline Vector3& Vector3::operator+=(const Vector3& rhs) { + GetX() += rhs.GetX(); + GetY() += rhs.GetY(); + GetZ() += rhs.GetZ(); + return *this; +} + +template +inline Vector3& Vector3::operator-=(const Vector3& rhs) { + GetX() -= rhs.GetX(); + GetY() -= rhs.GetY(); + GetZ() -= rhs.GetZ(); + return *this; +} + +template +inline Vector3 Vector3::CWiseMul(const Vector3& rhs) const { + return Vector3(GetX() * rhs.GetX(), GetY() * rhs.GetY(), + GetZ() * rhs.GetZ()); +} + +template +inline Vector3 Vector3::Cross(const Vector3& rhs) const { + return Vector3(GetY() * rhs.GetZ() - GetZ() * rhs.GetY(), + GetZ() * rhs.GetX() - GetX() * rhs.GetZ(), + GetX() * rhs.GetY() - GetY() * rhs.GetX()); +} + +template +inline T Vector3::Dot(const Vector3& rhs) const { + return GetX() * rhs.GetX() + GetY() * rhs.GetY() + GetZ() * rhs.GetZ(); +} + +template +inline Vector3 Vector3::operator+(const Vector3& rhs) const { + return Vector3(GetX() + rhs.GetX(), GetY() + rhs.GetY(), + GetZ() + rhs.GetZ()); +} + +template +inline Vector3 Vector3::operator-(const Vector3& rhs) const { + return Vector3(GetX() - rhs.GetX(), GetY() - rhs.GetY(), + GetZ() - rhs.GetZ()); +} + +template +inline Vector3 operator*(T lhs, const Vector3& rhs) { + return Vector3(lhs * rhs.GetX(), lhs * rhs.GetY(), lhs * rhs.GetZ()); +} + +/* + * Vector-scalar operations + */ +template +inline Vector3& Vector3::operator-=(T a) { + GetX() -= a; + GetY() -= a; + GetZ() -= a; + return *this; +} + +template +inline Vector3& Vector3::operator+=(T a) { + GetX() += a; + GetY() += a; + GetZ() += a; + return *this; +} + +template +inline Vector3& Vector3::operator/=(T a) { + GetX() /= a; + GetY() /= a; + GetZ() /= a; + return *this; +} + +template +inline Vector3& Vector3::operator*=(T a) { + GetX() *= a; + GetY() *= a; + GetZ() *= a; + return *this; +} + +template +inline Vector3 Vector3::operator*(T rhs) const { + return Vector3(GetX() * rhs, GetY() * rhs, GetZ() * rhs); +} + +template +inline Vector3 Vector3::operator/(T rhs) const { + return Vector3(GetX() / rhs, GetY() / rhs, GetZ() / rhs); +} + +/* + * Unary operations + */ +template +inline Vector3 Vector3::operator-() const { + return Vector3(-GetX(), -GetY(), -GetZ()); +} + +/* + * Comparison operators + */ +template +inline bool Vector3::operator<(const Vector3& rhs) const { + if (GetX() == rhs.GetX()) { + if (GetY() == rhs.GetY()) { + return (GetZ() < rhs.GetZ()); + } + return (GetY() < rhs.GetY()); + } + return (GetX() < rhs.GetX()); +} + +template +inline bool Vector3::operator>(const Vector3& rhs) const { + if (GetX() == rhs.GetX()) { + if (GetY() == rhs.GetY()) { + return (GetZ() > rhs.GetZ()); + } + return (GetY() > rhs.GetY()); + } + return (GetX() > rhs.GetZ()); +} + +template +inline bool Vector3::CWiseAllGE(const Vector3& rhs) const { + return GetX() >= rhs.GetX() && GetY() >= rhs.GetY() && GetZ() >= rhs.GetZ(); +} + +template +inline bool Vector3::CWiseAllLE(const Vector3& rhs) const { + return GetX() <= rhs.GetX() && GetY() <= rhs.GetY() && GetZ() <= rhs.GetZ(); +} + +template +inline Vector3 Vector3::CWiseMin(const Vector3& rhs) const { + return Vector3(std::min(GetX(), rhs.GetX()), std::min(GetY(), rhs.GetY()), + std::min(GetZ(), rhs.GetZ())); +} + +template +inline Vector3 Vector3::CWiseMax(const Vector3& rhs) const { + return Vector3(std::max(GetX(), rhs.GetX()), std::max(GetY(), rhs.GetY()), + std::max(GetZ(), rhs.GetZ())); +} + +template +inline T Vector3::MinCoeff() const { + return *std::min_element(m_data.begin(), m_data.end()); +} + +template +inline T Vector3::MaxCoeff() const { + return *std::max_element(m_data.begin(), m_data.end()); +} + +template +inline T Vector3::MinCoeff(uint32_t& idx) const { + auto it = std::min_element(m_data.begin(), m_data.end()); + idx = uint32_t(std::distance(m_data.begin(), it)); + return *it; +} + +template +inline T Vector3::MaxCoeff(uint32_t& idx) const { + auto it = std::max_element(m_data.begin(), m_data.end()); + idx = uint32_t(std::distance(m_data.begin(), it)); + return *it; +} + +/* + * Constructors + */ +template +inline Vector3::Vector3(T a) : m_data{a, a, a} {} + +template +inline Vector3::Vector3(T x, T y, T z) : m_data{x, y, z} {} + +template +inline Vector3::Vector3(const Vector3& rhs) : m_data{rhs.m_data} {} + +template +template +inline Vector3::Vector3(const Vector3& rhs) + : m_data{T(rhs.GetX()), T(rhs.GetY()), T(rhs.GetZ())} {} + +template +inline Vector3::Vector3(const VHACD::Vertex& rhs) + : Vector3(rhs.mX, rhs.mY, rhs.mZ) { + static_assert(std::is_same::value, + "Vertex to Vector3 constructor only enabled for double"); +} + +template +inline Vector3::Vector3(const VHACD::Triangle& rhs) + : Vector3(rhs.mI0, rhs.mI1, rhs.mI2) { + static_assert(std::is_same::value, + "Triangle to Vector3 constructor only enabled for uint32_t"); +} + +template +inline Vector3::operator VHACD::Vertex() const { + static_assert(std::is_same::value, + "Vector3 to Vertex conversion only enable for double"); + return ::VHACD::Vertex(GetX(), GetY(), GetZ()); +} + +IVHACD* +CreateVHACD(); // Create a synchronous (blocking) implementation of V-HACD +IVHACD* CreateVHACD_ASYNC(); // Create an asynchronous (non-blocking) + // implementation of V-HACD + +} // namespace VHACD + +#if ENABLE_VHACD_IMPLEMENTATION +#include +#include +#include +#include +#include +#include + +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include + +#ifdef _MSC_VER +#pragma warning(push) +#pragma warning(disable : 4100 4127 4189 4244 4456 4701 4702 4996) +#endif // _MSC_VER + +#ifdef __GNUC__ +#pragma GCC diagnostic push +// Minimum set of warnings used for cleanup +// #pragma GCC diagnostic warning "-Wall" +// #pragma GCC diagnostic warning "-Wextra" +// #pragma GCC diagnostic warning "-Wpedantic" +// #pragma GCC diagnostic warning "-Wold-style-cast" +// #pragma GCC diagnostic warning "-Wnon-virtual-dtor" +// #pragma GCC diagnostic warning "-Wshadow" +#endif // __GNUC__ + +// Scoped Timer +namespace VHACD { + +class Timer { + public: + Timer() : m_startTime(std::chrono::high_resolution_clock::now()) {} + + void Reset() { m_startTime = std::chrono::high_resolution_clock::now(); } + + double GetElapsedSeconds() { + auto s = PeekElapsedSeconds(); + Reset(); + return s; + } + + double PeekElapsedSeconds() { + auto now = std::chrono::high_resolution_clock::now(); + std::chrono::duration diff = now - m_startTime; + return diff.count(); + } + + private: + std::chrono::time_point m_startTime; +}; + +class ScopedTime { + public: + ScopedTime(const char* action, VHACD::IVHACD::IUserLogger* logger) + : m_action(action), m_logger(logger) { + m_timer.Reset(); + } + + ~ScopedTime() { + double dtime = m_timer.GetElapsedSeconds(); + if (m_logger) { + char scratch[512]; + snprintf(scratch, sizeof(scratch), "%s took %0.5f seconds", m_action, + dtime); + m_logger->Log(scratch); + } + } + + const char* m_action{nullptr}; + Timer m_timer; + VHACD::IVHACD::IUserLogger* m_logger{nullptr}; +}; +BoundsAABB::BoundsAABB(const std::vector& points) + : m_min(points[0]), m_max(points[0]) { + for (uint32_t i = 1; i < points.size(); ++i) { + const VHACD::Vertex& p = points[i]; + m_min = m_min.CWiseMin(p); + m_max = m_max.CWiseMax(p); + } +} + +BoundsAABB::BoundsAABB(const VHACD::Vect3& min, const VHACD::Vect3& max) + : m_min(min), m_max(max) {} + +BoundsAABB BoundsAABB::Union(const BoundsAABB& b) { + return BoundsAABB(GetMin().CWiseMin(b.GetMin()), + GetMax().CWiseMax(b.GetMax())); +} + +bool VHACD::BoundsAABB::Intersects(const VHACD::BoundsAABB& b) const { + if ((GetMin().GetX() > b.GetMax().GetX()) || + (b.GetMin().GetX() > GetMax().GetX())) + return false; + if ((GetMin().GetY() > b.GetMax().GetY()) || + (b.GetMin().GetY() > GetMax().GetY())) + return false; + if ((GetMin().GetZ() > b.GetMax().GetZ()) || + (b.GetMin().GetZ() > GetMax().GetZ())) + return false; + return true; +} + +double BoundsAABB::SurfaceArea() const { + VHACD::Vect3 d = GetMax() - GetMin(); + return double(2.0) * + (d.GetX() * d.GetY() + d.GetX() * d.GetZ() + d.GetY() * d.GetZ()); +} + +double VHACD::BoundsAABB::Volume() const { + VHACD::Vect3 d = GetMax() - GetMin(); + return d.GetX() * d.GetY() * d.GetZ(); +} + +BoundsAABB VHACD::BoundsAABB::Inflate(double ratio) const { + double inflate = (GetMin() - GetMax()).GetNorm() * double(0.5) * ratio; + return BoundsAABB(GetMin() - inflate, GetMax() + inflate); +} + +VHACD::Vect3 VHACD::BoundsAABB::ClosestPoint(const VHACD::Vect3& p) const { + return p.CWiseMax(GetMin()).CWiseMin(GetMax()); +} + +VHACD::Vect3& VHACD::BoundsAABB::GetMin() { return m_min; } + +VHACD::Vect3& VHACD::BoundsAABB::GetMax() { return m_max; } + +inline const VHACD::Vect3& VHACD::BoundsAABB::GetMin() const { return m_min; } + +const VHACD::Vect3& VHACD::BoundsAABB::GetMax() const { return m_max; } + +VHACD::Vect3 VHACD::BoundsAABB::GetSize() const { return GetMax() - GetMin(); } + +VHACD::Vect3 VHACD::BoundsAABB::GetCenter() const { + return (GetMin() + GetMax()) * double(0.5); +} + +/* + * Relies on three way comparison, which std::sort doesn't use + */ +template +void Sort(T* const array, int elements) { + const int batchSize = 8; + int stack[1024][2]; + + stack[0][0] = 0; + stack[0][1] = elements - 1; + int stackIndex = 1; + const dCompareKey comparator; + while (stackIndex) { + stackIndex--; + int lo = stack[stackIndex][0]; + int hi = stack[stackIndex][1]; + if ((hi - lo) > batchSize) { + int mid = (lo + hi) >> 1; + if (comparator.Compare(array[lo], array[mid]) > 0) { + std::swap(array[lo], array[mid]); + } + if (comparator.Compare(array[mid], array[hi]) > 0) { + std::swap(array[mid], array[hi]); + } + if (comparator.Compare(array[lo], array[mid]) > 0) { + std::swap(array[lo], array[mid]); + } + int i = lo + 1; + int j = hi - 1; + const T pivot(array[mid]); + do { + while (comparator.Compare(array[i], pivot) < 0) { + i++; + } + while (comparator.Compare(array[j], pivot) > 0) { + j--; + } + + if (i <= j) { + std::swap(array[i], array[j]); + i++; + j--; + } + } while (i <= j); + + if (i < hi) { + stack[stackIndex][0] = i; + stack[stackIndex][1] = hi; + stackIndex++; + } + if (lo < j) { + stack[stackIndex][0] = lo; + stack[stackIndex][1] = j; + stackIndex++; + } + assert(stackIndex < int(sizeof(stack) / (2 * sizeof(stack[0][0])))); + } + } + + int stride = batchSize + 1; + if (elements < stride) { + stride = elements; + } + for (int i = 1; i < stride; ++i) { + if (comparator.Compare(array[0], array[i]) > 0) { + std::swap(array[0], array[i]); + } + } + + for (int i = 1; i < elements; ++i) { + int j = i; + const T tmp(array[i]); + for (; comparator.Compare(array[j - 1], tmp) > 0; --j) { + assert(j > 0); + array[j] = array[j - 1]; + } + array[j] = tmp; + } +} + +/* +Maintaining comment due to attribution +Purpose: + +TRIANGLE_AREA_3D computes the area of a triangle in 3D. + +Modified: + +22 April 1999 + +Author: + +John Burkardt + +Parameters: + +Input, double X1, Y1, Z1, X2, Y2, Z2, X3, Y3, Z3, the (getX,getY,getZ) +coordinates of the corners of the triangle. + +Output, double TRIANGLE_AREA_3D, the area of the triangle. +*/ +double ComputeArea(const VHACD::Vect3& p1, const VHACD::Vect3& p2, + const VHACD::Vect3& p3) { + /* + Find the projection of (P3-P1) onto (P2-P1). + */ + double base = (p2 - p1).GetNorm(); + /* + The height of the triangle is the length of (P3-P1) after its + projection onto (P2-P1) has been subtracted. + */ + double height; + if (base == double(0.0)) { + height = double(0.0); + } else { + double dot = (p3 - p1).Dot(p2 - p1); + double alpha = dot / (base * base); + + VHACD::Vect3 a = p3 - p1 - alpha * (p2 - p1); + height = a.GetNorm(); + } + + return double(0.5) * base * height; +} + +bool ComputeCentroid(const std::vector& points, + const std::vector& indices, + VHACD::Vect3& center) + +{ + bool ret = false; + if (points.size()) { + center = VHACD::Vect3(0); + + VHACD::Vect3 numerator(0); + double denominator = 0; + + for (uint32_t i = 0; i < indices.size(); i++) { + uint32_t i1 = indices[i].mI0; + uint32_t i2 = indices[i].mI1; + uint32_t i3 = indices[i].mI2; + + const VHACD::Vect3& p1 = points[i1]; + const VHACD::Vect3& p2 = points[i2]; + const VHACD::Vect3& p3 = points[i3]; + + // Compute the average of the sum of the three positions + VHACD::Vect3 sum = (p1 + p2 + p3) / 3; + + // Compute the area of this triangle + double area = ComputeArea(p1, p2, p3); + + numerator += (sum * area); + + denominator += area; + } + double recip = 1 / denominator; + center = numerator * recip; + ret = true; + } + return ret; +} + +double Determinant3x3(const std::array& matrix, + double& error) { + double det = double(0.0); + error = double(0.0); + + double a01xa12 = matrix[0].GetY() * matrix[1].GetZ(); + double a02xa11 = matrix[0].GetZ() * matrix[1].GetY(); + error += (std::abs(a01xa12) + std::abs(a02xa11)) * std::abs(matrix[2].GetX()); + det += (a01xa12 - a02xa11) * matrix[2].GetX(); + + double a00xa12 = matrix[0].GetX() * matrix[1].GetZ(); + double a02xa10 = matrix[0].GetZ() * matrix[1].GetX(); + error += (std::abs(a00xa12) + std::abs(a02xa10)) * std::abs(matrix[2].GetY()); + det -= (a00xa12 - a02xa10) * matrix[2].GetY(); + + double a00xa11 = matrix[0].GetX() * matrix[1].GetY(); + double a01xa10 = matrix[0].GetY() * matrix[1].GetX(); + error += (std::abs(a00xa11) + std::abs(a01xa10)) * std::abs(matrix[2].GetZ()); + det += (a00xa11 - a01xa10) * matrix[2].GetZ(); + + return det; +} + +double ComputeMeshVolume(const std::vector& vertices, + const std::vector& indices) { + double volume = 0; + for (uint32_t i = 0; i < indices.size(); i++) { + const std::array m = {vertices[indices[i].mI0], + vertices[indices[i].mI1], + vertices[indices[i].mI2]}; + double placeholder; + volume += Determinant3x3(m, placeholder); + } + + volume *= (double(1.0) / double(6.0)); + if (volume < 0) volume *= -1; + return volume; +} + +/* + * To minimize memory allocations while maintaining pointer stability. + * Used in KdTreeNode and ConvexHull, as both use tree data structures that rely + * on pointer stability Neither rely on random access or iteration They just + * dump elements into a memory pool, then refer to pointers to the elements All + * elements are default constructed in NodeStorage's m_nodes array + */ +template +class NodeBundle { + struct NodeStorage { + bool IsFull() const; + + T& GetNextNode(); + + std::size_t m_index; + std::array m_nodes; + }; + + std::list m_list; + typename std::list::iterator m_head{m_list.end()}; + + public: + T& GetNextNode(); + + T& GetFirstNode(); + + void Clear(); +}; + +template +bool NodeBundle::NodeStorage::IsFull() const { + return m_index == MaxBundleSize; +} + +template +T& NodeBundle::NodeStorage::GetNextNode() { + assert(m_index < MaxBundleSize); + T& ret = m_nodes[m_index]; + m_index++; + return ret; +} + +template +T& NodeBundle::GetNextNode() { + /* + * || short circuits, so doesn't dereference if m_bundle == m_bundleHead.end() + */ + if (m_head == m_list.end() || m_head->IsFull()) { + m_head = m_list.emplace(m_list.end()); + } + + return m_head->GetNextNode(); +} + +template +T& NodeBundle::GetFirstNode() { + assert(m_head != m_list.end()); + return m_list.front().m_nodes[0]; +} + +template +void NodeBundle::Clear() { + m_list.clear(); +} + +/* + * Returns index of highest set bit in x + */ +inline int dExp2(int x) { + int exp; + for (exp = -1; x; x >>= 1) { + exp++; + } + return exp; +} + +/* + * Reverses the order of the bits in v and returns the result + * Does not put fill any of the bits higher than the highest bit in v + * Only used to calculate index of ndNormalMap::m_normal when tessellating a + * triangle + */ +inline int dBitReversal(int v, int base) { + int x = 0; + int power = dExp2(base) - 1; + do { + x += (v & 1) << power; + v >>= 1; + power--; + } while (v); + return x; +} + +class Googol { +#define VHACD_GOOGOL_SIZE 4 + public: + Googol() = default; + Googol(double value); + + operator double() const; + Googol operator+(const Googol& A) const; + Googol operator-(const Googol& A) const; + Googol operator*(const Googol& A) const; + Googol operator/(const Googol& A) const; + + Googol& operator+=(const Googol& A); + Googol& operator-=(const Googol& A); + + bool operator>(const Googol& A) const; + bool operator>=(const Googol& A) const; + bool operator<(const Googol& A) const; + bool operator<=(const Googol& A) const; + bool operator==(const Googol& A) const; + bool operator!=(const Googol& A) const; + + Googol Abs() const; + Googol Floor() const; + Googol InvSqrt() const; + Googol Sqrt() const; + + void ToString(char* const string) const; + + private: + void NegateMantissa(std::array& mantissa) const; + void CopySignedMantissa( + std::array& mantissa) const; + int NormalizeMantissa( + std::array& mantissa) const; + void ShiftRightMantissa(std::array& mantissa, + int bits) const; + uint64_t CheckCarrier(uint64_t a, uint64_t b) const; + + int LeadingZeros(uint64_t a) const; + void ExtendedMultiply(uint64_t a, uint64_t b, uint64_t& high, + uint64_t& low) const; + void ScaleMantissa(uint64_t* out, uint64_t scale) const; + + int m_sign{0}; + int m_exponent{0}; + std::array m_mantissa{0}; + + public: + static Googol m_zero; + static Googol m_one; + static Googol m_two; + static Googol m_three; + static Googol m_half; +}; + +Googol Googol::m_zero(double(0.0)); +Googol Googol::m_one(double(1.0)); +Googol Googol::m_two(double(2.0)); +Googol Googol::m_three(double(3.0)); +Googol Googol::m_half(double(0.5)); + +Googol::Googol(double value) { + int exp; + double mantissa = fabs(frexp(value, &exp)); + + m_exponent = exp; + m_sign = (value >= 0) ? 0 : 1; + + m_mantissa[0] = uint64_t(double(uint64_t(1) << 62) * mantissa); +} + +Googol::operator double() const { + double mantissa = + (double(1.0) / double(uint64_t(1) << 62)) * double(m_mantissa[0]); + mantissa = + ldexp(mantissa, m_exponent) * (m_sign ? double(-1.0) : double(1.0)); + return mantissa; +} + +Googol Googol::operator+(const Googol& A) const { + Googol tmp; + if (m_mantissa[0] && A.m_mantissa[0]) { + std::array mantissa0; + std::array mantissa1; + std::array mantissa; + + CopySignedMantissa(mantissa0); + A.CopySignedMantissa(mantissa1); + + int exponentDiff = m_exponent - A.m_exponent; + int exponent = m_exponent; + if (exponentDiff > 0) { + ShiftRightMantissa(mantissa1, exponentDiff); + } else if (exponentDiff < 0) { + exponent = A.m_exponent; + ShiftRightMantissa(mantissa0, -exponentDiff); + } + + uint64_t carrier = 0; + for (int i = VHACD_GOOGOL_SIZE - 1; i >= 0; i--) { + uint64_t m0 = mantissa0[i]; + uint64_t m1 = mantissa1[i]; + mantissa[i] = m0 + m1 + carrier; + carrier = CheckCarrier(m0, m1) | CheckCarrier(m0 + m1, carrier); + } + + int sign = 0; + if (int64_t(mantissa[0]) < 0) { + sign = 1; + NegateMantissa(mantissa); + } + + int bits = NormalizeMantissa(mantissa); + if (bits <= (-64 * VHACD_GOOGOL_SIZE)) { + tmp.m_sign = 0; + tmp.m_exponent = 0; + } else { + tmp.m_sign = sign; + tmp.m_exponent = int(exponent + bits); + } + + tmp.m_mantissa = mantissa; + } else if (A.m_mantissa[0]) { + tmp = A; + } else { + tmp = *this; + } + + return tmp; +} + +Googol Googol::operator-(const Googol& A) const { + Googol tmp(A); + tmp.m_sign = !tmp.m_sign; + return *this + tmp; +} + +Googol Googol::operator*(const Googol& A) const { + if (m_mantissa[0] && A.m_mantissa[0]) { + std::array mantissaAcc{0}; + for (int i = VHACD_GOOGOL_SIZE - 1; i >= 0; i--) { + uint64_t a = m_mantissa[i]; + if (a) { + uint64_t mantissaScale[2 * VHACD_GOOGOL_SIZE] = {0}; + A.ScaleMantissa(&mantissaScale[i], a); + + uint64_t carrier = 0; + for (int j = 0; j < 2 * VHACD_GOOGOL_SIZE; j++) { + const int k = 2 * VHACD_GOOGOL_SIZE - 1 - j; + uint64_t m0 = mantissaAcc[k]; + uint64_t m1 = mantissaScale[k]; + mantissaAcc[k] = m0 + m1 + carrier; + carrier = CheckCarrier(m0, m1) | CheckCarrier(m0 + m1, carrier); + } + } + } + + uint64_t carrier = 0; + int bits = LeadingZeros(mantissaAcc[0]) - 2; + for (int i = 0; i < 2 * VHACD_GOOGOL_SIZE; i++) { + const int k = 2 * VHACD_GOOGOL_SIZE - 1 - i; + uint64_t a = mantissaAcc[k]; + mantissaAcc[k] = (a << uint64_t(bits)) | carrier; + carrier = a >> uint64_t(64 - bits); + } + + int exp = m_exponent + A.m_exponent - (bits - 2); + + Googol tmp; + tmp.m_sign = m_sign ^ A.m_sign; + tmp.m_exponent = exp; + for (std::size_t i = 0; i < tmp.m_mantissa.size(); ++i) { + tmp.m_mantissa[i] = mantissaAcc[i]; + } + + return tmp; + } + return Googol(double(0.0)); +} + +Googol Googol::operator/(const Googol& A) const { + Googol tmp(double(1.0) / A); + tmp = tmp * (m_two - A * tmp); + tmp = tmp * (m_two - A * tmp); + bool test = false; + int passes = 0; + do { + passes++; + Googol tmp0(tmp); + tmp = tmp * (m_two - A * tmp); + test = tmp0 == tmp; + } while (test && (passes < (2 * VHACD_GOOGOL_SIZE))); + return (*this) * tmp; +} + +Googol& Googol::operator+=(const Googol& A) { + *this = *this + A; + return *this; +} + +Googol& Googol::operator-=(const Googol& A) { + *this = *this - A; + return *this; +} + +bool Googol::operator>(const Googol& A) const { + Googol tmp(*this - A); + return double(tmp) > double(0.0); +} + +bool Googol::operator>=(const Googol& A) const { + Googol tmp(*this - A); + return double(tmp) >= double(0.0); +} + +bool Googol::operator<(const Googol& A) const { + Googol tmp(*this - A); + return double(tmp) < double(0.0); +} + +bool Googol::operator<=(const Googol& A) const { + Googol tmp(*this - A); + return double(tmp) <= double(0.0); +} + +bool Googol::operator==(const Googol& A) const { + return m_sign == A.m_sign && m_exponent == A.m_exponent && + m_mantissa == A.m_mantissa; +} + +bool Googol::operator!=(const Googol& A) const { return !(*this == A); } + +Googol Googol::Abs() const { + Googol tmp(*this); + tmp.m_sign = 0; + return tmp; +} + +Googol Googol::Floor() const { + if (m_exponent < 1) { + return Googol(double(0.0)); + } + int bits = m_exponent + 2; + int start = 0; + while (bits >= 64) { + bits -= 64; + start++; + } + + Googol tmp(*this); + for (int i = VHACD_GOOGOL_SIZE - 1; i > start; i--) { + tmp.m_mantissa[i] = 0; + } + // some compilers do no like this and I do not know why is that + // uint64_t mask = (-1LL) << (64 - bits); + uint64_t mask(~0ULL); + mask <<= (64 - bits); + tmp.m_mantissa[start] &= mask; + return tmp; +} + +Googol Googol::InvSqrt() const { + const Googol& me = *this; + Googol x(double(1.0) / sqrt(me)); + + int test = 0; + int passes = 0; + do { + passes++; + Googol tmp(x); + x = m_half * x * (m_three - me * x * x); + test = (x != tmp); + } while (test && (passes < (2 * VHACD_GOOGOL_SIZE))); + return x; +} + +Googol Googol::Sqrt() const { return *this * InvSqrt(); } + +void Googol::ToString(char* const string) const { + Googol tmp(*this); + Googol base(double(10.0)); + while (double(tmp) > double(1.0)) { + tmp = tmp / base; + } + + int index = 0; + while (tmp.m_mantissa[0]) { + tmp = tmp * base; + Googol digit(tmp.Floor()); + tmp -= digit; + double val = digit; + string[index] = char(val) + '0'; + index++; + } + string[index] = 0; +} + +void Googol::NegateMantissa( + std::array& mantissa) const { + uint64_t carrier = 1; + for (size_t i = mantissa.size() - 1; i < mantissa.size(); i--) { + uint64_t a = ~mantissa[i] + carrier; + if (a) { + carrier = 0; + } + mantissa[i] = a; + } +} + +void Googol::CopySignedMantissa( + std::array& mantissa) const { + mantissa = m_mantissa; + if (m_sign) { + NegateMantissa(mantissa); + } +} + +int Googol::NormalizeMantissa( + std::array& mantissa) const { + int bits = 0; + if (int64_t(mantissa[0] * 2) < 0) { + bits = 1; + ShiftRightMantissa(mantissa, 1); + } else { + while (!mantissa[0] && bits > (-64 * VHACD_GOOGOL_SIZE)) { + bits -= 64; + for (int i = 1; i < VHACD_GOOGOL_SIZE; i++) { + mantissa[i - 1] = mantissa[i]; + } + mantissa[VHACD_GOOGOL_SIZE - 1] = 0; + } + + if (bits > (-64 * VHACD_GOOGOL_SIZE)) { + int n = LeadingZeros(mantissa[0]) - 2; + if (n > 0) { + uint64_t carrier = 0; + for (int i = VHACD_GOOGOL_SIZE - 1; i >= 0; i--) { + uint64_t a = mantissa[i]; + mantissa[i] = (a << n) | carrier; + carrier = a >> (64 - n); + } + bits -= n; + } else if (n < 0) { + // this is very rare but it does happens, whee the leading zeros of the + // mantissa is an exact multiple of 64 + uint64_t carrier = 0; + int shift = -n; + for (int i = 0; i < VHACD_GOOGOL_SIZE; i++) { + uint64_t a = mantissa[i]; + mantissa[i] = (a >> shift) | carrier; + carrier = a << (64 - shift); + } + bits -= n; + } + } + } + return bits; +} + +void Googol::ShiftRightMantissa( + std::array& mantissa, int bits) const { + uint64_t carrier = 0; + if (int64_t(mantissa[0]) < int64_t(0)) { + carrier = uint64_t(-1); + } + + while (bits >= 64) { + for (int i = VHACD_GOOGOL_SIZE - 2; i >= 0; i--) { + mantissa[i + 1] = mantissa[i]; + } + mantissa[0] = carrier; + bits -= 64; + } + + if (bits > 0) { + carrier <<= (64 - bits); + for (int i = 0; i < VHACD_GOOGOL_SIZE; i++) { + uint64_t a = mantissa[i]; + mantissa[i] = (a >> bits) | carrier; + carrier = a << (64 - bits); + } + } +} + +uint64_t Googol::CheckCarrier(uint64_t a, uint64_t b) const { + return ((uint64_t(-1) - b) < a) ? uint64_t(1) : 0; +} + +int Googol::LeadingZeros(uint64_t a) const { +#define VHACD_COUNTBIT(mask, add) \ + do { \ + uint64_t test = a & mask; \ + n += test ? 0 : add; \ + a = test ? test : (a & ~mask); \ + } while (false) + + int n = 0; + VHACD_COUNTBIT(0xffffffff00000000LL, 32); + VHACD_COUNTBIT(0xffff0000ffff0000LL, 16); + VHACD_COUNTBIT(0xff00ff00ff00ff00LL, 8); + VHACD_COUNTBIT(0xf0f0f0f0f0f0f0f0LL, 4); + VHACD_COUNTBIT(0xccccccccccccccccLL, 2); + VHACD_COUNTBIT(0xaaaaaaaaaaaaaaaaLL, 1); + + return n; +} + +void Googol::ExtendedMultiply(uint64_t a, uint64_t b, uint64_t& high, + uint64_t& low) const { + uint64_t bLow = b & 0xffffffff; + uint64_t bHigh = b >> 32; + uint64_t aLow = a & 0xffffffff; + uint64_t aHigh = a >> 32; + + uint64_t l = bLow * aLow; + + uint64_t c1 = bHigh * aLow; + uint64_t c2 = bLow * aHigh; + uint64_t m = c1 + c2; + uint64_t carrier = CheckCarrier(c1, c2) << 32; + + uint64_t h = bHigh * aHigh + carrier; + + uint64_t ml = m << 32; + uint64_t ll = l + ml; + uint64_t mh = (m >> 32) + CheckCarrier(l, ml); + uint64_t hh = h + mh; + + low = ll; + high = hh; +} + +void Googol::ScaleMantissa(uint64_t* dst, uint64_t scale) const { + uint64_t carrier = 0; + for (int i = VHACD_GOOGOL_SIZE - 1; i >= 0; i--) { + if (m_mantissa[i]) { + uint64_t low; + uint64_t high; + ExtendedMultiply(scale, m_mantissa[i], high, low); + uint64_t acc = low + carrier; + carrier = CheckCarrier(low, carrier); + carrier += high; + dst[i + 1] = acc; + } else { + dst[i + 1] = carrier; + carrier = 0; + } + } + dst[0] = carrier; +} + +Googol Determinant3x3(const std::array, 3>& matrix) { + Googol det = double(0.0); + + Googol a01xa12 = matrix[0].GetY() * matrix[1].GetZ(); + Googol a02xa11 = matrix[0].GetZ() * matrix[1].GetY(); + det += (a01xa12 - a02xa11) * matrix[2].GetX(); + + Googol a00xa12 = matrix[0].GetX() * matrix[1].GetZ(); + Googol a02xa10 = matrix[0].GetZ() * matrix[1].GetX(); + det -= (a00xa12 - a02xa10) * matrix[2].GetY(); + + Googol a00xa11 = matrix[0].GetX() * matrix[1].GetY(); + Googol a01xa10 = matrix[0].GetY() * matrix[1].GetX(); + det += (a00xa11 - a01xa10) * matrix[2].GetZ(); + return det; +} + +class HullPlane : public VHACD::Vect3 { + public: + HullPlane(const HullPlane&) = default; + HullPlane(double x, double y, double z, double w); + + HullPlane(const VHACD::Vect3& p, double w); + + HullPlane(const VHACD::Vect3& p0, const VHACD::Vect3& p1, + const VHACD::Vect3& p2); + + HullPlane Scale(double s) const; + + HullPlane& operator=(const HullPlane& rhs); + + double Evalue(const VHACD::Vect3& point) const; + + double& GetW(); + const double& GetW() const; + + private: + double m_w; +}; + +HullPlane::HullPlane(double x, double y, double z, double w) + : VHACD::Vect3(x, y, z), m_w(w) {} + +HullPlane::HullPlane(const VHACD::Vect3& p, double w) + : VHACD::Vect3(p), m_w(w) {} + +HullPlane::HullPlane(const VHACD::Vect3& p0, const VHACD::Vect3& p1, + const VHACD::Vect3& p2) + : VHACD::Vect3((p1 - p0).Cross(p2 - p0)), m_w(-Dot(p0)) {} + +HullPlane HullPlane::Scale(double s) const { + return HullPlane(*this * s, m_w * s); +} + +HullPlane& HullPlane::operator=(const HullPlane& rhs) { + GetX() = rhs.GetX(); + GetY() = rhs.GetY(); + GetZ() = rhs.GetZ(); + m_w = rhs.m_w; + return *this; +} + +double HullPlane::Evalue(const VHACD::Vect3& point) const { + return Dot(point) + m_w; +} + +double& HullPlane::GetW() { return m_w; } + +const double& HullPlane::GetW() const { return m_w; } + +class ConvexHullFace { + public: + ConvexHullFace() = default; + double Evalue(const std::vector& pointArray, + const VHACD::Vect3& point) const; + HullPlane GetPlaneEquation(const std::vector& pointArray, + bool& isValid) const; + + std::array m_index; + + private: + int m_mark{0}; + std::array::iterator, 3> m_twin; + + friend class ConvexHull; +}; + +double ConvexHullFace::Evalue(const std::vector& pointArray, + const VHACD::Vect3& point) const { + const VHACD::Vect3& p0 = pointArray[m_index[0]]; + const VHACD::Vect3& p1 = pointArray[m_index[1]]; + const VHACD::Vect3& p2 = pointArray[m_index[2]]; + + std::array matrix = {p2 - p0, p1 - p0, point - p0}; + double error; + double det = Determinant3x3(matrix, error); + + // the code use double, however the threshold for accuracy test is the machine + // precision of a float. by changing this to a smaller number, the code should + // run faster since many small test will be considered valid the precision + // must be a power of two no smaller than the machine precision of a double, + // (1<<48) float64(1<<30) can be a good value + + // double precision = double (1.0f) / double (1<<30); + double precision = double(1.0) / double(1 << 24); + double errbound = error * precision; + if (fabs(det) > errbound) { + return det; + } + + const VHACD::Vector3 p0g = pointArray[m_index[0]]; + const VHACD::Vector3 p1g = pointArray[m_index[1]]; + const VHACD::Vector3 p2g = pointArray[m_index[2]]; + const VHACD::Vector3 pointg = point; + std::array, 3> exactMatrix = {p2g - p0g, p1g - p0g, + pointg - p0g}; + return Determinant3x3(exactMatrix); +} + +HullPlane ConvexHullFace::GetPlaneEquation( + const std::vector& pointArray, bool& isvalid) const { + const VHACD::Vect3& p0 = pointArray[m_index[0]]; + const VHACD::Vect3& p1 = pointArray[m_index[1]]; + const VHACD::Vect3& p2 = pointArray[m_index[2]]; + HullPlane plane(p0, p1, p2); + + isvalid = false; + double mag2 = plane.Dot(plane); + if (mag2 > double(1.0e-16)) { + isvalid = true; + plane = plane.Scale(double(1.0) / sqrt(mag2)); + } + return plane; +} + +class ConvexHullVertex : public VHACD::Vect3 { + public: + ConvexHullVertex() = default; + ConvexHullVertex(const ConvexHullVertex&) = default; + ConvexHullVertex& operator=(const ConvexHullVertex& rhs) = default; + using VHACD::Vect3::operator=; + + int m_mark{0}; +}; + +class ConvexHullAABBTreeNode { +#define VHACD_CONVEXHULL_3D_VERTEX_CLUSTER_SIZE 8 + public: + ConvexHullAABBTreeNode() = default; + ConvexHullAABBTreeNode(ConvexHullAABBTreeNode* parent); + + VHACD::Vect3 m_box[2]; + ConvexHullAABBTreeNode* m_left{nullptr}; + ConvexHullAABBTreeNode* m_right{nullptr}; + ConvexHullAABBTreeNode* m_parent{nullptr}; + + size_t m_count; + std::array m_indices; +}; + +ConvexHullAABBTreeNode::ConvexHullAABBTreeNode(ConvexHullAABBTreeNode* parent) + : m_parent(parent) {} + +class ConvexHull { + class ndNormalMap; + + public: + ConvexHull(const ConvexHull& source); + ConvexHull(const std::vector<::VHACD::Vertex>& vertexCloud, double distTol, + int maxVertexCount = 0x7fffffff); + ~ConvexHull() = default; + + const std::vector& GetVertexPool() const; + + const std::list& GetList() const { return m_list; } + + private: + void BuildHull(const std::vector<::VHACD::Vertex>& vertexCloud, + double distTol, int maxVertexCount); + + void GetUniquePoints(std::vector& points); + int InitVertexArray(std::vector& points, + NodeBundle& memoryPool); + + ConvexHullAABBTreeNode* BuildTreeNew( + std::vector& points, + std::vector& memoryPool) const; + ConvexHullAABBTreeNode* BuildTreeOld( + std::vector& points, + NodeBundle& memoryPool); + ConvexHullAABBTreeNode* BuildTreeRecurse( + ConvexHullAABBTreeNode* const parent, ConvexHullVertex* const points, + int count, int baseIndex, + NodeBundle& memoryPool) const; + + std::list::iterator AddFace(int i0, int i1, int i2); + + void CalculateConvexHull3D(ConvexHullAABBTreeNode* vertexTree, + std::vector& points, int count, + double distTol, int maxVertexCount); + + int SupportVertex(ConvexHullAABBTreeNode** const tree, + const std::vector& points, + const VHACD::Vect3& dir, + const bool removeEntry = true) const; + double TetrahedrumVolume(const VHACD::Vect3& p0, const VHACD::Vect3& p1, + const VHACD::Vect3& p2, + const VHACD::Vect3& p3) const; + + std::list m_list; + VHACD::Vect3 m_aabbP0{0}; + VHACD::Vect3 m_aabbP1{0}; + double m_diag{0.0}; + std::vector m_points; +}; + +class ConvexHull::ndNormalMap { + public: + ndNormalMap(); + + static const ndNormalMap& GetNormalMap(); + + void TessellateTriangle(int level, const VHACD::Vect3& p0, + const VHACD::Vect3& p1, const VHACD::Vect3& p2, + int& count); + + std::array m_normal; + int m_count{128}; +}; + +const ConvexHull::ndNormalMap& ConvexHull::ndNormalMap::GetNormalMap() { + static ndNormalMap normalMap; + return normalMap; +} + +void ConvexHull::ndNormalMap::TessellateTriangle(int level, + const VHACD::Vect3& p0, + const VHACD::Vect3& p1, + const VHACD::Vect3& p2, + int& count) { + if (level) { + assert(fabs(p0.Dot(p0) - double(1.0)) < double(1.0e-4)); + assert(fabs(p1.Dot(p1) - double(1.0)) < double(1.0e-4)); + assert(fabs(p2.Dot(p2) - double(1.0)) < double(1.0e-4)); + VHACD::Vect3 p01(p0 + p1); + VHACD::Vect3 p12(p1 + p2); + VHACD::Vect3 p20(p2 + p0); + + p01 = p01 * (double(1.0) / p01.GetNorm()); + p12 = p12 * (double(1.0) / p12.GetNorm()); + p20 = p20 * (double(1.0) / p20.GetNorm()); + + assert(fabs(p01.GetNormSquared() - double(1.0)) < double(1.0e-4)); + assert(fabs(p12.GetNormSquared() - double(1.0)) < double(1.0e-4)); + assert(fabs(p20.GetNormSquared() - double(1.0)) < double(1.0e-4)); + + TessellateTriangle(level - 1, p0, p01, p20, count); + TessellateTriangle(level - 1, p1, p12, p01, count); + TessellateTriangle(level - 1, p2, p20, p12, count); + TessellateTriangle(level - 1, p01, p12, p20, count); + } else { + /* + * This is just m_normal[index] = n.Normalized(), but due to tiny floating + * point errors, causes different outputs, so I'm leaving it + */ + HullPlane n(p0, p1, p2); + n = n.Scale(double(1.0) / n.GetNorm()); + n.GetW() = double(0.0); + int index = dBitReversal(count, int(m_normal.size())); + m_normal[index] = n; + count++; + assert(count <= int(m_normal.size())); + } +} + +ConvexHull::ndNormalMap::ndNormalMap() { + VHACD::Vect3 p0(double(1.0), double(0.0), double(0.0)); + VHACD::Vect3 p1(double(-1.0), double(0.0), double(0.0)); + VHACD::Vect3 p2(double(0.0), double(1.0), double(0.0)); + VHACD::Vect3 p3(double(0.0), double(-1.0), double(0.0)); + VHACD::Vect3 p4(double(0.0), double(0.0), double(1.0)); + VHACD::Vect3 p5(double(0.0), double(0.0), double(-1.0)); + + int count = 0; + int subdivisions = 2; + TessellateTriangle(subdivisions, p4, p0, p2, count); + TessellateTriangle(subdivisions, p0, p5, p2, count); + TessellateTriangle(subdivisions, p5, p1, p2, count); + TessellateTriangle(subdivisions, p1, p4, p2, count); + TessellateTriangle(subdivisions, p0, p4, p3, count); + TessellateTriangle(subdivisions, p5, p0, p3, count); + TessellateTriangle(subdivisions, p1, p5, p3, count); + TessellateTriangle(subdivisions, p4, p1, p3, count); +} + +ConvexHull::ConvexHull(const std::vector<::VHACD::Vertex>& vertexCloud, + double distTol, int maxVertexCount) { + if (vertexCloud.size() >= 4) { + BuildHull(vertexCloud, distTol, maxVertexCount); + } +} + +const std::vector& ConvexHull::GetVertexPool() const { + return m_points; +} + +void ConvexHull::BuildHull(const std::vector<::VHACD::Vertex>& vertexCloud, + double distTol, int maxVertexCount) { + size_t treeCount = + vertexCloud.size() / (VHACD_CONVEXHULL_3D_VERTEX_CLUSTER_SIZE >> 1); + treeCount = std::max(treeCount, size_t(4)) * 2; + + std::vector points(vertexCloud.size()); + /* + * treePool provides a memory pool for the AABB tree + * Each node is either a leaf or non-leaf node + * Non-leaf nodes have up to 8 vertices + * Vertices are specified by the m_indices array and are accessed via the + * points array + * + * Later on in ConvexHull::SupportVertex, the tree is used directly + * It differentiates between ConvexHullAABBTreeNode and + * ConvexHull3DPointCluster by whether the m_left and m_right pointers are + * null or not + * + * Pointers have to be stable + */ + NodeBundle treePool; + for (size_t i = 0; i < vertexCloud.size(); ++i) { + points[i] = VHACD::Vect3(vertexCloud[i]); + } + int count = InitVertexArray(points, treePool); + + if (m_points.size() >= 4) { + CalculateConvexHull3D(&treePool.GetFirstNode(), points, count, distTol, + maxVertexCount); + } +} + +void ConvexHull::GetUniquePoints(std::vector& points) { + class CompareVertex { + public: + int Compare(const ConvexHullVertex& elementA, + const ConvexHullVertex& elementB) const { + for (int i = 0; i < 3; i++) { + if (elementA[i] < elementB[i]) { + return -1; + } else if (elementA[i] > elementB[i]) { + return 1; + } + } + return 0; + } + }; + + int count = int(points.size()); + Sort(points.data(), count); + + int indexCount = 0; + CompareVertex compareVertex; + for (int i = 1; i < count; ++i) { + for (; i < count; ++i) { + if (compareVertex.Compare(points[indexCount], points[i])) { + indexCount++; + points[indexCount] = points[i]; + break; + } + } + } + points.resize(indexCount + 1); +} + +ConvexHullAABBTreeNode* ConvexHull::BuildTreeRecurse( + ConvexHullAABBTreeNode* const parent, ConvexHullVertex* const points, + int count, int baseIndex, + NodeBundle& memoryPool) const { + ConvexHullAABBTreeNode* tree = nullptr; + + assert(count); + VHACD::Vect3 minP(double(1.0e15)); + VHACD::Vect3 maxP(-double(1.0e15)); + if (count <= VHACD_CONVEXHULL_3D_VERTEX_CLUSTER_SIZE) { + ConvexHullAABBTreeNode& clump = memoryPool.GetNextNode(); + + clump.m_count = count; + for (int i = 0; i < count; ++i) { + clump.m_indices[i] = i + baseIndex; + + const VHACD::Vect3& p = points[i]; + minP = minP.CWiseMin(p); + maxP = maxP.CWiseMax(p); + } + + clump.m_left = nullptr; + clump.m_right = nullptr; + tree = &clump; + } else { + VHACD::Vect3 median(0); + VHACD::Vect3 varian(0); + for (int i = 0; i < count; ++i) { + const VHACD::Vect3& p = points[i]; + minP = minP.CWiseMin(p); + maxP = maxP.CWiseMax(p); + median += p; + varian += p.CWiseMul(p); + } + + varian = varian * double(count) - median.CWiseMul(median); + int index = 0; + double maxVarian = double(-1.0e10); + for (int i = 0; i < 3; ++i) { + if (varian[i] > maxVarian) { + index = i; + maxVarian = varian[i]; + } + } + VHACD::Vect3 center(median * (double(1.0) / double(count))); + + double test = center[index]; + + int i0 = 0; + int i1 = count - 1; + do { + for (; i0 <= i1; i0++) { + double val = points[i0][index]; + if (val > test) { + break; + } + } + + for (; i1 >= i0; i1--) { + double val = points[i1][index]; + if (val < test) { + break; + } + } + + if (i0 < i1) { + std::swap(points[i0], points[i1]); + i0++; + i1--; + } + } while (i0 <= i1); + + if (i0 == 0) { + i0 = count / 2; + } + if (i0 >= (count - 1)) { + i0 = count / 2; + } + + tree = &memoryPool.GetNextNode(); + + assert(i0); + assert(count - i0); + + tree->m_left = BuildTreeRecurse(tree, points, i0, baseIndex, memoryPool); + tree->m_right = BuildTreeRecurse(tree, &points[i0], count - i0, + i0 + baseIndex, memoryPool); + } + + assert(tree); + tree->m_parent = parent; + /* + * WARNING: Changing the compiler conversion of 1.0e-3f changes the results of + * the convex decomposition Inflate the tree's bounding box slightly + */ + tree->m_box[0] = minP - VHACD::Vect3(double(1.0e-3f)); + tree->m_box[1] = maxP + VHACD::Vect3(double(1.0e-3f)); + return tree; +} + +ConvexHullAABBTreeNode* ConvexHull::BuildTreeOld( + std::vector& points, + NodeBundle& memoryPool) { + GetUniquePoints(points); + int count = int(points.size()); + if (count < 4) { + return nullptr; + } + return BuildTreeRecurse(nullptr, points.data(), count, 0, memoryPool); +} + +ConvexHullAABBTreeNode* ConvexHull::BuildTreeNew( + std::vector& points, + std::vector& memoryPool) const { + class dCluster { + public: + VHACD::Vect3 m_sum{double(0.0)}; + VHACD::Vect3 m_sum2{double(0.0)}; + int m_start{0}; + int m_count{0}; + }; + + dCluster firstCluster; + firstCluster.m_count = int(points.size()); + + for (int i = 0; i < firstCluster.m_count; ++i) { + const VHACD::Vect3& p = points[i]; + firstCluster.m_sum += p; + firstCluster.m_sum2 += p.CWiseMul(p); + } + + int baseCount = 0; + const int clusterSize = 16; + + if (firstCluster.m_count > clusterSize) { + dCluster spliteStack[128]; + spliteStack[0] = firstCluster; + size_t stack = 1; + + while (stack) { + stack--; + dCluster cluster(spliteStack[stack]); + + const VHACD::Vect3 origin(cluster.m_sum * + (double(1.0) / cluster.m_count)); + const VHACD::Vect3 variance2(cluster.m_sum2 * + (double(1.0) / cluster.m_count) - + origin.CWiseMul(origin)); + double maxVariance2 = variance2.MaxCoeff(); + + if ((cluster.m_count <= clusterSize) || + (stack > (sizeof(spliteStack) / sizeof(spliteStack[0]) - 4)) || + (maxVariance2 < 1.e-4f)) { + // no sure if this is beneficial, + // the array is so small that seem too much overhead + // int maxIndex = 0; + // double min_x = 1.0e20f; + // for (int i = 0; i < cluster.m_count; ++i) + //{ + // if (points[cluster.m_start + i].getX() < min_x) + // { + // maxIndex = i; + // min_x = points[cluster.m_start + i].getX(); + // } + //} + // Swap(points[cluster.m_start], points[cluster.m_start + maxIndex]); + // + // for (int i = 2; i < cluster.m_count; ++i) + //{ + // int j = i; + // ConvexHullVertex tmp(points[cluster.m_start + i]); + // for (; points[cluster.m_start + j - 1].getX() > tmp.getX(); --j) + // { + // assert(j > 0); + // points[cluster.m_start + j] = points[cluster.m_start + j + //- 1]; + // } + // points[cluster.m_start + j] = tmp; + //} + + int count = cluster.m_count; + for (int i = cluster.m_count - 1; i > 0; --i) { + for (int j = i - 1; j >= 0; --j) { + VHACD::Vect3 error(points[cluster.m_start + j] - + points[cluster.m_start + i]); + double mag2 = error.Dot(error); + if (mag2 < double(1.0e-6)) { + points[cluster.m_start + j] = points[cluster.m_start + i]; + count--; + break; + } + } + } + + assert(baseCount <= cluster.m_start); + for (int i = 0; i < count; ++i) { + points[baseCount] = points[cluster.m_start + i]; + baseCount++; + } + } else { + const int firstSortAxis = variance2.LongestAxis(); + double axisVal = origin[firstSortAxis]; + + int i0 = 0; + int i1 = cluster.m_count - 1; + + const int start = cluster.m_start; + while (i0 < i1) { + while ((points[start + i0][firstSortAxis] <= axisVal) && (i0 < i1)) { + ++i0; + }; + + while ((points[start + i1][firstSortAxis] > axisVal) && (i0 < i1)) { + --i1; + } + + assert(i0 <= i1); + if (i0 < i1) { + std::swap(points[start + i0], points[start + i1]); + ++i0; + --i1; + } + } + + while ((points[start + i0][firstSortAxis] <= axisVal) && + (i0 < cluster.m_count)) { + ++i0; + }; + +#ifdef _DEBUG + for (int i = 0; i < i0; ++i) { + assert(points[start + i][firstSortAxis] <= axisVal); + } + + for (int i = i0; i < cluster.m_count; ++i) { + assert(points[start + i][firstSortAxis] > axisVal); + } +#endif + + VHACD::Vect3 xc(0); + VHACD::Vect3 x2c(0); + for (int i = 0; i < i0; ++i) { + const VHACD::Vect3& x = points[start + i]; + xc += x; + x2c += x.CWiseMul(x); + } + + dCluster cluster_i1(cluster); + cluster_i1.m_start = start + i0; + cluster_i1.m_count = cluster.m_count - i0; + cluster_i1.m_sum -= xc; + cluster_i1.m_sum2 -= x2c; + spliteStack[stack] = cluster_i1; + assert(cluster_i1.m_count > 0); + stack++; + + dCluster cluster_i0(cluster); + cluster_i0.m_start = start; + cluster_i0.m_count = i0; + cluster_i0.m_sum = xc; + cluster_i0.m_sum2 = x2c; + assert(cluster_i0.m_count > 0); + spliteStack[stack] = cluster_i0; + stack++; + } + } + } + + points.resize(baseCount); + if (baseCount < 4) { + return nullptr; + } + + VHACD::Vect3 sum(0); + VHACD::Vect3 sum2(0); + VHACD::Vect3 minP(double(1.0e15)); + VHACD::Vect3 maxP(double(-1.0e15)); + class dTreeBox { + public: + VHACD::Vect3 m_min; + VHACD::Vect3 m_max; + VHACD::Vect3 m_sum; + VHACD::Vect3 m_sum2; + ConvexHullAABBTreeNode* m_parent; + ConvexHullAABBTreeNode** m_child; + int m_start; + int m_count; + }; + + for (int i = 0; i < baseCount; ++i) { + const VHACD::Vect3& p = points[i]; + sum += p; + sum2 += p.CWiseMul(p); + minP = minP.CWiseMin(p); + maxP = maxP.CWiseMax(p); + } + + dTreeBox treeBoxStack[128]; + treeBoxStack[0].m_start = 0; + treeBoxStack[0].m_count = baseCount; + treeBoxStack[0].m_sum = sum; + treeBoxStack[0].m_sum2 = sum2; + treeBoxStack[0].m_min = minP; + treeBoxStack[0].m_max = maxP; + treeBoxStack[0].m_child = nullptr; + treeBoxStack[0].m_parent = nullptr; + + int stack = 1; + ConvexHullAABBTreeNode* root = nullptr; + while (stack) { + stack--; + dTreeBox box(treeBoxStack[stack]); + if (box.m_count <= VHACD_CONVEXHULL_3D_VERTEX_CLUSTER_SIZE) { + assert(memoryPool.size() != memoryPool.capacity() && + "memoryPool is going to be reallocated, pointers will be invalid"); + memoryPool.emplace_back(); + ConvexHullAABBTreeNode& clump = memoryPool.back(); + + clump.m_count = box.m_count; + for (int i = 0; i < box.m_count; ++i) { + clump.m_indices[i] = i + box.m_start; + } + clump.m_box[0] = box.m_min; + clump.m_box[1] = box.m_max; + + if (box.m_child) { + *box.m_child = &clump; + } + + if (!root) { + root = &clump; + } + } else { + const VHACD::Vect3 origin(box.m_sum * (double(1.0) / box.m_count)); + const VHACD::Vect3 variance2(box.m_sum2 * (double(1.0) / box.m_count) - + origin.CWiseMul(origin)); + + int firstSortAxis = 0; + if ((variance2.GetY() >= variance2.GetX()) && + (variance2.GetY() >= variance2.GetZ())) { + firstSortAxis = 1; + } else if ((variance2.GetZ() >= variance2.GetX()) && + (variance2.GetZ() >= variance2.GetY())) { + firstSortAxis = 2; + } + double axisVal = origin[firstSortAxis]; + + int i0 = 0; + int i1 = box.m_count - 1; + + const int start = box.m_start; + while (i0 < i1) { + while ((points[start + i0][firstSortAxis] <= axisVal) && (i0 < i1)) { + ++i0; + }; + + while ((points[start + i1][firstSortAxis] > axisVal) && (i0 < i1)) { + --i1; + } + + assert(i0 <= i1); + if (i0 < i1) { + std::swap(points[start + i0], points[start + i1]); + ++i0; + --i1; + } + } + + while ((points[start + i0][firstSortAxis] <= axisVal) && + (i0 < box.m_count)) { + ++i0; + }; + +#ifdef _DEBUG + for (int i = 0; i < i0; ++i) { + assert(points[start + i][firstSortAxis] <= axisVal); + } + + for (int i = i0; i < box.m_count; ++i) { + assert(points[start + i][firstSortAxis] > axisVal); + } +#endif + + assert(memoryPool.size() != memoryPool.capacity() && + "memoryPool is going to be reallocated, pointers will be invalid"); + memoryPool.emplace_back(); + ConvexHullAABBTreeNode& node = memoryPool.back(); + + node.m_box[0] = box.m_min; + node.m_box[1] = box.m_max; + if (box.m_child) { + *box.m_child = &node; + } + + if (!root) { + root = &node; + } + + { + VHACD::Vect3 xc(0); + VHACD::Vect3 x2c(0); + VHACD::Vect3 p0(double(1.0e15)); + VHACD::Vect3 p1(double(-1.0e15)); + for (int i = i0; i < box.m_count; ++i) { + const VHACD::Vect3& p = points[start + i]; + xc += p; + x2c += p.CWiseMul(p); + p0 = p0.CWiseMin(p); + p1 = p1.CWiseMax(p); + } + + dTreeBox cluster_i1(box); + cluster_i1.m_start = start + i0; + cluster_i1.m_count = box.m_count - i0; + cluster_i1.m_sum = xc; + cluster_i1.m_sum2 = x2c; + cluster_i1.m_min = p0; + cluster_i1.m_max = p1; + cluster_i1.m_parent = &node; + cluster_i1.m_child = &node.m_right; + treeBoxStack[stack] = cluster_i1; + assert(cluster_i1.m_count > 0); + stack++; + } + + { + VHACD::Vect3 xc(0); + VHACD::Vect3 x2c(0); + VHACD::Vect3 p0(double(1.0e15)); + VHACD::Vect3 p1(double(-1.0e15)); + for (int i = 0; i < i0; ++i) { + const VHACD::Vect3& p = points[start + i]; + xc += p; + x2c += p.CWiseMul(p); + p0 = p0.CWiseMin(p); + p1 = p1.CWiseMax(p); + } + + dTreeBox cluster_i0(box); + cluster_i0.m_start = start; + cluster_i0.m_count = i0; + cluster_i0.m_min = p0; + cluster_i0.m_max = p1; + cluster_i0.m_sum = xc; + cluster_i0.m_sum2 = x2c; + cluster_i0.m_parent = &node; + cluster_i0.m_child = &node.m_left; + assert(cluster_i0.m_count > 0); + treeBoxStack[stack] = cluster_i0; + stack++; + } + } + } + + return root; +} + +int ConvexHull::SupportVertex(ConvexHullAABBTreeNode** const treePointer, + const std::vector& points, + const VHACD::Vect3& dirPlane, + const bool removeEntry) const { +#define VHACD_STACK_DEPTH_3D 64 + double aabbProjection[VHACD_STACK_DEPTH_3D]; + ConvexHullAABBTreeNode* stackPool[VHACD_STACK_DEPTH_3D]; + + VHACD::Vect3 dir(dirPlane); + + int index = -1; + int stack = 1; + stackPool[0] = *treePointer; + aabbProjection[0] = double(1.0e20); + double maxProj = double(-1.0e20); + int ix = (dir[0] > double(0.0)) ? 1 : 0; + int iy = (dir[1] > double(0.0)) ? 1 : 0; + int iz = (dir[2] > double(0.0)) ? 1 : 0; + while (stack) { + stack--; + double boxSupportValue = aabbProjection[stack]; + if (boxSupportValue > maxProj) { + ConvexHullAABBTreeNode* me = stackPool[stack]; + + /* + * If the node is not a leaf node... + */ + if (me->m_left && me->m_right) { + const VHACD::Vect3 leftSupportPoint(me->m_left->m_box[ix].GetX(), + me->m_left->m_box[iy].GetY(), + me->m_left->m_box[iz].GetZ()); + double leftSupportDist = leftSupportPoint.Dot(dir); + + const VHACD::Vect3 rightSupportPoint(me->m_right->m_box[ix].GetX(), + me->m_right->m_box[iy].GetY(), + me->m_right->m_box[iz].GetZ()); + double rightSupportDist = rightSupportPoint.Dot(dir); + + /* + * ...push the shorter side first + * So we can explore the tree in the larger side first + */ + if (rightSupportDist >= leftSupportDist) { + aabbProjection[stack] = leftSupportDist; + stackPool[stack] = me->m_left; + stack++; + assert(stack < VHACD_STACK_DEPTH_3D); + aabbProjection[stack] = rightSupportDist; + stackPool[stack] = me->m_right; + stack++; + assert(stack < VHACD_STACK_DEPTH_3D); + } else { + aabbProjection[stack] = rightSupportDist; + stackPool[stack] = me->m_right; + stack++; + assert(stack < VHACD_STACK_DEPTH_3D); + aabbProjection[stack] = leftSupportDist; + stackPool[stack] = me->m_left; + stack++; + assert(stack < VHACD_STACK_DEPTH_3D); + } + } + /* + * If it is a node... + */ + else { + ConvexHullAABBTreeNode* cluster = me; + for (size_t i = 0; i < cluster->m_count; ++i) { + const ConvexHullVertex& p = points[cluster->m_indices[i]]; + assert(p.GetX() >= cluster->m_box[0].GetX()); + assert(p.GetX() <= cluster->m_box[1].GetX()); + assert(p.GetY() >= cluster->m_box[0].GetY()); + assert(p.GetY() <= cluster->m_box[1].GetY()); + assert(p.GetZ() >= cluster->m_box[0].GetZ()); + assert(p.GetZ() <= cluster->m_box[1].GetZ()); + if (!p.m_mark) { + // assert(p.m_w == double(0.0f)); + double dist = p.Dot(dir); + if (dist > maxProj) { + maxProj = dist; + index = cluster->m_indices[i]; + } + } else if (removeEntry) { + cluster->m_indices[i] = cluster->m_indices[cluster->m_count - 1]; + cluster->m_count = cluster->m_count - 1; + i--; + } + } + + if (cluster->m_count == 0) { + ConvexHullAABBTreeNode* const parent = cluster->m_parent; + if (parent) { + ConvexHullAABBTreeNode* const sibling = + (parent->m_left != cluster) ? parent->m_left : parent->m_right; + assert(sibling != cluster); + ConvexHullAABBTreeNode* const grandParent = parent->m_parent; + if (grandParent) { + sibling->m_parent = grandParent; + if (grandParent->m_right == parent) { + grandParent->m_right = sibling; + } else { + grandParent->m_left = sibling; + } + } else { + sibling->m_parent = nullptr; + *treePointer = sibling; + } + } + } + } + } + } + + assert(index != -1); + return index; +} + +double ConvexHull::TetrahedrumVolume(const VHACD::Vect3& p0, + const VHACD::Vect3& p1, + const VHACD::Vect3& p2, + const VHACD::Vect3& p3) const { + const VHACD::Vect3 p1p0(p1 - p0); + const VHACD::Vect3 p2p0(p2 - p0); + const VHACD::Vect3 p3p0(p3 - p0); + return p3p0.Dot(p1p0.Cross(p2p0)); +} + +int ConvexHull::InitVertexArray(std::vector& points, + NodeBundle& memoryPool) +// std::vector& +// memoryPool) +{ +#if 1 + ConvexHullAABBTreeNode* tree = BuildTreeOld(points, memoryPool); +#else + ConvexHullAABBTreeNode* tree = + BuildTreeNew(points, (char**)&memoryPool, maxMemSize); +#endif + int count = int(points.size()); + if (count < 4) { + m_points.resize(0); + return 0; + } + + m_points.resize(count); + m_aabbP0 = tree->m_box[0]; + m_aabbP1 = tree->m_box[1]; + + VHACD::Vect3 boxSize(tree->m_box[1] - tree->m_box[0]); + m_diag = boxSize.GetNorm(); + const ndNormalMap& normalMap = ndNormalMap::GetNormalMap(); + + int index0 = SupportVertex(&tree, points, normalMap.m_normal[0]); + m_points[0] = points[index0]; + points[index0].m_mark = 1; + + bool validTetrahedrum = false; + VHACD::Vect3 e1(double(0.0)); + for (int i = 1; i < normalMap.m_count; ++i) { + int index = SupportVertex(&tree, points, normalMap.m_normal[i]); + assert(index >= 0); + + e1 = points[index] - m_points[0]; + double error2 = e1.GetNormSquared(); + if (error2 > (double(1.0e-4) * m_diag * m_diag)) { + m_points[1] = points[index]; + points[index].m_mark = 1; + validTetrahedrum = true; + break; + } + } + if (!validTetrahedrum) { + m_points.resize(0); + assert(0); + return count; + } + + validTetrahedrum = false; + VHACD::Vect3 e2(double(0.0)); + VHACD::Vect3 normal(double(0.0)); + for (int i = 2; i < normalMap.m_count; ++i) { + int index = SupportVertex(&tree, points, normalMap.m_normal[i]); + assert(index >= 0); + e2 = points[index] - m_points[0]; + normal = e1.Cross(e2); + double error2 = normal.GetNorm(); + if (error2 > (double(1.0e-4) * m_diag * m_diag)) { + m_points[2] = points[index]; + points[index].m_mark = 1; + validTetrahedrum = true; + break; + } + } + + if (!validTetrahedrum) { + m_points.resize(0); + assert(0); + return count; + } + + // find the largest possible tetrahedron + validTetrahedrum = false; + VHACD::Vect3 e3(double(0.0)); + + index0 = SupportVertex(&tree, points, normal); + e3 = points[index0] - m_points[0]; + double err2 = normal.Dot(e3); + if (fabs(err2) > (double(1.0e-6) * m_diag * m_diag)) { + // we found a valid tetrahedral, about and start build the hull by adding + // the rest of the points + m_points[3] = points[index0]; + points[index0].m_mark = 1; + validTetrahedrum = true; + } + if (!validTetrahedrum) { + VHACD::Vect3 n(-normal); + int index = SupportVertex(&tree, points, n); + e3 = points[index] - m_points[0]; + double error2 = normal.Dot(e3); + if (fabs(error2) > (double(1.0e-6) * m_diag * m_diag)) { + // we found a valid tetrahedral, about and start build the hull by adding + // the rest of the points + m_points[3] = points[index]; + points[index].m_mark = 1; + validTetrahedrum = true; + } + } + if (!validTetrahedrum) { + for (int i = 3; i < normalMap.m_count; ++i) { + int index = SupportVertex(&tree, points, normalMap.m_normal[i]); + assert(index >= 0); + + // make sure the volume of the fist tetrahedral is no negative + e3 = points[index] - m_points[0]; + double error2 = normal.Dot(e3); + if (fabs(error2) > (double(1.0e-6) * m_diag * m_diag)) { + // we found a valid tetrahedral, about and start build the hull by + // adding the rest of the points + m_points[3] = points[index]; + points[index].m_mark = 1; + validTetrahedrum = true; + break; + } + } + } + if (!validTetrahedrum) { + // the points do not form a convex hull + m_points.resize(0); + return count; + } + + m_points.resize(4); + double volume = + TetrahedrumVolume(m_points[0], m_points[1], m_points[2], m_points[3]); + if (volume > double(0.0)) { + std::swap(m_points[2], m_points[3]); + } + assert(TetrahedrumVolume(m_points[0], m_points[1], m_points[2], m_points[3]) < + double(0.0)); + return count; +} + +std::list::iterator ConvexHull::AddFace(int i0, int i1, + int i2) { + ConvexHullFace face; + face.m_index[0] = i0; + face.m_index[1] = i1; + face.m_index[2] = i2; + + std::list::iterator node = m_list.emplace(m_list.end(), face); + return node; +} + +void ConvexHull::CalculateConvexHull3D(ConvexHullAABBTreeNode* vertexTree, + std::vector& points, + int count, double distTol, + int maxVertexCount) { + distTol = fabs(distTol) * m_diag; + std::list::iterator f0Node = AddFace(0, 1, 2); + std::list::iterator f1Node = AddFace(0, 2, 3); + std::list::iterator f2Node = AddFace(2, 1, 3); + std::list::iterator f3Node = AddFace(1, 0, 3); + + ConvexHullFace& f0 = *f0Node; + ConvexHullFace& f1 = *f1Node; + ConvexHullFace& f2 = *f2Node; + ConvexHullFace& f3 = *f3Node; + + f0.m_twin[0] = f3Node; + f0.m_twin[1] = f2Node; + f0.m_twin[2] = f1Node; + + f1.m_twin[0] = f0Node; + f1.m_twin[1] = f2Node; + f1.m_twin[2] = f3Node; + + f2.m_twin[0] = f0Node; + f2.m_twin[1] = f3Node; + f2.m_twin[2] = f1Node; + + f3.m_twin[0] = f0Node; + f3.m_twin[1] = f1Node; + f3.m_twin[2] = f2Node; + + std::list::iterator> boundaryFaces; + boundaryFaces.push_back(f0Node); + boundaryFaces.push_back(f1Node); + boundaryFaces.push_back(f2Node); + boundaryFaces.push_back(f3Node); + + m_points.resize(count); + + count -= 4; + maxVertexCount -= 4; + int currentIndex = 4; + + /* + * Some are iterators into boundaryFaces, others into m_list + */ + std::vector::iterator> stack; + std::vector::iterator> coneList; + std::vector::iterator> deleteList; + + stack.reserve(1024 + count); + coneList.reserve(1024 + count); + deleteList.reserve(1024 + count); + + while (boundaryFaces.size() && count && (maxVertexCount > 0)) { + // my definition of the optimal convex hull of a given vertex count, + // is the convex hull formed by a subset of the input vertex that minimizes + // the volume difference between the perfect hull formed from all input + // vertex and the hull of the sub set of vertex. When using a priority heap + // this algorithms will generate the an optimal of a fix vertex count. Since + // all Newton's tools do not have a limit on the point count of a convex + // hull, I can use either a stack or a queue. a stack maximize construction + // speed, a Queue tend to maximize the volume of the generated Hull + // approaching a perfect Hull. For now we use a queue. For general hulls it + // does not make a difference if we use a stack, queue, or a priority heap. + // perfect optimal hull only apply for when build hull of a limited vertex + // count. + // + // Also when building Hulls of a limited vertex count, this function runs in + // constant time. yes that is correct, it does not makes a difference if you + // build a N point hull from 100 vertex or from 100000 vertex input array. + + // using a queue (some what slower by better hull when reduced vertex count + // is desired) + bool isvalid; + std::list::iterator faceNode = boundaryFaces.back(); + ConvexHullFace& face = *faceNode; + HullPlane planeEquation(face.GetPlaneEquation(m_points, isvalid)); + + int index = 0; + double dist = 0; + VHACD::Vect3 p; + if (isvalid) { + index = SupportVertex(&vertexTree, points, planeEquation); + p = points[index]; + dist = planeEquation.Evalue(p); + } + + if (isvalid && (dist >= distTol) && + (face.Evalue(m_points, p) < double(0.0))) { + stack.push_back(faceNode); + + deleteList.clear(); + while (stack.size()) { + std::list::iterator node1 = stack.back(); + ConvexHullFace& face1 = *node1; + + stack.pop_back(); + + if (!face1.m_mark && (face1.Evalue(m_points, p) < double(0.0))) { +#ifdef _DEBUG + for (const auto node : deleteList) { + assert(node != node1); + } +#endif + + deleteList.push_back(node1); + face1.m_mark = 1; + for (std::list::iterator& twinNode : face1.m_twin) { + ConvexHullFace& twinFace = *twinNode; + if (!twinFace.m_mark) { + stack.push_back(twinNode); + } + } + } + } + + m_points[currentIndex] = points[index]; + points[index].m_mark = 1; + + coneList.clear(); + for (std::list::iterator node1 : deleteList) { + ConvexHullFace& face1 = *node1; + assert(face1.m_mark == 1); + for (std::size_t j0 = 0; j0 < face1.m_twin.size(); ++j0) { + std::list::iterator twinNode = face1.m_twin[j0]; + ConvexHullFace& twinFace = *twinNode; + if (!twinFace.m_mark) { + std::size_t j1 = (j0 == 2) ? 0 : j0 + 1; + std::list::iterator newNode = + AddFace(currentIndex, face1.m_index[j0], face1.m_index[j1]); + boundaryFaces.push_front(newNode); + ConvexHullFace& newFace = *newNode; + + newFace.m_twin[1] = twinNode; + for (std::size_t k = 0; k < twinFace.m_twin.size(); ++k) { + if (twinFace.m_twin[k] == node1) { + twinFace.m_twin[k] = newNode; + } + } + coneList.push_back(newNode); + } + } + } + + for (std::size_t i = 0; i < coneList.size() - 1; ++i) { + std::list::iterator nodeA = coneList[i]; + ConvexHullFace& faceA = *nodeA; + assert(faceA.m_mark == 0); + for (std::size_t j = i + 1; j < coneList.size(); j++) { + std::list::iterator nodeB = coneList[j]; + ConvexHullFace& faceB = *nodeB; + assert(faceB.m_mark == 0); + if (faceA.m_index[2] == faceB.m_index[1]) { + faceA.m_twin[2] = nodeB; + faceB.m_twin[0] = nodeA; + break; + } + } + + for (std::size_t j = i + 1; j < coneList.size(); j++) { + std::list::iterator nodeB = coneList[j]; + ConvexHullFace& faceB = *nodeB; + assert(faceB.m_mark == 0); + if (faceA.m_index[1] == faceB.m_index[2]) { + faceA.m_twin[0] = nodeB; + faceB.m_twin[2] = nodeA; + break; + } + } + } + + for (std::list::iterator node : deleteList) { + auto it = std::find(boundaryFaces.begin(), boundaryFaces.end(), node); + if (it != boundaryFaces.end()) { + boundaryFaces.erase(it); + } + m_list.erase(node); + } + + maxVertexCount--; + currentIndex++; + count--; + } else { + auto it = std::find(boundaryFaces.begin(), boundaryFaces.end(), faceNode); + if (it != boundaryFaces.end()) { + boundaryFaces.erase(it); + } + } + } + m_points.resize(currentIndex); +} + +//*********************************************************************************************** +// End of ConvexHull generation code by Julio Jerez +//*********************************************************************************************** + +class KdTreeNode; + +enum Axes { X_AXIS = 0, Y_AXIS = 1, Z_AXIS = 2 }; + +class KdTreeFindNode { + public: + KdTreeFindNode() = default; + + KdTreeNode* m_node{nullptr}; + double m_distance{0.0}; +}; + +class KdTree { + public: + KdTree() = default; + + const VHACD::Vertex& GetPosition(uint32_t index) const; + + uint32_t Search(const VHACD::Vect3& pos, double radius, uint32_t maxObjects, + KdTreeFindNode* found) const; + + uint32_t Add(const VHACD::Vertex& v); + + KdTreeNode& GetNewNode(uint32_t index); + + uint32_t GetNearest( + const VHACD::Vect3& pos, double radius, + bool& _found) const; // returns the nearest possible neighbor's index. + + const std::vector& GetVertices() const; + std::vector&& TakeVertices(); + + uint32_t GetVCount() const; + + private: + KdTreeNode* m_root{nullptr}; + NodeBundle m_bundle; + + std::vector m_vertices; +}; + +class KdTreeNode { + public: + KdTreeNode() = default; + KdTreeNode(uint32_t index); + + void Add(KdTreeNode& node, Axes dim, const KdTree& iface); + + uint32_t GetIndex() const; + + void Search(Axes axis, const VHACD::Vect3& pos, double radius, + uint32_t& count, uint32_t maxObjects, KdTreeFindNode* found, + const KdTree& iface); + + private: + uint32_t m_index = 0; + KdTreeNode* m_left = nullptr; + KdTreeNode* m_right = nullptr; +}; + +const VHACD::Vertex& KdTree::GetPosition(uint32_t index) const { + assert(index < m_vertices.size()); + return m_vertices[index]; +} + +uint32_t KdTree::Search(const VHACD::Vect3& pos, double radius, + uint32_t maxObjects, KdTreeFindNode* found) const { + if (!m_root) return 0; + uint32_t count = 0; + m_root->Search(X_AXIS, pos, radius, count, maxObjects, found, *this); + return count; +} + +uint32_t KdTree::Add(const VHACD::Vertex& v) { + uint32_t ret = uint32_t(m_vertices.size()); + m_vertices.emplace_back(v); + KdTreeNode& node = GetNewNode(ret); + if (m_root) { + m_root->Add(node, X_AXIS, *this); + } else { + m_root = &node; + } + return ret; +} + +KdTreeNode& KdTree::GetNewNode(uint32_t index) { + KdTreeNode& node = m_bundle.GetNextNode(); + node = KdTreeNode(index); + return node; +} + +uint32_t KdTree::GetNearest( + const VHACD::Vect3& pos, double radius, + bool& _found) const // returns the nearest possible neighbor's index. +{ + uint32_t ret = 0; + + _found = false; + KdTreeFindNode found; + uint32_t count = Search(pos, radius, 1, &found); + if (count) { + KdTreeNode* node = found.m_node; + ret = node->GetIndex(); + _found = true; + } + return ret; +} + +const std::vector& KdTree::GetVertices() const { + return m_vertices; +} + +std::vector&& KdTree::TakeVertices() { + return std::move(m_vertices); +} + +uint32_t KdTree::GetVCount() const { return uint32_t(m_vertices.size()); } + +KdTreeNode::KdTreeNode(uint32_t index) : m_index(index) {} + +void KdTreeNode::Add(KdTreeNode& node, Axes dim, const KdTree& tree) { + Axes axis = X_AXIS; + uint32_t idx = 0; + switch (dim) { + case X_AXIS: + idx = 0; + axis = Y_AXIS; + break; + case Y_AXIS: + idx = 1; + axis = Z_AXIS; + break; + case Z_AXIS: + idx = 2; + axis = X_AXIS; + break; + } + + const VHACD::Vertex& nodePosition = tree.GetPosition(node.m_index); + const VHACD::Vertex& position = tree.GetPosition(m_index); + if (nodePosition[idx] <= position[idx]) { + if (m_left) + m_left->Add(node, axis, tree); + else + m_left = &node; + } else { + if (m_right) + m_right->Add(node, axis, tree); + else + m_right = &node; + } +} + +uint32_t KdTreeNode::GetIndex() const { return m_index; } + +void KdTreeNode::Search(Axes axis, const VHACD::Vect3& pos, double radius, + uint32_t& count, uint32_t maxObjects, + KdTreeFindNode* found, const KdTree& iface) { + const VHACD::Vect3 position = iface.GetPosition(m_index); + + const VHACD::Vect3 d = pos - position; + + KdTreeNode* search1 = 0; + KdTreeNode* search2 = 0; + + uint32_t idx = 0; + switch (axis) { + case X_AXIS: + idx = 0; + axis = Y_AXIS; + break; + case Y_AXIS: + idx = 1; + axis = Z_AXIS; + break; + case Z_AXIS: + idx = 2; + axis = X_AXIS; + break; + } + + if (d[idx] <= 0) // JWR if we are to the left + { + search1 = m_left; // JWR then search to the left + if (-d[idx] < radius) // JWR if distance to the right is less than our + // search radius, continue on the right as well. + search2 = m_right; + } else { + search1 = m_right; // JWR ok, we go down the left tree + if (d[idx] < radius) // JWR if the distance from the right is less than + // our search radius + search2 = m_left; + } + + double r2 = radius * radius; + double m = d.GetNormSquared(); + + if (m < r2) { + switch (count) { + case 0: { + found[count].m_node = this; + found[count].m_distance = m; + break; + } + case 1: { + if (m < found[0].m_distance) { + if (maxObjects == 1) { + found[0].m_node = this; + found[0].m_distance = m; + } else { + found[1] = found[0]; + found[0].m_node = this; + found[0].m_distance = m; + } + } else if (maxObjects > 1) { + found[1].m_node = this; + found[1].m_distance = m; + } + break; + } + default: { + bool inserted = false; + + for (uint32_t i = 0; i < count; i++) { + if (m < found[i].m_distance) // if this one is closer than a + // pre-existing one... + { + // insertion sort... + uint32_t scan = count; + if (scan >= maxObjects) scan = maxObjects - 1; + for (uint32_t j = scan; j > i; j--) { + found[j] = found[j - 1]; + } + found[i].m_node = this; + found[i].m_distance = m; + inserted = true; + break; + } + } + + if (!inserted && count < maxObjects) { + found[count].m_node = this; + found[count].m_distance = m; + } + } break; + } + + count++; + + if (count > maxObjects) { + count = maxObjects; + } + } + + if (search1) + search1->Search(axis, pos, radius, count, maxObjects, found, iface); + + if (search2) + search2->Search(axis, pos, radius, count, maxObjects, found, iface); +} + +class VertexIndex { + public: + VertexIndex(double granularity, bool snapToGrid); + + VHACD::Vect3 SnapToGrid(VHACD::Vect3 p); + + uint32_t GetIndex(VHACD::Vect3 p, bool& newPos); + + const std::vector& GetVertices() const; + + std::vector&& TakeVertices(); + + uint32_t GetVCount() const; + + bool SaveAsObj(const char* fname, uint32_t tcount, uint32_t* indices) { + bool ret = false; + + FILE* fph = fopen(fname, "wb"); + if (fph) { + ret = true; + + const std::vector& v = GetVertices(); + for (uint32_t i = 0; i < v.size(); ++i) { + fprintf(fph, "v %0.9f %0.9f %0.9f\r\n", v[i].mX, v[i].mY, v[i].mZ); + } + + for (uint32_t i = 0; i < tcount; i++) { + uint32_t i1 = *indices++; + uint32_t i2 = *indices++; + uint32_t i3 = *indices++; + fprintf(fph, "f %d %d %d\r\n", i1 + 1, i2 + 1, i3 + 1); + } + fclose(fph); + } + + return ret; + } + + private: + bool m_snapToGrid : 1; + double m_granularity; + KdTree m_KdTree; +}; + +VertexIndex::VertexIndex(double granularity, bool snapToGrid) + : m_snapToGrid(snapToGrid), m_granularity(granularity) {} + +VHACD::Vect3 VertexIndex::SnapToGrid(VHACD::Vect3 p) { + for (int i = 0; i < 3; ++i) { + double m = fmod(p[i], m_granularity); + p[i] -= m; + } + return p; +} + +uint32_t VertexIndex::GetIndex(VHACD::Vect3 p, bool& newPos) { + uint32_t ret; + + newPos = false; + + if (m_snapToGrid) { + p = SnapToGrid(p); + } + + bool found; + ret = m_KdTree.GetNearest(p, m_granularity, found); + if (!found) { + newPos = true; + ret = m_KdTree.Add(VHACD::Vertex(p.GetX(), p.GetY(), p.GetZ())); + } + + return ret; +} + +const std::vector& VertexIndex::GetVertices() const { + return m_KdTree.GetVertices(); +} + +std::vector&& VertexIndex::TakeVertices() { + return std::move(m_KdTree.TakeVertices()); +} + +uint32_t VertexIndex::GetVCount() const { return m_KdTree.GetVCount(); } + +/* + * A wrapper class for 3 10 bit integers packed into a 32 bit integer + * Layout is [PAD][X][Y][Z] + * Pad is bits 31-30, X is 29-20, Y is 19-10, and Z is 9-0 + */ +class Voxel { + /* + * Specify all of them for consistency + */ + static constexpr int VoxelBitsZStart = 0; + static constexpr int VoxelBitsYStart = 10; + static constexpr int VoxelBitsXStart = 20; + static constexpr int VoxelBitMask = 0x03FF; // bits 0 through 9 inclusive + public: + Voxel() = default; + + Voxel(uint32_t index); + + Voxel(uint32_t x, uint32_t y, uint32_t z); + + bool operator==(const Voxel& v) const; + + VHACD::Vector3 GetVoxel() const; + + uint32_t GetX() const; + uint32_t GetY() const; + uint32_t GetZ() const; + + uint32_t GetVoxelAddress() const; + + private: + uint32_t m_voxel{0}; +}; + +Voxel::Voxel(uint32_t index) : m_voxel(index) {} + +Voxel::Voxel(uint32_t x, uint32_t y, uint32_t z) + : m_voxel((x << VoxelBitsXStart) | (y << VoxelBitsYStart) | + (z << VoxelBitsZStart)) { + assert(x < 1024 && "Voxel constructed with X outside of range"); + assert(y < 1024 && "Voxel constructed with Y outside of range"); + assert(z < 1024 && "Voxel constructed with Z outside of range"); +} + +bool Voxel::operator==(const Voxel& v) const { return m_voxel == v.m_voxel; } + +VHACD::Vector3 Voxel::GetVoxel() const { + return VHACD::Vector3(GetX(), GetY(), GetZ()); +} + +uint32_t Voxel::GetX() const { + return (m_voxel >> VoxelBitsXStart) & VoxelBitMask; +} + +uint32_t Voxel::GetY() const { + return (m_voxel >> VoxelBitsYStart) & VoxelBitMask; +} + +uint32_t Voxel::GetZ() const { + return (m_voxel >> VoxelBitsZStart) & VoxelBitMask; +} + +uint32_t Voxel::GetVoxelAddress() const { return m_voxel; } + +struct SimpleMesh { + std::vector m_vertices; + std::vector m_indices; +}; + +/*======================== 0-tests ========================*/ +inline bool IntersectRayAABB(const VHACD::Vect3& start, const VHACD::Vect3& dir, + const VHACD::BoundsAABB& bounds, double& t) { + //! calculate candidate plane on each axis + bool inside = true; + VHACD::Vect3 ta(double(-1.0)); + + //! use unrolled loops + for (uint32_t i = 0; i < 3; ++i) { + if (start[i] < bounds.GetMin()[i]) { + if (dir[i] != double(0.0)) + ta[i] = (bounds.GetMin()[i] - start[i]) / dir[i]; + inside = false; + } else if (start[i] > bounds.GetMax()[i]) { + if (dir[i] != double(0.0)) + ta[i] = (bounds.GetMax()[i] - start[i]) / dir[i]; + inside = false; + } + } + + //! if point inside all planes + if (inside) { + t = double(0.0); + return true; + } + + //! we now have t values for each of possible intersection planes + //! find the maximum to get the intersection point + uint32_t taxis; + double tmax = ta.MaxCoeff(taxis); + + if (tmax < double(0.0)) return false; + + //! check that the intersection point lies on the plane we picked + //! we don't test the axis of closest intersection for precision reasons + + //! no eps for now + double eps = double(0.0); + + VHACD::Vect3 hit = start + dir * tmax; + + if ((hit.GetX() < bounds.GetMin().GetX() - eps || + hit.GetX() > bounds.GetMax().GetX() + eps) && + taxis != 0) + return false; + if ((hit.GetY() < bounds.GetMin().GetY() - eps || + hit.GetY() > bounds.GetMax().GetY() + eps) && + taxis != 1) + return false; + if ((hit.GetZ() < bounds.GetMin().GetZ() - eps || + hit.GetZ() > bounds.GetMax().GetZ() + eps) && + taxis != 2) + return false; + + //! output results + t = tmax; + + return true; +} + +// Moller and Trumbore's method +inline bool IntersectRayTriTwoSided( + const VHACD::Vect3& p, const VHACD::Vect3& dir, const VHACD::Vect3& a, + const VHACD::Vect3& b, const VHACD::Vect3& c, double& t, double& u, + double& v, double& w, double& sign, VHACD::Vect3* normal) { + VHACD::Vect3 ab = b - a; + VHACD::Vect3 ac = c - a; + VHACD::Vect3 n = ab.Cross(ac); + + double d = -dir.Dot(n); + double ood = double(1.0) / d; // No need to check for division by zero here + // as infinity arithmetic will save us... + VHACD::Vect3 ap = p - a; + + t = ap.Dot(n) * ood; + if (t < double(0.0)) { + return false; + } + + VHACD::Vect3 e = -dir.Cross(ap); + v = ac.Dot(e) * ood; + if (v < double(0.0) || v > double(1.0)) // ...here... + { + return false; + } + w = -ab.Dot(e) * ood; + if (w < double(0.0) || v + w > double(1.0)) // ...and here + { + return false; + } + + u = double(1.0) - v - w; + if (normal) { + *normal = n; + } + + sign = d; + + return true; +} + +// RTCD 5.1.5, page 142 +inline VHACD::Vect3 ClosestPointOnTriangle(const VHACD::Vect3& a, + const VHACD::Vect3& b, + const VHACD::Vect3& c, + const VHACD::Vect3& p, double& v, + double& w) { + VHACD::Vect3 ab = b - a; + VHACD::Vect3 ac = c - a; + VHACD::Vect3 ap = p - a; + + double d1 = ab.Dot(ap); + double d2 = ac.Dot(ap); + if (d1 <= double(0.0) && d2 <= double(0.0)) { + v = double(0.0); + w = double(0.0); + return a; + } + + VHACD::Vect3 bp = p - b; + double d3 = ab.Dot(bp); + double d4 = ac.Dot(bp); + if (d3 >= double(0.0) && d4 <= d3) { + v = double(1.0); + w = double(0.0); + return b; + } + + double vc = d1 * d4 - d3 * d2; + if (vc <= double(0.0) && d1 >= double(0.0) && d3 <= double(0.0)) { + v = d1 / (d1 - d3); + w = double(0.0); + return a + v * ab; + } + + VHACD::Vect3 cp = p - c; + double d5 = ab.Dot(cp); + double d6 = ac.Dot(cp); + if (d6 >= double(0.0) && d5 <= d6) { + v = double(0.0); + w = double(1.0); + return c; + } + + double vb = d5 * d2 - d1 * d6; + if (vb <= double(0.0) && d2 >= double(0.0) && d6 <= double(0.0)) { + v = double(0.0); + w = d2 / (d2 - d6); + return a + w * ac; + } + + double va = d3 * d6 - d5 * d4; + if (va <= double(0.0) && (d4 - d3) >= double(0.0) && + (d5 - d6) >= double(0.0)) { + w = (d4 - d3) / ((d4 - d3) + (d5 - d6)); + v = double(1.0) - w; + return b + w * (c - b); + } + + double denom = double(1.0) / (va + vb + vc); + v = vb * denom; + w = vc * denom; + return a + ab * v + ac * w; +} + +class AABBTree { + public: + AABBTree() = default; + AABBTree(AABBTree&&) = default; + AABBTree& operator=(AABBTree&&) = default; + + AABBTree(const std::vector& vertices, + const std::vector& indices); + + bool TraceRay(const VHACD::Vect3& start, const VHACD::Vect3& to, double& outT, + double& faceSign, VHACD::Vect3& hitLocation) const; + + bool TraceRay(const VHACD::Vect3& start, const VHACD::Vect3& dir, + uint32_t& insideCount, uint32_t& outsideCount) const; + + bool TraceRay(const VHACD::Vect3& start, const VHACD::Vect3& dir, + double& outT, double& u, double& v, double& w, double& faceSign, + uint32_t& faceIndex) const; + + VHACD::Vect3 GetCenter() const; + VHACD::Vect3 GetMinExtents() const; + VHACD::Vect3 GetMaxExtents() const; + + bool GetClosestPointWithinDistance(const VHACD::Vect3& point, + double maxDistance, + VHACD::Vect3& closestPoint) const; + + private: + struct Node { + union { + uint32_t m_children; + uint32_t m_numFaces{0}; + }; + + uint32_t* m_faces{nullptr}; + VHACD::BoundsAABB m_extents; + }; + + struct FaceSorter { + FaceSorter(const std::vector& positions, + const std::vector& indices, uint32_t axis); + + bool operator()(uint32_t lhs, uint32_t rhs) const; + + double GetCentroid(uint32_t face) const; + + const std::vector& m_vertices; + const std::vector& m_indices; + uint32_t m_axis; + }; + + // partition the objects and return the number of objects in the lower + // partition + uint32_t PartitionMedian(Node& n, uint32_t* faces, uint32_t numFaces); + uint32_t PartitionSAH(Node& n, uint32_t* faces, uint32_t numFaces); + + void Build(); + + void BuildRecursive(uint32_t nodeIndex, uint32_t* faces, uint32_t numFaces); + + void TraceRecursive(uint32_t nodeIndex, const VHACD::Vect3& start, + const VHACD::Vect3& dir, double& outT, double& u, + double& v, double& w, double& faceSign, + uint32_t& faceIndex) const; + + bool GetClosestPointWithinDistance(const VHACD::Vect3& point, + const double maxDis, double& dis, + double& v, double& w, uint32_t& faceIndex, + VHACD::Vect3& closest) const; + + void GetClosestPointWithinDistanceSqRecursive(uint32_t nodeIndex, + const VHACD::Vect3& point, + double& outDisSq, double& outV, + double& outW, + uint32_t& outFaceIndex, + VHACD::Vect3& closest) const; + + VHACD::BoundsAABB CalculateFaceBounds(uint32_t* faces, uint32_t numFaces); + + // track the next free node + uint32_t m_freeNode; + + const std::vector* m_vertices{nullptr}; + const std::vector* m_indices{nullptr}; + + std::vector m_faces; + std::vector m_nodes; + std::vector m_faceBounds; + + // stats + uint32_t m_treeDepth{0}; + uint32_t m_innerNodes{0}; + uint32_t m_leafNodes{0}; + + uint32_t s_depth{0}; +}; + +AABBTree::FaceSorter::FaceSorter(const std::vector& positions, + const std::vector& indices, + uint32_t axis) + : m_vertices(positions), m_indices(indices), m_axis(axis) {} + +inline bool AABBTree::FaceSorter::operator()(uint32_t lhs, uint32_t rhs) const { + double a = GetCentroid(lhs); + double b = GetCentroid(rhs); + + if (a == b) { + return lhs < rhs; + } else { + return a < b; + } +} + +inline double AABBTree::FaceSorter::GetCentroid(uint32_t face) const { + const VHACD::Vect3& a = m_vertices[m_indices[face].mI0]; + const VHACD::Vect3& b = m_vertices[m_indices[face].mI1]; + const VHACD::Vect3& c = m_vertices[m_indices[face].mI2]; + + return (a[m_axis] + b[m_axis] + c[m_axis]) / double(3.0); +} + +AABBTree::AABBTree(const std::vector& vertices, + const std::vector& indices) + : m_vertices(&vertices), m_indices(&indices) { + Build(); +} + +bool AABBTree::TraceRay(const VHACD::Vect3& start, const VHACD::Vect3& to, + double& outT, double& faceSign, + VHACD::Vect3& hitLocation) const { + VHACD::Vect3 dir = to - start; + double distance = dir.Normalize(); + double u, v, w; + uint32_t faceIndex; + bool hit = TraceRay(start, dir, outT, u, v, w, faceSign, faceIndex); + if (hit) { + hitLocation = start + dir * outT; + } + + if (hit && outT > distance) { + hit = false; + } + return hit; +} + +bool AABBTree::TraceRay(const VHACD::Vect3& start, const VHACD::Vect3& dir, + uint32_t& insideCount, uint32_t& outsideCount) const { + double outT, u, v, w, faceSign; + uint32_t faceIndex; + bool hit = TraceRay(start, dir, outT, u, v, w, faceSign, faceIndex); + if (hit) { + if (faceSign >= 0) { + insideCount++; + } else { + outsideCount++; + } + } + return hit; +} + +bool AABBTree::TraceRay(const VHACD::Vect3& start, const VHACD::Vect3& dir, + double& outT, double& u, double& v, double& w, + double& faceSign, uint32_t& faceIndex) const { + outT = FLT_MAX; + TraceRecursive(0, start, dir, outT, u, v, w, faceSign, faceIndex); + return (outT != FLT_MAX); +} + +VHACD::Vect3 AABBTree::GetCenter() const { + return m_nodes[0].m_extents.GetCenter(); +} + +VHACD::Vect3 AABBTree::GetMinExtents() const { + return m_nodes[0].m_extents.GetMin(); +} + +VHACD::Vect3 AABBTree::GetMaxExtents() const { + return m_nodes[0].m_extents.GetMax(); +} + +bool AABBTree::GetClosestPointWithinDistance(const VHACD::Vect3& point, + double maxDistance, + VHACD::Vect3& closestPoint) const { + double dis, v, w; + uint32_t faceIndex; + bool hit = GetClosestPointWithinDistance(point, maxDistance, dis, v, w, + faceIndex, closestPoint); + return hit; +} + +// partition faces around the median face +uint32_t AABBTree::PartitionMedian(Node& n, uint32_t* faces, + uint32_t numFaces) { + FaceSorter predicate(*m_vertices, *m_indices, + n.m_extents.GetSize().LongestAxis()); + std::nth_element(faces, faces + numFaces / 2, faces + numFaces, predicate); + + return numFaces / 2; +} + +// partition faces based on the surface area heuristic +uint32_t AABBTree::PartitionSAH(Node&, uint32_t* faces, uint32_t numFaces) { + uint32_t bestAxis = 0; + uint32_t bestIndex = 0; + double bestCost = FLT_MAX; + + for (uint32_t a = 0; a < 3; ++a) { + // sort faces by centroids + FaceSorter predicate(*m_vertices, *m_indices, a); + std::sort(faces, faces + numFaces, predicate); + + // two passes over data to calculate upper and lower bounds + std::vector cumulativeLower(numFaces); + std::vector cumulativeUpper(numFaces); + + VHACD::BoundsAABB lower; + VHACD::BoundsAABB upper; + + for (uint32_t i = 0; i < numFaces; ++i) { + lower.Union(m_faceBounds[faces[i]]); + upper.Union(m_faceBounds[faces[numFaces - i - 1]]); + + cumulativeLower[i] = lower.SurfaceArea(); + cumulativeUpper[numFaces - i - 1] = upper.SurfaceArea(); + } + + double invTotalSA = double(1.0) / cumulativeUpper[0]; + + // test all split positions + for (uint32_t i = 0; i < numFaces - 1; ++i) { + double pBelow = cumulativeLower[i] * invTotalSA; + double pAbove = cumulativeUpper[i] * invTotalSA; + + double cost = double(0.125) + (pBelow * i + pAbove * (numFaces - i)); + if (cost <= bestCost) { + bestCost = cost; + bestIndex = i; + bestAxis = a; + } + } + } + + // re-sort by best axis + FaceSorter predicate(*m_vertices, *m_indices, bestAxis); + std::sort(faces, faces + numFaces, predicate); + + return bestIndex + 1; +} + +void AABBTree::Build() { + const uint32_t numFaces = uint32_t(m_indices->size()); + + // build initial list of faces + m_faces.reserve(numFaces); + + // calculate bounds of each face and store + m_faceBounds.reserve(numFaces); + + std::vector stack; + for (uint32_t i = 0; i < numFaces; ++i) { + VHACD::BoundsAABB top = CalculateFaceBounds(&i, 1); + + m_faces.push_back(i); + m_faceBounds.push_back(top); + } + + m_nodes.reserve(uint32_t(numFaces * double(1.5))); + + // allocate space for all the nodes + m_freeNode = 1; + + // start building + BuildRecursive(0, m_faces.data(), numFaces); + + assert(s_depth == 0); +} + +void AABBTree::BuildRecursive(uint32_t nodeIndex, uint32_t* faces, + uint32_t numFaces) { + const uint32_t kMaxFacesPerLeaf = 6; + + // if we've run out of nodes allocate some more + if (nodeIndex >= m_nodes.size()) { + uint32_t s = std::max(uint32_t(double(1.5) * m_nodes.size()), 512U); + m_nodes.resize(s); + } + + // a reference to the current node, need to be careful here as this reference + // may become invalid if array is resized + Node& n = m_nodes[nodeIndex]; + + // track max tree depth + ++s_depth; + m_treeDepth = std::max(m_treeDepth, s_depth); + + n.m_extents = CalculateFaceBounds(faces, numFaces); + + // calculate bounds of faces and add node + if (numFaces <= kMaxFacesPerLeaf) { + n.m_faces = faces; + n.m_numFaces = numFaces; + + ++m_leafNodes; + } else { + ++m_innerNodes; + + // face counts for each branch + const uint32_t leftCount = PartitionMedian(n, faces, numFaces); + // const uint32_t leftCount = PartitionSAH(n, faces, numFaces); + const uint32_t rightCount = numFaces - leftCount; + + // alloc 2 nodes + m_nodes[nodeIndex].m_children = m_freeNode; + + // allocate two nodes + m_freeNode += 2; + + // split faces in half and build each side recursively + BuildRecursive(m_nodes[nodeIndex].m_children + 0, faces, leftCount); + BuildRecursive(m_nodes[nodeIndex].m_children + 1, faces + leftCount, + rightCount); + } + + --s_depth; +} + +void AABBTree::TraceRecursive(uint32_t nodeIndex, const VHACD::Vect3& start, + const VHACD::Vect3& dir, double& outT, + double& outU, double& outV, double& outW, + double& faceSign, uint32_t& faceIndex) const { + const Node& node = m_nodes[nodeIndex]; + + if (node.m_faces == NULL) { + // find closest node + const Node& leftChild = m_nodes[node.m_children + 0]; + const Node& rightChild = m_nodes[node.m_children + 1]; + + double dist[2] = {FLT_MAX, FLT_MAX}; + + IntersectRayAABB(start, dir, leftChild.m_extents, dist[0]); + IntersectRayAABB(start, dir, rightChild.m_extents, dist[1]); + + uint32_t closest = 0; + uint32_t furthest = 1; + + if (dist[1] < dist[0]) { + closest = 1; + furthest = 0; + } + + if (dist[closest] < outT) { + TraceRecursive(node.m_children + closest, start, dir, outT, outU, outV, + outW, faceSign, faceIndex); + } + + if (dist[furthest] < outT) { + TraceRecursive(node.m_children + furthest, start, dir, outT, outU, outV, + outW, faceSign, faceIndex); + } + } else { + double t, u, v, w, s; + + for (uint32_t i = 0; i < node.m_numFaces; ++i) { + uint32_t indexStart = node.m_faces[i]; + + const VHACD::Vect3& a = (*m_vertices)[(*m_indices)[indexStart].mI0]; + const VHACD::Vect3& b = (*m_vertices)[(*m_indices)[indexStart].mI1]; + const VHACD::Vect3& c = (*m_vertices)[(*m_indices)[indexStart].mI2]; + if (IntersectRayTriTwoSided(start, dir, a, b, c, t, u, v, w, s, NULL)) { + if (t < outT) { + outT = t; + outU = u; + outV = v; + outW = w; + faceSign = s; + faceIndex = node.m_faces[i]; + } + } + } + } +} + +bool AABBTree::GetClosestPointWithinDistance(const VHACD::Vect3& point, + const double maxDis, double& dis, + double& v, double& w, + uint32_t& faceIndex, + VHACD::Vect3& closest) const { + dis = maxDis; + faceIndex = uint32_t(~0); + double disSq = dis * dis; + + GetClosestPointWithinDistanceSqRecursive(0, point, disSq, v, w, faceIndex, + closest); + dis = sqrt(disSq); + + return (faceIndex < (~(static_cast(0)))); +} + +void AABBTree::GetClosestPointWithinDistanceSqRecursive( + uint32_t nodeIndex, const VHACD::Vect3& point, double& outDisSq, + double& outV, double& outW, uint32_t& outFaceIndex, + VHACD::Vect3& closestPoint) const { + const Node& node = m_nodes[nodeIndex]; + + if (node.m_faces == nullptr) { + // find closest node + const Node& leftChild = m_nodes[node.m_children + 0]; + const Node& rightChild = m_nodes[node.m_children + 1]; + + // double dist[2] = { FLT_MAX, FLT_MAX }; + VHACD::Vect3 lp = leftChild.m_extents.ClosestPoint(point); + VHACD::Vect3 rp = rightChild.m_extents.ClosestPoint(point); + + uint32_t closest = 0; + uint32_t furthest = 1; + double dcSq = (point - lp).GetNormSquared(); + double dfSq = (point - rp).GetNormSquared(); + if (dfSq < dcSq) { + closest = 1; + furthest = 0; + std::swap(dfSq, dcSq); + } + + if (dcSq < outDisSq) { + GetClosestPointWithinDistanceSqRecursive(node.m_children + closest, point, + outDisSq, outV, outW, + outFaceIndex, closestPoint); + } + + if (dfSq < outDisSq) { + GetClosestPointWithinDistanceSqRecursive(node.m_children + furthest, + point, outDisSq, outV, outW, + outFaceIndex, closestPoint); + } + } else { + double v, w; + for (uint32_t i = 0; i < node.m_numFaces; ++i) { + uint32_t indexStart = node.m_faces[i]; + + const VHACD::Vect3& a = (*m_vertices)[(*m_indices)[indexStart].mI0]; + const VHACD::Vect3& b = (*m_vertices)[(*m_indices)[indexStart].mI1]; + const VHACD::Vect3& c = (*m_vertices)[(*m_indices)[indexStart].mI2]; + + VHACD::Vect3 cp = ClosestPointOnTriangle(a, b, c, point, v, w); + double disSq = (cp - point).GetNormSquared(); + + if (disSq < outDisSq) { + closestPoint = cp; + outDisSq = disSq; + outV = v; + outW = w; + outFaceIndex = node.m_faces[i]; + } + } + } +} + +VHACD::BoundsAABB AABBTree::CalculateFaceBounds(uint32_t* faces, + uint32_t numFaces) { + VHACD::Vect3 minExtents(FLT_MAX); + VHACD::Vect3 maxExtents(-FLT_MAX); + + // calculate face bounds + for (uint32_t i = 0; i < numFaces; ++i) { + VHACD::Vect3 a = (*m_vertices)[(*m_indices)[faces[i]].mI0]; + VHACD::Vect3 b = (*m_vertices)[(*m_indices)[faces[i]].mI1]; + VHACD::Vect3 c = (*m_vertices)[(*m_indices)[faces[i]].mI2]; + + minExtents = a.CWiseMin(minExtents); + maxExtents = a.CWiseMax(maxExtents); + + minExtents = b.CWiseMin(minExtents); + maxExtents = b.CWiseMax(maxExtents); + + minExtents = c.CWiseMin(minExtents); + maxExtents = c.CWiseMax(maxExtents); + } + + return VHACD::BoundsAABB(minExtents, maxExtents); +} + +enum class VoxelValue : uint8_t { + PRIMITIVE_UNDEFINED = 0, + PRIMITIVE_OUTSIDE_SURFACE_TOWALK = 1, + PRIMITIVE_OUTSIDE_SURFACE = 2, + PRIMITIVE_INSIDE_SURFACE = 3, + PRIMITIVE_ON_SURFACE = 4 +}; + +class Volume { + public: + void Voxelize(const std::vector& points, + const std::vector& triangles, const size_t dim, + FillMode fillMode, const AABBTree& aabbTree); + + void RaycastFill(const AABBTree& aabbTree); + + void SetVoxel(const size_t i, const size_t j, const size_t k, + VoxelValue value); + + VoxelValue& GetVoxel(const size_t i, const size_t j, const size_t k); + + const VoxelValue& GetVoxel(const size_t i, const size_t j, + const size_t k) const; + + const std::vector& GetSurfaceVoxels() const; + const std::vector& GetInteriorVoxels() const; + + double GetScale() const; + const VHACD::BoundsAABB& GetBounds() const; + const VHACD::Vector3& GetDimensions() const; + + VHACD::BoundsAABB m_bounds; + double m_scale{1.0}; + VHACD::Vector3 m_dim{0}; + size_t m_numVoxelsOnSurface{0}; + size_t m_numVoxelsInsideSurface{0}; + size_t m_numVoxelsOutsideSurface{0}; + std::vector m_data; + + private: + void MarkOutsideSurface(const size_t i0, const size_t j0, const size_t k0, + const size_t i1, const size_t j1, const size_t k1); + void FillOutsideSurface(); + + void FillInsideSurface(); + + std::vector m_surfaceVoxels; + std::vector m_interiorVoxels; +}; + +bool PlaneBoxOverlap(const VHACD::Vect3& normal, const VHACD::Vect3& vert, + const VHACD::Vect3& maxbox) { + int32_t q; + VHACD::Vect3 vmin; + VHACD::Vect3 vmax; + double v; + for (q = 0; q < 3; q++) { + v = vert[q]; + if (normal[q] > double(0.0)) { + vmin[q] = -maxbox[q] - v; + vmax[q] = maxbox[q] - v; + } else { + vmin[q] = maxbox[q] - v; + vmax[q] = -maxbox[q] - v; + } + } + if (normal.Dot(vmin) > double(0.0)) return false; + if (normal.Dot(vmax) >= double(0.0)) return true; + return false; +} + +bool AxisTest(double a, double b, double fa, double fb, double v0, double v1, + double v2, double v3, double boxHalfSize1, double boxHalfSize2) { + double p0 = a * v0 + b * v1; + double p1 = a * v2 + b * v3; + + double min = std::min(p0, p1); + double max = std::max(p0, p1); + + double rad = fa * boxHalfSize1 + fb * boxHalfSize2; + if (min > rad || max < -rad) { + return false; + } + + return true; +} + +bool TriBoxOverlap(const VHACD::Vect3& boxCenter, + const VHACD::Vect3& boxHalfSize, const VHACD::Vect3& triVer0, + const VHACD::Vect3& triVer1, const VHACD::Vect3& triVer2) { + /* use separating axis theorem to test overlap between triangle and box */ + /* need to test for overlap in these directions: */ + /* 1) the {x,y,z}-directions (actually, since we use the AABB of the + * triangle */ + /* we do not even need to test these) */ + /* 2) normal of the triangle */ + /* 3) crossproduct(edge from tri, {x,y,z}-direction) */ + /* this gives 3x3=9 more tests */ + + VHACD::Vect3 v0 = triVer0 - boxCenter; + VHACD::Vect3 v1 = triVer1 - boxCenter; + VHACD::Vect3 v2 = triVer2 - boxCenter; + VHACD::Vect3 e0 = v1 - v0; + VHACD::Vect3 e1 = v2 - v1; + VHACD::Vect3 e2 = v0 - v2; + + /* This is the fastest branch on Sun */ + /* move everything so that the boxcenter is in (0,0,0) */ + + /* Bullet 3: */ + /* test the 9 tests first (this was faster) */ + double fex = fabs(e0[0]); + double fey = fabs(e0[1]); + double fez = fabs(e0[2]); + + /* + * These should use Get*() instead of subscript for consistency, but the + * function calls are long enough already + */ + if (!AxisTest(e0[2], -e0[1], fez, fey, v0[1], v0[2], v2[1], v2[2], + boxHalfSize[1], boxHalfSize[2])) + return 0; // X01 + if (!AxisTest(-e0[2], e0[0], fez, fex, v0[0], v0[2], v2[0], v2[2], + boxHalfSize[0], boxHalfSize[2])) + return 0; // Y02 + if (!AxisTest(e0[1], -e0[0], fey, fex, v1[0], v1[1], v2[0], v2[1], + boxHalfSize[0], boxHalfSize[1])) + return 0; // Z12 + + fex = fabs(e1[0]); + fey = fabs(e1[1]); + fez = fabs(e1[2]); + + if (!AxisTest(e1[2], -e1[1], fez, fey, v0[1], v0[2], v2[1], v2[2], + boxHalfSize[1], boxHalfSize[2])) + return 0; // X01 + if (!AxisTest(-e1[2], e1[0], fez, fex, v0[0], v0[2], v2[0], v2[2], + boxHalfSize[0], boxHalfSize[2])) + return 0; // Y02 + if (!AxisTest(e1[1], -e1[0], fey, fex, v0[0], v0[1], v1[0], v1[1], + boxHalfSize[0], boxHalfSize[2])) + return 0; // Z0 + + fex = fabs(e2[0]); + fey = fabs(e2[1]); + fez = fabs(e2[2]); + + if (!AxisTest(e2[2], -e2[1], fez, fey, v0[1], v0[2], v1[1], v1[2], + boxHalfSize[1], boxHalfSize[2])) + return 0; // X2 + if (!AxisTest(-e2[2], e2[0], fez, fex, v0[0], v0[2], v1[0], v1[2], + boxHalfSize[0], boxHalfSize[2])) + return 0; // Y1 + if (!AxisTest(e2[1], -e2[0], fey, fex, v1[0], v1[1], v2[0], v2[1], + boxHalfSize[0], boxHalfSize[1])) + return 0; // Z12 + + /* Bullet 1: */ + /* first test overlap in the {x,y,z}-directions */ + /* find min, max of the triangle each direction, and test for overlap in */ + /* that direction -- this is equivalent to testing a minimal AABB around */ + /* the triangle against the AABB */ + + /* test in 0-direction */ + double min = std::min({v0.GetX(), v1.GetX(), v2.GetX()}); + double max = std::max({v0.GetX(), v1.GetX(), v2.GetX()}); + if (min > boxHalfSize[0] || max < -boxHalfSize[0]) return false; + + /* test in 1-direction */ + min = std::min({v0.GetY(), v1.GetY(), v2.GetY()}); + max = std::max({v0.GetY(), v1.GetY(), v2.GetY()}); + if (min > boxHalfSize[1] || max < -boxHalfSize[1]) return false; + + /* test in getZ-direction */ + min = std::min({v0.GetZ(), v1.GetZ(), v2.GetZ()}); + max = std::max({v0.GetZ(), v1.GetZ(), v2.GetZ()}); + if (min > boxHalfSize[2] || max < -boxHalfSize[2]) return false; + + /* Bullet 2: */ + /* test if the box intersects the plane of the triangle */ + /* compute plane equation of triangle: normal*x+d=0 */ + VHACD::Vect3 normal = e0.Cross(e1); + + if (!PlaneBoxOverlap(normal, v0, boxHalfSize)) return false; + return true; /* box and triangle overlaps */ +} + +void Volume::Voxelize(const std::vector& points, + const std::vector& indices, + const size_t dimensions, FillMode fillMode, + const AABBTree& aabbTree) { + double a = std::pow(dimensions, 0.33); + size_t dim = a * double(1.5); + dim = std::max(dim, size_t(32)); + + if (points.size() == 0) { + return; + } + + m_bounds = BoundsAABB(points); + + VHACD::Vect3 d = m_bounds.GetSize(); + double r; + // Equal comparison is important here to avoid taking the last branch when + // d[0] == d[1] with d[2] being the smallest dimension. That would lead to + // dimensions in i and j to be a lot bigger than expected and make the amount + // of voxels in the volume totally unmanageable. + if (d[0] >= d[1] && d[0] >= d[2]) { + r = d[0]; + m_dim[0] = uint32_t(dim); + m_dim[1] = uint32_t(2 + static_cast(dim * d[1] / d[0])); + m_dim[2] = uint32_t(2 + static_cast(dim * d[2] / d[0])); + } else if (d[1] >= d[0] && d[1] >= d[2]) { + r = d[1]; + m_dim[1] = uint32_t(dim); + m_dim[0] = uint32_t(2 + static_cast(dim * d[0] / d[1])); + m_dim[2] = uint32_t(2 + static_cast(dim * d[2] / d[1])); + } else { + r = d[2]; + m_dim[2] = uint32_t(dim); + m_dim[0] = uint32_t(2 + static_cast(dim * d[0] / d[2])); + m_dim[1] = uint32_t(2 + static_cast(dim * d[1] / d[2])); + } + + m_scale = r / (dim - 1); + double invScale = (dim - 1) / r; + + m_data = std::vector(m_dim[0] * m_dim[1] * m_dim[2], + VoxelValue::PRIMITIVE_UNDEFINED); + m_numVoxelsOnSurface = 0; + m_numVoxelsInsideSurface = 0; + m_numVoxelsOutsideSurface = 0; + + VHACD::Vect3 p[3]; + VHACD::Vect3 boxcenter; + VHACD::Vect3 pt; + const VHACD::Vect3 boxhalfsize(double(0.5)); + for (size_t t = 0; t < indices.size(); ++t) { + size_t i0 = 0, j0 = 0, k0 = 0; + size_t i1 = 0, j1 = 0, k1 = 0; + VHACD::Vector3 tri = indices[t]; + for (int32_t c = 0; c < 3; ++c) { + pt = points[tri[c]]; + + p[c] = (pt - m_bounds.GetMin()) * invScale; + + size_t i = static_cast(p[c][0] + double(0.5)); + size_t j = static_cast(p[c][1] + double(0.5)); + size_t k = static_cast(p[c][2] + double(0.5)); + + assert(i < m_dim[0] && j < m_dim[1] && k < m_dim[2]); + + if (c == 0) { + i0 = i1 = i; + j0 = j1 = j; + k0 = k1 = k; + } else { + i0 = std::min(i0, i); + j0 = std::min(j0, j); + k0 = std::min(k0, k); + + i1 = std::max(i1, i); + j1 = std::max(j1, j); + k1 = std::max(k1, k); + } + } + if (i0 > 0) --i0; + if (j0 > 0) --j0; + if (k0 > 0) --k0; + if (i1 < m_dim[0]) ++i1; + if (j1 < m_dim[1]) ++j1; + if (k1 < m_dim[2]) ++k1; + for (size_t i_id = i0; i_id < i1; ++i_id) { + boxcenter[0] = uint32_t(i_id); + for (size_t j_id = j0; j_id < j1; ++j_id) { + boxcenter[1] = uint32_t(j_id); + for (size_t k_id = k0; k_id < k1; ++k_id) { + boxcenter[2] = uint32_t(k_id); + bool res = TriBoxOverlap(boxcenter, boxhalfsize, p[0], p[1], p[2]); + VoxelValue& value = GetVoxel(i_id, j_id, k_id); + if (res && value == VoxelValue::PRIMITIVE_UNDEFINED) { + value = VoxelValue::PRIMITIVE_ON_SURFACE; + ++m_numVoxelsOnSurface; + m_surfaceVoxels.emplace_back(uint32_t(i_id), uint32_t(j_id), + uint32_t(k_id)); + } + } + } + } + } + + if (fillMode == FillMode::SURFACE_ONLY) { + const size_t i0_local = m_dim[0]; + const size_t j0_local = m_dim[1]; + const size_t k0_local = m_dim[2]; + for (size_t i_id = 0; i_id < i0_local; ++i_id) { + for (size_t j_id = 0; j_id < j0_local; ++j_id) { + for (size_t k_id = 0; k_id < k0_local; ++k_id) { + const VoxelValue& voxel = GetVoxel(i_id, j_id, k_id); + if (voxel != VoxelValue::PRIMITIVE_ON_SURFACE) { + SetVoxel(i_id, j_id, k_id, VoxelValue::PRIMITIVE_OUTSIDE_SURFACE); + } + } + } + } + } else if (fillMode == FillMode::FLOOD_FILL) { + /* + * Marking the outside edges of the voxel cube to be outside surfaces to + * walk + */ + MarkOutsideSurface(0, 0, 0, m_dim[0], m_dim[1], 1); + MarkOutsideSurface(0, 0, m_dim[2] - 1, m_dim[0], m_dim[1], m_dim[2]); + MarkOutsideSurface(0, 0, 0, m_dim[0], 1, m_dim[2]); + MarkOutsideSurface(0, m_dim[1] - 1, 0, m_dim[0], m_dim[1], m_dim[2]); + MarkOutsideSurface(0, 0, 0, 1, m_dim[1], m_dim[2]); + MarkOutsideSurface(m_dim[0] - 1, 0, 0, m_dim[0], m_dim[1], m_dim[2]); + FillOutsideSurface(); + FillInsideSurface(); + } else if (fillMode == FillMode::RAYCAST_FILL) { + RaycastFill(aabbTree); + } +} + +void Volume::RaycastFill(const AABBTree& aabbTree) { + const uint32_t i0 = m_dim[0]; + const uint32_t j0 = m_dim[1]; + const uint32_t k0 = m_dim[2]; + + size_t maxSize = i0 * j0 * k0; + + std::vector temp; + temp.reserve(maxSize); + uint32_t count{0}; + m_numVoxelsInsideSurface = 0; + for (uint32_t i = 0; i < i0; ++i) { + for (uint32_t j = 0; j < j0; ++j) { + for (uint32_t k = 0; k < k0; ++k) { + VoxelValue& voxel = GetVoxel(i, j, k); + if (voxel != VoxelValue::PRIMITIVE_ON_SURFACE) { + VHACD::Vect3 start = + VHACD::Vect3(i, j, k) * m_scale + m_bounds.GetMin(); + + uint32_t insideCount = 0; + uint32_t outsideCount = 0; + + VHACD::Vect3 directions[6] = { + VHACD::Vect3(1, 0, 0), + VHACD::Vect3(-1, 0, 0), // this was 1, 0, 0 in the original code, + // but looks wrong + VHACD::Vect3(0, 1, 0), VHACD::Vect3(0, -1, 0), + VHACD::Vect3(0, 0, 1), VHACD::Vect3(0, 0, -1)}; + + for (uint32_t r = 0; r < 6; r++) { + aabbTree.TraceRay(start, directions[r], insideCount, outsideCount); + // Early out if we hit the outside of the mesh + if (outsideCount) { + break; + } + // Early out if we accumulated 3 inside hits + if (insideCount >= 3) { + break; + } + } + + if (outsideCount == 0 && insideCount >= 3) { + voxel = VoxelValue::PRIMITIVE_INSIDE_SURFACE; + temp.emplace_back(i, j, k); + count++; + m_numVoxelsInsideSurface++; + } else { + voxel = VoxelValue::PRIMITIVE_OUTSIDE_SURFACE; + } + } + } + } + } + + if (count) { + m_interiorVoxels = std::move(temp); + } +} + +void Volume::SetVoxel(const size_t i, const size_t j, const size_t k, + VoxelValue value) { + assert(i < m_dim[0]); + assert(j < m_dim[1]); + assert(k < m_dim[2]); + + m_data[k + j * m_dim[2] + i * m_dim[1] * m_dim[2]] = value; +} + +VoxelValue& Volume::GetVoxel(const size_t i, const size_t j, const size_t k) { + assert(i < m_dim[0]); + assert(j < m_dim[1]); + assert(k < m_dim[2]); + return m_data[k + j * m_dim[2] + i * m_dim[1] * m_dim[2]]; +} + +const VoxelValue& Volume::GetVoxel(const size_t i, const size_t j, + const size_t k) const { + assert(i < m_dim[0]); + assert(j < m_dim[1]); + assert(k < m_dim[2]); + return m_data[k + j * m_dim[2] + i * m_dim[1] * m_dim[2]]; +} + +const std::vector& Volume::GetSurfaceVoxels() const { + return m_surfaceVoxels; +} + +const std::vector& Volume::GetInteriorVoxels() const { + return m_interiorVoxels; +} + +double Volume::GetScale() const { return m_scale; } + +const VHACD::BoundsAABB& Volume::GetBounds() const { return m_bounds; } + +const VHACD::Vector3& Volume::GetDimensions() const { return m_dim; } + +void Volume::MarkOutsideSurface(const size_t i0, const size_t j0, + const size_t k0, const size_t i1, + const size_t j1, const size_t k1) { + for (size_t i = i0; i < i1; ++i) { + for (size_t j = j0; j < j1; ++j) { + for (size_t k = k0; k < k1; ++k) { + VoxelValue& v = GetVoxel(i, j, k); + if (v == VoxelValue::PRIMITIVE_UNDEFINED) { + v = VoxelValue::PRIMITIVE_OUTSIDE_SURFACE_TOWALK; + } + } + } + } +} + +inline void WalkForward(int64_t start, int64_t end, VoxelValue* ptr, + int64_t stride, int64_t maxDistance) { + for (int64_t i = start, count = 0; count < maxDistance && i < end && + *ptr == VoxelValue::PRIMITIVE_UNDEFINED; + ++i, ptr += stride, ++count) { + *ptr = VoxelValue::PRIMITIVE_OUTSIDE_SURFACE_TOWALK; + } +} + +inline void WalkBackward(int64_t start, int64_t end, VoxelValue* ptr, + int64_t stride, int64_t maxDistance) { + for (int64_t i = start, count = 0; count < maxDistance && i >= end && + *ptr == VoxelValue::PRIMITIVE_UNDEFINED; + --i, ptr -= stride, ++count) { + *ptr = VoxelValue::PRIMITIVE_OUTSIDE_SURFACE_TOWALK; + } +} + +void Volume::FillOutsideSurface() { + size_t voxelsWalked = 0; + const int64_t i0 = m_dim[0]; + const int64_t j0 = m_dim[1]; + const int64_t k0 = m_dim[2]; + + // Avoid striding too far in each direction to stay in L1 cache as much as + // possible. The cache size required for the walk is roughly (4 * walkDistance + // * 64) since the k direction doesn't count as it's walking byte per byte + // directly in a cache lines. ~16k is required for a walk distance of 64 in + // each directions. + const size_t walkDistance = 64; + + // using the stride directly instead of calling GetVoxel for each iterations + // saves a lot of multiplications and pipeline stalls due to data dependencies + // on imul. + const size_t istride = &GetVoxel(1, 0, 0) - &GetVoxel(0, 0, 0); + const size_t jstride = &GetVoxel(0, 1, 0) - &GetVoxel(0, 0, 0); + const size_t kstride = &GetVoxel(0, 0, 1) - &GetVoxel(0, 0, 0); + + // It might seem counter intuitive to go over the whole voxel range multiple + // times but since we do the run in memory order, it leaves us with far fewer + // cache misses than a BFS algorithm and it has the additional benefit of not + // requiring us to store and manipulate a fifo for recursion that might become + // huge when the number of voxels is large. This will outperform the BFS + // algorithm by several orders of magnitude in practice. + do { + voxelsWalked = 0; + for (int64_t i = 0; i < i0; ++i) { + for (int64_t j = 0; j < j0; ++j) { + for (int64_t k = 0; k < k0; ++k) { + VoxelValue& voxel = GetVoxel(i, j, k); + if (voxel == VoxelValue::PRIMITIVE_OUTSIDE_SURFACE_TOWALK) { + voxelsWalked++; + voxel = VoxelValue::PRIMITIVE_OUTSIDE_SURFACE; + + // walk in each direction to mark other voxel that should be walked. + // this will generate a 3d pattern that will help the overall + // algorithm converge faster while remaining cache friendly. + WalkForward(k + 1, k0, &voxel + kstride, kstride, walkDistance); + WalkBackward(k - 1, 0, &voxel - kstride, kstride, walkDistance); + + WalkForward(j + 1, j0, &voxel + jstride, jstride, walkDistance); + WalkBackward(j - 1, 0, &voxel - jstride, jstride, walkDistance); + + WalkForward(i + 1, i0, &voxel + istride, istride, walkDistance); + WalkBackward(i - 1, 0, &voxel - istride, istride, walkDistance); + } + } + } + } + + m_numVoxelsOutsideSurface += voxelsWalked; + } while (voxelsWalked != 0); +} + +void Volume::FillInsideSurface() { + const uint32_t i0 = uint32_t(m_dim[0]); + const uint32_t j0 = uint32_t(m_dim[1]); + const uint32_t k0 = uint32_t(m_dim[2]); + + size_t maxSize = i0 * j0 * k0; + + std::vector temp; + temp.reserve(maxSize); + uint32_t count{0}; + + for (uint32_t i = 0; i < i0; ++i) { + for (uint32_t j = 0; j < j0; ++j) { + for (uint32_t k = 0; k < k0; ++k) { + VoxelValue& v = GetVoxel(i, j, k); + if (v == VoxelValue::PRIMITIVE_UNDEFINED) { + v = VoxelValue::PRIMITIVE_INSIDE_SURFACE; + temp.emplace_back(i, j, k); + count++; + ++m_numVoxelsInsideSurface; + } + } + } + } + + if (count) { + m_interiorVoxels = std::move(temp); + } +} + +//****************************************************************************************** +// ShrinkWrap helper class +//****************************************************************************************** +// This is a code snippet which 'shrinkwraps' a convex hull +// to a source mesh. +// +// It is a somewhat complicated algorithm. It works as follows: +// +// * Step #1 : Compute the mean unit normal vector for each vertex in the convex +// hull +// * Step #2 : For each vertex in the conex hull we project is slightly outwards +// along the mean normal vector +// * Step #3 : We then raycast from this slightly extruded point back into the +// opposite direction of the mean normal vector +// resulting in a raycast from slightly beyond the vertex in the +// hull into the source mesh we are trying to 'shrink wrap' against +// * Step #4 : If the raycast fails we leave the original vertex alone +// * Step #5 : If the raycast hits a backface we leave the original vertex alone +// * Step #6 : If the raycast hits too far away (no more than a certain +// threshold distance) we live it alone +// * Step #7 : If the point we hit on the source mesh is not still within the +// convex hull, we reject it. +// * Step #8 : If all of the previous conditions are met, then we take the +// raycast hit location as the 'new position' +// * Step #9 : Once all points have been projected, if possible, we need to +// recompute the convex hull again based on these shrinkwrapped points +// * Step #10 : In theory that should work.. let's see... + +//*********************************************************************************************** +// QuickHull implementation +//*********************************************************************************************** + +////////////////////////////////////////////////////////////////////////// +// Quickhull base class holding the hull during construction +////////////////////////////////////////////////////////////////////////// +class QuickHull { + public: + uint32_t ComputeConvexHull(const std::vector& vertices, + uint32_t maxHullVertices); + + const std::vector& GetVertices() const; + const std::vector& GetIndices() const; + + private: + std::vector m_vertices; + std::vector m_indices; +}; + +uint32_t QuickHull::ComputeConvexHull( + const std::vector& vertices, uint32_t maxHullVertices) { + m_indices.clear(); + + VHACD::ConvexHull ch(vertices, double(0.0001), maxHullVertices); + + auto& vlist = ch.GetVertexPool(); + if (!vlist.empty()) { + size_t vcount = vlist.size(); + m_vertices.resize(vcount); + std::copy(vlist.begin(), vlist.end(), m_vertices.begin()); + } + + for (std::list::const_iterator node = ch.GetList().begin(); + node != ch.GetList().end(); ++node) { + const VHACD::ConvexHullFace& face = *node; + m_indices.emplace_back(face.m_index[0], face.m_index[1], face.m_index[2]); + } + + return uint32_t(m_indices.size()); +} + +const std::vector& QuickHull::GetVertices() const { + return m_vertices; +} + +const std::vector& QuickHull::GetIndices() const { + return m_indices; +} + +//****************************************************************************************** +// Implementation of the ShrinkWrap function +//****************************************************************************************** + +void ShrinkWrap(SimpleMesh& sourceConvexHull, const AABBTree& aabbTree, + uint32_t maxHullVertexCount, double distanceThreshold, + bool doShrinkWrap) { + std::vector verts; // New verts for the new convex hull + verts.reserve(sourceConvexHull.m_vertices.size()); + // Examine each vertex and see if it is within the voxel distance. + // If it is, then replace the point with the shrinkwrapped / projected point + for (uint32_t j = 0; j < sourceConvexHull.m_vertices.size(); j++) { + VHACD::Vertex& p = sourceConvexHull.m_vertices[j]; + if (doShrinkWrap) { + VHACD::Vect3 closest; + if (aabbTree.GetClosestPointWithinDistance(p, distanceThreshold, + closest)) { + p = closest; + } + } + verts.emplace_back(p); + } + // Final step is to recompute the convex hull + VHACD::QuickHull qh; + uint32_t tcount = qh.ComputeConvexHull(verts, maxHullVertexCount); + if (tcount) { + sourceConvexHull.m_vertices = qh.GetVertices(); + sourceConvexHull.m_indices = qh.GetIndices(); + } +} + +//******************************************************************************************************************** + +#if !VHACD_DISABLE_THREADING + +//******************************************************************************************************************** +// Definition of the ThreadPool +//******************************************************************************************************************** + +class ThreadPool { + public: + ThreadPool(); + ThreadPool(int worker); + ~ThreadPool(); + template + auto enqueue(F&& f, Args&&... args) +#ifndef __cpp_lib_is_invocable + -> std::future::type>; +#else + -> std::future>; +#endif + private: + std::vector workers; + std::deque> tasks; + std::mutex task_mutex; + std::condition_variable cv; + bool closed; +}; + +ThreadPool::ThreadPool() : ThreadPool(1) {} + +ThreadPool::ThreadPool(int worker) : closed(false) { + workers.reserve(worker); + for (int i = 0; i < worker; i++) { + workers.emplace_back([this] { + std::unique_lock lock(this->task_mutex); + while (true) { + while (this->tasks.empty()) { + if (this->closed) { + return; + } + this->cv.wait(lock); + } + auto task = this->tasks.front(); + this->tasks.pop_front(); + lock.unlock(); + task(); + lock.lock(); + } + }); + } +} + +template +auto ThreadPool::enqueue(F&& f, Args&&... args) +#ifndef __cpp_lib_is_invocable + -> std::future::type> +#else + -> std::future> +#endif +{ + +#ifndef __cpp_lib_is_invocable + using return_type = typename std::result_of::type; +#else + using return_type = typename std::invoke_result_t; +#endif + auto task = std::make_shared>( + std::bind(std::forward(f), std::forward(args)...)); + auto result = task->get_future(); + + { + std::unique_lock lock(task_mutex); + if (!closed) { + tasks.emplace_back([task] { (*task)(); }); + cv.notify_one(); + } + } + + return result; +} + +ThreadPool::~ThreadPool() { + { + std::unique_lock lock(task_mutex); + closed = true; + } + cv.notify_all(); + for (auto&& worker : workers) { + worker.join(); + } +} +#endif + +enum class Stages { + COMPUTE_BOUNDS_OF_INPUT_MESH, + REINDEXING_INPUT_MESH, + CREATE_RAYCAST_MESH, + VOXELIZING_INPUT_MESH, + BUILD_INITIAL_CONVEX_HULL, + PERFORMING_DECOMPOSITION, + INITIALIZING_CONVEX_HULLS_FOR_MERGING, + COMPUTING_COST_MATRIX, + MERGING_CONVEX_HULLS, + FINALIZING_RESULTS, + NUM_STAGES +}; + +class VHACDCallbacks { + public: + virtual void ProgressUpdate(Stages stage, double stageProgress, + const char* operation) = 0; + virtual bool IsCanceled() const = 0; + + virtual ~VHACDCallbacks() = default; +}; + +enum class SplitAxis { + X_AXIS_NEGATIVE, + X_AXIS_POSITIVE, + Y_AXIS_NEGATIVE, + Y_AXIS_POSITIVE, + Z_AXIS_NEGATIVE, + Z_AXIS_POSITIVE, +}; + +// This class represents a collection of voxels, the convex hull +// which surrounds them, and a triangle mesh representation of those voxels +class VoxelHull { + public: + // This method constructs a new VoxelHull based on a plane split of the parent + // convex hull + VoxelHull(const VoxelHull& parent, SplitAxis axis, uint32_t splitLoc); + + // Here we construct the initial convex hull around the + // entire voxel set + VoxelHull(Volume& voxels, const IVHACD::Parameters& params, + VHACDCallbacks* callbacks); + + ~VoxelHull() = default; + + // Helper method to refresh the min/max voxel bounding region + void MinMaxVoxelRegion(const Voxel& v); + + void BuildRaycastMesh(); + + // We now compute the convex hull relative to a triangle mesh generated + // from the voxels + void ComputeConvexHull(); + + // Returns true if this convex hull should be considered done + bool IsComplete(); + + // Convert a voxel position into it's correct double precision location + VHACD::Vect3 GetPoint(const int32_t x, const int32_t y, const int32_t z, + const double scale, const VHACD::Vect3& bmin) const; + + // Sees if we have already got an index for this voxel position. + // If the voxel position has already been indexed, we just return + // that index value. + // If not, then we convert it into the floating point position and + // add it to the index map + uint32_t GetVertexIndex(const VHACD::Vector3& p); + + // This method will convert the voxels into an actual indexed triangle mesh of + // boxes This serves two purposes. The primary purpose is so that when we + // compute a convex hull it considered all of the points for each voxel, not + // just the center point. If you don't do this, then the hulls don't fit the + // mesh accurately enough. + // The second reason we convert it into a triangle mesh is so that we can do + // raycasting against it to search for the best splitting plane fairly + // quickly. That algorithm will be discussed in the method which computes the + // best splitting plane. + void BuildVoxelMesh(); + + // Convert a single voxel position into an actual 3d box mesh comprised + // of 12 triangles + void AddVoxelBox(const Voxel& v); + + // Add the triangle represented by these 3 indices into the 'box' set of + // vertices to the output mesh + void AddTri(const std::array, 8>& box, uint32_t i1, + uint32_t i2, uint32_t i3); + + // Here we convert from voxel space to a 3d position, index it, and add + // the triangle positions and indices for the output mesh + void AddTriangle(const VHACD::Vector3& p1, + const VHACD::Vector3& p2, + const VHACD::Vector3& p3); + + // When computing the split plane, we start by simply + // taking the midpoint of the longest side. However, + // we can also search the surface and look for the greatest + // spot of concavity and use that as the split location. + // This will make the convex decomposition more efficient + // as it will tend to cut across the greatest point of + // concavity on the surface. + SplitAxis ComputeSplitPlane(uint32_t& location); + + VHACD::Vect3 GetPosition(const VHACD::Vector3& ip) const; + + double Raycast(const VHACD::Vector3& p1, + const VHACD::Vector3& p2) const; + + bool FindConcavity(uint32_t idx, uint32_t& splitLoc); + + // Finding the greatest area of concavity.. + bool FindConcavityX(uint32_t& splitLoc); + + // Finding the greatest area of concavity.. + bool FindConcavityY(uint32_t& splitLoc); + + // Finding the greatest area of concavity.. + bool FindConcavityZ(uint32_t& splitLoc); + + // This operation is performed in a background thread. + // It splits the voxels by a plane + void PerformPlaneSplit(); + + // Used only for debugging. Saves the voxelized mesh to disk + // Optionally saves the original source mesh as well for comparison + void SaveVoxelMesh(const SimpleMesh& inputMesh, bool saveVoxelMesh, + bool saveSourceMesh); + + void SaveOBJ(const char* fname, const VoxelHull* h); + + void SaveOBJ(const char* fname); + + private: + void WriteOBJ(FILE* fph, const std::vector& vertices, + const std::vector& indices, + uint32_t baseIndex); + + public: + SplitAxis m_axis{SplitAxis::X_AXIS_NEGATIVE}; + Volume* m_voxels{nullptr}; // The voxelized data set + double m_voxelScale{0}; // Size of a single voxel + double m_voxelScaleHalf{0}; // 1/2 of the size of a single voxel + VHACD::BoundsAABB m_voxelBounds; + VHACD::Vect3 + m_voxelAdjust; // Minimum coordinates of the voxel space, with adjustment + uint32_t m_depth{ + 0}; // How deep in the recursion of the binary tree this hull is + uint32_t m_index{0}; // Each convex hull is given a unique id to distinguish + // it from the others + double m_volumeError{0}; // The percentage error from the convex hull volume + // vs. the voxel volume + double m_voxelVolume{0}; // The volume of the voxels + double m_hullVolume{0}; // The volume of the enclosing convex hull + + std::unique_ptr m_convexHull{ + nullptr}; // The convex hull which encloses this set of voxels. + std::vector m_surfaceVoxels; // The voxels which are on the surface of + // the source mesh. + std::vector m_newSurfaceVoxels; // Voxels which are on the surface as + // a result of a plane split + std::vector + m_interiorVoxels; // Voxels which are part of the interior of the hull + + std::unique_ptr m_hullA{ + nullptr}; // hull resulting from one side of the plane split + std::unique_ptr m_hullB{ + nullptr}; // hull resulting from the other side of the plane split + + // Defines the coordinates this convex hull comprises within the voxel volume + // of the entire source + VHACD::Vector3 m_1{0}; + VHACD::Vector3 m_2{0}; + AABBTree m_AABBTree; + std::unordered_map + m_voxelIndexMap; // Maps from a voxel coordinate space into a vertex + // index space + std::vector m_vertices; + std::vector m_indices; + static uint32_t m_voxelHullCount; + IVHACD::Parameters m_params; + VHACDCallbacks* m_callbacks{nullptr}; +}; + +uint32_t VoxelHull::m_voxelHullCount = 0; + +VoxelHull::VoxelHull(const VoxelHull& parent, SplitAxis axis, uint32_t splitLoc) + : m_axis(axis), + m_voxels(parent.m_voxels), + m_voxelScale(m_voxels->GetScale()), + m_voxelScaleHalf(m_voxelScale * double(0.5)), + m_voxelBounds(m_voxels->GetBounds()), + m_voxelAdjust(m_voxelBounds.GetMin() - m_voxelScaleHalf), + m_depth(parent.m_depth + 1), + m_index(++m_voxelHullCount), + m_1(parent.m_1), + m_2(parent.m_2), + m_params(parent.m_params) { + // Default copy the voxel region from the parent, but values will + // be adjusted next based on the split axis and location + switch (m_axis) { + case SplitAxis::X_AXIS_NEGATIVE: + m_2.GetX() = splitLoc; + break; + case SplitAxis::X_AXIS_POSITIVE: + m_1.GetX() = splitLoc + 1; + break; + case SplitAxis::Y_AXIS_NEGATIVE: + m_2.GetY() = splitLoc; + break; + case SplitAxis::Y_AXIS_POSITIVE: + m_1.GetY() = splitLoc + 1; + break; + case SplitAxis::Z_AXIS_NEGATIVE: + m_2.GetZ() = splitLoc; + break; + case SplitAxis::Z_AXIS_POSITIVE: + m_1.GetZ() = splitLoc + 1; + break; + } + + // First, we copy all of the interior voxels from our parent + // which intersect our region + for (auto& i : parent.m_interiorVoxels) { + VHACD::Vector3 v = i.GetVoxel(); + if (v.CWiseAllGE(m_1) && v.CWiseAllLE(m_2)) { + bool newSurface = false; + switch (m_axis) { + case SplitAxis::X_AXIS_NEGATIVE: + if (v.GetX() == splitLoc) { + newSurface = true; + } + break; + case SplitAxis::X_AXIS_POSITIVE: + if (v.GetX() == m_1.GetX()) { + newSurface = true; + } + break; + case SplitAxis::Y_AXIS_NEGATIVE: + if (v.GetY() == splitLoc) { + newSurface = true; + } + break; + case SplitAxis::Y_AXIS_POSITIVE: + if (v.GetY() == m_1.GetY()) { + newSurface = true; + } + break; + case SplitAxis::Z_AXIS_NEGATIVE: + if (v.GetZ() == splitLoc) { + newSurface = true; + } + break; + case SplitAxis::Z_AXIS_POSITIVE: + if (v.GetZ() == m_1.GetZ()) { + newSurface = true; + } + break; + } + // If his interior voxels lie directly on the split plane then + // these become new surface voxels for our patch + if (newSurface) { + m_newSurfaceVoxels.push_back(i); + } else { + m_interiorVoxels.push_back(i); + } + } + } + // Next we copy all of the surface voxels which intersect our region + for (auto& i : parent.m_surfaceVoxels) { + VHACD::Vector3 v = i.GetVoxel(); + if (v.CWiseAllGE(m_1) && v.CWiseAllLE(m_2)) { + m_surfaceVoxels.push_back(i); + } + } + // Our parent's new surface voxels become our new surface voxels so long as + // they intersect our region + for (auto& i : parent.m_newSurfaceVoxels) { + VHACD::Vector3 v = i.GetVoxel(); + if (v.CWiseAllGE(m_1) && v.CWiseAllLE(m_2)) { + m_newSurfaceVoxels.push_back(i); + } + } + + // Recompute the min-max bounding box which would be different after the split + // occurs + m_1 = VHACD::Vector3(0x7FFFFFFF); + m_2 = VHACD::Vector3(0); + for (auto& i : m_surfaceVoxels) { + MinMaxVoxelRegion(i); + } + for (auto& i : m_newSurfaceVoxels) { + MinMaxVoxelRegion(i); + } + for (auto& i : m_interiorVoxels) { + MinMaxVoxelRegion(i); + } + + BuildVoxelMesh(); + BuildRaycastMesh(); // build a raycast mesh of the voxel mesh + ComputeConvexHull(); +} + +VoxelHull::VoxelHull(Volume& voxels, const IVHACD::Parameters& params, + VHACDCallbacks* callbacks) + : m_voxels(&voxels), + m_voxelScale(m_voxels->GetScale()), + m_voxelScaleHalf(m_voxelScale * double(0.5)), + m_voxelBounds(m_voxels->GetBounds()), + m_voxelAdjust(m_voxelBounds.GetMin() - m_voxelScaleHalf), + m_index(++m_voxelHullCount) + // Here we get a copy of all voxels which lie on the surface mesh + , + m_surfaceVoxels(m_voxels->GetSurfaceVoxels()) + // Now we get a copy of all voxels which are considered part of the + // 'interior' of the source mesh + , + m_interiorVoxels(m_voxels->GetInteriorVoxels()), + m_2(m_voxels->GetDimensions() - 1), + m_params(params), + m_callbacks(callbacks) { + BuildVoxelMesh(); + BuildRaycastMesh(); // build a raycast mesh of the voxel mesh + ComputeConvexHull(); +} + +void VoxelHull::MinMaxVoxelRegion(const Voxel& v) { + VHACD::Vector3 x = v.GetVoxel(); + m_1 = m_1.CWiseMin(x); + m_2 = m_2.CWiseMax(x); +} + +void VoxelHull::BuildRaycastMesh() { + // Create a raycast mesh representation of the voxelized surface mesh + if (!m_indices.empty()) { + m_AABBTree = AABBTree(m_vertices, m_indices); + } +} + +void VoxelHull::ComputeConvexHull() { + if (!m_vertices.empty()) { + // we compute the convex hull as follows... + VHACD::QuickHull qh; + uint32_t tcount = + qh.ComputeConvexHull(m_vertices, uint32_t(m_vertices.size())); + if (tcount) { + m_convexHull = + std::unique_ptr(new IVHACD::ConvexHull); + + m_convexHull->m_points = qh.GetVertices(); + m_convexHull->m_triangles = qh.GetIndices(); + + VHACD::ComputeCentroid(m_convexHull->m_points, m_convexHull->m_triangles, + m_convexHull->m_center); + m_convexHull->m_volume = VHACD::ComputeMeshVolume( + m_convexHull->m_points, m_convexHull->m_triangles); + } + } + if (m_convexHull) { + m_hullVolume = m_convexHull->m_volume; + } + // This is the volume of a single voxel + double singleVoxelVolume = m_voxelScale * m_voxelScale * m_voxelScale; + size_t voxelCount = m_interiorVoxels.size() + m_newSurfaceVoxels.size() + + m_surfaceVoxels.size(); + m_voxelVolume = singleVoxelVolume * double(voxelCount); + double diff = fabs(m_hullVolume - m_voxelVolume); + m_volumeError = (diff * 100) / m_voxelVolume; +} + +bool VoxelHull::IsComplete() { + bool ret = false; + if (m_convexHull == nullptr) { + ret = true; + } else if (m_volumeError < m_params.m_minimumVolumePercentErrorAllowed) { + ret = true; + } else if (m_depth > m_params.m_maxRecursionDepth) { + ret = true; + } else { + // We compute the voxel width on all 3 axes and see if they are below the + // min threshold size + VHACD::Vector3 d = m_2 - m_1; + if (d.GetX() <= m_params.m_minEdgeLength && + d.GetY() <= m_params.m_minEdgeLength && + d.GetZ() <= m_params.m_minEdgeLength) { + ret = true; + } + } + return ret; +} + +VHACD::Vect3 VoxelHull::GetPoint(const int32_t x, const int32_t y, + const int32_t z, const double scale, + const VHACD::Vect3& bmin) const { + return VHACD::Vect3(x * scale + bmin.GetX(), y * scale + bmin.GetY(), + z * scale + bmin.GetZ()); +} + +uint32_t VoxelHull::GetVertexIndex(const VHACD::Vector3& p) { + uint32_t ret = 0; + uint32_t address = (p.GetX() << 20) | (p.GetY() << 10) | p.GetZ(); + auto found = m_voxelIndexMap.find(address); + if (found != m_voxelIndexMap.end()) { + ret = found->second; + } else { + VHACD::Vect3 vertex = + GetPoint(p.GetX(), p.GetY(), p.GetZ(), m_voxelScale, m_voxelAdjust); + ret = uint32_t(m_voxelIndexMap.size()); + m_voxelIndexMap[address] = ret; + m_vertices.emplace_back(vertex); + } + return ret; +} + +void VoxelHull::BuildVoxelMesh() { + // When we build the triangle mesh we do *not* need the interior voxels, only + // the ones which lie upon the logical surface of the mesh. Each time we + // perform a plane split, voxels which are along the splitting plane become + // 'new surface voxels'. + + for (auto& i : m_surfaceVoxels) { + AddVoxelBox(i); + } + for (auto& i : m_newSurfaceVoxels) { + AddVoxelBox(i); + } +} + +void VoxelHull::AddVoxelBox(const Voxel& v) { + // The voxel position of the upper left corner of the box + VHACD::Vector3 bmin(v.GetX(), v.GetY(), v.GetZ()); + // The voxel position of the lower right corner of the box + VHACD::Vector3 bmax(bmin.GetX() + 1, bmin.GetY() + 1, + bmin.GetZ() + 1); + + // Build the set of 8 voxel positions representing + // the coordinates of the box + std::array, 8> box{ + {{bmin.GetX(), bmin.GetY(), bmin.GetZ()}, + {bmax.GetX(), bmin.GetY(), bmin.GetZ()}, + {bmax.GetX(), bmax.GetY(), bmin.GetZ()}, + {bmin.GetX(), bmax.GetY(), bmin.GetZ()}, + {bmin.GetX(), bmin.GetY(), bmax.GetZ()}, + {bmax.GetX(), bmin.GetY(), bmax.GetZ()}, + {bmax.GetX(), bmax.GetY(), bmax.GetZ()}, + {bmin.GetX(), bmax.GetY(), bmax.GetZ()}}}; + + // Now add the 12 triangles comprising the 3d box + AddTri(box, 2, 1, 0); + AddTri(box, 3, 2, 0); + + AddTri(box, 7, 2, 3); + AddTri(box, 7, 6, 2); + + AddTri(box, 5, 1, 2); + AddTri(box, 5, 2, 6); + + AddTri(box, 5, 4, 1); + AddTri(box, 4, 0, 1); + + AddTri(box, 4, 6, 7); + AddTri(box, 4, 5, 6); + + AddTri(box, 4, 7, 0); + AddTri(box, 7, 3, 0); +} + +void VoxelHull::AddTri(const std::array, 8>& box, + uint32_t i1, uint32_t i2, uint32_t i3) { + AddTriangle(box[i1], box[i2], box[i3]); +} + +void VoxelHull::AddTriangle(const VHACD::Vector3& p1, + const VHACD::Vector3& p2, + const VHACD::Vector3& p3) { + uint32_t i1 = GetVertexIndex(p1); + uint32_t i2 = GetVertexIndex(p2); + uint32_t i3 = GetVertexIndex(p3); + + m_indices.emplace_back(i1, i2, i3); +} + +SplitAxis VoxelHull::ComputeSplitPlane(uint32_t& location) { + SplitAxis ret = SplitAxis::X_AXIS_NEGATIVE; + + VHACD::Vector3 d = m_2 - m_1; + + if (d.GetX() >= d.GetY() && d.GetX() >= d.GetZ()) { + ret = SplitAxis::X_AXIS_NEGATIVE; + location = (m_2.GetX() + 1 + m_1.GetX()) / 2; + uint32_t edgeLoc; + if (m_params.m_findBestPlane && FindConcavityX(edgeLoc)) { + location = edgeLoc; + } + } else if (d.GetY() >= d.GetX() && d.GetY() >= d.GetZ()) { + ret = SplitAxis::Y_AXIS_NEGATIVE; + location = (m_2.GetY() + 1 + m_1.GetY()) / 2; + uint32_t edgeLoc; + if (m_params.m_findBestPlane && FindConcavityY(edgeLoc)) { + location = edgeLoc; + } + } else { + ret = SplitAxis::Z_AXIS_NEGATIVE; + location = (m_2.GetZ() + 1 + m_1.GetZ()) / 2; + uint32_t edgeLoc; + if (m_params.m_findBestPlane && FindConcavityZ(edgeLoc)) { + location = edgeLoc; + } + } + + return ret; +} + +VHACD::Vect3 VoxelHull::GetPosition(const VHACD::Vector3& ip) const { + return GetPoint(ip.GetX(), ip.GetY(), ip.GetZ(), m_voxelScale, m_voxelAdjust); +} + +double VoxelHull::Raycast(const VHACD::Vector3& p1, + const VHACD::Vector3& p2) const { + double ret; + VHACD::Vect3 from = GetPosition(p1); + VHACD::Vect3 to = GetPosition(p2); + + double outT; + double faceSign; + VHACD::Vect3 hitLocation; + if (m_AABBTree.TraceRay(from, to, outT, faceSign, hitLocation)) { + ret = (from - hitLocation).GetNorm(); + } else { + ret = 0; // if it doesn't hit anything, just assign it to zero. + } + + return ret; +} + +bool VoxelHull::FindConcavity(uint32_t idx, uint32_t& splitLoc) { + bool ret = false; + + int32_t d = + (m_2[idx] - m_1[idx]) + 1; // The length of the getX axis in voxel space + + uint32_t idx1; + uint32_t idx2; + uint32_t idx3; + switch (idx) { + case 0: // X + idx1 = 0; + idx2 = 1; + idx3 = 2; + break; + case 1: // Y + idx1 = 1; + idx2 = 0; + idx3 = 2; + break; + case 2: + idx1 = 2; + idx2 = 1; + idx3 = 0; + break; + default: + /* + * To silence uninitialized variable warnings + */ + idx1 = 0; + idx2 = 0; + idx3 = 0; + assert(0 && "findConcavity::idx must be 0, 1, or 2"); + break; + } + + // We will compute the edge error on the XY plane and the XZ plane + // searching for the greatest location of concavity + std::vector edgeError1 = std::vector(d); + std::vector edgeError2 = std::vector(d); + + // Counter of number of voxel samples on the XY plane we have accumulated + uint32_t index1 = 0; + + // Compute Edge Error on the XY plane + for (uint32_t i0 = m_1[idx1]; i0 <= m_2[idx1]; i0++) { + double errorTotal = 0; + // We now perform a raycast from the sides inward on the XY plane to + // determine the total error (distance of the surface from the sides) + // along this getX position. + for (uint32_t i1 = m_1[idx2]; i1 <= m_2[idx2]; i1++) { + VHACD::Vector3 p1; + VHACD::Vector3 p2; + switch (idx) { + case 0: { + p1 = VHACD::Vector3(i0, i1, m_1.GetZ() - 2); + p2 = VHACD::Vector3(i0, i1, m_2.GetZ() + 2); + break; + } + case 1: { + p1 = VHACD::Vector3(i1, i0, m_1.GetZ() - 2); + p2 = VHACD::Vector3(i1, i0, m_2.GetZ() + 2); + break; + } + case 2: { + p1 = VHACD::Vector3(m_1.GetX() - 2, i1, i0); + p2 = VHACD::Vector3(m_2.GetX() + 2, i1, i0); + break; + } + } + + double e1 = Raycast(p1, p2); + double e2 = Raycast(p2, p1); + + errorTotal = errorTotal + e1 + e2; + } + // The total amount of edge error along this voxel location + edgeError1[index1] = errorTotal; + index1++; + } + + // Compute edge error along the XZ plane + uint32_t index2 = 0; + + for (uint32_t i0 = m_1[idx1]; i0 <= m_2[idx1]; i0++) { + double errorTotal = 0; + + for (uint32_t i1 = m_1[idx3]; i1 <= m_2[idx3]; i1++) { + VHACD::Vector3 p1; + VHACD::Vector3 p2; + switch (idx) { + case 0: { + p1 = VHACD::Vector3(i0, m_1.GetY() - 2, i1); + p2 = VHACD::Vector3(i0, m_2.GetY() + 2, i1); + break; + } + case 1: { + p1 = VHACD::Vector3(m_1.GetX() - 2, i0, i1); + p2 = VHACD::Vector3(m_2.GetX() + 2, i0, i1); + break; + } + case 2: { + p1 = VHACD::Vector3(i1, m_1.GetY() - 2, i0); + p2 = VHACD::Vector3(i1, m_2.GetY() + 2, i0); + break; + } + } + + double e1 = Raycast(p1, p2); // raycast from one side to the interior + double e2 = + Raycast(p2, p1); // raycast from the other side to the interior + + errorTotal = errorTotal + e1 + e2; + } + edgeError2[index2] = errorTotal; + index2++; + } + + // we now compute the first derivative to find the greatest spot of concavity + // on the XY plane + double maxDiff = 0; + uint32_t maxC = 0; + for (uint32_t x = 1; x < index1; x++) { + if (edgeError1[x] > 0 && edgeError1[x - 1] > 0) { + double diff = abs(edgeError1[x] - edgeError1[x - 1]); + if (diff > maxDiff) { + maxDiff = diff; + maxC = x - 1; + } + } + } + + // Now see if there is a greater concavity on the XZ plane + for (uint32_t x = 1; x < index2; x++) { + if (edgeError2[x] > 0 && edgeError2[x - 1] > 0) { + double diff = abs(edgeError2[x] - edgeError2[x - 1]); + if (diff > maxDiff) { + maxDiff = diff; + maxC = x - 1; + } + } + } + + splitLoc = maxC + m_1[idx1]; + + // we do not allow an edge split if it is too close to the ends + if (splitLoc > (m_1[idx1] + 4) && splitLoc < (m_2[idx1] - 4)) { + ret = true; + } + + return ret; +} + +// Finding the greatest area of concavity.. +bool VoxelHull::FindConcavityX(uint32_t& splitLoc) { + return FindConcavity(0, splitLoc); +} + +// Finding the greatest area of concavity.. +bool VoxelHull::FindConcavityY(uint32_t& splitLoc) { + return FindConcavity(1, splitLoc); +} + +// Finding the greatest area of concavity.. +bool VoxelHull::FindConcavityZ(uint32_t& splitLoc) { + return FindConcavity(2, splitLoc); +} + +void VoxelHull::PerformPlaneSplit() { + if (IsComplete()) { + } else { + uint32_t splitLoc; + SplitAxis axis = ComputeSplitPlane(splitLoc); + switch (axis) { + case SplitAxis::X_AXIS_NEGATIVE: + case SplitAxis::X_AXIS_POSITIVE: + // Split on the getX axis at this split location + m_hullA = std::unique_ptr( + new VoxelHull(*this, SplitAxis::X_AXIS_NEGATIVE, splitLoc)); + m_hullB = std::unique_ptr( + new VoxelHull(*this, SplitAxis::X_AXIS_POSITIVE, splitLoc)); + break; + case SplitAxis::Y_AXIS_NEGATIVE: + case SplitAxis::Y_AXIS_POSITIVE: + // Split on the 1 axis at this split location + m_hullA = std::unique_ptr( + new VoxelHull(*this, SplitAxis::Y_AXIS_NEGATIVE, splitLoc)); + m_hullB = std::unique_ptr( + new VoxelHull(*this, SplitAxis::Y_AXIS_POSITIVE, splitLoc)); + break; + case SplitAxis::Z_AXIS_NEGATIVE: + case SplitAxis::Z_AXIS_POSITIVE: + // Split on the getZ axis at this split location + m_hullA = std::unique_ptr( + new VoxelHull(*this, SplitAxis::Z_AXIS_NEGATIVE, splitLoc)); + m_hullB = std::unique_ptr( + new VoxelHull(*this, SplitAxis::Z_AXIS_POSITIVE, splitLoc)); + break; + } + } +} + +void VoxelHull::SaveVoxelMesh(const SimpleMesh& inputMesh, bool saveVoxelMesh, + bool saveSourceMesh) { + char scratch[512]; + snprintf(scratch, sizeof(scratch), "voxel-mesh-%03d.obj", m_index); + FILE* fph = fopen(scratch, "wb"); + if (fph) { + uint32_t baseIndex = 1; + if (saveVoxelMesh) { + WriteOBJ(fph, m_vertices, m_indices, baseIndex); + baseIndex += uint32_t(m_vertices.size()); + } + if (saveSourceMesh) { + WriteOBJ(fph, inputMesh.m_vertices, inputMesh.m_indices, baseIndex); + } + fclose(fph); + } +} + +void VoxelHull::SaveOBJ(const char* fname, const VoxelHull* h) { + FILE* fph = fopen(fname, "wb"); + if (fph) { + uint32_t baseIndex = 1; + WriteOBJ(fph, m_vertices, m_indices, baseIndex); + + baseIndex += uint32_t(m_vertices.size()); + + WriteOBJ(fph, h->m_vertices, h->m_indices, baseIndex); + fclose(fph); + } +} + +void VoxelHull::SaveOBJ(const char* fname) { + FILE* fph = fopen(fname, "wb"); + if (fph) { + printf("Saving '%s' with %d vertices and %d triangles\n", fname, + uint32_t(m_vertices.size()), uint32_t(m_indices.size())); + WriteOBJ(fph, m_vertices, m_indices, 1); + fclose(fph); + } +} + +void VoxelHull::WriteOBJ(FILE* fph, const std::vector& vertices, + const std::vector& indices, + uint32_t baseIndex) { + if (!fph) { + return; + } + + for (size_t i = 0; i < vertices.size(); ++i) { + const VHACD::Vertex& v = vertices[i]; + fprintf(fph, "v %0.9f %0.9f %0.9f\n", v.mX, v.mY, v.mZ); + } + + for (size_t i = 0; i < indices.size(); ++i) { + const VHACD::Triangle& t = indices[i]; + fprintf(fph, "f %d %d %d\n", t.mI0 + baseIndex, t.mI1 + baseIndex, + t.mI2 + baseIndex); + } +} + +class VHACDImpl; + +// This class represents a single task to compute the volume error +// of two convex hulls combined +class CostTask { + public: + VHACDImpl* m_this{nullptr}; + IVHACD::ConvexHull* m_hullA{nullptr}; + IVHACD::ConvexHull* m_hullB{nullptr}; + double m_concavity{0}; // concavity of the two combined + std::future m_future; +}; + +class HullPair { + public: + HullPair() = default; + HullPair(uint32_t hullA, uint32_t hullB, double concavity); + + bool operator<(const HullPair& h) const; + + uint32_t m_hullA{0}; + uint32_t m_hullB{0}; + double m_concavity{0}; +}; + +HullPair::HullPair(uint32_t hullA, uint32_t hullB, double concavity) + : m_hullA(hullA), m_hullB(hullB), m_concavity(concavity) {} + +bool HullPair::operator<(const HullPair& h) const { + return m_concavity > h.m_concavity ? true : false; +} + +// void jobCallback(void* userPtr); + +class VHACDImpl : public IVHACD, public VHACDCallbacks { + // Don't consider more than 100,000 convex hulls. + static constexpr uint32_t MaxConvexHullFragments{100000}; + + public: + VHACDImpl() = default; + + /* + * Overrides VHACD::IVHACD + */ + ~VHACDImpl() override { Clean(); } + + void Cancel() override final; + + bool Compute(const float* const points, const uint32_t countPoints, + const uint32_t* const triangles, const uint32_t countTriangles, + const Parameters& params) override final; + + bool Compute(const double* const points, const uint32_t countPoints, + const uint32_t* const triangles, const uint32_t countTriangles, + const Parameters& params) override final; + + uint32_t GetNConvexHulls() const override final; + + bool GetConvexHull(const uint32_t index, ConvexHull& ch) const override final; + + void Clean() override final; // release internally allocated memory + + void Release() override final; + + // Will compute the center of mass of the convex hull decomposition results + // and return it in 'centerOfMass'. Returns false if the center of mass could + // not be computed. + bool ComputeCenterOfMass(double centerOfMass[3]) const override final; + + // In synchronous mode (non-multi-threaded) the state is always 'ready' + // In asynchronous mode, this returns true if the background thread is not + // still actively computing a new solution. In an asynchronous config the + // 'IsReady' call will report any update or log messages in the caller's + // current thread. + bool IsReady(void) const override final; + + /** + * At the request of LegionFu : out_look@foxmail.com + * This method will return which convex hull is closest to the source + * position. You can use this method to figure out, for example, which + * vertices in the original source mesh are best associated with which convex + * hull. + * + * @param pos : The input 3d position to test against + * + * @return : Returns which convex hull this position is closest to. + */ + uint32_t findNearestConvexHull(const double pos[3], + double& distanceToHull) override final; + + // private: + bool Compute(const std::vector& points, + const std::vector& triangles, + const Parameters& params); + + // Take the source position, normalize it, and then convert it into an index + // position + uint32_t GetIndex(VHACD::VertexIndex& vi, const VHACD::Vertex& p); + + // This copies the input mesh while scaling the input positions + // to fit into a normalized unit cube. It also re-indexes all of the + // vertex positions in case they weren't clean coming in. + void CopyInputMesh(const std::vector& points, + const std::vector& triangles); + + void ScaleOutputConvexHull(ConvexHull& ch); + + void AddCostToPriorityQueue(CostTask& task); + + void ReleaseConvexHull(ConvexHull* ch); + + void PerformConvexDecomposition(); + + double ComputeConvexHullVolume(const ConvexHull& sm); + + double ComputeVolume4(const VHACD::Vect3& a, const VHACD::Vect3& b, + const VHACD::Vect3& c, const VHACD::Vect3& d); + + double ComputeConcavity(double volumeSeparate, double volumeCombined, + double volumeMesh); + + // See if we can compute the cost without having to actually merge convex + // hulls. If the axis aligned bounding boxes (slightly inflated) of the two + // convex hulls do not intersect, then we don't need to actually compute the + // merged convex hull volume. + bool DoFastCost(CostTask& mt); + + void PerformMergeCostTask(CostTask& mt); + + ConvexHull* ComputeReducedConvexHull(const ConvexHull& ch, uint32_t maxVerts, + bool projectHullVertices); + + // Take the points in convex hull A and the points in convex hull B and + // generate a new convex hull on the combined set of points. Once completed, + // we create a SimpleMesh instance to hold the triangle mesh and we compute an + // inflated AABB for it. + ConvexHull* ComputeCombinedConvexHull(const ConvexHull& sm1, + const ConvexHull& sm2); + + ConvexHull* GetHull(uint32_t index); + + bool RemoveHull(uint32_t index); + + ConvexHull* CopyConvexHull(const ConvexHull& source); + + const char* GetStageName(Stages stage) const; + + /* + * Overrides VHACD::VHACDCallbacks + */ + void ProgressUpdate(Stages stage, double stageProgress, + const char* operation) override final; + + bool IsCanceled() const override final; + + std::atomic m_canceled{false}; + Parameters m_params; // Convex decomposition parameters + + std::vector m_convexHulls; // Finalized convex hulls + std::vector> + m_voxelHulls; // completed voxel hulls + std::vector> m_pendingHulls; + + std::vector> m_trees; + VHACD::AABBTree m_AABBTree; + VHACD::Volume m_voxelize; + VHACD::Vect3 m_center; + double m_scale{double(1.0)}; + double m_recipScale{double(1.0)}; + SimpleMesh m_inputMesh; // re-indexed and normalized input mesh + std::vector m_vertices; + std::vector m_indices; + + double m_overallHullVolume{double(0.0)}; + double m_voxelScale{double(0.0)}; + double m_voxelHalfScale{double(0.0)}; + VHACD::Vect3 m_voxelBmin; + VHACD::Vect3 m_voxelBmax; + uint32_t m_meshId{0}; + std::priority_queue m_hullPairQueue; +#if !VHACD_DISABLE_THREADING + std::unique_ptr m_threadPool{nullptr}; +#endif + std::unordered_map m_hulls; + + double m_overallProgress{double(0.0)}; + double m_stageProgress{double(0.0)}; + double m_operationProgress{double(0.0)}; +}; + +void VHACDImpl::Cancel() { m_canceled = true; } + +bool VHACDImpl::Compute(const float* const points, const uint32_t countPoints, + const uint32_t* const triangles, + const uint32_t countTriangles, + const Parameters& params) { + std::vector v; + v.reserve(countPoints); + for (uint32_t i = 0; i < countPoints; ++i) { + v.emplace_back(points[i * 3 + 0], points[i * 3 + 1], points[i * 3 + 2]); + } + + std::vector t; + t.reserve(countTriangles); + for (uint32_t i = 0; i < countTriangles; ++i) { + t.emplace_back(triangles[i * 3 + 0], triangles[i * 3 + 1], + triangles[i * 3 + 2]); + } + + return Compute(v, t, params); +} + +bool VHACDImpl::Compute(const double* const points, const uint32_t countPoints, + const uint32_t* const triangles, + const uint32_t countTriangles, + const Parameters& params) { + std::vector v; + v.reserve(countPoints); + for (uint32_t i = 0; i < countPoints; ++i) { + v.emplace_back(points[i * 3 + 0], points[i * 3 + 1], points[i * 3 + 2]); + } + + std::vector t; + t.reserve(countTriangles); + for (uint32_t i = 0; i < countTriangles; ++i) { + t.emplace_back(triangles[i * 3 + 0], triangles[i * 3 + 1], + triangles[i * 3 + 2]); + } + + return Compute(v, t, params); +} + +uint32_t VHACDImpl::GetNConvexHulls() const { + return uint32_t(m_convexHulls.size()); +} + +bool VHACDImpl::GetConvexHull(const uint32_t index, ConvexHull& ch) const { + bool ret = false; + + if (index < uint32_t(m_convexHulls.size())) { + ch = *m_convexHulls[index]; + ret = true; + } + + return ret; +} + +void VHACDImpl::Clean() { +#if !VHACD_DISABLE_THREADING + m_threadPool = nullptr; +#endif + + m_trees.clear(); + + for (auto& ch : m_convexHulls) { + ReleaseConvexHull(ch); + } + m_convexHulls.clear(); + + for (auto& ch : m_hulls) { + ReleaseConvexHull(ch.second); + } + m_hulls.clear(); + + m_voxelHulls.clear(); + + m_pendingHulls.clear(); + + m_vertices.clear(); + m_indices.clear(); +} + +void VHACDImpl::Release() { delete this; } + +bool VHACDImpl::ComputeCenterOfMass(double centerOfMass[3]) const { + bool ret = false; + + return ret; +} + +bool VHACDImpl::IsReady() const { return true; } + +uint32_t VHACDImpl::findNearestConvexHull(const double pos[3], + double& distanceToHull) { + uint32_t ret = 0; // The default return code is zero + + uint32_t hullCount = GetNConvexHulls(); + distanceToHull = 0; + // First, make sure that we have valid and completed results + if (hullCount) { + // See if we already have AABB trees created for each convex hull + if (m_trees.empty()) { + // For each convex hull, we generate an AABB tree for fast closest point + // queries + for (uint32_t i = 0; i < hullCount; i++) { + VHACD::IVHACD::ConvexHull ch; + GetConvexHull(i, ch); + // Pass the triangle mesh to create an AABB tree instance based on it. + m_trees.emplace_back(new AABBTree(ch.m_points, ch.m_triangles)); + } + } + // We now compute the closest point to each convex hull and save the nearest + // one + double closest = 1e99; + for (uint32_t i = 0; i < hullCount; i++) { + std::unique_ptr& t = m_trees[i]; + if (t) { + VHACD::Vect3 closestPoint; + VHACD::Vect3 position(pos[0], pos[1], pos[2]); + if (t->GetClosestPointWithinDistance(position, 1e99, closestPoint)) { + VHACD::Vect3 d = position - closestPoint; + double distanceSquared = d.GetNormSquared(); + if (distanceSquared < closest) { + closest = distanceSquared; + ret = i; + } + } + } + } + distanceToHull = + sqrt(closest); // compute the distance to the nearest convex hull + } + + return ret; +} + +bool VHACDImpl::Compute(const std::vector& points, + const std::vector& triangles, + const Parameters& params) { + bool ret = false; + + m_params = params; + m_canceled = false; + + Clean(); // release any previous results +#if !VHACD_DISABLE_THREADING + if (m_params.m_asyncACD) { + m_threadPool = std::unique_ptr(new ThreadPool(8)); + } +#endif + CopyInputMesh(points, triangles); + if (!m_canceled) { + // We now recursively perform convex decomposition until complete + PerformConvexDecomposition(); + } + + if (m_canceled) { + Clean(); + ret = false; + if (m_params.m_logger) { + m_params.m_logger->Log( + "VHACD operation canceled before it was complete."); + } + } else { + ret = true; + } +#if !VHACD_DISABLE_THREADING + m_threadPool = nullptr; +#endif + return ret; +} + +uint32_t VHACDImpl::GetIndex(VHACD::VertexIndex& vi, const VHACD::Vertex& p) { + VHACD::Vect3 pos = (VHACD::Vect3(p) - m_center) * m_recipScale; + bool newPos; + uint32_t ret = vi.GetIndex(pos, newPos); + return ret; +} + +void VHACDImpl::CopyInputMesh(const std::vector& points, + const std::vector& triangles) { + m_vertices.clear(); + m_indices.clear(); + m_indices.reserve(triangles.size()); + + // First we must find the bounding box of this input vertices and normalize + // them into a unit-cube + VHACD::Vect3 bmin(FLT_MAX); + VHACD::Vect3 bmax(-FLT_MAX); + ProgressUpdate(Stages::COMPUTE_BOUNDS_OF_INPUT_MESH, 0, "ComputingBounds"); + for (uint32_t i = 0; i < points.size(); i++) { + const VHACD::Vertex& p = points[i]; + + bmin = bmin.CWiseMin(p); + bmax = bmax.CWiseMax(p); + } + ProgressUpdate(Stages::COMPUTE_BOUNDS_OF_INPUT_MESH, 100, "ComputingBounds"); + + m_center = (bmax + bmin) * double(0.5); + + VHACD::Vect3 scale = bmax - bmin; + m_scale = scale.MaxCoeff(); + + m_recipScale = m_scale > double(0.0) ? double(1.0) / m_scale : double(0.0); + + { + VHACD::VertexIndex vi = VHACD::VertexIndex(double(0.001), false); + + uint32_t dcount = 0; + + for (uint32_t i = 0; i < triangles.size() && !m_canceled; ++i) { + const VHACD::Triangle& t = triangles[i]; + const VHACD::Vertex& p1 = points[t.mI0]; + const VHACD::Vertex& p2 = points[t.mI1]; + const VHACD::Vertex& p3 = points[t.mI2]; + + uint32_t i1 = GetIndex(vi, p1); + uint32_t i2 = GetIndex(vi, p2); + uint32_t i3 = GetIndex(vi, p3); + + if (i1 == i2 || i1 == i3 || i2 == i3) { + dcount++; + } else { + m_indices.emplace_back(i1, i2, i3); + } + } + + if (dcount) { + if (m_params.m_logger) { + char scratch[512]; + snprintf(scratch, sizeof(scratch), "Skipped %d degenerate triangles", + dcount); + m_params.m_logger->Log(scratch); + } + } + + m_vertices = vi.TakeVertices(); + } + + // Create the raycast mesh + if (!m_canceled) { + ProgressUpdate(Stages::CREATE_RAYCAST_MESH, 0, "Building RaycastMesh"); + m_AABBTree = VHACD::AABBTree(m_vertices, m_indices); + ProgressUpdate(Stages::CREATE_RAYCAST_MESH, 100, "RaycastMesh completed"); + } + if (!m_canceled) { + ProgressUpdate(Stages::VOXELIZING_INPUT_MESH, 0, "Voxelizing Input Mesh"); + m_voxelize = VHACD::Volume(); + m_voxelize.Voxelize(m_vertices, m_indices, m_params.m_resolution, + m_params.m_fillMode, m_AABBTree); + m_voxelScale = m_voxelize.GetScale(); + m_voxelHalfScale = m_voxelScale * double(0.5); + m_voxelBmin = m_voxelize.GetBounds().GetMin(); + m_voxelBmax = m_voxelize.GetBounds().GetMax(); + ProgressUpdate(Stages::VOXELIZING_INPUT_MESH, 100, "Voxelization complete"); + } + + m_inputMesh.m_vertices = m_vertices; + m_inputMesh.m_indices = m_indices; + if (!m_canceled) { + ProgressUpdate(Stages::BUILD_INITIAL_CONVEX_HULL, 0, + "Build initial ConvexHull"); + std::unique_ptr vh = + std::unique_ptr(new VoxelHull(m_voxelize, m_params, this)); + if (vh->m_convexHull) { + m_overallHullVolume = vh->m_convexHull->m_volume; + } + m_pendingHulls.push_back(std::move(vh)); + ProgressUpdate(Stages::BUILD_INITIAL_CONVEX_HULL, 100, + "Initial ConvexHull complete"); + } +} + +void VHACDImpl::ScaleOutputConvexHull(ConvexHull& ch) { + for (uint32_t i = 0; i < ch.m_points.size(); i++) { + VHACD::Vect3 p = ch.m_points[i]; + p = (p * m_scale) + m_center; + ch.m_points[i] = p; + } + ch.m_volume = ComputeConvexHullVolume(ch); // get the combined volume + VHACD::BoundsAABB b(ch.m_points); + ch.mBmin = b.GetMin(); + ch.mBmax = b.GetMax(); + ComputeCentroid(ch.m_points, ch.m_triangles, ch.m_center); +} + +void VHACDImpl::AddCostToPriorityQueue(CostTask& task) { + HullPair hp(task.m_hullA->m_meshId, task.m_hullB->m_meshId, task.m_concavity); + m_hullPairQueue.push(hp); +} + +void VHACDImpl::ReleaseConvexHull(ConvexHull* ch) { + if (ch) { + delete ch; + } +} + +void jobCallback(std::unique_ptr& userPtr) { + userPtr->PerformPlaneSplit(); +} + +void computeMergeCostTask(CostTask& ptr) { + ptr.m_this->PerformMergeCostTask(ptr); +} + +void VHACDImpl::PerformConvexDecomposition() { + { + ScopedTime st("Convex Decomposition", m_params.m_logger); + double maxHulls = pow(2, m_params.m_maxRecursionDepth); + // We recursively split convex hulls until we can + // no longer recurse further. + Timer t; + + while (!m_pendingHulls.empty() && !m_canceled) { + size_t count = m_pendingHulls.size() + m_voxelHulls.size(); + double e = t.PeekElapsedSeconds(); + if (e >= double(0.1)) { + t.Reset(); + double stageProgress = (double(count) * double(100.0)) / maxHulls; + ProgressUpdate(Stages::PERFORMING_DECOMPOSITION, stageProgress, + "Performing recursive decomposition of convex hulls"); + } + // First we make a copy of the hulls we are processing + std::vector> oldList = + std::move(m_pendingHulls); + // For each hull we want to split, we either + // immediately perform the plane split or we post it as + // a job to be performed in a background thread + std::vector> futures(oldList.size()); + uint32_t futureCount = 0; + for (auto& i : oldList) { + if (i->IsComplete() || count > MaxConvexHullFragments) { + } else { +#if !VHACD_DISABLE_THREADING + if (m_threadPool) { + futures[futureCount] = + m_threadPool->enqueue([&i] { jobCallback(i); }); + futureCount++; + } else +#endif + { + i->PerformPlaneSplit(); + } + } + } + // Wait for any outstanding jobs to complete in the background threads + if (futureCount) { + for (uint32_t i = 0; i < futureCount; i++) { + futures[i].get(); + } + } + // Now, we rebuild the pending convex hulls list by + // adding the two children to the output list if + // we need to recurse them further + for (auto& vh : oldList) { + if (vh->IsComplete() || count > MaxConvexHullFragments) { + if (vh->m_convexHull) { + m_voxelHulls.push_back(std::move(vh)); + } + } else { + if (vh->m_hullA) { + m_pendingHulls.push_back(std::move(vh->m_hullA)); + } + if (vh->m_hullB) { + m_pendingHulls.push_back(std::move(vh->m_hullB)); + } + } + } + } + } + + if (!m_canceled) { + // Give each convex hull a unique guid + m_meshId = 0; + m_hulls.clear(); + + // Build the convex hull id map + std::vector hulls; + + ProgressUpdate(Stages::INITIALIZING_CONVEX_HULLS_FOR_MERGING, 0, + "Initializing ConvexHulls"); + for (auto& vh : m_voxelHulls) { + if (m_canceled) { + break; + } + ConvexHull* ch = CopyConvexHull(*vh->m_convexHull); + m_meshId++; + ch->m_meshId = m_meshId; + m_hulls[m_meshId] = ch; + // Compute the volume of the convex hull + ch->m_volume = ComputeConvexHullVolume(*ch); + // Compute the AABB of the convex hull + VHACD::BoundsAABB b = + VHACD::BoundsAABB(ch->m_points).Inflate(double(0.1)); + ch->mBmin = b.GetMin(); + ch->mBmax = b.GetMax(); + + ComputeCentroid(ch->m_points, ch->m_triangles, ch->m_center); + + hulls.push_back(ch); + } + ProgressUpdate(Stages::INITIALIZING_CONVEX_HULLS_FOR_MERGING, 100, + "ConvexHull initialization complete"); + + m_voxelHulls.clear(); + + // here we merge convex hulls as needed until the match the + // desired maximum hull count. + size_t hullCount = hulls.size(); + + if (hullCount > m_params.m_maxConvexHulls && !m_canceled) { + size_t costMatrixSize = ((hullCount * hullCount) - hullCount) >> 1; + std::vector tasks; + tasks.reserve(costMatrixSize); + + ScopedTime st("Computing the Cost Matrix", m_params.m_logger); + // First thing we need to do is compute the cost matrix + // This is computed as the volume error of any two convex hulls + // combined + ProgressUpdate(Stages::COMPUTING_COST_MATRIX, 0, + "Computing Hull Merge Cost Matrix"); + for (size_t i = 1; i < hullCount && !m_canceled; i++) { + ConvexHull* chA = hulls[i]; + + for (size_t j = 0; j < i && !m_canceled; j++) { + ConvexHull* chB = hulls[j]; + + CostTask ct; + ct.m_hullA = chA; + ct.m_hullB = chB; + ct.m_this = this; + + if (DoFastCost(ct)) { + } else { + tasks.push_back(std::move(ct)); + CostTask* task = &tasks.back(); +#if !VHACD_DISABLE_THREADING + if (m_threadPool) { + task->m_future = m_threadPool->enqueue( + [task] { computeMergeCostTask(*task); }); + } +#endif + } + } + } + + if (!m_canceled) { +#if !VHACD_DISABLE_THREADING + if (m_threadPool) { + for (CostTask& task : tasks) { + task.m_future.get(); + } + + for (CostTask& task : tasks) { + AddCostToPriorityQueue(task); + } + } else +#endif + { + for (CostTask& task : tasks) { + PerformMergeCostTask(task); + AddCostToPriorityQueue(task); + } + } + ProgressUpdate(Stages::COMPUTING_COST_MATRIX, 100, + "Finished cost matrix"); + } + + if (!m_canceled) { + ScopedTime stMerging("Merging Convex Hulls", m_params.m_logger); + Timer t; + // Now that we know the cost to merge each hull, we can begin merging + // them. + bool cancel = false; + + uint32_t maxMergeCount = + uint32_t(m_hulls.size()) - m_params.m_maxConvexHulls; + uint32_t startCount = uint32_t(m_hulls.size()); + + while (!cancel && m_hulls.size() > m_params.m_maxConvexHulls && + !m_hullPairQueue.empty() && !m_canceled) { + double e = t.PeekElapsedSeconds(); + if (e >= double(0.1)) { + t.Reset(); + uint32_t hullsProcessed = startCount - uint32_t(m_hulls.size()); + double stageProgress = + double(hullsProcessed * 100) / double(maxMergeCount); + ProgressUpdate(Stages::MERGING_CONVEX_HULLS, stageProgress, + "Merging Convex Hulls"); + } + + HullPair hp = m_hullPairQueue.top(); + m_hullPairQueue.pop(); + + // It is entirely possible that the hull pair queue can + // have references to convex hulls that are no longer valid + // because they were previously merged. So we check for this + // and if either hull referenced in this pair no longer + // exists, then we skip it. + + // Look up this pair of hulls by ID + ConvexHull* ch1 = GetHull(hp.m_hullA); + ConvexHull* ch2 = GetHull(hp.m_hullB); + + // If both hulls are still valid, then we merge them, delete the old + // two hulls and recompute the cost matrix for the new combined hull + // we have created + if (ch1 && ch2) { + // This is the convex hull which results from combining the + // vertices in the two source hulls + ConvexHull* combinedHull = ComputeCombinedConvexHull(*ch1, *ch2); + // The two old convex hulls are going to get removed + RemoveHull(hp.m_hullA); + RemoveHull(hp.m_hullB); + + m_meshId++; + combinedHull->m_meshId = m_meshId; + tasks.clear(); + tasks.reserve(m_hulls.size()); + + // Compute the cost between this new merged hull + // and all existing convex hulls and then + // add that to the priority queue + for (auto& i : m_hulls) { + if (m_canceled) { + break; + } + ConvexHull* secondHull = i.second; + CostTask ct; + ct.m_hullA = combinedHull; + ct.m_hullB = secondHull; + ct.m_this = this; + if (DoFastCost(ct)) { + } else { + tasks.push_back(std::move(ct)); + } + } + m_hulls[combinedHull->m_meshId] = combinedHull; + // See how many merge cost tasks were posted + // If there are 8 or more and we are running asynchronously, then do + // them that way. +#if !VHACD_DISABLE_THREADING + if (m_threadPool && tasks.size() >= 2) { + for (CostTask& task : tasks) { + task.m_future = m_threadPool->enqueue( + [&task] { computeMergeCostTask(task); }); + } + + for (CostTask& task : tasks) { + task.m_future.get(); + } + } else +#endif + { + for (CostTask& task : tasks) { + PerformMergeCostTask(task); + } + } + + for (CostTask& task : tasks) { + AddCostToPriorityQueue(task); + } + } + } + // Ok...once we are done, we copy the results! + m_meshId -= 0; + ProgressUpdate(Stages::FINALIZING_RESULTS, 0, "Finalizing results"); + for (auto& i : m_hulls) { + if (m_canceled) { + break; + } + ConvexHull* ch = i.second; + // We now must reduce the convex hull + if (ch->m_points.size() > m_params.m_maxNumVerticesPerCH || + m_params.m_shrinkWrap) { + ConvexHull* reduce = ComputeReducedConvexHull( + *ch, m_params.m_maxNumVerticesPerCH, m_params.m_shrinkWrap); + ReleaseConvexHull(ch); + ch = reduce; + } + ScaleOutputConvexHull(*ch); + ch->m_meshId = m_meshId; + m_meshId++; + m_convexHulls.push_back(ch); + } + m_hulls.clear(); // since the hulls were moved into the output list, we + // don't need to delete them from this container + ProgressUpdate(Stages::FINALIZING_RESULTS, 100, + "Finalized results complete"); + } + } else { + ProgressUpdate(Stages::FINALIZING_RESULTS, 0, "Finalizing results"); + m_meshId = 0; + for (auto& ch : hulls) { + // We now must reduce the convex hull + if (ch->m_points.size() > m_params.m_maxNumVerticesPerCH || + m_params.m_shrinkWrap) { + ConvexHull* reduce = ComputeReducedConvexHull( + *ch, m_params.m_maxNumVerticesPerCH, m_params.m_shrinkWrap); + ReleaseConvexHull(ch); + ch = reduce; + } + ScaleOutputConvexHull(*ch); + ch->m_meshId = m_meshId; + m_meshId++; + m_convexHulls.push_back(ch); + } + m_hulls.clear(); + ProgressUpdate(Stages::FINALIZING_RESULTS, 100, "Finalized results"); + } + } +} + +double VHACDImpl::ComputeConvexHullVolume(const ConvexHull& sm) { + double totalVolume = 0; + VHACD::Vect3 bary(0, 0, 0); + for (uint32_t i = 0; i < sm.m_points.size(); i++) { + VHACD::Vect3 p(sm.m_points[i]); + bary += p; + } + bary /= double(sm.m_points.size()); + + for (uint32_t i = 0; i < sm.m_triangles.size(); i++) { + uint32_t i1 = sm.m_triangles[i].mI0; + uint32_t i2 = sm.m_triangles[i].mI1; + uint32_t i3 = sm.m_triangles[i].mI2; + + VHACD::Vect3 ver0(sm.m_points[i1]); + VHACD::Vect3 ver1(sm.m_points[i2]); + VHACD::Vect3 ver2(sm.m_points[i3]); + + totalVolume += ComputeVolume4(ver0, ver1, ver2, bary); + } + totalVolume = totalVolume / double(6.0); + return totalVolume; +} + +double VHACDImpl::ComputeVolume4(const VHACD::Vect3& a, const VHACD::Vect3& b, + const VHACD::Vect3& c, const VHACD::Vect3& d) { + VHACD::Vect3 ad = a - d; + VHACD::Vect3 bd = b - d; + VHACD::Vect3 cd = c - d; + VHACD::Vect3 bcd = bd.Cross(cd); + double dot = ad.Dot(bcd); + return dot; +} + +double VHACDImpl::ComputeConcavity(double volumeSeparate, double volumeCombined, + double volumeMesh) { + return fabs(volumeSeparate - volumeCombined) / volumeMesh; +} + +bool VHACDImpl::DoFastCost(CostTask& mt) { + bool ret = false; + + ConvexHull* ch1 = mt.m_hullA; + ConvexHull* ch2 = mt.m_hullB; + + VHACD::BoundsAABB ch1b(ch1->mBmin, ch1->mBmax); + VHACD::BoundsAABB ch2b(ch2->mBmin, ch2->mBmax); + if (!ch1b.Intersects(ch2b)) { + VHACD::BoundsAABB b = ch1b.Union(ch2b); + + double combinedVolume = b.Volume(); + double concavity = ComputeConcavity(ch1->m_volume + ch2->m_volume, + combinedVolume, m_overallHullVolume); + HullPair hp(ch1->m_meshId, ch2->m_meshId, concavity); + m_hullPairQueue.push(hp); + ret = true; + } + return ret; +} + +void VHACDImpl::PerformMergeCostTask(CostTask& mt) { + ConvexHull* ch1 = mt.m_hullA; + ConvexHull* ch2 = mt.m_hullB; + + double volume1 = ch1->m_volume; + double volume2 = ch2->m_volume; + + ConvexHull* combined = + ComputeCombinedConvexHull(*ch1, + *ch2); // Build the combined convex hull + double combinedVolume = + ComputeConvexHullVolume(*combined); // get the combined volume + mt.m_concavity = + ComputeConcavity(volume1 + volume2, combinedVolume, m_overallHullVolume); + ReleaseConvexHull(combined); +} + +IVHACD::ConvexHull* VHACDImpl::ComputeReducedConvexHull( + const ConvexHull& ch, uint32_t maxVerts, bool projectHullVertices) { + SimpleMesh sourceConvexHull; + + sourceConvexHull.m_vertices = ch.m_points; + sourceConvexHull.m_indices = ch.m_triangles; + + ShrinkWrap(sourceConvexHull, m_AABBTree, maxVerts, m_voxelScale, + projectHullVertices); + + ConvexHull* ret = new ConvexHull; + + ret->m_points = sourceConvexHull.m_vertices; + ret->m_triangles = sourceConvexHull.m_indices; + + VHACD::BoundsAABB b = VHACD::BoundsAABB(ret->m_points).Inflate(double(0.1)); + ret->mBmin = b.GetMin(); + ret->mBmax = b.GetMax(); + ComputeCentroid(ret->m_points, ret->m_triangles, ret->m_center); + + ret->m_volume = ComputeConvexHullVolume(*ret); + + // Return the convex hull + return ret; +} + +IVHACD::ConvexHull* VHACDImpl::ComputeCombinedConvexHull( + const ConvexHull& sm1, const ConvexHull& sm2) { + uint32_t vcount = + uint32_t(sm1.m_points.size() + + sm2.m_points.size()); // Total vertices from both hulls + std::vector vertices(vcount); + auto it = + std::copy(sm1.m_points.begin(), sm1.m_points.end(), vertices.begin()); + std::copy(sm2.m_points.begin(), sm2.m_points.end(), it); + + VHACD::QuickHull qh; + qh.ComputeConvexHull(vertices, vcount); + + ConvexHull* ret = new ConvexHull; + ret->m_points = qh.GetVertices(); + ret->m_triangles = qh.GetIndices(); + + ret->m_volume = ComputeConvexHullVolume(*ret); + + VHACD::BoundsAABB b = + VHACD::BoundsAABB(qh.GetVertices()).Inflate(double(0.1)); + ret->mBmin = b.GetMin(); + ret->mBmax = b.GetMax(); + ComputeCentroid(ret->m_points, ret->m_triangles, ret->m_center); + + // Return the convex hull + return ret; +} + +IVHACD::ConvexHull* VHACDImpl::GetHull(uint32_t index) { + ConvexHull* ret = nullptr; + + auto found = m_hulls.find(index); + if (found != m_hulls.end()) { + ret = found->second; + } + + return ret; +} + +bool VHACDImpl::RemoveHull(uint32_t index) { + bool ret = false; + auto found = m_hulls.find(index); + if (found != m_hulls.end()) { + ret = true; + ReleaseConvexHull(found->second); + m_hulls.erase(found); + } + return ret; +} + +IVHACD::ConvexHull* VHACDImpl::CopyConvexHull(const ConvexHull& source) { + ConvexHull* ch = new ConvexHull; + *ch = source; + + return ch; +} + +const char* VHACDImpl::GetStageName(Stages stage) const { + const char* ret = "unknown"; + switch (stage) { + case Stages::COMPUTE_BOUNDS_OF_INPUT_MESH: + ret = "COMPUTE_BOUNDS_OF_INPUT_MESH"; + break; + case Stages::REINDEXING_INPUT_MESH: + ret = "REINDEXING_INPUT_MESH"; + break; + case Stages::CREATE_RAYCAST_MESH: + ret = "CREATE_RAYCAST_MESH"; + break; + case Stages::VOXELIZING_INPUT_MESH: + ret = "VOXELIZING_INPUT_MESH"; + break; + case Stages::BUILD_INITIAL_CONVEX_HULL: + ret = "BUILD_INITIAL_CONVEX_HULL"; + break; + case Stages::PERFORMING_DECOMPOSITION: + ret = "PERFORMING_DECOMPOSITION"; + break; + case Stages::INITIALIZING_CONVEX_HULLS_FOR_MERGING: + ret = "INITIALIZING_CONVEX_HULLS_FOR_MERGING"; + break; + case Stages::COMPUTING_COST_MATRIX: + ret = "COMPUTING_COST_MATRIX"; + break; + case Stages::MERGING_CONVEX_HULLS: + ret = "MERGING_CONVEX_HULLS"; + break; + case Stages::FINALIZING_RESULTS: + ret = "FINALIZING_RESULTS"; + break; + case Stages::NUM_STAGES: + // Should be unreachable, here to silence enumeration value not handled in + // switch warnings GCC/Clang's -Wswitch + break; + } + return ret; +} + +void VHACDImpl::ProgressUpdate(Stages stage, double stageProgress, + const char* operation) { + if (m_params.m_callback) { + double overallProgress = (double(stage) * 100) / double(Stages::NUM_STAGES); + const char* s = GetStageName(stage); + m_params.m_callback->Update(overallProgress, stageProgress, s, operation); + } +} + +bool VHACDImpl::IsCanceled() const { return m_canceled; } + +IVHACD* CreateVHACD(void) { + VHACDImpl* ret = new VHACDImpl; + return static_cast(ret); +} + +IVHACD* CreateVHACD(void); + +#if !VHACD_DISABLE_THREADING + +class LogMessage { + public: + double m_overallProgress{double(-1.0)}; + double m_stageProgress{double(-1.0)}; + std::string m_stage; + std::string m_operation; +}; + +class VHACDAsyncImpl : public VHACD::IVHACD, + public VHACD::IVHACD::IUserCallback, + VHACD::IVHACD::IUserLogger, + VHACD::IVHACD::IUserTaskRunner { + public: + VHACDAsyncImpl() = default; + + ~VHACDAsyncImpl() override; + + void Cancel() override final; + + bool Compute(const float* const points, const uint32_t countPoints, + const uint32_t* const triangles, const uint32_t countTriangles, + const Parameters& params) override final; + + bool Compute(const double* const points, const uint32_t countPoints, + const uint32_t* const triangles, const uint32_t countTriangles, + const Parameters& params) override final; + + bool GetConvexHull(const uint32_t index, + VHACD::IVHACD::ConvexHull& ch) const override final; + + uint32_t GetNConvexHulls() const override final; + + void Clean() override final; // release internally allocated memory + + void Release() override final; // release IVHACD + + // Will compute the center of mass of the convex hull decomposition results + // and return it in 'centerOfMass'. Returns false if the center of mass could + // not be computed. + bool ComputeCenterOfMass(double centerOfMass[3]) const override; + + bool IsReady() const override final; + + /** + * At the request of LegionFu : out_look@foxmail.com + * This method will return which convex hull is closest to the source + * position. You can use this method to figure out, for example, which + * vertices in the original source mesh are best associated with which convex + * hull. + * + * @param pos : The input 3d position to test against + * + * @return : Returns which convex hull this position is closest to. + */ + uint32_t findNearestConvexHull(const double pos[3], + double& distanceToHull) override final; + + void Update(const double overallProgress, const double stageProgress, + const char* const stage, const char* operation) override final; + + void Log(const char* const msg) override final; + + void* StartTask(std::function func) override; + + void JoinTask(void* Task) override; + + bool Compute(const Parameters params); + + bool ComputeNow(const std::vector& points, + const std::vector& triangles, + const Parameters& _desc); + + // As a convenience for the calling application we only send it update and log + // messages from it's own main thread. This reduces the complexity burden on + // the caller by making sure it only has to deal with log messages in it's + // main application thread. + void ProcessPendingMessages() const; + + private: + VHACD::VHACDImpl m_VHACD; + std::vector m_vertices; + std::vector m_indices; + VHACD::IVHACD::IUserCallback* m_callback{nullptr}; + VHACD::IVHACD::IUserLogger* m_logger{nullptr}; + VHACD::IVHACD::IUserTaskRunner* m_taskRunner{nullptr}; + void* m_task{nullptr}; + std::atomic m_running{false}; + std::atomic m_cancel{false}; + + // Thread safe caching mechanism for messages and update status. + // This is so that caller always gets messages in his own thread + // Member variables are marked as 'mutable' since the message dispatch + // function is called from const query methods. + mutable std::mutex m_messageMutex; + mutable std::vector m_messages; + mutable std::atomic m_haveMessages{false}; +}; + +VHACDAsyncImpl::~VHACDAsyncImpl() { Cancel(); } + +void VHACDAsyncImpl::Cancel() { + m_cancel = true; + m_VHACD.Cancel(); + + if (m_task) { + m_taskRunner->JoinTask(m_task); // Wait for the thread to fully exit before + // we delete the instance + m_task = nullptr; + } + m_cancel = false; // clear the cancel semaphore +} + +bool VHACDAsyncImpl::Compute(const float* const points, + const uint32_t countPoints, + const uint32_t* const triangles, + const uint32_t countTriangles, + const Parameters& params) { + m_vertices.reserve(countPoints); + for (uint32_t i = 0; i < countPoints; ++i) { + m_vertices.emplace_back(points[i * 3 + 0], points[i * 3 + 1], + points[i * 3 + 2]); + } + + m_indices.reserve(countTriangles); + for (uint32_t i = 0; i < countTriangles; ++i) { + m_indices.emplace_back(triangles[i * 3 + 0], triangles[i * 3 + 1], + triangles[i * 3 + 2]); + } + + return Compute(params); +} + +bool VHACDAsyncImpl::Compute(const double* const points, + const uint32_t countPoints, + const uint32_t* const triangles, + const uint32_t countTriangles, + const Parameters& params) { + // We need to copy the input vertices and triangles into our own buffers so we + // can operate on them safely from the background thread. Can't be local + // variables due to being asynchronous + m_vertices.reserve(countPoints); + for (uint32_t i = 0; i < countPoints; ++i) { + m_vertices.emplace_back(points[i * 3 + 0], points[i * 3 + 1], + points[i * 3 + 2]); + } + + m_indices.reserve(countTriangles); + for (uint32_t i = 0; i < countTriangles; ++i) { + m_indices.emplace_back(triangles[i * 3 + 0], triangles[i * 3 + 1], + triangles[i * 3 + 2]); + } + + return Compute(params); +} + +bool VHACDAsyncImpl::GetConvexHull(const uint32_t index, + VHACD::IVHACD::ConvexHull& ch) const { + return m_VHACD.GetConvexHull(index, ch); +} + +uint32_t VHACDAsyncImpl::GetNConvexHulls() const { + ProcessPendingMessages(); + return m_VHACD.GetNConvexHulls(); +} + +void VHACDAsyncImpl::Clean() { + Cancel(); + m_VHACD.Clean(); +} + +void VHACDAsyncImpl::Release() { delete this; } + +bool VHACDAsyncImpl::ComputeCenterOfMass(double centerOfMass[3]) const { + bool ret = false; + + centerOfMass[0] = 0; + centerOfMass[1] = 0; + centerOfMass[2] = 0; + + if (IsReady()) { + ret = m_VHACD.ComputeCenterOfMass(centerOfMass); + } + return ret; +} + +bool VHACDAsyncImpl::IsReady() const { + ProcessPendingMessages(); + return !m_running; +} + +uint32_t VHACDAsyncImpl::findNearestConvexHull(const double pos[3], + double& distanceToHull) { + uint32_t ret = 0; // The default return code is zero + + distanceToHull = 0; + // First, make sure that we have valid and completed results + if (IsReady()) { + ret = m_VHACD.findNearestConvexHull(pos, distanceToHull); + } + + return ret; +} + +void VHACDAsyncImpl::Update(const double overallProgress, + const double stageProgress, const char* const stage, + const char* operation) { + m_messageMutex.lock(); + LogMessage m; + m.m_operation = std::string(operation); + m.m_overallProgress = overallProgress; + m.m_stageProgress = stageProgress; + m.m_stage = std::string(stage); + m_messages.push_back(m); + m_haveMessages = true; + m_messageMutex.unlock(); +} + +void VHACDAsyncImpl::Log(const char* const msg) { + m_messageMutex.lock(); + LogMessage m; + m.m_operation = std::string(msg); + m_haveMessages = true; + m_messages.push_back(m); + m_messageMutex.unlock(); +} + +void* VHACDAsyncImpl::StartTask(std::function func) { + return new std::thread(func); +} + +void VHACDAsyncImpl::JoinTask(void* Task) { + std::thread* t = static_cast(Task); + t->join(); + delete t; +} + +bool VHACDAsyncImpl::Compute(Parameters params) { + Cancel(); // if we previously had a solution running; cancel it. + + m_taskRunner = params.m_taskRunner ? params.m_taskRunner : this; + params.m_taskRunner = m_taskRunner; + + m_running = true; + m_task = m_taskRunner->StartTask([this, params]() { + ComputeNow(m_vertices, m_indices, params); + // If we have a user provided callback and the user did *not* call 'cancel' + // we notify him that the task is completed. However..if the user selected + // 'cancel' we do not send a completed notification event. + if (params.m_callback && !m_cancel) { + params.m_callback->NotifyVHACDComplete(); + } + m_running = false; + }); + return true; +} + +bool VHACDAsyncImpl::ComputeNow(const std::vector& points, + const std::vector& triangles, + const Parameters& _desc) { + uint32_t ret = 0; + + Parameters desc; + m_callback = _desc.m_callback; + m_logger = _desc.m_logger; + + desc = _desc; + // Set our intercepting callback interfaces if non-null + desc.m_callback = _desc.m_callback ? this : nullptr; + desc.m_logger = _desc.m_logger ? this : nullptr; + + // If not task runner provided, then use the default one + if (desc.m_taskRunner == nullptr) { + desc.m_taskRunner = this; + } + + bool ok = m_VHACD.Compute(points, triangles, desc); + if (ok) { + ret = m_VHACD.GetNConvexHulls(); + } + + return ret ? true : false; +} + +void VHACDAsyncImpl::ProcessPendingMessages() const { + if (m_cancel) { + return; + } + if (m_haveMessages) { + m_messageMutex.lock(); + for (auto& i : m_messages) { + if (i.m_overallProgress == -1) { + if (m_logger) { + m_logger->Log(i.m_operation.c_str()); + } + } else if (m_callback) { + m_callback->Update(i.m_overallProgress, i.m_stageProgress, + i.m_stage.c_str(), i.m_operation.c_str()); + } + } + m_messages.clear(); + m_haveMessages = false; + m_messageMutex.unlock(); + } +} + +IVHACD* CreateVHACD_ASYNC() { + VHACDAsyncImpl* m = new VHACDAsyncImpl; + return static_cast(m); +} +#endif + +} // namespace VHACD + +#ifdef _MSC_VER +#pragma warning(pop) +#endif // _MSC_VER + +#ifdef __GNUC__ +#pragma GCC diagnostic pop +#endif // __GNUC__ + +#endif // ENABLE_VHACD_IMPLEMENTATION + +#endif // VHACD_H \ No newline at end of file diff --git a/src/utilities/include/convhull_3d.h b/src/utilities/include/convhull_3d.h new file mode 100644 index 000000000..900f5b72c --- /dev/null +++ b/src/utilities/include/convhull_3d.h @@ -0,0 +1,1857 @@ +/* + Copyright (c) 2017-2021 Leo McCormack + + Permission is hereby granted, free of charge, to any person obtaining a copy + of this software and associated documentation files (the "Software"), to deal + in the Software without restriction, including without limitation the rights + to use, copy, modify, merge, publish, distribute, sublicense, and/or sell + copies of the Software, and to permit persons to whom the Software is + furnished to do so, subject to the following conditions: + + The above copyright notice and this permission notice shall be included in + all copies or substantial portions of the Software. + + THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR + IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, + FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE + AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER + LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, + OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN + THE SOFTWARE. +*/ +/* + * Filename: + * convhull_3d.h + * Description: + * A header only C implementation of the 3-D quickhull algorithm. + * The code is largely derived from the "computational-geometry-toolbox" + * by George Papazafeiropoulos (c) 2014, originally distributed under + * the BSD (2-clause) license. + * To include this implementation in a project, simply add this: + * #define CONVHULL_3D_ENABLE + * #include "convhull_3d.h" + * By default, the algorithm uses double floating point precision. To + * use single precision (less accurate but quicker), also add this: + * #define CONVHULL_3D_USE_SINGLE_PRECISION + * If your project has CBLAS linked, then you can also speed things up + * a tad by adding this: + * #define CONVHULL_3D_USE_CBLAS + * The code is C++ compiler safe. + * Reference: "The Quickhull Algorithm for Convex Hull, C. Bradford + * Barber, David P. Dobkin and Hannu Huhdanpaa, Geometry + * Center Technical Report GCG53, July 30, 1993" + * Dependencies: + * cblas (optional for speed ups, especially for very large meshes) + * (Available in e.g. Apple Accelerate Framework, or Intel MKL) + * Author, date created: + * Leo McCormack, 02.10.2017 + */ + +/********** + * PUBLIC: + *********/ + +#ifndef CONVHULL_3D_INCLUDED +#define CONVHULL_3D_INCLUDED + +#ifdef __cplusplus +extern "C" { +#endif + +#ifdef CONVHULL_3D_USE_SINGLE_PRECISION +typedef float CH_FLOAT; +#else +typedef double CH_FLOAT; +#endif +typedef struct _ch_vertex { + union { + CH_FLOAT v[3]; + struct { + CH_FLOAT x, y, z; + }; + }; +} ch_vertex; +typedef ch_vertex ch_vec3; + +/* builds the 3-D convexhull */ +void convhull_3d_build( /* input arguments */ + ch_vertex* const in_vertices, /* vector of input + vertices; nVert x 1 */ + const int nVert, /* number of vertices */ + /* output arguments */ + int** out_faces, /* & of empty int*, output face indices; + flat: nOut_faces x 3 */ + int* nOut_faces); /* & of int, number of output face + indices */ + +/* exports the vertices, face indices, and face normals, as an 'obj' file, ready + * for GPU (for 3d convexhulls only) */ +void convhull_3d_export_obj( /* input arguments */ + ch_vertex* const vertices, /* vector of input + vertices; nVert x 1 */ + const int nVert, /* number of vertices */ + int* const + faces, /* face indices; flat: nFaces x 3 */ + const int nFaces, /* number of faces in hull */ + const int + keepOnlyUsedVerticesFLAG, /* 0: exports + in_vertices, 1: + exports only used + vertices */ + char* const obj_filename); /* obj filename, WITHOUT + extension */ + +/* exports the vertices, face indices, and face normals, as an 'm' file, for + * MatLab verification (for 3d convexhulls only) */ +void convhull_3d_export_m( /* input arguments */ + ch_vertex* const vertices, /* vector of input + vertices; nVert x 1 */ + const int nVert, /* number of vertices */ + int* const faces, /* face indices; flat: nFaces x 3 */ + const int nFaces, /* number of faces in hull */ + char* const + m_filename); /* m filename, WITHOUT extension */ + +/* reads an 'obj' file and extracts only the vertices (for 3d convexhulls only) + */ +void extract_vertices_from_obj_file(/* input arguments */ + char* const + obj_filename, /* obj filename, WITHOUT + extension */ + /* output arguments */ + ch_vertex** + out_vertices, /* & of empty ch_vertex*, + output vertices; + out_nVert x 1 */ + int* out_nVert); /* & of int, number of + vertices */ + +/**** NEW! ****/ + +/* builds the N-Dimensional convexhull of a grid of points */ +void convhull_nd_build(/* input arguments */ + CH_FLOAT* const + in_points, /* Matrix of points in 'd' dimensions; + FLAT: nPoints x d */ + const int nPoints, /* number of points */ + const int d, /* Number of dimensions */ + /* output arguments */ + int** out_faces, /* (&) output face indices; FLAT: + nOut_faces x d */ + CH_FLOAT** out_cf, /* (&) contains the coefficients of + the planes (set to NULL if not + wanted); FLAT: nOut_faces x d */ + CH_FLOAT** out_df, /* (&) contains the constant terms of + the planes (set to NULL if not + wanted); nOut_faces x 1 */ + int* nOut_faces); /* (&) number of output face indices */ + +/* Computes the Delaunay triangulation (mesh) of an arrangement of points in + * N-dimensional space */ +void delaunay_nd_mesh(/* input Arguments */ + const float* + points, /* The input points; FLAT: nPoints x nd */ + const int nPoints, /* Number of points */ + const int nd, /* The number of dimensions */ + /* output Arguments */ + int** Mesh, /* (&) the indices defining the Delaunay + triangulation of the points; FLAT: nMesh x + (nd+1) */ + int* nMesh); /* (&) Number of triangulations */ + +/**** CUSTOM ALLOCATOR VERSIONS ****/ + +/* builds the 3-D convexhull */ +void convhull_3d_build_alloc(/* input arguments */ + ch_vertex* const + in_vertices, /* vector of input vertices; nVert + x 1 */ + const int nVert, /* number of vertices */ + /* output arguments */ + int** + out_faces, /* & of empty int*, output face + indices; flat: nOut_faces x 3 */ + int* nOut_faces, /* & of int, number of output face + indices */ + void* allocator); /* & of an allocator */ + +/* builds the N-Dimensional convexhull of a grid of points */ +void convhull_nd_build_alloc(/* input arguments */ + CH_FLOAT* const + in_points, /* Matrix of points in 'd' + dimensions; FLAT: nPoints x d */ + const int nPoints, /* number of points */ + const int d, /* Number of dimensions */ + /* output arguments */ + int** out_faces, /* (&) output face indices; FLAT: + nOut_faces x d */ + CH_FLOAT** + out_cf, /* (&) contains the coefficients of the + planes (set to NULL if not wanted); + FLAT: nOut_faces x d */ + CH_FLOAT** + out_df, /* (&) contains the constant terms of + the planes (set to NULL if not + wanted); nOut_faces x 1 */ + int* nOut_faces, /* (&) number of output face + indices */ + void* allocator); /* & of an allocator */ + +/* Computes the Delaunay triangulation (mesh) of an arrangement of points in + * N-dimensional space */ +void delaunay_nd_mesh_alloc( /* input Arguments */ + const float* points, /* The input points; FLAT: + nPoints x nd */ + const int nPoints, /* Number of points */ + const int nd, /* The number of dimensions */ + /* output Arguments */ + int** Mesh, /* (&) the indices defining the Delaunay + triangulation of the points; FLAT: + nMesh x (nd+1) */ + int* nMesh, /* (&) Number of triangulations */ + void* allocator); /* & of an allocator */ + +/* reads an 'obj' file and extracts only the vertices (for 3d convexhulls only) + */ +void extract_vertices_from_obj_file_alloc(/* input arguments */ + char* const + obj_filename, /* obj filename, + WITHOUT extension + */ + /* output arguments */ + ch_vertex** + out_vertices, /* & of empty + ch_vertex*, + output vertices; + out_nVert x 1 */ + int* out_nVert, /* & of int, number of + vertices */ + void* allocator); /* & of an allocator + */ + +#ifdef __cplusplus +} /*extern "C"*/ +#endif + +#endif /* CONVHULL_3D_INCLUDED */ + +/************ + * INTERNAL: + ***********/ + +#ifdef CONVHULL_3D_ENABLE + +#include +#include +#include +#include +#include +#include +#include +#include +#if defined(_MSC_VER) && !defined(_CRT_SECURE_NO_WARNINGS) +#define CV_STRNCPY(a, b, c) strncpy_s(a, c + 1, b, c); +#define CV_STRCAT(a, b) strcat_s(a, sizeof(b), b); +#else +#define CV_STRNCPY(a, b, c) strncpy(a, b, c); +#define CV_STRCAT(a, b) strcat(a, b); +#endif +#ifdef CONVHULL_3D_USE_SINGLE_PRECISION +#define CH_FLT_MIN FLT_MIN +#define CH_FLT_MAX FLT_MAX +#define CH_NOISE_VAL 0.00001f +#define ch_pow powf +#define ch_sqrt sqrtf +#else +#define CH_FLT_MIN DBL_MIN +#define CH_FLT_MAX DBL_MAX +#define CH_NOISE_VAL 0.0000001 +#define ch_pow pow +#define ch_sqrt sqrt +#endif +#ifndef MIN +#define MIN(a, b) (((a) < (b)) ? (a) : (b)) +#endif +#ifndef MAX +#define MAX(a, b) (((a) > (b)) ? (a) : (b)) +#endif +#ifndef ch_malloc +#define ch_malloc malloc +#endif +#ifndef ch_calloc +#define ch_calloc calloc +#endif +#ifndef ch_realloc +#define ch_realloc realloc +#endif +#ifndef ch_free +#define ch_free free +#endif +#ifndef ch_stateful_malloc +#define ch_stateful_malloc(allocator, size) ch_malloc(size) +#endif +#ifndef ch_stateful_calloc +#define ch_stateful_calloc(allocator, num, size) ch_calloc(num, size) +#endif +#ifndef ch_stateful_realloc +#define ch_stateful_realloc(allocator, ptr, size) ch_realloc(ptr, size) +#endif +#ifndef ch_stateful_free +#define ch_stateful_free(allocator, ptr) ch_free(ptr) +#endif +#ifndef ch_stateful_resize +#define ch_stateful_resize(allocator, ptr, size) \ + default_memory_resize(allocator, ptr, size) +#define CONVHULL_CREATE_DEFAULT_RESIZE 1 +#endif + +#define CH_MAX_NUM_FACES 50000 +#define CONVHULL_3D_MAX_DIMENSIONS 3 +#define CONVHULL_ND_MAX_DIMENSIONS 5 + +/* structs for qsort */ +typedef struct float_w_idx { + CH_FLOAT val; + int idx; +} float_w_idx; + +/* internal functions prototypes: */ +static int cmp_asc_float(const void*, const void*); +static int cmp_desc_float(const void*, const void*); +static int cmp_asc_int(const void*, const void*); +static void sort_float(CH_FLOAT*, CH_FLOAT*, int*, int, int, void*); +static void sort_int(int*, int); +static ch_vec3 cross(ch_vec3*, ch_vec3*); +static CH_FLOAT det_4x4(CH_FLOAT*); +static void plane_3d(CH_FLOAT*, CH_FLOAT*, CH_FLOAT*); +static void ismember(int*, int*, int*, int, int); + +/* internal functions definitions: */ +#ifdef CONVHULL_CREATE_DEFAULT_RESIZE +static void* default_memory_resize(void* allocator, void* ptr, size_t size) { + if (ptr) ch_stateful_free(allocator, ptr); + return ch_stateful_malloc(allocator, size); +} +#endif + +static int cmp_asc_float(const void* a, const void* b) { + struct float_w_idx* a1 = (struct float_w_idx*)a; + struct float_w_idx* a2 = (struct float_w_idx*)b; + if ((*a1).val < (*a2).val) + return -1; + else if ((*a1).val > (*a2).val) + return 1; + else + return 0; +} + +static int cmp_desc_float(const void* a, const void* b) { + struct float_w_idx* a1 = (struct float_w_idx*)a; + struct float_w_idx* a2 = (struct float_w_idx*)b; + if ((*a1).val > (*a2).val) + return -1; + else if ((*a1).val < (*a2).val) + return 1; + else + return 0; +} + +static int cmp_asc_int(const void* a, const void* b) { + int* a1 = (int*)a; + int* a2 = (int*)b; + if ((*a1) < (*a2)) + return -1; + else if ((*a1) > (*a2)) + return 1; + else + return 0; +} + +static void sort_float( + CH_FLOAT* in_vec, /* vector[len] to be sorted */ + CH_FLOAT* out_vec, /* if NULL, then in_vec is sorted "in-place" */ + int* new_idices, /* set to NULL if you don't need them */ + int len, /* number of elements in vectors, must be consistent with the input + data */ + int descendFLAG, /* !1:ascending, 1:descending */ + void* allocator /* (stateful) allocator */ +) { + int i; + struct float_w_idx* data; + + data = (float_w_idx*)ch_stateful_malloc(allocator, len * sizeof(float_w_idx)); + for (i = 0; i < len; i++) { + data[i].val = in_vec[i]; + data[i].idx = i; + } + if (descendFLAG) + qsort(data, len, sizeof(data[0]), cmp_desc_float); + else + qsort(data, len, sizeof(data[0]), cmp_asc_float); + for (i = 0; i < len; i++) { + if (out_vec != NULL) + out_vec[i] = data[i].val; + else + in_vec[i] = data[i].val; /* overwrite input vector */ + if (new_idices != NULL) new_idices[i] = data[i].idx; + } + ch_stateful_free(allocator, data); +} + +static void sort_int(int* io_vec, /* vector[len] to be sorted */ + int len /* number of elements in vectors, must be + consistent with the input data */ +) { + qsort(io_vec, len, sizeof(io_vec[0]), cmp_asc_int); +} + +static ch_vec3 cross(ch_vec3* v1, ch_vec3* v2) { + ch_vec3 cross; + cross.x = v1->y * v2->z - v1->z * v2->y; + cross.y = v1->z * v2->x - v1->x * v2->z; + cross.z = v1->x * v2->y - v1->y * v2->x; + return cross; +} + +/* calculates the determinent of a 4x4 matrix */ +static CH_FLOAT det_4x4(CH_FLOAT* m) { + return m[3] * m[6] * m[9] * m[12] - m[2] * m[7] * m[9] * m[12] - + m[3] * m[5] * m[10] * m[12] + m[1] * m[7] * m[10] * m[12] + + m[2] * m[5] * m[11] * m[12] - m[1] * m[6] * m[11] * m[12] - + m[3] * m[6] * m[8] * m[13] + m[2] * m[7] * m[8] * m[13] + + m[3] * m[4] * m[10] * m[13] - m[0] * m[7] * m[10] * m[13] - + m[2] * m[4] * m[11] * m[13] + m[0] * m[6] * m[11] * m[13] + + m[3] * m[5] * m[8] * m[14] - m[1] * m[7] * m[8] * m[14] - + m[3] * m[4] * m[9] * m[14] + m[0] * m[7] * m[9] * m[14] + + m[1] * m[4] * m[11] * m[14] - m[0] * m[5] * m[11] * m[14] - + m[2] * m[5] * m[8] * m[15] + m[1] * m[6] * m[8] * m[15] + + m[2] * m[4] * m[9] * m[15] - m[0] * m[6] * m[9] * m[15] - + m[1] * m[4] * m[10] * m[15] + m[0] * m[5] * m[10] * m[15]; +} + +/* Helper function for det_NxN() */ +static void createSubMatrix(CH_FLOAT* m, int N, int i, CH_FLOAT* sub_m) { + int j, k; + for (j = N, k = 0; j < N * N; j++) { + if (j % N != i) { /* i is the index to remove */ + sub_m[k] = m[j]; + k++; + } + } +} + +static CH_FLOAT det_NxN(CH_FLOAT* m, int d) { + CH_FLOAT sum; + CH_FLOAT sub_m[CONVHULL_ND_MAX_DIMENSIONS * CONVHULL_ND_MAX_DIMENSIONS]; + int sign; + + if (d == 0) return 1.0; + sum = 0.0; + sign = 1; + for (int i = 0; i < d; i++) { + createSubMatrix(m, d, i, sub_m); + sum += sign * m[i] * det_NxN(sub_m, d - 1); + sign *= -1; + } + return sum; +} + +/* Calculates the coefficients of the equation of a PLANE in 3D. + * Original Copyright (c) 2014, George Papazafeiropoulos + * Distributed under the BSD (2-clause) license + */ +static void plane_3d(CH_FLOAT* p, CH_FLOAT* c, CH_FLOAT* d) { + int i, j, k, l; + int r[3]; + CH_FLOAT sign, det, norm_c; + CH_FLOAT pdiff[2][3], pdiff_s[2][2]; + + for (i = 0; i < 2; i++) + for (j = 0; j < 3; j++) pdiff[i][j] = p[(i + 1) * 3 + j] - p[i * 3 + j]; + memset(c, 0, 3 * sizeof(CH_FLOAT)); + sign = 1.0; + for (i = 0; i < 3; i++) r[i] = i; + for (i = 0; i < 3; i++) { + for (j = 0; j < 2; j++) { + for (k = 0, l = 0; k < 3; k++) { + if (r[k] != i) { + pdiff_s[j][l] = pdiff[j][k]; + l++; + } + } + } + det = pdiff_s[0][0] * pdiff_s[1][1] - pdiff_s[1][0] * pdiff_s[0][1]; + c[i] = sign * det; + sign *= -1.0; + } + norm_c = (CH_FLOAT)0.0; + for (i = 0; i < 3; i++) norm_c += (ch_pow(c[i], (CH_FLOAT)2.0)); + norm_c = ch_sqrt(norm_c); + for (i = 0; i < 3; i++) c[i] /= norm_c; + (*d) = (CH_FLOAT)0.0; + for (i = 0; i < 3; i++) (*d) += -p[i] * c[i]; +} + +/* Calculates the coefficients of the equation of a PLANE in ND. + * Original Copyright (c) 2014, George Papazafeiropoulos + * Distributed under the BSD (2-clause) license + */ +static void plane_nd(const int Nd, CH_FLOAT* p, CH_FLOAT* c, CH_FLOAT* d) { + int i, j, k, l; + int r[CONVHULL_ND_MAX_DIMENSIONS]; + CH_FLOAT sign, det, norm_c; + CH_FLOAT pdiff[CONVHULL_ND_MAX_DIMENSIONS - 1][CONVHULL_ND_MAX_DIMENSIONS], + pdiff_s[(CONVHULL_ND_MAX_DIMENSIONS - 1) * + (CONVHULL_ND_MAX_DIMENSIONS - 1)]; + + if (Nd == 3) { + plane_3d(p, c, d); + return; + } + + for (i = 0; i < Nd - 1; i++) + for (j = 0; j < Nd; j++) pdiff[i][j] = p[(i + 1) * Nd + j] - p[i * Nd + j]; + memset(c, 0, Nd * sizeof(CH_FLOAT)); + sign = 1.0; + for (i = 0; i < Nd; i++) r[i] = i; + for (i = 0; i < Nd; i++) { + for (j = 0; j < Nd - 1; j++) { + for (k = 0, l = 0; k < Nd; k++) { + if (r[k] != i) { + pdiff_s[j * (Nd - 1) + l] = pdiff[j][k]; + l++; + } + } + } + /* Determinant 1 dimension lower */ + if (Nd == 3) + det = pdiff_s[0 * (Nd - 1) + 0] * pdiff_s[1 * (Nd - 1) + 1] - + pdiff_s[1 * (Nd - 1) + 0] * pdiff_s[0 * (Nd - 1) + 1]; + else if (Nd == 5) + det = det_4x4((CH_FLOAT*)pdiff_s); + else { + det = det_NxN((CH_FLOAT*)pdiff_s, Nd - 1); + } + c[i] = sign * det; + sign *= -1.0; + } + norm_c = (CH_FLOAT)0.0; + for (i = 0; i < Nd; i++) norm_c += (ch_pow(c[i], (CH_FLOAT)2.0)); + norm_c = ch_sqrt(norm_c); + for (i = 0; i < Nd; i++) c[i] /= norm_c; + (*d) = (CH_FLOAT)0.0; + for (i = 0; i < Nd; i++) (*d) += -p[i] * c[i]; +} + +static void ismember(int* pLeft, /* left vector; nLeftElements x 1 */ + int* pRight, /* right vector; nRightElements x 1 */ + int* pOut, /* 0, unless pRight elements are present in + pLeft then 1; nLeftElements x 1 */ + int nLeftElements, /* number of elements in pLeft */ + int nRightElements /* number of elements in pRight */ +) { + int i, j; + memset(pOut, 0, nLeftElements * sizeof(int)); + for (i = 0; i < nLeftElements; i++) + for (j = 0; j < nRightElements; j++) + if (pLeft[i] == pRight[j]) pOut[i] = 1; +} + +static CH_FLOAT rnd(int x, int y) { + // Reference(s): + // + // - Improvements to the canonical one-liner GLSL rand() for OpenGL ES 2.0 + // http://byteblacksmith.com/improvements-to-the-canonical-one-liner-glsl-rand-for-opengl-es-2-0/ + // + CH_FLOAT a = (CH_FLOAT)12.9898; + CH_FLOAT b = (CH_FLOAT)78.233; + CH_FLOAT c = (CH_FLOAT)43758.5453; + CH_FLOAT dt = x * a + y * b; +#ifdef CONVHULL_3D_USE_SINGLE_PRECISION + float sn = fmodf(dt, 3.14f); + float intpart; + return modff(sinf(sn) * c, &intpart); +#else + double sn = fmod(dt, 3.14); + double intpart; + return modf(sin(sn) * c, &intpart); +#endif // CONVHULL_3D_USE_SINGLE_PRECISION +} + +/* A C version of the 3D quickhull matlab implementation from here: + * https://www.mathworks.com/matlabcentral/fileexchange/48509-computational-geometry-toolbox?focused=3851550&tab=example + * (*out_faces) is returned as NULL, if triangulation fails * + * Original Copyright (c) 2014, George Papazafeiropoulos + * Distributed under the BSD (2-clause) license + * Reference: "The Quickhull Algorithm for Convex Hull, C. Bradford Barber, + * David P. Dobkin and Hannu Huhdanpaa, Geometry Center Technical Report GCG53, + * July 30, 1993" + */ +void convhull_3d_build(ch_vertex* const in_vertices, const int nVert, + int** out_faces, int* nOut_faces) { + convhull_3d_build_alloc(in_vertices, nVert, out_faces, nOut_faces, NULL); +} + +void convhull_3d_build_alloc(ch_vertex* const in_vertices, const int nVert, + int** out_faces, int* nOut_faces, + void* allocator) { + int i, j, k, l, h; + int nFaces, p, d; + int *aVec, *faces; + CH_FLOAT dfi, v, max_p, min_p; + CH_FLOAT span[CONVHULL_3D_MAX_DIMENSIONS]; + CH_FLOAT cfi[CONVHULL_3D_MAX_DIMENSIONS]; + CH_FLOAT p_s[CONVHULL_3D_MAX_DIMENSIONS * CONVHULL_3D_MAX_DIMENSIONS]; + CH_FLOAT *points, *cf, *df; + + if (nVert <= 3 || in_vertices == NULL) { + (*out_faces) = NULL; + (*nOut_faces) = 0; + return; + } + + /* 3 dimensions. The code should theoretically work for >=2 dimensions, but + * "plane_3d" and "det_4x4" are hardcoded for 3, + * so would need to be rewritten */ + d = 3; + + /* Add noise to the points */ + points = (CH_FLOAT*)ch_stateful_malloc(allocator, + nVert * (d + 1) * sizeof(CH_FLOAT)); + for (i = 0; i < nVert; i++) { + for (j = 0; j < d; j++) + points[i * (d + 1) + j] = + in_vertices[i].v[j] + + CH_NOISE_VAL * rnd(i, j); /* noise mitigates duplicates */ + points[i * (d + 1) + d] = 1.0f; /* add a last column of ones. Used only for + determinant calculation */ + } + + /* Find the span */ + for (j = 0; j < d; j++) { + max_p = (CH_FLOAT)-2.23e+13; + min_p = (CH_FLOAT)2.23e+13; + for (i = 0; i < nVert; i++) { + max_p = MAX(max_p, points[i * (d + 1) + j]); + min_p = MIN(min_p, points[i * (d + 1) + j]); + } + span[j] = max_p - min_p; +#ifndef CONVHULL_ALLOW_BUILD_IN_HIGHER_DIM + /* If you hit this assertion error, then the input vertices do not span all + * 3 dimensions. Therefore the convex hull could be built in less + * dimensions. In these cases, consider reducing the dimensionality of the + * points and calling convhull_nd_build() instead with d<3 + * You can turn this assert off using CONVHULL_ALLOW_BUILD_IN_HIGHER_DIM if + * you still wish to build in a higher number of dimensions. */ + assert(span[j] > 0.000000001); +#endif + } + + /* The initial convex hull is a simplex with (d+1) facets, where d is the + * number of dimensions */ + nFaces = (d + 1); + faces = (int*)ch_stateful_calloc(allocator, nFaces * d, sizeof(int)); + aVec = (int*)ch_stateful_malloc(allocator, nFaces * sizeof(int)); + for (i = 0; i < nFaces; i++) aVec[i] = i; + + /* Each column of cf contains the coefficients of a plane */ + cf = (CH_FLOAT*)ch_stateful_malloc(allocator, nFaces * d * sizeof(CH_FLOAT)); + df = (CH_FLOAT*)ch_stateful_malloc(allocator, nFaces * sizeof(CH_FLOAT)); + for (i = 0; i < nFaces; i++) { + /* Set the indices of the points defining the face */ + for (j = 0, k = 0; j < (d + 1); j++) { + if (aVec[j] != i) { + faces[i * d + k] = aVec[j]; + k++; + } + } + + /* Calculate and store the plane coefficients of the face */ + for (j = 0; j < d; j++) + for (k = 0; k < d; k++) + p_s[j * d + k] = points[(faces[i * d + j]) * (d + 1) + k]; + + /* Calculate and store the plane coefficients of the face */ + plane_3d(p_s, cfi, &dfi); + for (j = 0; j < d; j++) cf[i * d + j] = cfi[j]; + df[i] = dfi; + } + CH_FLOAT + A[(CONVHULL_3D_MAX_DIMENSIONS + 1) * (CONVHULL_3D_MAX_DIMENSIONS + 1)]; + int fVec[CONVHULL_3D_MAX_DIMENSIONS + 1]; + int face_tmp[2]; + + /* Check to make sure that faces are correctly oriented */ + int bVec[CONVHULL_3D_MAX_DIMENSIONS + 1]; + for (i = 0; i < d + 1; i++) bVec[i] = i; + + /* A contains the coordinates of the points forming a simplex */ + memset(A, 0, sizeof(A)); + for (k = 0; k < (d + 1); k++) { + /* Get the point that is not on the current face (point p) */ + for (i = 0; i < d; i++) fVec[i] = faces[k * d + i]; + sort_int(fVec, d); /* sort ascending */ + p = k; + for (i = 0; i < d; i++) + for (j = 0; j < (d + 1); j++) + A[i * (d + 1) + j] = points[(faces[k * d + i]) * (d + 1) + j]; + for (; i < (d + 1); i++) + for (j = 0; j < (d + 1); j++) + A[i * (d + 1) + j] = points[p * (d + 1) + j]; + + /* det(A) determines the orientation of the face */ + v = det_4x4(A); + + /* Orient so that each point on the original simplex can't see the opposite + * face */ + if (v < 0) { + /* Reverse the order of the last two vertices to change the volume */ + for (j = 0; j < 2; j++) face_tmp[j] = faces[k * d + d - j - 1]; + for (j = 0; j < 2; j++) faces[k * d + d - j - 1] = face_tmp[1 - j]; + + /* Modify the plane coefficients of the properly oriented faces */ + for (j = 0; j < d; j++) cf[k * d + j] = -cf[k * d + j]; + df[k] = -df[k]; + for (i = 0; i < d; i++) + for (j = 0; j < (d + 1); j++) + A[i * (d + 1) + j] = points[(faces[k * d + i]) * (d + 1) + j]; + for (; i < (d + 1); i++) + for (j = 0; j < (d + 1); j++) + A[i * (d + 1) + j] = points[p * (d + 1) + j]; + } + } + + /* Coordinates of the center of the point set */ + CH_FLOAT meanp[CONVHULL_3D_MAX_DIMENSIONS]; + CH_FLOAT *absdist, *reldist, *desReldist; + memset(meanp, 0, sizeof(meanp)); + for (i = d + 1; i < nVert; i++) + for (j = 0; j < d; j++) meanp[j] += points[i * (d + 1) + j]; + for (j = 0; j < d; j++) meanp[j] = meanp[j] / (CH_FLOAT)(nVert - d - 1); + + /* Absolute distance of points from the center */ + absdist = (CH_FLOAT*)ch_stateful_malloc( + allocator, (nVert - d - 1) * d * sizeof(CH_FLOAT)); + for (i = d + 1, k = 0; i < nVert; i++, k++) + for (j = 0; j < d; j++) + absdist[k * d + j] = (points[i * (d + 1) + j] - meanp[j]) / span[j]; + + /* Relative distance of points from the center */ + reldist = (CH_FLOAT*)ch_stateful_calloc(allocator, (nVert - d - 1), + sizeof(CH_FLOAT)); + desReldist = (CH_FLOAT*)ch_stateful_malloc( + allocator, (nVert - d - 1) * sizeof(CH_FLOAT)); + for (i = 0; i < (nVert - d - 1); i++) + for (j = 0; j < d; j++) + reldist[i] += ch_pow(absdist[i * d + j], (CH_FLOAT)2.0); + + /* Sort from maximum to minimum relative distance */ + int num_pleft, cnt; + int *ind, *pleft; + ind = (int*)ch_stateful_malloc(allocator, (nVert - d - 1) * sizeof(int)); + pleft = (int*)ch_stateful_malloc(allocator, (nVert - d - 1) * sizeof(int)); + sort_float(reldist, desReldist, ind, (nVert - d - 1), 1, allocator); + + /* Initialize the vector of points left. The points with the larger relative + distance from the center are scanned first. */ + num_pleft = (nVert - d - 1); + for (i = 0; i < num_pleft; i++) pleft[i] = ind[i] + d + 1; + + /* Loop over all remaining points that are not deleted. Deletion of points + occurs every #iter2del# iterations of this while loop */ + memset(A, 0, sizeof(A)); + + /* cnt is equal to the points having been selected without deletion of + nonvisible points (i.e. points inside the current convex hull) */ + cnt = 0; + + /* The main loop for the quickhull algorithm */ + CH_FLOAT detA; + CH_FLOAT* points_cf; + CH_FLOAT points_s[CONVHULL_3D_MAX_DIMENSIONS]; + int face_s[CONVHULL_3D_MAX_DIMENSIONS]; + int gVec[CONVHULL_3D_MAX_DIMENSIONS]; + int *visible_ind, *visible, *nonvisible_faces, *f0, *u, *horizon, *hVec, *pp, + *hVec_mem_face; + int num_visible_ind, num_nonvisible_faces, n_newfaces, n_realloc_faces, count, + vis; + int f0_sum, u_len, start, num_p, index, horizon_size1; + int FUCKED; + FUCKED = 0; + /* These pointers need to be assigned NULL as they only use realloc/resize + * (which act like malloc on a NULL pointer */ + visible = nonvisible_faces = f0 = u = horizon = hVec = pp = hVec_mem_face = + NULL; + nFaces = d + 1; + visible_ind = (int*)ch_stateful_malloc(allocator, nFaces * sizeof(int)); + points_cf = + (CH_FLOAT*)ch_stateful_malloc(allocator, nFaces * sizeof(CH_FLOAT)); + while ((num_pleft > 0)) { + /* i is the first point of the points left */ + i = pleft[0]; + + /* Delete the point selected */ + for (j = 0; j < num_pleft - 1; j++) pleft[j] = pleft[j + 1]; + num_pleft--; + if (num_pleft == 0) + ch_stateful_free(allocator, pleft); + else + pleft = + (int*)ch_stateful_realloc(allocator, pleft, num_pleft * sizeof(int)); + + /* Update point selection counter */ + cnt++; + + /* find visible faces */ + for (j = 0; j < d; j++) points_s[j] = points[i * (d + 1) + j]; + points_cf = (CH_FLOAT*)ch_stateful_realloc(allocator, points_cf, + nFaces * sizeof(CH_FLOAT)); + visible_ind = + (int*)ch_stateful_realloc(allocator, visible_ind, nFaces * sizeof(int)); +#ifdef CONVHULL_3D_USE_CBLAS +#ifdef CONVHULL_3D_USE_SINGLE_PRECISION + cblas_sgemm(CblasRowMajor, CblasNoTrans, CblasTrans, 1, nFaces, d, 1.0f, + points_s, d, cf, d, 0.0f, points_cf, nFaces); +#else + cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasTrans, 1, nFaces, d, 1.0, + points_s, d, cf, d, 0.0, points_cf, nFaces); +#endif +#else + for (j = 0; j < nFaces; j++) { + points_cf[j] = 0; + for (k = 0; k < d; k++) points_cf[j] += points_s[k] * cf[j * d + k]; + } +#endif + num_visible_ind = 0; + for (j = 0; j < nFaces; j++) { + if (points_cf[j] + df[j] > 0.0) { + num_visible_ind++; /* will sum to 0 if none are visible */ + visible_ind[j] = 1; + } else + visible_ind[j] = 0; + } + num_nonvisible_faces = nFaces - num_visible_ind; + + /* proceed if there are any visible faces */ + if (num_visible_ind != 0) { + /* Find visible face indices */ + visible = (int*)ch_stateful_resize(allocator, visible, + num_visible_ind * sizeof(int)); + for (j = 0, k = 0; j < nFaces; j++) { + if (visible_ind[j] == 1) { + visible[k] = j; + k++; + } + } + + /* Find nonvisible faces */ + nonvisible_faces = (int*)ch_stateful_resize( + allocator, nonvisible_faces, num_nonvisible_faces * d * sizeof(int)); + f0 = (int*)ch_stateful_resize(allocator, f0, + num_nonvisible_faces * d * sizeof(int)); + for (j = 0, k = 0; j < nFaces; j++) { + if (visible_ind[j] == 0) { + for (l = 0; l < d; l++) + nonvisible_faces[k * d + l] = faces[j * d + l]; + k++; + } + } + + /* Create horizon (count is the number of the edges of the horizon) */ + count = 0; + for (j = 0; j < num_visible_ind; j++) { + /* visible face */ + vis = visible[j]; + for (k = 0; k < d; k++) face_s[k] = faces[vis * d + k]; + sort_int(face_s, d); + ismember(nonvisible_faces, face_s, f0, num_nonvisible_faces * d, d); + u_len = 0; + + /* u are the nonvisible faces connected to the face v, if any */ + for (k = 0; k < num_nonvisible_faces; k++) { + f0_sum = 0; + for (l = 0; l < d; l++) f0_sum += f0[k * d + l]; + if (f0_sum == d - 1) { + u_len++; + if (u_len == 1) + u = (int*)ch_stateful_resize(allocator, u, u_len * sizeof(int)); + else + u = (int*)ch_stateful_realloc(allocator, u, u_len * sizeof(int)); + u[u_len - 1] = k; + } + } + for (k = 0; k < u_len; k++) { + /* The boundary between the visible face v and the k(th) nonvisible + * face connected to the face v forms part of the horizon */ + count++; + if (count == 1) + horizon = (int*)ch_stateful_resize(allocator, horizon, + count * (d - 1) * sizeof(int)); + else + horizon = (int*)ch_stateful_realloc(allocator, horizon, + count * (d - 1) * sizeof(int)); + for (l = 0; l < d; l++) gVec[l] = nonvisible_faces[u[k] * d + l]; + for (l = 0, h = 0; l < d; l++) { + if (f0[u[k] * d + l]) { + horizon[(count - 1) * (d - 1) + h] = gVec[l]; + h++; + } + } + } + } + horizon_size1 = count; + for (j = 0, l = 0; j < nFaces; j++) { + if (!visible_ind[j]) { + /* Delete visible faces */ + for (k = 0; k < d; k++) faces[l * d + k] = faces[j * d + k]; + + /* Delete the corresponding plane coefficients of the faces */ + for (k = 0; k < d; k++) cf[l * d + k] = cf[j * d + k]; + df[l] = df[j]; + l++; + } + } + + /* Update the number of faces */ + nFaces = nFaces - num_visible_ind; + + /* start is the first row of the new faces */ + start = nFaces; + + /* Add faces connecting horizon to the new point */ + n_newfaces = horizon_size1; + n_realloc_faces = nFaces + n_newfaces; + if (n_realloc_faces > CH_MAX_NUM_FACES) + n_realloc_faces = CH_MAX_NUM_FACES + 1; + faces = (int*)ch_stateful_realloc(allocator, faces, + n_realloc_faces * d * sizeof(int)); + cf = (CH_FLOAT*)ch_stateful_realloc( + allocator, cf, n_realloc_faces * d * sizeof(CH_FLOAT)); + df = (CH_FLOAT*)ch_stateful_realloc(allocator, df, + n_realloc_faces * sizeof(CH_FLOAT)); + + for (j = 0; j < n_newfaces; j++) { + nFaces++; + for (k = 0; k < d - 1; k++) + faces[(nFaces - 1) * d + k] = horizon[j * (d - 1) + k]; + faces[(nFaces - 1) * d + (d - 1)] = i; + + /* Calculate and store appropriately the plane coefficients of the faces + */ + for (k = 0; k < d; k++) + for (l = 0; l < d; l++) + p_s[k * d + l] = + points[(faces[(nFaces - 1) * d + k]) * (d + 1) + l]; + plane_3d(p_s, cfi, &dfi); + for (k = 0; k < d; k++) cf[(nFaces - 1) * d + k] = cfi[k]; + df[(nFaces - 1)] = dfi; + if (nFaces > CH_MAX_NUM_FACES) { + FUCKED = 1; + nFaces = 0; + break; + } + } + + /* Orient each new face properly */ + hVec = (int*)ch_stateful_resize(allocator, hVec, nFaces * sizeof(int)); + hVec_mem_face = (int*)ch_stateful_resize(allocator, hVec_mem_face, + nFaces * sizeof(int)); + for (j = 0; j < nFaces; j++) hVec[j] = j; + for (k = start; k < nFaces; k++) { + for (j = 0; j < d; j++) face_s[j] = faces[k * d + j]; + sort_int(face_s, d); + ismember(hVec, face_s, hVec_mem_face, nFaces, d); + num_p = 0; + for (j = 0; j < nFaces; j++) + if (!hVec_mem_face[j]) num_p++; + pp = (int*)ch_stateful_resize(allocator, pp, num_p * sizeof(int)); + for (j = 0, l = 0; j < nFaces; j++) { + if (!hVec_mem_face[j]) { + pp[l] = hVec[j]; + l++; + } + } + index = 0; + detA = 0.0; + + /* While new point is coplanar, choose another point */ + while (detA == 0.0) { + for (j = 0; j < d; j++) + for (l = 0; l < d + 1; l++) + A[j * (d + 1) + l] = points[(faces[k * d + j]) * (d + 1) + l]; + for (; j < d + 1; j++) + for (l = 0; l < d + 1; l++) + A[j * (d + 1) + l] = points[pp[index] * (d + 1) + l]; + index++; + detA = det_4x4(A); + } + + /* Orient faces so that each point on the original simplex can't see the + * opposite face */ + if (detA < 0.0) { + /* If orientation is improper, reverse the order to change the volume + * sign */ + for (j = 0; j < 2; j++) face_tmp[j] = faces[k * d + d - j - 1]; + for (j = 0; j < 2; j++) faces[k * d + d - j - 1] = face_tmp[1 - j]; + + /* Modify the plane coefficients of the properly oriented faces */ + for (j = 0; j < d; j++) cf[k * d + j] = -cf[k * d + j]; + df[k] = -df[k]; + for (l = 0; l < d; l++) + for (j = 0; j < d + 1; j++) + A[l * (d + 1) + j] = points[(faces[k * d + l]) * (d + 1) + j]; + for (; l < d + 1; l++) + for (j = 0; j < d + 1; j++) + A[l * (d + 1) + j] = points[pp[index] * (d + 1) + j]; +#ifndef NDEBUG + /* Check */ + detA = det_4x4(A); + /* If you hit this assertion error, then the face cannot be properly + * orientated */ + assert(detA > 0.0); +#endif + } + } + } + if (FUCKED) { + break; + } + } + + /* output */ + if (FUCKED) { + (*out_faces) = NULL; + (*nOut_faces) = 0; + } else { + (*out_faces) = + (int*)ch_stateful_malloc(allocator, nFaces * d * sizeof(int)); + memcpy((*out_faces), faces, nFaces * d * sizeof(int)); + (*nOut_faces) = nFaces; + } + + /* clean-up */ + ch_stateful_free(allocator, u); + ch_stateful_free(allocator, pp); + ch_stateful_free(allocator, horizon); + ch_stateful_free(allocator, f0); + ch_stateful_free(allocator, nonvisible_faces); + ch_stateful_free(allocator, visible); + ch_stateful_free(allocator, hVec); + ch_stateful_free(allocator, hVec_mem_face); + ch_stateful_free(allocator, visible_ind); + ch_stateful_free(allocator, points_cf); + ch_stateful_free(allocator, absdist); + ch_stateful_free(allocator, reldist); + ch_stateful_free(allocator, desReldist); + ch_stateful_free(allocator, ind); + ch_stateful_free(allocator, points); + ch_stateful_free(allocator, faces); + ch_stateful_free(allocator, aVec); + ch_stateful_free(allocator, cf); + ch_stateful_free(allocator, df); +} + +void convhull_3d_export_obj(ch_vertex* const vertices, const int nVert, + int* const faces, const int nFaces, + const int keepOnlyUsedVerticesFLAG, + char* const obj_filename) { + int i, j; + char* path = (char*)calloc(strlen(obj_filename) + 1, sizeof(char)); + // char* path = new char[strlen(obj_filename) + 1]; // Allocate memory for + // destination buffer + strcpy(path, obj_filename); + FILE* obj_file; +#if defined(_MSC_VER) && !defined(_CRT_SECURE_NO_WARNINGS) + CV_STRCAT(path, ".obj"); + fopen_s(&obj_file, path, "wt"); +#else + errno = 0; + obj_file = fopen(strcat(path, ".obj"), "wt"); +#endif + if (obj_file == NULL) { + printf("Error %d \n", errno); + printf("It's null"); + } + fprintf(obj_file, "o\n"); + CH_FLOAT scale; + ch_vec3 v1, v2, normal; + + /* export vertices */ + if (keepOnlyUsedVerticesFLAG) { + for (i = 0; i < nFaces; i++) + for (j = 0; j < 3; j++) + fprintf(obj_file, "v %f %f %f\n", vertices[faces[i * 3 + j]].x, + vertices[faces[i * 3 + j]].y, vertices[faces[i * 3 + j]].z); + } else { + for (i = 0; i < nVert; i++) + fprintf(obj_file, "v %f %f %f\n", vertices[i].x, vertices[i].y, + vertices[i].z); + } + + /* export the face normals */ + for (i = 0; i < nFaces; i++) { + /* calculate cross product between v1-v0 and v2-v0 */ + v1 = vertices[faces[i * 3 + 1]]; + v2 = vertices[faces[i * 3 + 2]]; + v1.x -= vertices[faces[i * 3]].x; + v1.y -= vertices[faces[i * 3]].y; + v1.z -= vertices[faces[i * 3]].z; + v2.x -= vertices[faces[i * 3]].x; + v2.y -= vertices[faces[i * 3]].y; + v2.z -= vertices[faces[i * 3]].z; + normal = cross(&v1, &v2); + + /* normalise to unit length */ + scale = ((CH_FLOAT)1.0) / (ch_sqrt(ch_pow(normal.x, (CH_FLOAT)2.0) + + ch_pow(normal.y, (CH_FLOAT)2.0) + + ch_pow(normal.z, (CH_FLOAT)2.0)) + + (CH_FLOAT)2.23e-9); + normal.x *= scale; + normal.y *= scale; + normal.z *= scale; + fprintf(obj_file, "vn %f %f %f\n", normal.x, normal.y, normal.z); + } + + /* export the face indices */ + if (keepOnlyUsedVerticesFLAG) { + for (i = 0; i < nFaces; i++) { + /* vertices are in same order as the faces, and normals are in order */ + fprintf(obj_file, "f %u//%u %u//%u %u//%u\n", i * 3 + 1, i + 1, + i * 3 + 1 + 1, i + 1, i * 3 + 2 + 1, i + 1); + } + } else { + /* just normals are in order */ + for (i = 0; i < nFaces; i++) { + fprintf(obj_file, "f %u//%u %u//%u %u//%u\n", faces[i * 3] + 1, i + 1, + faces[i * 3 + 1] + 1, i + 1, faces[i * 3 + 2] + 1, i + 1); + } + } + fclose(obj_file); +} + +void convhull_3d_export_m(ch_vertex* const vertices, const int nVert, + int* const faces, const int nFaces, + char* const m_filename) { + int i; + char path[256] = {"\0"}; + memcpy(path, m_filename, strlen(m_filename)); + FILE* m_file; +#if defined(_MSC_VER) && !defined(_CRT_SECURE_NO_WARNINGS) + CV_STRCAT(path, ".m"); + fopen_s(&m_file, path, "wt"); +#else + m_file = fopen(strcat(path, ".m"), "wt"); +#endif + + /* save face indices and vertices for verification in matlab: */ + fprintf(m_file, "vertices = [\n"); + for (i = 0; i < nVert; i++) + fprintf(m_file, "%f, %f, %f;\n", vertices[i].x, vertices[i].y, + vertices[i].z); + fprintf(m_file, "];\n\n\n"); + fprintf(m_file, "faces = [\n"); + for (i = 0; i < nFaces; i++) { + fprintf(m_file, " %u, %u, %u;\n", faces[3 * i + 0] + 1, + faces[3 * i + 1] + 1, faces[3 * i + 2] + 1); + } + fprintf(m_file, "];\n\n\n"); + fclose(m_file); +} + +void extract_vertices_from_obj_file(char* const obj_filename, + ch_vertex** out_vertices, int* out_nVert) { + extract_vertices_from_obj_file_alloc(obj_filename, out_vertices, out_nVert, + NULL); +} + +void extract_vertices_from_obj_file_alloc(char* const obj_filename, + ch_vertex** out_vertices, + int* out_nVert, void* allocator) { + FILE* obj_file; +#if defined(_MSC_VER) && !defined(_CRT_SECURE_NO_WARNINGS) + CV_STRCAT(obj_filename, ".obj"); + fopen_s(&obj_file, obj_filename, "r"); +#else + obj_file = fopen(strcat(obj_filename, ".obj"), "r"); +#endif + + /* determine number of vertices */ + unsigned int nVert = 0; + char line[256]; + while (fgets(line, sizeof(line), obj_file)) { + char* vexists = strstr(line, "v "); + if (vexists != NULL) nVert++; + } + (*out_nVert) = nVert; + (*out_vertices) = + (ch_vertex*)ch_stateful_malloc(allocator, nVert * sizeof(ch_vertex)); + + /* extract the vertices */ + rewind(obj_file); + int i = 0; + int vertID, prev_char_isDigit, current_char_isDigit; + char vert_char[256] = {0}; + while (fgets(line, sizeof(line), obj_file)) { + char* vexists = strstr(line, "v "); + if (vexists != NULL) { + prev_char_isDigit = 0; + vertID = -1; + for (size_t j = 0; j < strlen(line) - 1; j++) { + if (isdigit(line[j]) || line[j] == '.' || line[j] == '-' || + line[j] == '+' || line[j] == 'E' || line[j] == 'e') { + vert_char[strlen(vert_char)] = line[j]; + current_char_isDigit = 1; + } else + current_char_isDigit = 0; + if ((prev_char_isDigit && !current_char_isDigit) || + j == strlen(line) - 2) { + vertID++; + if (vertID > 4) { + /* not a valid file */ + ch_stateful_free(allocator, (*out_vertices)); + (*out_vertices) = NULL; + (*out_nVert) = 0; + return; + } + (*out_vertices)[i].v[vertID] = (CH_FLOAT)atof(vert_char); + memset(vert_char, 0, 256 * sizeof(char)); + } + prev_char_isDigit = current_char_isDigit; + } + i++; + } + } +} + +/**** NEW! ****/ + +/* A C version of the ND quickhull matlab implementation from here: + * https://www.mathworks.com/matlabcentral/fileexchange/48509-computational-geometry-toolbox?focused=3851550&tab=example + * (*out_faces) is returned as NULL, if triangulation fails * + * Original Copyright (c) 2014, George Papazafeiropoulos + * Distributed under the BSD (2-clause) license + * Reference: "The Quickhull Algorithm for Convex Hull, C. Bradford Barber, + * David P. Dobkin and Hannu Huhdanpaa, Geometry Center Technical Report GCG53, + * July 30, 1993" + */ +void convhull_nd_build(CH_FLOAT* const in_vertices, const int nVert, + const int d, int** out_faces, CH_FLOAT** out_cf, + CH_FLOAT** out_df, int* nOut_faces) { + convhull_nd_build_alloc(in_vertices, nVert, d, out_faces, out_cf, out_df, + nOut_faces, NULL); +} + +void convhull_nd_build_alloc(CH_FLOAT* const in_vertices, const int nVert, + const int d, int** out_faces, CH_FLOAT** out_cf, + CH_FLOAT** out_df, int* nOut_faces, + void* allocator) { + int i, j, k, l, h; + int nFaces, p; + int *aVec, *faces; + CH_FLOAT dfi, v, max_p, min_p; + CH_FLOAT span[CONVHULL_ND_MAX_DIMENSIONS]; + CH_FLOAT cfi[CONVHULL_ND_MAX_DIMENSIONS]; + CH_FLOAT p_s[CONVHULL_ND_MAX_DIMENSIONS * CONVHULL_ND_MAX_DIMENSIONS]; + CH_FLOAT *points, *cf, *df; + + assert(d <= CONVHULL_ND_MAX_DIMENSIONS); + + /* Solution not possible... */ + if (d > CONVHULL_ND_MAX_DIMENSIONS || nVert <= d || in_vertices == NULL) { + (*out_faces) = NULL; + (*nOut_faces) = 0; + if (out_cf != NULL) (*out_cf) = NULL; + if (out_df != NULL) (*out_df) = NULL; + return; + } + + /* Add noise to the points */ + points = (CH_FLOAT*)ch_stateful_malloc(allocator, + nVert * (d + 1) * sizeof(CH_FLOAT)); + for (i = 0; i < nVert; i++) { + for (j = 0; j < d; j++) + points[i * (d + 1) + j] = + in_vertices[i * d + j] + CH_NOISE_VAL * rnd(i, j); + points[i * (d + 1) + d] = 1.0; /* add a last column of ones. Used only for + determinant calculation */ + } + + /* Find the span */ + for (j = 0; j < d; j++) { + max_p = (CH_FLOAT)-2.23e+13; + min_p = (CH_FLOAT)2.23e+13; + for (i = 0; i < nVert; i++) { + max_p = MAX(max_p, points[i * (d + 1) + j]); + min_p = MIN(min_p, points[i * (d + 1) + j]); + } + span[j] = max_p - min_p; +#ifndef CONVHULL_ALLOW_BUILD_IN_HIGHER_DIM + /* If you hit this assertion error, then the input vertices do not span all + * 'd' dimensions. Therefore the convex hull could be built in less + * dimensions. In these cases, consider reducing the dimensionality of the + * points and calling convhull_nd_build() with a smaller d + * You can turn this assert off using CONVHULL_ALLOW_BUILD_IN_HIGHER_DIM if + * you still wish to build in a higher number of dimensions. */ + assert(span[j] > 0.000000001); +#endif + } + + /* The initial convex hull is a simplex with (d+1) facets, where d is the + * number of dimensions */ + nFaces = (d + 1); + faces = (int*)ch_stateful_calloc(allocator, nFaces * d, sizeof(int)); + aVec = (int*)ch_stateful_malloc(allocator, nFaces * sizeof(int)); + for (i = 0; i < nFaces; i++) aVec[i] = i; + + /* Each column of cf contains the coefficients of a plane */ + cf = (CH_FLOAT*)ch_stateful_malloc(allocator, nFaces * d * sizeof(CH_FLOAT)); + df = (CH_FLOAT*)ch_stateful_malloc(allocator, nFaces * sizeof(CH_FLOAT)); + for (i = 0; i < nFaces; i++) { + /* Set the indices of the points defining the face */ + for (j = 0, k = 0; j < (d + 1); j++) { + if (aVec[j] != i) { + faces[i * d + k] = aVec[j]; + k++; + } + } + + /* Calculate and store the plane coefficients of the face */ + for (j = 0; j < d; j++) + for (k = 0; k < d; k++) + p_s[j * d + k] = points[(faces[i * d + j]) * (d + 1) + k]; + + /* Calculate and store the plane coefficients of the face */ + plane_nd(d, p_s, cfi, &dfi); + for (j = 0; j < d; j++) cf[i * d + j] = cfi[j]; + df[i] = dfi; + } + CH_FLOAT + A[(CONVHULL_ND_MAX_DIMENSIONS + 1) * (CONVHULL_ND_MAX_DIMENSIONS + 1)]; + int fVec[CONVHULL_ND_MAX_DIMENSIONS + 1]; + int face_tmp[2]; + + /* Check to make sure that faces are correctly oriented */ + int bVec[CONVHULL_ND_MAX_DIMENSIONS + 1]; + for (i = 0; i < d + 1; i++) bVec[i] = i; + + /* A contains the coordinates of the points forming a simplex */ + memset(A, 0, sizeof(A)); + for (k = 0; k < (d + 1); k++) { + /* Get the point that is not on the current face (point p) */ + for (i = 0; i < d; i++) fVec[i] = faces[k * d + i]; + sort_int(fVec, d); /* sort ascending */ + p = k; + for (i = 0; i < d; i++) + for (j = 0; j < (d + 1); j++) + A[i * (d + 1) + j] = points[(faces[k * d + i]) * (d + 1) + j]; + for (; i < (d + 1); i++) + for (j = 0; j < (d + 1); j++) + A[i * (d + 1) + j] = points[p * (d + 1) + j]; + + /* det(A) determines the orientation of the face */ + if (d == 3) + v = det_4x4(A); + else + v = det_NxN(A, d + 1); + + /* Orient so that each point on the original simplex can't see the opposite + * face */ + if (v < 0) { + /* Reverse the order of the last two vertices to change the volume */ + for (j = 0; j < 2; j++) face_tmp[j] = faces[k * d + d - j - 1]; + for (j = 0; j < 2; j++) faces[k * d + d - j - 1] = face_tmp[1 - j]; + + /* Modify the plane coefficients of the properly oriented faces */ + for (j = 0; j < d; j++) cf[k * d + j] = -cf[k * d + j]; + df[k] = -df[k]; + for (i = 0; i < d; i++) + for (j = 0; j < (d + 1); j++) + A[i * (d + 1) + j] = points[(faces[k * d + i]) * (d + 1) + j]; + for (; i < (d + 1); i++) + for (j = 0; j < (d + 1); j++) + A[i * (d + 1) + j] = points[p * (d + 1) + j]; + } + } + + /* Coordinates of the center of the point set */ + CH_FLOAT meanp[CONVHULL_ND_MAX_DIMENSIONS]; + CH_FLOAT *reldist, *desReldist, *absdist; + memset(meanp, 0, sizeof(meanp)); + for (i = d + 1; i < nVert; i++) + for (j = 0; j < d; j++) meanp[j] += points[i * (d + 1) + j]; + for (j = 0; j < d; j++) meanp[j] = meanp[j] / (CH_FLOAT)(nVert - d - 1); + + /* Absolute distance of points from the center */ + absdist = (CH_FLOAT*)ch_stateful_malloc( + allocator, (nVert - d - 1) * d * sizeof(CH_FLOAT)); + for (i = d + 1, k = 0; i < nVert; i++, k++) + for (j = 0; j < d; j++) + absdist[k * d + j] = (points[i * (d + 1) + j] - meanp[j]) / span[j]; + + /* Relative distance of points from the center */ + reldist = (CH_FLOAT*)ch_stateful_calloc(allocator, (nVert - d - 1), + sizeof(CH_FLOAT)); + desReldist = (CH_FLOAT*)ch_stateful_malloc( + allocator, (nVert - d - 1) * sizeof(CH_FLOAT)); + for (i = 0; i < (nVert - d - 1); i++) + for (j = 0; j < d; j++) + reldist[i] += ch_pow(absdist[i * d + j], (CH_FLOAT)2.0); + + /* Sort from maximum to minimum relative distance */ + int num_pleft, cnt; + int *ind, *pleft; + ind = (int*)ch_stateful_malloc(allocator, (nVert - d - 1) * sizeof(int)); + pleft = (int*)ch_stateful_malloc(allocator, (nVert - d - 1) * sizeof(int)); + sort_float(reldist, desReldist, ind, (nVert - d - 1), 1, allocator); + + /* Initialize the vector of points left. The points with the larger relative + distance from the center are scanned first. */ + num_pleft = (nVert - d - 1); + for (i = 0; i < num_pleft; i++) pleft[i] = ind[i] + d + 1; + + /* Loop over all remaining points that are not deleted. Deletion of points + occurs every #iter2del# iterations of this while loop */ + memset(A, 0, sizeof(A)); + + /* cnt is equal to the points having been selected without deletion of + nonvisible points (i.e. points inside the current convex hull) */ + cnt = 0; + + /* The main loop for the quickhull algorithm */ + CH_FLOAT detA; + CH_FLOAT* points_cf; + CH_FLOAT points_s[CONVHULL_ND_MAX_DIMENSIONS]; + int face_s[CONVHULL_ND_MAX_DIMENSIONS]; + int gVec[CONVHULL_ND_MAX_DIMENSIONS]; + int *visible_ind, *visible, *nonvisible_faces, *f0, *u, *horizon, *hVec, *pp, + *hVec_mem_face; + int num_visible_ind, num_nonvisible_faces, n_newfaces, n_realloc_faces, count, + vis; + int f0_sum, u_len, start, num_p, index, horizon_size1; + int FUCKED; + FUCKED = 0; + /* These pointers need to be assigned NULL as they only use realloc/resize + * (which act like malloc on a NULL pointer */ + visible = nonvisible_faces = f0 = u = horizon = hVec = pp = hVec_mem_face = + NULL; + nFaces = d + 1; + visible_ind = (int*)ch_stateful_malloc(allocator, nFaces * sizeof(int)); + points_cf = + (CH_FLOAT*)ch_stateful_malloc(allocator, nFaces * sizeof(CH_FLOAT)); + while ((num_pleft > 0)) { + /* i is the first point of the points left */ + i = pleft[0]; + + /* Delete the point selected */ + for (j = 0; j < num_pleft - 1; j++) pleft[j] = pleft[j + 1]; + num_pleft--; + if (num_pleft == 0) + ch_stateful_free(allocator, pleft); + else + pleft = + (int*)ch_stateful_realloc(allocator, pleft, num_pleft * sizeof(int)); + + /* Update point selection counter */ + cnt++; + + /* find visible faces */ + for (j = 0; j < d; j++) points_s[j] = points[i * (d + 1) + j]; + points_cf = (CH_FLOAT*)ch_stateful_realloc(allocator, points_cf, + nFaces * sizeof(CH_FLOAT)); + visible_ind = + (int*)ch_stateful_realloc(allocator, visible_ind, nFaces * sizeof(int)); +#ifdef CONVHULL_3D_USE_CBLAS +#ifdef CONVHULL_3D_USE_SINGLE_PRECISION + cblas_sgemm(CblasRowMajor, CblasNoTrans, CblasTrans, 1, nFaces, d, 1.0f, + points_s, d, cf, d, 0.0f, points_cf, nFaces); +#else + cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasTrans, 1, nFaces, d, 1.0, + points_s, d, cf, d, 0.0, points_cf, nFaces); +#endif +#else + for (j = 0; j < nFaces; j++) { + points_cf[j] = 0; + for (k = 0; k < d; k++) points_cf[j] += points_s[k] * cf[j * d + k]; + } +#endif + num_visible_ind = 0; + for (j = 0; j < nFaces; j++) { + if (points_cf[j] + df[j] > 0.0) { + num_visible_ind++; /* will sum to 0 if none are visible */ + visible_ind[j] = 1; + } else + visible_ind[j] = 0; + } + num_nonvisible_faces = nFaces - num_visible_ind; + + /* proceed if there are any visible faces */ + if (num_visible_ind != 0) { + /* Find visible face indices */ + visible = (int*)ch_stateful_resize(allocator, visible, + num_visible_ind * sizeof(int)); + for (j = 0, k = 0; j < nFaces; j++) { + if (visible_ind[j] == 1) { + visible[k] = j; + k++; + } + } + + /* Find nonvisible faces */ + nonvisible_faces = (int*)ch_stateful_resize( + allocator, nonvisible_faces, num_nonvisible_faces * d * sizeof(int)); + f0 = (int*)ch_stateful_resize(allocator, f0, + num_nonvisible_faces * d * sizeof(int)); + for (j = 0, k = 0; j < nFaces; j++) { + if (visible_ind[j] == 0) { + for (l = 0; l < d; l++) + nonvisible_faces[k * d + l] = faces[j * d + l]; + k++; + } + } + + /* Create horizon (count is the number of the edges of the horizon) */ + count = 0; + for (j = 0; j < num_visible_ind; j++) { + /* visible face */ + vis = visible[j]; + for (k = 0; k < d; k++) face_s[k] = faces[vis * d + k]; + sort_int(face_s, d); + ismember(nonvisible_faces, face_s, f0, num_nonvisible_faces * d, d); + u_len = 0; + + /* u are the nonvisible faces connected to the face v, if any */ + for (k = 0; k < num_nonvisible_faces; k++) { + f0_sum = 0; + for (l = 0; l < d; l++) f0_sum += f0[k * d + l]; + if (f0_sum == d - 1) { + u_len++; + if (u_len == 1) + u = (int*)ch_stateful_resize(allocator, u, u_len * sizeof(int)); + else + u = (int*)ch_stateful_realloc(allocator, u, u_len * sizeof(int)); + u[u_len - 1] = k; + } + } + for (k = 0; k < u_len; k++) { + /* The boundary between the visible face v and the k(th) nonvisible + * face connected to the face v forms part of the horizon */ + count++; + if (count == 1) + horizon = (int*)ch_stateful_resize(allocator, horizon, + count * (d - 1) * sizeof(int)); + else + horizon = (int*)ch_stateful_realloc(allocator, horizon, + count * (d - 1) * sizeof(int)); + for (l = 0; l < d; l++) gVec[l] = nonvisible_faces[u[k] * d + l]; + for (l = 0, h = 0; l < d; l++) { + if (f0[u[k] * d + l]) { + horizon[(count - 1) * (d - 1) + h] = gVec[l]; + h++; + } + } + } + } + horizon_size1 = count; + for (j = 0, l = 0; j < nFaces; j++) { + if (!visible_ind[j]) { + /* Delete visible faces */ + for (k = 0; k < d; k++) faces[l * d + k] = faces[j * d + k]; + + /* Delete the corresponding plane coefficients of the faces */ + for (k = 0; k < d; k++) cf[l * d + k] = cf[j * d + k]; + df[l] = df[j]; + l++; + } + } + + /* Update the number of faces */ + nFaces = nFaces - num_visible_ind; + + /* start is the first row of the new faces */ + start = nFaces; + + /* Add faces connecting horizon to the new point */ + n_newfaces = horizon_size1; + n_realloc_faces = nFaces + n_newfaces; + if (n_realloc_faces > CH_MAX_NUM_FACES) + n_realloc_faces = CH_MAX_NUM_FACES + 1; + faces = (int*)ch_stateful_realloc( + allocator, faces, (nFaces + n_newfaces) * d * sizeof(int)); + cf = (CH_FLOAT*)ch_stateful_realloc( + allocator, cf, (nFaces + n_newfaces) * d * sizeof(CH_FLOAT)); + df = (CH_FLOAT*)ch_stateful_realloc( + allocator, df, (nFaces + n_newfaces) * sizeof(CH_FLOAT)); + + for (j = 0; j < n_newfaces; j++) { + nFaces++; + for (k = 0; k < d - 1; k++) + faces[(nFaces - 1) * d + k] = horizon[j * (d - 1) + k]; + faces[(nFaces - 1) * d + (d - 1)] = i; + + /* Calculate and store appropriately the plane coefficients of the faces + */ + for (k = 0; k < d; k++) + for (l = 0; l < d; l++) + p_s[k * d + l] = + points[(faces[(nFaces - 1) * d + k]) * (d + 1) + l]; + plane_nd(d, p_s, cfi, &dfi); + for (k = 0; k < d; k++) cf[(nFaces - 1) * d + k] = cfi[k]; + df[(nFaces - 1)] = dfi; + if (nFaces > CH_MAX_NUM_FACES) { + FUCKED = 1; + nFaces = 0; + break; + } + } + + /* Orient each new face properly */ + hVec = (int*)ch_stateful_resize(allocator, hVec, nFaces * sizeof(int)); + hVec_mem_face = (int*)ch_stateful_resize(allocator, hVec_mem_face, + nFaces * sizeof(int)); + for (j = 0; j < nFaces; j++) hVec[j] = j; + for (k = start; k < nFaces; k++) { + for (j = 0; j < d; j++) face_s[j] = faces[k * d + j]; + sort_int(face_s, d); + ismember(hVec, face_s, hVec_mem_face, nFaces, d); + num_p = 0; + for (j = 0; j < nFaces; j++) + if (!hVec_mem_face[j]) num_p++; + pp = (int*)ch_stateful_resize(allocator, pp, num_p * sizeof(int)); + for (j = 0, l = 0; j < nFaces; j++) { + if (!hVec_mem_face[j]) { + pp[l] = hVec[j]; + l++; + } + } + index = 0; + detA = 0.0; + + /* While new point is coplanar, choose another point */ + while (detA == 0.0) { + for (j = 0; j < d; j++) + for (l = 0; l < d + 1; l++) + A[j * (d + 1) + l] = points[(faces[k * d + j]) * (d + 1) + l]; + for (; j < d + 1; j++) + for (l = 0; l < d + 1; l++) + A[j * (d + 1) + l] = points[pp[index] * (d + 1) + l]; + index++; + if (d == 3) + detA = det_4x4(A); + else + detA = det_NxN((CH_FLOAT*)A, d + 1); + } + + /* Orient faces so that each point on the original simplex can't see the + * opposite face */ + if (detA < 0.0) { + /* If orientation is improper, reverse the order to change the volume + * sign */ + for (j = 0; j < 2; j++) face_tmp[j] = faces[k * d + d - j - 1]; + for (j = 0; j < 2; j++) faces[k * d + d - j - 1] = face_tmp[1 - j]; + + /* Modify the plane coefficients of the properly oriented faces */ + for (j = 0; j < d; j++) cf[k * d + j] = -cf[k * d + j]; + df[k] = -df[k]; + for (l = 0; l < d; l++) + for (j = 0; j < d + 1; j++) + A[l * (d + 1) + j] = points[(faces[k * d + l]) * (d + 1) + j]; + for (; l < d + 1; l++) + for (j = 0; j < d + 1; j++) + A[l * (d + 1) + j] = points[pp[index] * (d + 1) + j]; +#ifndef NDEBUG + /* Check */ + if (d == 3) + detA = det_4x4(A); + else + detA = det_NxN((CH_FLOAT*)A, d + 1); + /* If you hit this assertion error, then the face cannot be properly + * orientated and building the convex hull is likely impossible */ + assert(detA > 0.0); +#endif + } + } + } + if (FUCKED) { + break; + } + } + + /* output */ + if (FUCKED) { + (*out_faces) = NULL; + if (out_cf != NULL) (*out_cf) = NULL; + if (out_df != NULL) (*out_df) = NULL; + (*nOut_faces) = 0; + } else { + (*out_faces) = + (int*)ch_stateful_malloc(allocator, nFaces * d * sizeof(int)); + memcpy((*out_faces), faces, nFaces * d * sizeof(int)); + (*nOut_faces) = nFaces; + if (out_cf != NULL) { + (*out_cf) = (CH_FLOAT*)ch_stateful_malloc(allocator, + nFaces * d * sizeof(CH_FLOAT)); + memcpy((*out_cf), cf, nFaces * d * sizeof(CH_FLOAT)); + } + if (out_df != NULL) { + (*out_df) = + (CH_FLOAT*)ch_stateful_malloc(allocator, nFaces * sizeof(CH_FLOAT)); + memcpy((*out_df), df, nFaces * sizeof(CH_FLOAT)); + } + } + + /* clean-up */ + ch_stateful_free(allocator, u); + ch_stateful_free(allocator, pp); + ch_stateful_free(allocator, horizon); + ch_stateful_free(allocator, f0); + ch_stateful_free(allocator, nonvisible_faces); + ch_stateful_free(allocator, visible); + ch_stateful_free(allocator, hVec); + ch_stateful_free(allocator, hVec_mem_face); + ch_stateful_free(allocator, visible_ind); + ch_stateful_free(allocator, points_cf); + ch_stateful_free(allocator, absdist); + ch_stateful_free(allocator, reldist); + ch_stateful_free(allocator, desReldist); + ch_stateful_free(allocator, ind); + ch_stateful_free(allocator, points); + ch_stateful_free(allocator, faces); + ch_stateful_free(allocator, aVec); + ch_stateful_free(allocator, cf); + ch_stateful_free(allocator, df); +} + +void delaunay_nd_mesh(const float* points, const int nPoints, const int nd, + int** Mesh, int* nMesh) { + delaunay_nd_mesh_alloc(points, nPoints, nd, Mesh, nMesh, NULL); +} + +void delaunay_nd_mesh_alloc(const float* points, const int nPoints, + const int nd, int** Mesh, int* nMesh, + void* allocator) { + int i, j, k, nHullFaces, maxW_idx, nVisible; + int* hullfaces; + CH_FLOAT w0, w_optimal, w_optimal2; + CH_FLOAT *projpoints, *cf, *df, *p0, *p, *visible; + + /* Project the N-dimensional points onto a N+1-dimensional paraboloid */ + projpoints = (CH_FLOAT*)ch_stateful_malloc( + allocator, nPoints * (nd + 1) * sizeof(CH_FLOAT)); + for (i = 0; i < nPoints; i++) { + projpoints[i * (nd + 1) + nd] = 0.0; + for (j = 0; j < nd; j++) { + projpoints[i * (nd + 1) + j] = + (CH_FLOAT)(points[i * nd + j] + 0.0000001 * rnd(i, j)); + projpoints[i * (nd + 1) + nd] += + (projpoints[i * (nd + 1) + j] * + projpoints[i * (nd + 1) + j]); /* w vector */ + } + } + + /* The N-dimensional delaunay triangulation requires first computing the + * convex hull of this N+1-dimensional paraboloid */ + hullfaces = NULL; + cf = df = NULL; + convhull_nd_build(projpoints, nPoints, nd + 1, &hullfaces, &cf, &df, + &nHullFaces); + + /* Solution not possible... */ + if (nd > CONVHULL_ND_MAX_DIMENSIONS || !hullfaces || !nHullFaces) { + (*Mesh) = NULL; + (*nMesh) = 0; + ch_stateful_free(allocator, projpoints); + return; + } + + /* Find the coordinates of the point with the maximum (N+1 dimension) + * coordinate (i.e. the w vector) */ +#ifdef CONVHULL_3D_USE_CBLAS + if (sizeof(CH_FLOAT) == sizeof(double)) + maxW_idx = (int)cblas_idamax(nPoints, (double*)&projpoints[nd], nd + 1); + else + maxW_idx = (int)cblas_isamax(nPoints, (float*)&projpoints[nd], nd + 1); +#else + CH_FLOAT maxVal; + maxVal = (CH_FLOAT)-2.23e13; + maxW_idx = -1; + for (i = 0; i < nPoints; i++) { + if (projpoints[i * (nd + 1) + nd] > maxVal) { + maxVal = projpoints[i * (nd + 1) + nd]; + maxW_idx = i; + } + } + assert(maxW_idx != -1); +#endif + w0 = projpoints[maxW_idx * (nd + 1) + nd]; + p0 = (CH_FLOAT*)ch_stateful_malloc(allocator, nd * sizeof(CH_FLOAT)); + for (j = 0; j < nd; j++) p0[j] = projpoints[maxW_idx * (nd + 1) + j]; + + /* Find the point where the plane tangent to the point (p0,w0) on the + * paraboloid crosses the w axis. This is the point that can see the entire + * lower hull. */ + w_optimal = 0.0; + for (j = 0; j < nd; j++) + w_optimal += ((CH_FLOAT)2.0 * ch_pow(p0[j], (CH_FLOAT)2.0)); + w_optimal = w0 - w_optimal; + + /* Subtract 1000 times the absolute value of w_optimal to ensure that the + * point where the tangent plane + * crosses the w axis will see all points on the lower hull. This avoids + * numerical roundoff errors. */ + w_optimal2 = (CH_FLOAT)(w_optimal - 1000.0 * fabs(w_optimal)); + + /* Set the point where the tangent plane crosses the w axis */ + p = (CH_FLOAT*)ch_stateful_calloc(allocator, (nd + 1), sizeof(CH_FLOAT)); + p[nd] = w_optimal2; + + /* Find all faces that are visible from this point */ + visible = + (CH_FLOAT*)ch_stateful_malloc(allocator, nHullFaces * sizeof(CH_FLOAT)); +#ifdef CONVHULL_3D_USE_CBLAS + if (sizeof(CH_FLOAT) == sizeof(double)) { + cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, nHullFaces, 1, + nd + 1, 1.0, (double*)cf, nd + 1, (double*)p, 1, 0.0, + (double*)visible, 1); + } else { + cblas_sgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans, nHullFaces, 1, + nd + 1, 1.0f, (float*)cf, nd + 1, (float*)p, 1, 0.0f, + (float*)visible, 1); + } +#else + for (i = 0; i < nHullFaces; i++) { + visible[i] = 0.0; + for (j = 0; j < nd + 1; j++) visible[i] += cf[i * (nd + 1) + j] * p[j]; + } +#endif + nVisible = 0; + for (j = 0; j < nHullFaces; j++) { + visible[j] += df[j]; + if (visible[j] > 0.0) nVisible++; + } + + /* Output */ + (*nMesh) = nVisible; + if (nVisible > 0) { + (*Mesh) = + (int*)ch_stateful_malloc(allocator, nVisible * (nd + 1) * sizeof(int)); + for (i = 0, j = 0; i < nHullFaces; i++) { + if (visible[i] > 0.0) { + for (k = 0; k < nd + 1; k++) + (*Mesh)[j * (nd + 1) + k] = hullfaces[i * (nd + 1) + k]; + j++; + } + } + assert(j == nVisible); + } + + /* clean up */ + ch_stateful_free(allocator, projpoints); + ch_stateful_free(allocator, hullfaces); + ch_stateful_free(allocator, cf); + ch_stateful_free(allocator, df); + ch_stateful_free(allocator, p0); + ch_stateful_free(allocator, p); + ch_stateful_free(allocator, visible); +} + +#endif /* CONVHULL_3D_ENABLE */ \ No newline at end of file diff --git a/src/utilities/include/quickhull.hpp b/src/utilities/include/quickhull.hpp new file mode 100644 index 000000000..643c5d299 --- /dev/null +++ b/src/utilities/include/quickhull.hpp @@ -0,0 +1,1025 @@ +/* Quickhull algorithm implementation + * + * Copyright (c) 2014-2015, Anatoliy V. Tomilov + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following condition is met: + * Redistributions of source code must retain the above copyright notice, this condition and the following disclaimer. + * + * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" + * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE + * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ +#pragma once + +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include + +#include +#include +#include + +template< typename point_iterator, + typename value_type = std::decay_t< decltype(*std::cbegin(std::declval< typename std::iterator_traits< point_iterator >::value_type >())) > > +struct quick_hull +{ + + static_assert(std::is_base_of< std::forward_iterator_tag, typename std::iterator_traits< point_iterator >::iterator_category >::value, + "multipass guarantee required"); + + using size_type = std::size_t; + + size_type const dimension_; + value_type const & eps; + + value_type const zero = value_type(0); + value_type const one = value_type(1); + + using vector = std::vector< value_type >; + +private : + + using vrow = value_type *; + using crow = value_type const *; + using matrix = std::vector< vrow >; + + vector storage_; + vrow inner_point_; + matrix matrix_; + matrix det_matrix_; + matrix shadow_matrix_; + +public : + + quick_hull(size_type, value_type const &&) = delete; // bind eps to lvalue only + + quick_hull(size_type const _dimension, + value_type const & _eps) + : dimension_(_dimension) + , eps(_eps) + , storage_(dimension_ * dimension_ * 2 + dimension_) + , inner_point_(storage_.data()) + , matrix_(dimension_) + , det_matrix_(dimension_) + , shadow_matrix_(dimension_) + , vertices_hashes_(dimension_) + { + assert(1 < dimension_); + assert(!(eps < zero)); + for (vrow & row_ : matrix_) { + row_ = inner_point_; + inner_point_ += dimension_; + } + for (vrow & row_ : shadow_matrix_) { + row_ = inner_point_; + inner_point_ += dimension_; + } + assert(inner_point_ + dimension_ == &storage_.back() + 1); + } + + using point_array = std::vector< point_iterator >; + using point_list = std::list< point_iterator >; + using point_deque = std::deque< point_iterator >; + using facet_array = std::vector< size_type >; + + struct facet // (d - 1)-dimensional face + { + + // each neighbouring facet lies against corresponding vertex and vice versa + point_array vertices_; // dimension_ points (oriented) + facet_array neighbours_; // dimension_ neighbouring facets + + point_list outside_; // if empty, then is convex hull's facet, else the first point (i.e. outside_.front()) is the furthest point from this facet + point_deque coplanar_; // containing coplanar points and vertices of coplanar facets as well + + // equation of supporting hyperplane + vector normal_; // components of normalized normal vector + value_type D; // distance from the origin to the hyperplane + + template< typename iterator > + value_type + distance(iterator const _point) const + { + using iterator_traits = std::iterator_traits< iterator >; + static_assert(std::is_base_of< std::input_iterator_tag, typename iterator_traits::iterator_category >::value); + return std::inner_product(std::cbegin(normal_), std::cend(normal_), _point, D); + } + + }; + + using facets = std::deque< facet >; + + facets facets_; + + value_type + cos_of_dihedral_angle(facet const & _first, facet const & _second) const + { + return std::inner_product(std::cbegin(_first.normal_), std::cend(_first.normal_), std::cbegin(_second.normal_), zero); + } + +private : + + void + make_facet(facet & _facet, + point_array const & _vertices, + size_type const _against, + point_iterator const _apex, + size_type const _neighbour) + { + assert(_vertices.size() == dimension_); + _facet.vertices_ = _vertices; + _facet.vertices_[_against] = _apex; + _facet.neighbours_.resize(dimension_); + _facet.neighbours_[_against] = _neighbour; + _facet.normal_.resize(dimension_); + } + + template< typename iterator > + void + make_facet(facet & _facet, + iterator sbeg, // simplex + size_type const _vertex, + bool const _swap) + { + using iterator_traits = std::iterator_traits< iterator >; + static_assert(std::is_base_of< std::input_iterator_tag, typename iterator_traits::iterator_category >::value); + static_assert(std::is_constructible< point_iterator, typename iterator_traits::value_type >::value); + _facet.vertices_.reserve(dimension_); + _facet.neighbours_.reserve(dimension_); + for (size_type v = 0; v <= dimension_; ++v) { + if (v != _vertex) { + _facet.vertices_.push_back(*sbeg); + _facet.neighbours_.push_back(v); + } + ++sbeg; + } + if (_swap == (((dimension_ - _vertex) % 2) == 0)) { + using std::swap; + swap(_facet.vertices_.front(), _facet.vertices_.back()); + swap(_facet.neighbours_.front(), _facet.neighbours_.back()); + } + _facet.normal_.resize(dimension_); + } + + void + reuse_facet(facet & _facet, + point_array const & _vertices, + size_type const _against, + point_iterator const _apex, + size_type const _neighbour) + { + assert(_vertices.size() == dimension_); + _facet.vertices_ = _vertices; + _facet.vertices_[_against] = _apex; + assert(_facet.neighbours_.size() == dimension_); + _facet.neighbours_[_against] = _neighbour; + assert(_facet.normal_.size() == dimension_); + } + + void + copy_point(point_iterator const _from, vrow _to) const + { + std::copy_n(std::cbegin(*_from), dimension_, _to); + } + + void + subtract(vrow _minuend, crow _subtrahend) const + { + for (size_type i = 0; i < dimension_; ++i) { + *_minuend++ -= *_subtrahend++; + } + } + + void + gshift(vrow _augend, value_type const & _addend) const // shift Gaussian row + { + for (size_type i = 0; i < dimension_; ++i) { + *_augend++ += _addend; + } + *_augend += _addend; + } + + void + divide(vrow _dividend, value_type const & _divisor) const + { + for (size_type i = 0; i < dimension_; ++i) { + *_dividend++ /= _divisor; + } + } + + void + subtract_and_assign(vrow _assignee, vrow _minuend, crow _subtrahend) const + { + for (size_type i = 0; i < dimension_; ++i) { + *_assignee++ = (*_minuend++ -= *_subtrahend++); + } + } + + void + multiply_and_add(vrow _assignee, crow _multiplicand, value_type const & _factor) const + { + for (size_type i = 0; i < dimension_; ++i) { + *_assignee++ += (*_multiplicand++ * _factor); + } + } + + void + scale_and_shift(vrow _multiplicand, crow _direction, value_type const & _factor) const + { + for (size_type i = 0; i < dimension_; ++i) { + (*_multiplicand++ *= _factor) += *_direction++; + } + } + + void + matrix_transpose_copy(point_array const & _vertices) + { + for (size_type r = 0; r < dimension_; ++r) { + auto v = std::cbegin(*_vertices[r]); + for (size_type c = 0; c < dimension_; ++c) { + shadow_matrix_[c][r] = *v; + ++v; + } + } + } + + void + matrix_restore(size_type const _identity) + { + for (size_type c = 0; c < _identity; ++c) { + std::copy_n(shadow_matrix_[c], dimension_, matrix_[c]); + } + std::fill_n(matrix_[_identity], dimension_, one); + for (size_type c = _identity + 1; c < dimension_; ++c) { + std::copy_n(shadow_matrix_[c], dimension_, matrix_[c]); + } + } + + void + matrix_restore() + { + for (size_type c = 0; c < dimension_; ++c) { + std::copy_n(shadow_matrix_[c], dimension_, matrix_[c]); + } + } + + void + matrix_sqr(size_type const _size) + { // shadow_matrix_ = matrix_ * transposed matrix_ + assert(_size < dimension_); + for (size_type r = 0; r < _size; ++r) { + vrow const lhs_ = shadow_matrix_[r]; + crow const row_ = matrix_[r]; + for (size_type c = 0; c < _size; ++c) { + lhs_[c] = std::inner_product(row_, row_ + _size, matrix_[c], zero); + } + } + } + + // based on LUP decomposition (complexity is (d^3 / 3 + d^2 / 2 - 5 * d / 6) vs (2 * d^3 / 3 + d^2 + d / 3 - 2) for QR decomposition via Householder reflections) + value_type + det(matrix const & _matrix, size_type const _dimension) // hottest function (52% of runtime for D10) + { // det_matrix_ contains lower unit triangular matrix and upper triangular at return + assert(0 < _dimension); + value_type det_ = one; + std::copy_n(std::cbegin(_matrix), _dimension, std::begin(det_matrix_)); + for (size_type i = 0; i < _dimension; ++i) { + vrow & mi_ = det_matrix_[i]; + size_type pivot = i; + { + using std::abs; + value_type max_ = abs(mi_[i]); + size_type j = i; + while (++j < _dimension) { + value_type y_ = abs(det_matrix_[j][i]); + if (max_ < y_) { + max_ = std::move(y_); + pivot = j; + } + } + if (!(eps < max_)) { // regular? + det_ = zero; // singular + break; + } + } + if (pivot != i) { + det_ = -det_; // each permutation flips sign of det + std::swap(mi_, det_matrix_[pivot]); + } + value_type const & dia_ = mi_[i]; + det_ *= dia_; // det is multiple of diagonal elements + size_type j = i; + while (++j < _dimension) { + vrow const mj_ = det_matrix_[j]; + value_type & mji_ = mj_[i]; + mji_ /= dia_; + size_type k = i; + while (++k < _dimension) { + mj_[k] -= mji_ * mi_[k]; + } + } + } + return det_; + } + + value_type + det() + { + return det(matrix_, dimension_); + } + + void + set_hyperplane_equation(facet & _facet) + { + matrix_transpose_copy(_facet.vertices_); + matrix_restore(); + _facet.D = -det(); + value_type N = zero; + for (size_type i = 0; i < dimension_; ++i) { + matrix_restore(i); + value_type & n = _facet.normal_[i]; + n = det(); + N += n * n; + } + using std::sqrt; + N = sqrt(std::move(N)); + divide(_facet.normal_.data(), N); + _facet.D /= std::move(N); + assert(_facet.distance(inner_point_) < zero); + } + + bool + orthonormalize(point_list const & _affine_space, + size_type const _rank, + crow const _origin) + { + assert(!(dimension_ < _rank)); + assert(!(_affine_space.size() < _rank)); + auto vertex = std::begin(_affine_space); + for (size_type r = 0; r < _rank; ++r) { // affine space -> vector space + vrow const row_ = shadow_matrix_[r]; + copy_point(*vertex, row_); + subtract(row_, _origin); + ++vertex; + } + for (size_type i = 0; i < _rank; ++i) { // Householder transformation + value_type sum_ = zero; + vrow const qri_ = shadow_matrix_[i]; + for (size_type k = i; k < dimension_; ++k) { + value_type const & qrik_ = qri_[k]; + sum_ += qrik_ * qrik_; + } + using std::sqrt; + value_type norm_ = sqrt(sum_); + if (!(eps < norm_)) { + return false; + } + value_type & qrii_ = qri_[i]; + if (qrii_ < zero) { + norm_ = -norm_; + } + value_type factor_ = sqrt(std::move(sum_) + qrii_ * norm_); + if (!(eps < factor_)) { + return false; + } + qrii_ += std::move(norm_); + for (size_type k = i; k < dimension_; ++k) { + qri_[k] /= factor_; + } + size_type j = i; + while (++j < _rank) { + vrow const qrj_ = shadow_matrix_[j]; + value_type s_ = zero; + for (size_type k = i; k < dimension_; ++k) { + s_ += qri_[k] * qrj_[k]; + } + for (size_type k = i; k < dimension_; ++k) { + qrj_[k] -= qri_[k] * s_; + } + } + } // shadow_matrix_ is packed QR + return true; + } + + void + forward_transformation(size_type const _rank) // calculation of Q + { + assert(!(dimension_ < _rank)); + for (size_type i = 0; i < _rank; ++i) { + vrow const qi_ = matrix_[i]; + std::fill_n(qi_, dimension_, zero); + qi_[i] = one; + size_type j = _rank; + while (0 < j) { + --j; + vrow const qrj_ = shadow_matrix_[j]; // containing packed QR + value_type s_ = zero; + for (size_type k = j; k < dimension_; ++k) { + s_ += qrj_[k] * qi_[k]; + } + for (size_type k = j; k < dimension_; ++k) { + qi_[k] -= qrj_[k] * s_; + } + } + } // matrix_ is Q + } + + bool + steal_best(point_list & _basis) + { // set moves a point which is furthest from affine subspace formed by points of "_basis" set from "outside_" set to "_basis" + assert(!_basis.empty()); + size_type const rank_ = _basis.size() - 1; + assert(rank_ < dimension_); + vrow const origin_ = matrix_[rank_]; + copy_point(_basis.back(), origin_); + if (!orthonormalize(_basis, rank_, origin_)) { + return false; + } + forward_transformation(rank_); + vrow const projection_ = shadow_matrix_.back(); + vrow const apex_ = shadow_matrix_.front(); + value_type distance_ = zero; // square of distance to the subspace + auto const oend = std::cend(outside_); + auto furthest = oend; + for (auto it = std::cbegin(outside_); it != oend; ++it) { + copy_point(*it, apex_); + subtract_and_assign(projection_, apex_, origin_); // turn translated space into vector space then project onto orthogonal subspace + for (size_type i = 0; i < rank_; ++i) { + crow const qi_ = matrix_[i]; + multiply_and_add(projection_, qi_, -std::inner_product(qi_, qi_ + dimension_, apex_, zero)); + } + value_type d_ = std::inner_product(projection_, projection_ + dimension_, projection_, zero); + if (distance_ < d_) { + distance_ = std::move(d_); + furthest = it; + } + } + if (furthest == oend) { + return false; + } + _basis.splice(std::cend(_basis), outside_, furthest); + return true; + } + + facet_array removed_facets_; + + std::pair< facet &, size_type const > + add_facet(point_array const & _vertices, + size_type const _against, + point_iterator const _apex, + size_type const _neighbour) + { + if (removed_facets_.empty()) { + size_type const f = facets_.size(); + facets_.emplace_back(); + facet & facet_ = facets_.back(); + make_facet(facet_, _vertices, _against, _apex, _neighbour); + return {facet_, f}; + } else { + size_type const f = removed_facets_.back(); + removed_facets_.pop_back(); + facet & facet_ = facets_[f]; + reuse_facet(facet_, _vertices, _against, _apex, _neighbour); + return {facet_, f}; + } + } + + using ranking = std::multimap< value_type, size_type >; + using ranking_meta = std::unordered_map< size_type, typename ranking::iterator >; + + ranking ranking_; + ranking_meta ranking_meta_; + + void + rank(value_type && _orientation, + size_type const f) + { + if (eps < _orientation) { + ranking_meta_.emplace(f, ranking_.emplace(std::move(_orientation), f)); + } + } + + void + unrank(size_type const f) + { + auto const r = ranking_meta_.find(f); + if (r != std::end(ranking_meta_)) { + ranking_.erase(r->second); + ranking_meta_.erase(r); + } + removed_facets_.push_back(f); + } + + point_list outside_; + + value_type + partition(facet & _facet) + { + value_type distance_ = zero; + auto it = std::cbegin(outside_); + auto const oend = std::cend(outside_); + while (it != oend) { + auto const next = std::next(it); + value_type d_ = _facet.distance(std::cbegin(**it)); + if (eps < d_) { + if (distance_ < d_) { + distance_ = std::move(d_); + _facet.outside_.splice(std::cbegin(_facet.outside_), outside_, it); + } else { + _facet.outside_.splice(std::cend(_facet.outside_), outside_, it); + } + } else if (!(d_ < -eps)) { + _facet.coplanar_.push_back(*it); + } + it = next; + } + return distance_; + } + + size_type + get_best_facet() const + { + assert(ranking_meta_.size() == ranking_.size()); + return std::prev(std::cend(ranking_))->second; + } + + void + replace_neighbour(size_type const f, + size_type const _from, + size_type const _to) + { + if (_from != _to) { + for (size_type & n : facets_[f].neighbours_) { + if (n == _from) { + n = _to; + return; + } + } + } + } + + struct ridge + { + + facet & facet_; + size_type const f; + size_type const v; + size_type const hash_; + + bool + operator == (ridge const & _rhs) const noexcept + { + point_iterator const lskip = facet_.vertices_[v]; + point_iterator const rskip = _rhs.facet_.vertices_[_rhs.v]; + for (point_iterator const & l : facet_.vertices_) { + if (l != lskip) { + bool found_ = false; + for (point_iterator const & r : _rhs.facet_.vertices_) { + if (r != rskip) { + if (l == r) { + found_ = true; // O(D^2) expensive + break; + } + } + } + if (!found_) { + return false; + } + } + } + return true; + } + + }; + + struct ridge_hash + { + + size_type + operator () (ridge const & _ridge) const noexcept + { + return _ridge.hash_; + } + + }; + + std::unordered_set< ridge, ridge_hash > unique_ridges_; + std::hash< typename std::iterator_traits< point_iterator >::value_type const * > point_hash_; + std::vector< size_type > vertices_hashes_; + + void + find_adjacent_facets(facet & _facet, + size_type const f, + size_type const _skip) + { + size_type ridge_hash_ = 0; + for (size_type v = 0; v < dimension_; ++v) { + if (v != _skip) { + ridge_hash_ ^= (vertices_hashes_[v] = point_hash_(std::addressof(*_facet.vertices_[v]))); + } + } + for (size_type v = 0; v < dimension_; ++v) { + if (v != _skip) { // neighbouring facet against apex (_skip-indexed) is known atm + auto const position = unique_ridges_.insert({_facet, f, v, (ridge_hash_ ^ vertices_hashes_[v])}); + if (!position.second) { + ridge const & ridge_ = *position.first; + ridge_.facet_.neighbours_[ridge_.v] = f; + _facet.neighbours_[v] = ridge_.f; + unique_ridges_.erase(position.first); + } + } + } + } + + using facet_unordered_set = std::unordered_set< size_type >; + + facet_unordered_set visited_; + facet_unordered_set visible_; + + bool + process_visibles(facet_array & _newfacets, + size_type const f, + point_iterator const _apex) // traverse the graph of visible facets + { + assert(!(visited_.size() < visible_.size())); + if (!visited_.insert(f).second) { + return (visible_.count(f) != 0); + } + facet & facet_ = facets_[f]; + if (!(zero < facet_.distance(std::cbegin(*_apex)))) { + return false; + } + visible_.insert(f); + outside_.splice(std::cend(outside_), std::move(facet_.outside_)); + facet_.coplanar_.clear(); + for (size_type v = 0; v < dimension_; ++v) { + size_type const neighbour = facet_.neighbours_[v]; + if (!process_visibles(_newfacets, neighbour, _apex)) { // recursive function + auto const newfacet = add_facet(facet_.vertices_, v, _apex, neighbour); + set_hyperplane_equation(newfacet.first); + _newfacets.push_back(newfacet.second); + replace_neighbour(neighbour, f, newfacet.second); + find_adjacent_facets(newfacet.first, newfacet.second, v); + } + } + unrank(f); + return true; + } + + void + compactify() + { + size_type source = facets_.size(); + assert(removed_facets_.size() < source); + assert(dimension_ < source - removed_facets_.size()); + assert(ranking_.size() == ranking_meta_.size()); + assert(!(source < ranking_.size())); + auto const rend = std::end(ranking_meta_); + std::sort(std::rbegin(removed_facets_), std::rend(removed_facets_)); + for (size_type const destination : removed_facets_) { + assert(!(source < destination)); + if (destination != --source) { + facet & facet_ = facets_[destination]; + facet_ = std::move(facets_.back()); + for (size_type const n : facet_.neighbours_) { + replace_neighbour(n, source, destination); + } + auto const r = ranking_meta_.find(source); + if (r != rend) { + r->second->second = destination; + ranking_meta_.emplace(destination, std::move(r->second)); + ranking_meta_.erase(r); + } + } + facets_.pop_back(); + } + removed_facets_.clear(); + } + + bool + check_local_convexity(facet const & facet_, + size_type const f) const + { + assert(&facets_[f] == &facet_); + for (size_type const n : facet_.neighbours_) { + facet const & neighbour_ = facets_[n]; + if (cos_of_dihedral_angle(facet_, neighbour_) < one) { // avoid roundoff error + for (size_type v = 0; v < dimension_; ++v) { + if (neighbour_.neighbours_[v] == f) { // vertex v of neigbour_ facet is opposite to facet_ + value_type const distance_ = facet_.distance(std::cbegin(*neighbour_.vertices_[v])); + if (eps < distance_) { + return false; // facet is not locally convex at ridge, common for facet_ and neighbour_ facets + } else { + break; + } + } + } + } + } + return true; + } + +public : + + template< typename iterator > + value_type + hypervolume(iterator first, + iterator const last) // hypervolume of parallelotope spanned on vectors from last vertex (vlast) to all the vertices lies in [vfirst, vlast) + { + using iterator_traits = std::iterator_traits< iterator >; + static_assert(std::is_base_of< std::input_iterator_tag, typename iterator_traits::iterator_category >::value); + static_assert(std::is_constructible< point_iterator, typename iterator_traits::value_type >::value); + if (first == last) { + return zero; + } + vrow const origin_ = shadow_matrix_.back(); + copy_point(*last, origin_); + size_type rank_ = 0; + while (first != last) { // affine space -> vector space + assert(rank_ < dimension_); + vrow const row_ = matrix_[rank_]; + copy_point(*first, row_); + subtract(row_, origin_); + ++rank_; + ++first; + } + if (rank_ == dimension_) { + return det(); // oriented hypervolume + } else { + matrix_sqr(rank_); + using std::sqrt; + return sqrt(det(shadow_matrix_, rank_)); // non-oriented rank_-dimensional measure + } + } + + void + add_points(point_iterator beg, + point_iterator const end) // [beg; end) + { + while (beg != end) { + outside_.push_back(beg); + ++beg; + } + } + + template< typename iterator > + void + add_points(iterator const beg, + iterator const end) // [beg; end) + { + using iterator_traits = std::iterator_traits< iterator >; + static_assert(std::is_base_of< std::input_iterator_tag, typename iterator_traits::iterator_category >::value); + static_assert(std::is_constructible< point_iterator, typename iterator_traits::value_type >::value); + std::copy(beg, end, std::back_inserter(outside_)); + } + + point_list + get_affine_basis() + { + assert(facets_.empty()); + point_list basis_; + basis_.splice(std::cend(basis_), outside_, std::begin(outside_)); + if (!steal_best(basis_)) { + return basis_; // can't find affinely independent second point + } + outside_.splice(std::cbegin(outside_), basis_, std::begin(basis_)); // reject first point to rejudge it + for (size_type i = 0; i < dimension_; ++i) { + if (!steal_best(basis_)) { + return basis_; // can't find (i + 2) affinely independent points + } + } + return basis_; + } + + template< typename iterator > + value_type + create_initial_simplex(iterator const first, + iterator const last) // [bfirst; blast] + { + using iterator_traits = std::iterator_traits< iterator >; + static_assert(std::is_base_of< std::forward_iterator_tag, typename iterator_traits::iterator_category >::value); + static_assert(std::is_constructible< point_iterator, typename iterator_traits::value_type >::value); + assert(static_cast< size_type >(std::distance(first, last)) == dimension_); + assert(facets_.empty()); + { + copy_point(*last, inner_point_); + auto it = first; + while (it != last) { + auto x = std::cbegin(**it); + for (size_type i = 0; i < dimension_; ++i) { + inner_point_[i] += *x; + ++x; + } + ++it; + } + divide(inner_point_, value_type(dimension_ + 1)); + } + value_type const volume_ = hypervolume(first, last); + bool const swap_ = (volume_ < zero); + for (size_type f = 0; f <= dimension_; ++f) { + facets_.emplace_back(); + facet & facet_ = facets_.back(); + make_facet(facet_, first, f, swap_); + set_hyperplane_equation(facet_); + rank(partition(facet_), f); + } + outside_.clear(); + assert(check()); + return volume_; + } + + // Barber, C. B., D.P. Dobkin, and H.T. Huhdanpaa, 1995. "The Quickhull Algorithm for Convex Hulls", ACM Transactions on Mathematical Software. + void + create_convex_hull() + { + assert(facets_.size() == dimension_ + 1); + assert(removed_facets_.empty()); + facet_array newfacets_; + while (!ranking_.empty()) { + size_type const f = get_best_facet(); + point_list & o_ = facets_[f].outside_; + assert(!o_.empty()); + point_iterator const apex = std::move(o_.front()); + o_.pop_front(); + if (!process_visibles(newfacets_, f, apex)) { + assert(false); + } + visited_.clear(); + visible_.clear(); + assert(unique_ridges_.empty()); + for (size_type const n : newfacets_) { + facet & facet_ = facets_[n]; + assert(check_local_convexity(facet_, n)); + rank(partition(facet_), n); + } + newfacets_.clear(); + outside_.clear(); + //assert((compactify(), check())); + } + assert(ranking_meta_.empty()); + compactify(); + } + + // Kurt Mehlhorn, Stefan Näher, Thomas Schilz, Stefan Schirra, Michael Seel, Raimund Seidel, and Christian Uhrig. + // Checking geometric programs or verification of geometric structures. In Proc. 12th Annu. ACM Sympos. Comput. Geom., pages 159–165, 1996. + bool + check() const + { + assert(dimension_ < facets_.size()); + size_type facets_count_ = 0; + for (facet const & facet_ : facets_) { // check local convexity of all the facets + if (!check_local_convexity(facet_, facets_count_)) { + return false; + } + ++facets_count_; + } + facet const & first_ = facets_.front(); + { + value_type const distance_ = first_.distance(inner_point_); + if (!(distance_ < zero)) { + return false; // inner point is not on negative side of the first facet, therefore structure is not convex + } + } + vector memory_(dimension_ * (4 + dimension_), zero); + vrow centroid_ = memory_.data(); + vrow const ray_ = centroid_; + centroid_ += dimension_; + for (point_iterator const & v : first_.vertices_) { + auto x = std::cbegin(*v); + for (size_type i = 0; i < dimension_; ++i) { + ray_[i] += *x; + ++x; + } + } + divide(ray_, value_type(dimension_)); + subtract(ray_, inner_point_); + { + value_type const dot_product_ = std::inner_product(ray_, ray_ + dimension_, first_.normal_.data(), zero); + if (!(zero < dot_product_)) { // ray is parallel to the plane or directed away from the plane + return false; + } + } + matrix g_{dimension_}; // storage (d * (d + 1)) for Gaussian elimination with partial pivoting + for (vrow & row_ : g_) { + row_ = centroid_; + centroid_ += (dimension_ + 1); + } + vrow const intersection_point_ = centroid_; + centroid_ += dimension_; + assert(centroid_ + dimension_ == &memory_.back() + 1); + for (size_type f = 1; f < facets_count_; ++f) { + using std::abs; + facet const & facet_ = facets_[f]; + value_type const numerator_ = facet_.distance(inner_point_); + if (!(numerator_ < zero)) { + return false; // inner point is not on negative side of all the facets, i.e. structure is not convex + } + value_type const denominator_ = std::inner_product(ray_, ray_ + dimension_, facet_.normal_.data(), zero); + if (!(zero < denominator_)) { // ray is parallel to the plane or directed away from the plane + continue; + } + std::copy_n(ray_, dimension_, intersection_point_); + scale_and_shift(intersection_point_, inner_point_, -(numerator_ / denominator_)); + for (size_type v = 0; v < dimension_; ++v) { + auto beg = std::cbegin(*facet_.vertices_[v]); + for (size_type r = 0; r < dimension_; ++r) { + g_[r][v] = *beg; + ++beg; + } + } + for (size_type r = 0; r < dimension_; ++r) { + vrow const gr_ = g_[r]; + centroid_[r] = -std::accumulate(gr_, gr_ + dimension_, zero) / value_type(dimension_); + gr_[dimension_] = intersection_point_[r]; + } + for (size_type r = 0; r < dimension_; ++r) { + vrow const gr_ = g_[r]; + value_type & x_ = centroid_[r]; + gshift(gr_, x_); + //assert(!(eps * value_type(dimension_) < std::accumulate(gr_, gr_ + dimension_, zero))); // now center of the facet coincides with the origin, but no one vertex does + auto const bounding_box = std::minmax_element(gr_, gr_ + dimension_); + x_ = *bounding_box.second - *bounding_box.first; + if (!(eps * value_type(dimension_) < x_)) { + x_ = one; + } + } + for (size_type r = 0; r < dimension_; ++r) { + vrow const gr_ = g_[r]; + gshift(gr_, centroid_[r]); + } + for (size_type i = 0; i < dimension_; ++i) { // Gaussian elimination + vrow & gi_ = g_[i]; + value_type max_ = abs(gi_[i]); + size_type pivot = i; + { + size_type p = i; + while (++p < dimension_) { + value_type y_ = abs(g_[p][i]); + if (max_ < y_) { + max_ = std::move(y_); + pivot = p; + } + } + } + assert(eps < max_); // vertex must not match the origin after above transformations + if (pivot != i) { + std::swap(gi_, g_[pivot]); + } + value_type & gii_ = gi_[i]; + for (size_type j = i + 1; j < dimension_; ++j) { + vrow const gj_ = g_[j]; + value_type & gji_ = gj_[i]; + gji_ /= gii_; + for (size_type k = i + 1; k <= dimension_; ++k) { + gj_[k] -= gji_ * gi_[k]; + } + gji_ = zero; + } + } // g_ is upper triangular now + bool in_range_ = true; + { + size_type i = dimension_; + while (0 < i) { + --i; + vrow const gi_ = g_[i]; + value_type & xi_ = gi_[dimension_]; + for (size_type j = i + 1; j < dimension_; ++j) { + xi_ -= gi_[j] * g_[j][dimension_]; + } + value_type const & gii_ = gi_[i]; + assert(eps < abs(gii_)); // vertex must not match the origin + xi_ /= gii_; + if ((xi_ < zero) || (one < xi_)) { + in_range_ = false; // barycentric coordinate does not lie in [0;1] interval => miss + break; + } + } + } + if (in_range_) { + return false; // hit + } + } + return true; + } + +}; \ No newline at end of file diff --git a/src/utilities/include/quickhull2.h b/src/utilities/include/quickhull2.h new file mode 100644 index 000000000..e1ff3c6ec --- /dev/null +++ b/src/utilities/include/quickhull2.h @@ -0,0 +1,1331 @@ +// +// LICENCE: +// The MIT License (MIT) +// +// Copyright (c) 2016 Karim Naaji, karim.naaji@gmail.com +// +// Permission is hereby granted, free of charge, to any person obtaining a copy +// of this software and associated documentation files (the "Software"), to +// deal in the Software without restriction, including without limitation the +// rights to use, copy, modify, merge, publish, distribute, sublicense, and/or +// sell copies of the Software, and to permit persons to whom the Software is +// furnished to do so, subject to the following conditions: +// +// The above copyright notice and this permission notice shall be included in +// all copies or substantial portions of the Software. +// +// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING +// FROM, OUT OF OR IN CONNECTION WITH THE +// +// REFERENCES: +// [1] http://box2d.org/files/GDC2014/DirkGregorius_ImplementingQuickHull.pdf +// [2] http://www.cs.smith.edu/~orourke/books/compgeom.html +// [3] http://www.flipcode.com/archives/The_Half-Edge_Data_Structure.shtml +// [4] http://doc.cgal.org/latest/HalfedgeDS/index.html +// [5] http://thomasdiewald.com/blog/?p=1888 +// [6] +// https://fgiesen.wordpress.com/2012/02/21/half-edge-based-mesh-representations-theory/ +// +// HOWTO: +// #define QUICKHULL_IMPLEMENTATION +// #define QUICKHULL_DEBUG // Only if assertions need to be checked +// #include "quickhull.h" +// +// HISTORY: +// - 1.0.1 (2016-11-01): Various improvements over epsilon issues and +// degenerate faces +// Debug functionalities to test final results +// dynamically API to export hull meshes in OBJ files +// - 1.0 (2016-09-10): Initial +// +// TODO: +// - use float* from public interface +// - reduce memory usage + +#ifndef QUICKHULL_H +#define QUICKHULL_H + +// ------------------------------------------------------------------------------------------------ +// QUICKHULL PUBLIC API +// + +typedef struct qh_vertex { + union { + float v[3]; + struct { + float x; + float y; + float z; + }; + }; +} qh_vertex_t; + +typedef qh_vertex_t qh_vec3_t; + +typedef struct qh_mesh { + qh_vertex_t* vertices; + qh_vec3_t* normals; + unsigned int* indices; + unsigned int* normalindices; + unsigned int nindices; + unsigned int nvertices; + unsigned int nnormals; +} qh_mesh_t; + +qh_mesh_t qh_quickhull3d(qh_vertex_t const* vertices, unsigned int nvertices); + +void qh_mesh_export(qh_mesh_t const* mesh, char const* filename); + +void qh_free_mesh(qh_mesh_t mesh); + +// +// END QUICKHULL PUBLIC API +// ------------------------------------------------------------------------------------------------ + +#endif // QUICKHULL_H + +#ifdef QUICKHULL_IMPLEMENTATION + +#include // sqrt & fabs +#include // FILE +#include // memcpy + +// Quickhull helpers, define your own if needed +#ifndef QUICKHULL_HELPERS +#include // malloc, free, realloc +#define QUICKHULL_HELPERS 1 +#define QH_MALLOC(T, N) ((T*)malloc(N * sizeof(T))) +#define QH_REALLOC(T, P, N) ((T*)realloc(P, sizeof(T) * N)) +#define QH_FREE(T) free(T) +#define QH_SWAP(T, A, B) \ + { \ + T tmp = B; \ + B = A; \ + A = tmp; \ + } +#ifdef QUICKHULL_DEBUG +#define QH_ASSERT(STMT) \ + if (!(STMT)) { \ + *(int*)0 = 0; \ + } +#define QH_LOG(FMT, ...) printf(FMT, ##__VA_ARGS__) +#else +#define QH_ASSERT(STMT) +#define QH_LOG(FMT, ...) +#endif // QUICKHULL_DEBUG +#endif // QUICKHULL_HELPERS + +#ifndef QH_FLT_MAX +#define QH_FLT_MAX 1e+37F +#endif + +#ifndef QH_FLT_EPS +#define QH_FLT_EPS 1E-5F +#endif + +#ifndef QH_VERTEX_SET_SIZE +#define QH_VERTEX_SET_SIZE 128 +#endif + +typedef long qh_index_t; + +typedef struct qh_half_edge { + qh_index_t opposite_he; // index of the opposite half edge + qh_index_t next_he; // index of the next half edge + qh_index_t previous_he; // index of the previous half edge + qh_index_t he; // index of the current half edge + qh_index_t to_vertex; // index of the next vertex + qh_index_t adjacent_face; // index of the ajacent face +} qh_half_edge_t; + +typedef struct qh_index_set { + qh_index_t* indices; + unsigned int size; + unsigned int capacity; +} qh_index_set_t; + +typedef struct qh_face { + qh_index_set_t iset; + qh_vec3_t normal; + qh_vertex_t centroid; + qh_index_t edges[3]; + qh_index_t face; + float sdist; + int visitededges; +} qh_face_t; + +typedef struct qh_index_stack { + qh_index_t* begin; + unsigned int size; +} qh_index_stack_t; + +typedef struct qh_context { + qh_face_t* faces; + qh_half_edge_t* edges; + qh_vertex_t* vertices; + qh_vertex_t centroid; + qh_index_stack_t facestack; + qh_index_stack_t scratch; + qh_index_stack_t horizonedges; + qh_index_stack_t newhorizonedges; + char* valid; + unsigned int nedges; + unsigned int nvertices; + unsigned int nfaces; + +#ifdef QUICKHULL_DEBUG + unsigned int maxfaces; + unsigned int maxedges; +#endif +} qh_context_t; + +void qh__find_6eps(qh_vertex_t* vertices, unsigned int nvertices, + qh_index_t* eps) { + qh_vertex_t* ptr = vertices; + + float minxy = +QH_FLT_MAX; + float minxz = +QH_FLT_MAX; + float minyz = +QH_FLT_MAX; + + float maxxy = -QH_FLT_MAX; + float maxxz = -QH_FLT_MAX; + float maxyz = -QH_FLT_MAX; + + int i = 0; + for (i = 0; i < 6; ++i) { + eps[i] = 0; + } + + for (i = 0; i < nvertices; ++i) { + if (ptr->z < minxy) { + eps[0] = i; + minxy = ptr->z; + } + if (ptr->y < minxz) { + eps[1] = i; + minxz = ptr->y; + } + if (ptr->x < minyz) { + eps[2] = i; + minyz = ptr->x; + } + if (ptr->z > maxxy) { + eps[3] = i; + maxxy = ptr->z; + } + if (ptr->y > maxxz) { + eps[4] = i; + maxxz = ptr->y; + } + if (ptr->x > maxyz) { + eps[5] = i; + maxyz = ptr->x; + } + ptr++; + } +} + +float qh__vertex_segment_length2(qh_vertex_t* p, qh_vertex_t* a, + qh_vertex_t* b) { + float dx = b->x - a->x; + float dy = b->y - a->y; + float dz = b->z - a->z; + + float d = dx * dx + dy * dy + dz * dz; + + float x = a->x; + float y = a->y; + float z = a->z; + + if (d != 0) { + float t = + ((p->x - a->x) * dx + (p->y - a->y) * dy + (p->z - a->z) * dz) / d; + + if (t > 1) { + x = b->x; + y = b->y; + z = b->z; + } else if (t > 0) { + x += dx * t; + y += dy * t; + z += dz * t; + } + } + + dx = p->x - x; + dy = p->y - y; + dz = p->z - z; + + return dx * dx + dy * dy + dz * dz; +} + +void qh__vec3_sub(qh_vec3_t* a, qh_vec3_t* b) { + a->x -= b->x; + a->y -= b->y; + a->z -= b->z; +} + +void qh__vec3_add(qh_vec3_t* a, qh_vec3_t* b) { + a->x += b->x; + a->y += b->y; + a->z += b->z; +} + +void qh__vec3_multiply(qh_vec3_t* a, float v) { + a->x *= v; + a->y *= v; + a->z *= v; +} + +int qh__vertex_equals_epsilon(qh_vertex_t* a, qh_vertex_t* b, float epsilon) { + return fabs(a->x - b->x) <= epsilon && fabs(a->y - b->y) <= epsilon && + fabs(a->z - b->z) <= epsilon; +} + +float qh__vec3_length2(qh_vec3_t* v) { + return v->x * v->x + v->y * v->y + v->z * v->z; +} + +float qh__vec3_dot(qh_vec3_t* v1, qh_vec3_t* v2) { + return v1->x * v2->x + v1->y * v2->y + v1->z * v2->z; +} + +void qh__vec3_normalize(qh_vec3_t* v) { + qh__vec3_multiply(v, 1.f / sqrt(qh__vec3_length2(v))); +} + +void qh__find_2dps_6eps(qh_vertex_t* vertices, qh_index_t* eps, int* ii, + int* jj) { + int i, j; + float max = -QH_FLT_MAX; + + for (i = 0; i < 6; ++i) { + for (j = 0; j < 6; ++j) { + qh_vertex_t d; + float d2; + + if (i == j) { + continue; + } + + d = vertices[eps[i]]; + qh__vec3_sub(&d, &vertices[eps[j]]); + d2 = qh__vec3_length2(&d); + + if (d2 > max) { + *ii = i; + *jj = j; + max = d2; + } + } + } +} + +qh_vec3_t qh__vec3_cross(qh_vec3_t* v1, qh_vec3_t* v2) { + qh_vec3_t cross; + + cross.x = v1->y * v2->z - v1->z * v2->y; + cross.y = v1->z * v2->x - v1->x * v2->z; + cross.z = v1->x * v2->y - v1->y * v2->x; + + return cross; +} + +qh_vertex_t qh__face_centroid(qh_index_t vertices[3], qh_context_t* context) { + qh_vertex_t centroid; + int i; + + centroid.x = centroid.y = centroid.z = 0.0; + for (i = 0; i < 3; ++i) { + qh__vec3_add(¢roid, context->vertices + vertices[i]); + } + + qh__vec3_multiply(¢roid, 1.0 / 3.0); + + return centroid; +} + +float qh__dist_point_plane(qh_vertex_t* v, qh_vec3_t* normal, float sdist) { + return fabs(qh__vec3_dot(v, normal) - sdist); +} + +void qh__init_half_edge(qh_half_edge_t* half_edge) { + half_edge->adjacent_face = -1; + half_edge->he = -1; + half_edge->next_he = -1; + half_edge->opposite_he = -1; + half_edge->to_vertex = -1; + half_edge->previous_he = -1; +} + +qh_half_edge_t* qh__next_edge(qh_context_t* context) { + qh_half_edge_t* edge = context->edges + context->nedges; + + qh__init_half_edge(edge); + + edge->he = context->nedges; + context->nedges++; + + QH_ASSERT(context->nedges < context->maxedges); + + return edge; +} + +qh_face_t* qh__next_face(qh_context_t* context) { + qh_face_t* face = context->faces + context->nfaces; + + face->face = context->nfaces; + face->iset.indices = NULL; + context->valid[context->nfaces] = 1; + context->nfaces++; + + QH_ASSERT(context->nfaces < context->maxfaces); + + return face; +} + +qh_vec3_t qh__edge_vec3(qh_half_edge_t* edge, qh_context_t* context) { + qh_half_edge_t prevhe = context->edges[edge->previous_he]; + qh_vec3_t v0, v1; + + v0 = context->vertices[prevhe.to_vertex]; + v1 = context->vertices[edge->to_vertex]; + + qh__vec3_sub(&v1, &v0); + qh__vec3_normalize(&v1); + + return v1; +} + +void qh__face_init(qh_face_t* face, qh_index_t vertices[3], + qh_context_t* context) { + qh_half_edge_t* e0 = qh__next_edge(context); + qh_half_edge_t* e1 = qh__next_edge(context); + qh_half_edge_t* e2 = qh__next_edge(context); + qh_vec3_t v0, v1; + qh_vertex_t centroid, normal; + + e2->to_vertex = vertices[0]; + e0->to_vertex = vertices[1]; + e1->to_vertex = vertices[2]; + + e0->next_he = e1->he; + e2->previous_he = e1->he; + face->edges[1] = e1->he; + + e1->next_he = e2->he; + e0->previous_he = e2->he; + face->edges[2] = e2->he; + v1 = qh__edge_vec3(e2, context); + + e2->next_he = e0->he; + e1->previous_he = e0->he; + face->edges[0] = e0->he; + v0 = qh__edge_vec3(e0, context); + + e2->adjacent_face = face->face; + e1->adjacent_face = face->face; + e0->adjacent_face = face->face; + + qh__vec3_multiply(&v1, -1.f); + normal = qh__vec3_cross(&v0, &v1); + + qh__vec3_normalize(&normal); + centroid = qh__face_centroid(vertices, context); + face->centroid = centroid; + face->sdist = qh__vec3_dot(&normal, ¢roid); + face->normal = normal; + face->iset.indices = QH_MALLOC(qh_index_t, QH_VERTEX_SET_SIZE); + face->iset.capacity = QH_VERTEX_SET_SIZE; + face->iset.size = 0; + face->visitededges = 0; +} + +void qh__tetrahedron_basis(qh_context_t* context, qh_index_t vertices[3]) { + qh_index_t eps[6]; + int i, j, k, l = 0; + float max = -QH_FLT_MAX; + + qh__find_6eps(context->vertices, context->nvertices, eps); + qh__find_2dps_6eps(context->vertices, eps, &j, &k); + + for (i = 0; i < 6; ++i) { + float d2; + + if (i == j || i == k) { + continue; + } + + d2 = qh__vertex_segment_length2(context->vertices + eps[i], + context->vertices + eps[j], + context->vertices + eps[k]); + + if (d2 > max) { + max = d2; + l = i; + } + } + + vertices[0] = eps[j]; + vertices[1] = eps[k]; + vertices[2] = eps[l]; +} + +void qh__push_stack(qh_index_stack_t* stack, qh_index_t index) { + stack->begin[stack->size] = index; + stack->size++; +} + +qh_index_t qh__pop_stack(qh_index_stack_t* stack) { + qh_index_t top = -1; + + if (stack->size > 0) { + top = stack->begin[stack->size - 1]; + stack->size--; + } + + return top; +} + +qh_index_t qh__furthest_point_from_plane(qh_context_t* context, + qh_index_t* indices, int nindices, + qh_vec3_t* normal, float sdist) { + int i, j = 0; + float max = -QH_FLT_MAX; + + for (i = 0; i < nindices; ++i) { + qh_index_t index = indices ? *(indices + i) : i; + float dist = qh__dist_point_plane(context->vertices + index, normal, sdist); + + if (dist > max) { + j = i; + max = dist; + } + } + + return j; +} + +int qh__face_can_see_vertex(qh_face_t* face, qh_vertex_t* v) { + qh_vec3_t tov = *v; + + qh__vec3_sub(&tov, &face->centroid); + return qh__vec3_dot(&tov, &face->normal) > 0; +} + +int qh__face_can_see_vertex_epsilon(qh_context_t* context, qh_face_t* face, + qh_vertex_t* v, float epsilon) { + float dot; + qh_vec3_t tov = *v; + + qh__vec3_sub(&tov, &face->centroid); + dot = qh__vec3_dot(&tov, &face->normal); + + if (dot > epsilon) { + return 1; + } else { + dot = fabsf(dot); + + if (dot <= epsilon && dot >= 0) { + qh_vec3_t n = face->normal; + + // allow epsilon degeneration along the face normal + qh__vec3_multiply(&n, epsilon); + qh__vec3_add(v, &n); + + return 1; + } + } + + return 0; +} + +static inline void qh__assert_half_edge(qh_half_edge_t* edge, + qh_context_t* context) { + QH_ASSERT(edge->opposite_he != -1); + QH_ASSERT(edge->he != -1); + QH_ASSERT(edge->adjacent_face != -1); + QH_ASSERT(edge->next_he != -1); + QH_ASSERT(edge->previous_he != -1); + QH_ASSERT(edge->to_vertex != -1); + QH_ASSERT(context->edges[edge->opposite_he].to_vertex != edge->to_vertex); +} + +static inline void qh__assert_face(qh_face_t* face, qh_context_t* context) { + int i; + + for (i = 0; i < 3; ++i) { + qh__assert_half_edge(context->edges + face->edges[i], context); + } + + QH_ASSERT(context->valid[face->face]); +} + +#ifdef QUICKHULL_DEBUG + +void qh__log_face(qh_context_t* context, qh_face_t const* face) { + QH_LOG("Face %ld:\n", face->face); + for (int i = 0; i < 3; ++i) { + qh_half_edge_t edge = context->edges[face->edges[i]]; + QH_LOG("\te%d %ld\n", i, edge.he); + QH_LOG("\t\te%d.opposite_he %ld\n", i, edge.opposite_he); + QH_LOG("\t\te%d.next_he %ld\n", i, edge.next_he); + QH_LOG("\t\te%d.previous_he %ld\n", i, edge.previous_he); + QH_LOG("\t\te%d.to_vertex %ld\n", i, edge.to_vertex); + QH_LOG("\t\te%d.adjacent_face %ld\n", i, edge.adjacent_face); + } + QH_LOG("\tnormal %f %f %f\n", face->normal.x, face->normal.y, face->normal.z); + QH_LOG("\tsdist %f\n", face->sdist); + QH_LOG("\tcentroid %f %f %f\n", face->centroid.x, face->centroid.y, + face->centroid.z); +} + +#endif + +int qh__test_hull(qh_context_t* context, float epsilon, int testiset) { + unsigned int i, j, k; + + for (i = 0; i < context->nvertices; ++i) { + qh_index_t vindex = i; + char valid = 1; + + for (j = 0; j < context->nfaces; ++j) { + if (!context->valid[j]) { + continue; + } + qh_face_t* face = context->faces + j; + + qh_half_edge_t* e0 = context->edges + face->edges[0]; + qh_half_edge_t* e1 = context->edges + face->edges[1]; + qh_half_edge_t* e2 = context->edges + face->edges[2]; + + if (e0->to_vertex == vindex || e1->to_vertex == vindex || + e2->to_vertex == vindex) { + valid = 0; + break; + } + + if (testiset) { + for (k = 0; k < face->iset.size; ++k) { + if (vindex == face->iset.indices[k]) { + valid = 0; + } + } + } + } + + if (!valid) { + continue; + } + + for (j = 0; j < context->nfaces; ++j) { + if (!context->valid[j]) { + continue; + } + qh_face_t* face = context->faces + j; + + qh_vertex_t vertex = context->vertices[vindex]; + qh__vec3_sub(&vertex, &face->centroid); + if (qh__vec3_dot(&face->normal, &vertex) > epsilon) { +#ifdef QUICKHULL_DEBUG + qh__log_face(context, face); +#endif + return 0; + } + } + } + + return 1; +} + +#ifdef QUICKHULL_DEBUG +void qh__build_hull(qh_context_t* context, float epsilon, unsigned int step, + unsigned int* failurestep) +#else +void qh__build_hull(qh_context_t* context, float epsilon) +#endif +{ + qh_index_t topface = qh__pop_stack(&context->facestack); + int i, j, k; + +#ifdef QUICKHULL_DEBUG + unsigned int iteration = 0; +#endif + + while (topface != -1) { + qh_face_t* face = context->faces + topface; + qh_index_t fvi, apex; + qh_vertex_t* fv; + int reversed = 0; + +#ifdef QUICKHULL_DEBUG + if (!context->valid[topface] || face->iset.size == 0 || iteration == step) +#else + if (!context->valid[topface] || face->iset.size == 0) +#endif + { + topface = qh__pop_stack(&context->facestack); + continue; + } + +#ifdef QUICKHULL_DEBUG + if (failurestep != NULL && !qh__test_hull(context, epsilon, 1)) { + if (*failurestep == 0) { + *failurestep = iteration; + break; + } + } + + iteration++; +#endif + + fvi = qh__furthest_point_from_plane(context, face->iset.indices, + face->iset.size, &face->normal, + face->sdist); + fv = context->vertices + *(face->iset.indices + fvi); + + qh__assert_face(face, context); + + // Reset visited flag for faces + { + for (i = 0; i < context->nfaces; ++i) { + context->faces[i].visitededges = 0; + } + } + + // Find horizon edge + { + qh_index_t tovisit = topface; + qh_face_t* facetovisit = context->faces + tovisit; + + // Release scratch + context->scratch.size = 0; + + while (tovisit != -1) { + if (facetovisit->visitededges >= 3) { + context->valid[tovisit] = 0; + tovisit = qh__pop_stack(&context->scratch); + facetovisit = context->faces + tovisit; + } else { + qh_index_t edgeindex = facetovisit->edges[facetovisit->visitededges]; + qh_half_edge_t* edge; + qh_half_edge_t* oppedge; + qh_face_t* adjface; + + facetovisit->visitededges++; + + edge = context->edges + edgeindex; + oppedge = context->edges + edge->opposite_he; + adjface = context->faces + oppedge->adjacent_face; + + if (!context->valid[oppedge->adjacent_face]) { + continue; + } + + qh__assert_half_edge(oppedge, context); + qh__assert_half_edge(edge, context); + qh__assert_face(adjface, context); + + if (!qh__face_can_see_vertex(adjface, fv)) { + qh__push_stack(&context->horizonedges, edge->he); + } else { + context->valid[tovisit] = 0; + qh__push_stack(&context->scratch, adjface->face); + } + } + } + } + + apex = face->iset.indices[fvi]; + + // Sort horizon edges in CCW order + { + qh_vertex_t triangle[3]; + int vindex = 0; + qh_vec3_t v0, v1, toapex; + qh_vertex_t n; + + for (i = 0; i < context->horizonedges.size; ++i) { + qh_index_t he0 = context->horizonedges.begin[i]; + qh_index_t he0vert = context->edges[he0].to_vertex; + qh_index_t phe0 = context->edges[he0].previous_he; + qh_index_t phe0vert = context->edges[phe0].to_vertex; + + for (j = i + 2; j < context->horizonedges.size; ++j) { + qh_index_t he1 = context->horizonedges.begin[j]; + qh_index_t he1vert = context->edges[he1].to_vertex; + qh_index_t phe1 = context->edges[he1].previous_he; + qh_index_t phe1vert = context->edges[phe1].to_vertex; + + if (phe1vert == he0vert || phe0vert == he1vert) { + QH_SWAP(qh_index_t, context->horizonedges.begin[j], + context->horizonedges.begin[i + 1]); + break; + } + } + + if (vindex < 3) { + triangle[vindex++] = context->vertices[context->edges[he0].to_vertex]; + } + } + + if (vindex == 3) { + // Detect first triangle face ordering + v0 = triangle[0]; + v1 = triangle[2]; + + qh__vec3_sub(&v0, &triangle[1]); + qh__vec3_sub(&v1, &triangle[1]); + + n = qh__vec3_cross(&v0, &v1); + + // Get the vector to the apex + toapex = triangle[0]; + + qh__vec3_sub(&toapex, context->vertices + apex); + + reversed = qh__vec3_dot(&n, &toapex) < 0.f; + } + } + + // Create new faces + { + qh_index_t top = qh__pop_stack(&context->horizonedges); + qh_index_t last = qh__pop_stack(&context->horizonedges); + qh_index_t first = top; + int looped = 0; + + QH_ASSERT(context->newhorizonedges.size == 0); + + // Release scratch + context->scratch.size = 0; + + while (!looped) { + qh_half_edge_t* prevhe; + qh_half_edge_t* nexthe; + qh_half_edge_t* oppedge; + qh_vec3_t normal; + qh_vertex_t fcentroid; + qh_index_t verts[3]; + qh_face_t* newface; + + if (last == -1) { + looped = 1; + last = first; + } + + prevhe = context->edges + last; + nexthe = context->edges + top; + + if (reversed) { + QH_SWAP(qh_half_edge_t*, prevhe, nexthe); + } + + verts[0] = prevhe->to_vertex; + verts[1] = nexthe->to_vertex; + verts[2] = apex; + + context->valid[nexthe->adjacent_face] = 0; + + oppedge = context->edges + nexthe->opposite_he; + newface = qh__next_face(context); + + qh__face_init(newface, verts, context); + + oppedge->opposite_he = context->edges[newface->edges[0]].he; + context->edges[newface->edges[0]].opposite_he = oppedge->he; + + qh__push_stack(&context->scratch, newface->face); + qh__push_stack(&context->newhorizonedges, newface->edges[0]); + + top = last; + last = qh__pop_stack(&context->horizonedges); + } + } + + // Attach point sets to newly created faces + { + for (k = 0; k < context->nfaces; ++k) { + qh_face_t* f = context->faces + k; + + if (context->valid[k] || f->iset.size == 0) { + continue; + } + + if (f->visitededges == 3) { + context->valid[k] = 0; + } + + for (i = 0; i < f->iset.size; ++i) { + qh_index_t vertex = f->iset.indices[i]; + qh_vertex_t* v = context->vertices + vertex; + qh_face_t* dface = NULL; + + for (j = 0; j < context->scratch.size; ++j) { + qh_face_t* newface = context->faces + context->scratch.begin[j]; + qh_half_edge_t* e0 = context->edges + newface->edges[0]; + qh_half_edge_t* e1 = context->edges + newface->edges[1]; + qh_half_edge_t* e2 = context->edges + newface->edges[2]; + qh_vertex_t cv; + + if (e0->to_vertex == vertex || e1->to_vertex == vertex || + e2->to_vertex == vertex) { + continue; + } + + if (qh__face_can_see_vertex_epsilon( + context, newface, context->vertices + vertex, epsilon)) { + dface = newface; + break; + } + } + + if (dface) { + if (dface->iset.size + 1 >= dface->iset.capacity) { + dface->iset.capacity *= 2; + dface->iset.indices = QH_REALLOC(qh_index_t, dface->iset.indices, + dface->iset.capacity); + } + + dface->iset.indices[dface->iset.size++] = vertex; + } + } + + f->iset.size = 0; + } + } + + // Link new faces together + { + for (i = 0; i < context->newhorizonedges.size; ++i) { + qh_index_t phe0, nhe1; + qh_half_edge_t* he0; + qh_half_edge_t* he1; + int ii; + + if (reversed) { + ii = (i == 0) ? context->newhorizonedges.size - 1 : (i - 1); + } else { + ii = (i + 1) % context->newhorizonedges.size; + } + + phe0 = context->edges[context->newhorizonedges.begin[i]].previous_he; + nhe1 = context->edges[context->newhorizonedges.begin[ii]].next_he; + + he0 = context->edges + phe0; + he1 = context->edges + nhe1; + + QH_ASSERT(he1->to_vertex == apex); + QH_ASSERT(he0->opposite_he == -1); + QH_ASSERT(he1->opposite_he == -1); + + he0->opposite_he = he1->he; + he1->opposite_he = he0->he; + } + + context->newhorizonedges.size = 0; + } + + // Push new face to stack + { + for (i = 0; i < context->scratch.size; ++i) { + qh_face_t* face = context->faces + context->scratch.begin[i]; + + if (face->iset.size > 0) { + qh__push_stack(&context->facestack, face->face); + } + } + + // Release scratch + context->scratch.size = 0; + } + + topface = qh__pop_stack(&context->facestack); + + // TODO: push all non-valid faces for reuse in face stack memory pool + } +} + +void qh_mesh_export(qh_mesh_t const* mesh, char const* filename) { + FILE* objfile = fopen(filename, "wt"); + fprintf(objfile, "o\n"); + + for (int i = 0; i < mesh->nvertices; ++i) { + qh_vertex_t v = mesh->vertices[i]; + fprintf(objfile, "v %f %f %f\n", v.x, v.y, v.z); + } + + for (int i = 0; i < mesh->nnormals; ++i) { + qh_vec3_t n = mesh->normals[i]; + fprintf(objfile, "vn %f %f %f\n", n.x, n.y, n.z); + } + + for (int i = 0, j = 0; i < mesh->nindices; i += 3, j++) { + fprintf(objfile, "f %u/%u %u/%u %u/%u\n", mesh->indices[i + 0] + 1, + mesh->normalindices[j] + 1, mesh->indices[i + 1] + 1, + mesh->normalindices[j] + 1, mesh->indices[i + 2] + 1, + mesh->normalindices[j] + 1); + } + + fclose(objfile); +} + +qh_face_t* qh__build_tetrahedron(qh_context_t* context, float epsilon) { + int i, j; + qh_index_t vertices[3]; + qh_index_t apex; + qh_face_t* faces; + qh_vertex_t normal, centroid, vapex, tcentroid; + + // Get the initial tetrahedron basis (first face) + qh__tetrahedron_basis(context, &vertices[0]); + + // Find apex from the tetrahedron basis + { + float sdist; + qh_vec3_t v0, v1; + + v0 = context->vertices[vertices[1]]; + v1 = context->vertices[vertices[2]]; + + qh__vec3_sub(&v0, context->vertices + vertices[0]); + qh__vec3_sub(&v1, context->vertices + vertices[0]); + + normal = qh__vec3_cross(&v0, &v1); + qh__vec3_normalize(&normal); + + centroid = qh__face_centroid(vertices, context); + sdist = qh__vec3_dot(&normal, ¢roid); + + apex = qh__furthest_point_from_plane(context, NULL, context->nvertices, + &normal, sdist); + vapex = context->vertices[apex]; + + qh__vec3_sub(&vapex, ¢roid); + + // Whether the face is looking towards the apex + if (qh__vec3_dot(&vapex, &normal) > 0) { + QH_SWAP(qh_index_t, vertices[1], vertices[2]); + } + } + + faces = qh__next_face(context); + qh__face_init(&faces[0], vertices, context); + + // Build faces from the tetrahedron basis to the apex + { + qh_index_t facevertices[3]; + for (i = 0; i < 3; ++i) { + qh_half_edge_t* edge = context->edges + faces[0].edges[i]; + qh_half_edge_t prevedge = context->edges[edge->previous_he]; + qh_face_t* face = faces + i + 1; + qh_half_edge_t* e0; + + facevertices[0] = edge->to_vertex; + facevertices[1] = prevedge.to_vertex; + facevertices[2] = apex; + + qh__next_face(context); + qh__face_init(face, facevertices, context); + + e0 = context->edges + faces[i + 1].edges[0]; + edge->opposite_he = e0->he; + e0->opposite_he = edge->he; + } + } + + // Attach half edges to faces tied to the apex + { + for (i = 0; i < 3; ++i) { + qh_face_t* face; + qh_face_t* nextface; + qh_half_edge_t* e1; + qh_half_edge_t* e2; + + j = (i + 2) % 3; + + face = faces + i + 1; + nextface = faces + j + 1; + + e1 = context->edges + face->edges[1]; + e2 = context->edges + nextface->edges[2]; + + QH_ASSERT(e1->opposite_he == -1); + QH_ASSERT(e2->opposite_he == -1); + + e1->opposite_he = e2->he; + e2->opposite_he = e1->he; + + qh__assert_half_edge(e1, context); + qh__assert_half_edge(e2, context); + } + } + + // Create initial point set; every point is + // attached to the first face it can see + { + for (i = 0; i < context->nvertices; ++i) { + qh_vertex_t* v; + qh_face_t* dface = NULL; + + if (vertices[0] == i || vertices[1] == i || vertices[2] == i) { + continue; + } + + for (j = 0; j < 4; ++j) { + if (qh__face_can_see_vertex_epsilon(context, context->faces + j, + context->vertices + i, epsilon)) { + dface = context->faces + j; + break; + } + } + + if (dface) { + int valid = 1; + + for (int j = 0; j < 3; ++j) { + qh_half_edge_t* e = context->edges + dface->edges[j]; + if (i == e->to_vertex) { + valid = 0; + break; + } + } + + if (!valid) { + continue; + } + + if (dface->iset.size + 1 >= dface->iset.capacity) { + dface->iset.capacity *= 2; + dface->iset.indices = + QH_REALLOC(qh_index_t, dface->iset.indices, dface->iset.capacity); + } + + dface->iset.indices[dface->iset.size++] = i; + } + } + } + + // Add initial tetrahedron faces to the face stack + tcentroid.x = tcentroid.y = tcentroid.z = 0.0; + for (i = 0; i < 4; ++i) { + context->valid[i] = 1; + qh__assert_face(context->faces + i, context); + qh__push_stack(&context->facestack, i); + qh__vec3_add(&tcentroid, &context->faces[i].centroid); + } + + // Assign the tetrahedron centroid + qh__vec3_multiply(&tcentroid, 0.25); + context->centroid = tcentroid; + + QH_ASSERT(context->nedges == context->nfaces * 3); + QH_ASSERT(context->nfaces == 4); + QH_ASSERT(context->facestack.size == 4); + + return faces; +} + +void qh__remove_vertex_duplicates(qh_context_t* context, float epsilon) { + int i, j, k; + for (i = 0; i < context->nvertices; ++i) { + qh_vertex_t* v = context->vertices + i; + if (v->x == 0) v->x = 0; + if (v->y == 0) v->y = 0; + if (v->z == 0) v->z = 0; + for (j = i + 1; j < context->nvertices; ++j) { + if (qh__vertex_equals_epsilon(context->vertices + i, + context->vertices + j, epsilon)) { + for (k = j; k < context->nvertices - 1; ++k) { + context->vertices[k] = context->vertices[k + 1]; + } + context->nvertices--; + } + } + } +} + +void qh__init_context(qh_context_t* context, qh_vertex_t const* vertices, + unsigned int nvertices) { + // TODO: + // size_t nedges = 3 * nvertices - 6; + // size_t nfaces = 2 * nvertices - 4; + unsigned int nfaces = nvertices * (nvertices - 1); + unsigned int nedges = nfaces * 3; + + context->edges = QH_MALLOC(qh_half_edge_t, nedges); + context->faces = QH_MALLOC(qh_face_t, nfaces); + context->facestack.begin = QH_MALLOC(qh_index_t, nfaces); + context->scratch.begin = QH_MALLOC(qh_index_t, nfaces); + context->horizonedges.begin = QH_MALLOC(qh_index_t, nedges); + context->newhorizonedges.begin = QH_MALLOC(qh_index_t, nedges); + context->valid = QH_MALLOC(char, nfaces); + + context->vertices = QH_MALLOC(qh_vertex_t, nvertices); + memcpy(context->vertices, vertices, sizeof(qh_vertex_t) * nvertices); + + context->nvertices = nvertices; + context->nedges = 0; + context->nfaces = 0; + context->facestack.size = 0; + context->scratch.size = 0; + context->horizonedges.size = 0; + context->newhorizonedges.size = 0; + +#ifdef QUICKHULL_DEBUG + context->maxfaces = nfaces; + context->maxedges = nedges; +#endif +} + +void qh__free_context(qh_context_t* context) { + int i; + + for (i = 0; i < context->nfaces; ++i) { + QH_FREE(context->faces[i].iset.indices); + context->faces[i].iset.size = 0; + } + + context->nvertices = 0; + context->nfaces = 0; + + QH_FREE(context->edges); + + QH_FREE(context->faces); + QH_FREE(context->facestack.begin); + QH_FREE(context->scratch.begin); + QH_FREE(context->horizonedges.begin); + QH_FREE(context->newhorizonedges.begin); + QH_FREE(context->vertices); + QH_FREE(context->valid); +} + +void qh_free_mesh(qh_mesh_t mesh) { + QH_FREE(mesh.vertices); + QH_FREE(mesh.indices); + QH_FREE(mesh.normalindices); + QH_FREE(mesh.normals); +} + +float qh__compute_epsilon(qh_vertex_t const* vertices, unsigned int nvertices) { + float epsilon; + unsigned int i; + + float maxxi = -QH_FLT_MAX; + float maxyi = -QH_FLT_MAX; + + for (i = 0; i < nvertices; ++i) { + float fxi = fabsf(vertices[i].x); + float fyi = fabsf(vertices[i].y); + + if (fxi > maxxi) { + maxxi = fxi; + } + if (fyi > maxyi) { + maxyi = fyi; + } + } + + epsilon = 2 * (maxxi + maxyi) * QH_FLT_EPS; + + return epsilon; +} + +qh_mesh_t qh_quickhull3d(qh_vertex_t const* vertices, unsigned int nvertices) { + qh_mesh_t m; + qh_context_t context; + unsigned int* indices; + unsigned int nfaces = 0, i, index, nindices; + float epsilon; + + epsilon = qh__compute_epsilon(vertices, nvertices); + + qh__init_context(&context, vertices, nvertices); + + qh__remove_vertex_duplicates(&context, epsilon); + + // Build the initial tetrahedron + qh__build_tetrahedron(&context, epsilon); + +// Build the convex hull +#ifdef QUICKHULL_DEBUG + qh__build_hull(&context, epsilon, -1, NULL); +#else + qh__build_hull(&context, epsilon); +#endif + + // QH_ASSERT(qh__test_hull(&context, epsilon)); + + for (i = 0; i < context.nfaces; ++i) { + if (context.valid[i]) { + nfaces++; + } + } + + nindices = nfaces * 3; + + m.normals = QH_MALLOC(qh_vertex_t, nfaces); + m.normalindices = QH_MALLOC(unsigned int, nfaces); + m.vertices = QH_MALLOC(qh_vertex_t, nindices); + m.indices = QH_MALLOC(unsigned int, nindices); + m.nindices = nindices; + m.nnormals = nfaces; + m.nvertices = 0; + + { + index = 0; + for (i = 0; i < context.nfaces; ++i) { + if (!context.valid[i]) { + continue; + } + m.normals[index] = context.faces[i].normal; + index++; + } + + index = 0; + for (i = 0; i < context.nfaces; ++i) { + if (!context.valid[i]) { + continue; + } + m.normalindices[index] = index; + index++; + } + + index = 0; + for (i = 0; i < context.nfaces; ++i) { + if (!context.valid[i]) { + continue; + } + m.indices[index + 0] = context.faces[i].iset.indices[0]; + // m.indices[index + 0] = context.facestack.begin[index + 0]; + // m.indices[index + 1] = context.facestack.begin[index + 1]; + // m.indices[index + 2] = context.facestack.begin[index + 2]; + m.indices[index + 1] = context.faces[i].iset.indices[1]; + m.indices[index + 2] = context.faces[i].iset.indices[2]; + index += 3; + } + + for (i = 0; i < context.nfaces; ++i) { + if (!context.valid[i]) { + continue; + } + qh_half_edge_t e0 = context.edges[context.faces[i].edges[0]]; + qh_half_edge_t e1 = context.edges[context.faces[i].edges[1]]; + qh_half_edge_t e2 = context.edges[context.faces[i].edges[2]]; + + m.vertices[m.nvertices++] = context.vertices[e0.to_vertex]; + m.vertices[m.nvertices++] = context.vertices[e1.to_vertex]; + m.vertices[m.nvertices++] = context.vertices[e2.to_vertex]; + } + } + + qh__free_context(&context); + + return m; +} + +#endif // QUICKHULL_IMPLEMENTATION \ No newline at end of file diff --git a/test/edge_test.cpp b/test/edge_test.cpp index b1a5c0941..b51194dd1 100644 --- a/test/edge_test.cpp +++ b/test/edge_test.cpp @@ -105,4 +105,232 @@ TEST(Manifold, EmptyHull) { const std::vector coplanar{ {0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {1, 1, 0}}; EXPECT_TRUE(Manifold::Hull(coplanar).IsEmpty()); -} \ No newline at end of file +} + +TEST(Manifold, VHACDHULL) { + const float tictacRad = 100; + const float tictacHeight = 500; + const int tictacSeg = 100; + const float tictacMid = tictacHeight - 2 * tictacRad; + const auto sphere = Manifold::Sphere(tictacRad, tictacSeg); + const std::vector spheres{sphere, + sphere.Translate({0, 0, tictacMid})}; + const auto tictac = Manifold::Hull2(spheres); + +#ifdef MANIFOLD_EXPORT + if (options.exportModels) { + ExportMesh("tictac_hull2.glb", tictac.GetMesh(), {}); + } +#endif + + EXPECT_EQ(sphere.NumVert() + tictacSeg, tictac.NumVert()); +} + +TEST(Manifold, HollowHull2) { + auto sphere = Manifold::Sphere(100, 360); + auto hollow = sphere - sphere.Scale({0.8, 0.8, 0.8}); + const float sphere_vol = sphere.GetProperties().volume; + EXPECT_FLOAT_EQ(hollow.Hull2().GetProperties().volume, sphere_vol); +} + +TEST(Manifold, CubeHull2) { + std::vector cubePts = { + {0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {0, 0, 1}, // corners + {1, 1, 0}, {0, 1, 1}, {1, 0, 1}, {1, 1, 1}, // corners + {0.5, 0.5, 0.5}, {0.5, 0, 0}, {0.5, 0.7, 0.2} // internal points + }; + auto cube = Manifold::Hull2(cubePts); + EXPECT_FLOAT_EQ(cube.GetProperties().volume, 1); +} + +TEST(Manifold, EmptyHull2) { + const std::vector tooFew{{0, 0, 0}, {1, 0, 0}, {0, 1, 0}}; + EXPECT_TRUE(Manifold::Hull2(tooFew).IsEmpty()); + + const std::vector coplanar{ + {0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {1, 1, 0}}; + EXPECT_TRUE(Manifold::Hull2(coplanar).IsEmpty()); +} + +TEST(Manifold, QUICKHULL2) { + const float tictacRad = 100; + const float tictacHeight = 500; + const int tictacSeg = 50; + const float tictacMid = tictacHeight - 2 * tictacRad; + const auto sphere = Manifold::Sphere(tictacRad, tictacSeg); + const std::vector spheres{sphere, + sphere.Translate({0, 0, tictacMid})}; + const auto tictac = Manifold::Hull3(spheres); + +#ifdef MANIFOLD_EXPORT + if (options.exportModels) { + ExportMesh("tictac_hull3.glb", tictac.GetMesh(), {}); + } +#endif + + EXPECT_NEAR(sphere.NumVert() + tictacSeg, tictac.NumVert(), 3); +} + +// TEST(Manifold, HollowHull3) { +// auto sphere = Manifold::Sphere(100, 100); +// auto hollow = sphere - sphere.Scale({0.8, 0.8, 0.8}); +// const float sphere_vol = sphere.GetProperties().volume; +// EXPECT_FLOAT_EQ(hollow.Hull3().GetProperties().volume, sphere_vol); +// } + +// TEST(Manifold, CubeHull3) { +// std::vector cubePts = { +// {0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {0, 0, 1}, // corners +// {1, 1, 0}, {0, 1, 1}, {1, 0, 1}, {1, 1, 1}, // corners +// {0.5, 0.5, 0.5}, {0.5, 0, 0}, {0.5, 0.7, 0.2} // internal points +// }; +// auto cube = Manifold::Hull3(cubePts); +// EXPECT_FLOAT_EQ(cube.GetProperties().volume, 1); +// } + +// TEST(Manifold, EmptyHull3) { +// const std::vector tooFew{{0, 0, 0}, {1, 0, 0}, {0, 1, 0}}; +// EXPECT_TRUE(Manifold::Hull3(tooFew).IsEmpty()); + +// const std::vector coplanar{ +// {0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {1, 1, 0}}; +// EXPECT_TRUE(Manifold::Hull3(coplanar).IsEmpty()); +// } + +TEST(Manifold, TICTACHULL4) { + const float tictacRad = 100; + const float tictacHeight = 500; + const int tictacSeg = 50; + const float tictacMid = tictacHeight - 2 * tictacRad; + const auto sphere = Manifold::Sphere(tictacRad, tictacSeg); + const std::vector spheres{sphere, + sphere.Translate({0, 0, tictacMid})}; + const auto tictac = Manifold::Hull4(spheres); + +#ifdef MANIFOLD_EXPORT + if (options.exportModels) { + // std::cout << "Ok" << std::endl; + ExportMesh("tictac_hull4.glb", tictac.GetMesh(), {}); + } +#endif + + EXPECT_NEAR(sphere.NumVert() + tictacSeg, tictac.NumVert(), 3); +} + +TEST(Manifold, HollowHull4) { + auto sphere = Manifold::Sphere(100, 100); + auto hollow = sphere - sphere.Scale({0.8, 0.8, 0.8}); + const float sphere_vol = sphere.GetProperties().volume; + EXPECT_FLOAT_EQ(hollow.Hull4().GetProperties().volume, sphere_vol); +} + +TEST(Manifold, CubeHull4) { + std::vector cubePts = { + {0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {0, 0, 1}, // corners + {1, 1, 0}, {0, 1, 1}, {1, 0, 1}, {1, 1, 1}, // corners + {0.5, 0.5, 0.5}, {0.5, 0, 0}, {0.5, 0.7, 0.2} // internal points + }; + auto cube = Manifold::Hull4(cubePts); + EXPECT_FLOAT_EQ(cube.GetProperties().volume, 1); +} + +TEST(Manifold, EmptyHull4) { + const std::vector tooFew{{0, 0, 0}, {1, 0, 0}, {0, 1, 0}}; + EXPECT_TRUE(Manifold::Hull4(tooFew).IsEmpty()); + + const std::vector coplanar{ + {0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {1, 1, 0}}; + EXPECT_TRUE(Manifold::Hull4(coplanar).IsEmpty()); +} + +TEST(Manifold, TICTACHULL5) { + const float tictacRad = 100; + const float tictacHeight = 500; + const int tictacSeg = 50; + const float tictacMid = tictacHeight - 2 * tictacRad; + const auto sphere = Manifold::Sphere(tictacRad, tictacSeg); + const std::vector spheres{sphere, + sphere.Translate({0, 0, tictacMid})}; + const auto tictac = Manifold::Hull5(spheres); + +#ifdef MANIFOLD_EXPORT + if (options.exportModels) { + // std::cout << "Ok" << std::endl; + ExportMesh("tictac_hull5.glb", tictac.GetMesh(), {}); + } +#endif + + EXPECT_NEAR(sphere.NumVert() + tictacSeg, tictac.NumVert(), 3); +} + +TEST(Manifold, HollowHull5) { + auto sphere = Manifold::Sphere(100, 100); + auto hollow = sphere - sphere.Scale({0.8, 0.8, 0.8}); + const float sphere_vol = sphere.GetProperties().volume; + EXPECT_FLOAT_EQ(hollow.Hull5().GetProperties().volume, sphere_vol); +} + +TEST(Manifold, CubeHull5) { + std::vector cubePts = { + {0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {0, 0, 1}, // corners + {1, 1, 0}, {0, 1, 1}, {1, 0, 1}, {1, 1, 1}, // corners + {0.5, 0.5, 0.5}, {0.5, 0, 0}, {0.5, 0.7, 0.2} // internal points + }; + auto cube = Manifold::Hull5(cubePts); + EXPECT_FLOAT_EQ(cube.GetProperties().volume, 1); +} + +TEST(Manifold, EmptyHull5) { + const std::vector tooFew{{0, 0, 0}, {1, 0, 0}, {0, 1, 0}}; + EXPECT_TRUE(Manifold::Hull5(tooFew).IsEmpty()); + + const std::vector coplanar{ + {0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {1, 1, 0}}; + EXPECT_TRUE(Manifold::Hull5(coplanar).IsEmpty()); +} + +TEST(Manifold, TICTACHULL6) { + const float tictacRad = 100; + const float tictacHeight = 500; + const int tictacSeg = 50; + const float tictacMid = tictacHeight - 2 * tictacRad; + const auto sphere = Manifold::Sphere(tictacRad, tictacSeg); + const std::vector spheres{sphere, + sphere.Translate({0, 0, tictacMid})}; + const auto tictac = Manifold::Hull6(spheres); + +#ifdef MANIFOLD_EXPORT + if (options.exportModels) { + // std::cout << "Ok" << std::endl; + ExportMesh("tictac_hull6.glb", tictac.GetMesh(), {}); + } +#endif + + EXPECT_NEAR(sphere.NumVert() + tictacSeg, tictac.NumVert(), 3); +} + +TEST(Manifold, HollowHull6) { + auto sphere = Manifold::Sphere(100, 100); + auto hollow = sphere - sphere.Scale({0.8, 0.8, 0.8}); + const float sphere_vol = sphere.GetProperties().volume; + EXPECT_FLOAT_EQ(hollow.Hull6().GetProperties().volume, sphere_vol); +} + +TEST(Manifold, CubeHull6) { + std::vector cubePts = { + {0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {0, 0, 1}, // corners + {1, 1, 0}, {0, 1, 1}, {1, 0, 1}, {1, 1, 1}, // corners + {0.5, 0.5, 0.5}, {0.5, 0, 0}, {0.5, 0.7, 0.2} // internal points + }; + auto cube = Manifold::Hull6(cubePts); + EXPECT_FLOAT_EQ(cube.GetProperties().volume, 1); +} + +TEST(Manifold, EmptyHull6) { + const std::vector tooFew{{0, 0, 0}, {1, 0, 0}, {0, 1, 0}}; + EXPECT_TRUE(Manifold::Hull6(tooFew).IsEmpty()); + + const std::vector coplanar{ + {0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {1, 1, 0}}; + EXPECT_TRUE(Manifold::Hull6(coplanar).IsEmpty()); +} diff --git a/test/manifold_test.cpp b/test/manifold_test.cpp index 91ab10baf..afd777dbd 100644 --- a/test/manifold_test.cpp +++ b/test/manifold_test.cpp @@ -20,7 +20,6 @@ #include "samples.h" #include "sdf.h" #include "test.h" -#include "tri_dist.h" namespace { diff --git a/test/samples_test.cpp b/test/samples_test.cpp index 9146c81a6..9b29a8634 100644 --- a/test/samples_test.cpp +++ b/test/samples_test.cpp @@ -251,6 +251,19 @@ TEST(Samples, Sponge1) { // degree rotations. TEST(Samples, Sponge4) { Manifold sponge = MengerSponge(4); + // sponge = sponge.Rotate(30, 40, 50); + Mesh spongeMesh = sponge.GetMesh(); + const int nVert = spongeMesh.vertPos.size(); + std::vector spongePts; + for (int i = 0; i < nVert; ++i) { + spongePts.push_back(spongeMesh.vertPos[i]); + } + auto spongeHull = Manifold::Hull(spongePts); +#ifdef MANIFOLD_EXPORT + if (options.exportModels) { + ExportMesh("sponge_hull.glb", spongeHull.GetMesh(), {}); + } +#endif CheckNormals(sponge); EXPECT_LE(sponge.NumDegenerateTris(), 8); EXPECT_EQ(sponge.Genus(), 26433); // should be 1:5, 2:81, 3:1409, 4:26433 @@ -263,15 +276,6 @@ TEST(Samples, Sponge4) { CrossSection projection = cutSponge.first.Project(); Rect rect = projection.Bounds(); Box box = cutSponge.first.BoundingBox(); - EXPECT_EQ(rect.min.x, box.min.x); - EXPECT_EQ(rect.min.y, box.min.y); - EXPECT_EQ(rect.max.x, box.max.x); - EXPECT_EQ(rect.max.y, box.max.y); - EXPECT_NEAR(projection.Area(), 0.535, 0.001); - Manifold extrusion = Manifold::Extrude(projection, 1); - EXPECT_EQ(extrusion.NumDegenerateTris(), 0); - EXPECT_EQ(extrusion.Genus(), 502); - #ifdef MANIFOLD_EXPORT if (options.exportModels) { ExportMesh("mengerHalf.glb", cutSponge.first.GetMesh(), {}); @@ -287,6 +291,14 @@ TEST(Samples, Sponge4) { ExportMesh("mengerSponge.glb", out, options); } #endif + EXPECT_EQ(rect.min.x, box.min.x); + EXPECT_EQ(rect.min.y, box.min.y); + EXPECT_EQ(rect.max.x, box.max.x); + EXPECT_EQ(rect.max.y, box.max.y); + EXPECT_NEAR(projection.Area(), 0.535, 0.001); + Manifold extrusion = Manifold::Extrude(projection, 1); + EXPECT_EQ(extrusion.NumDegenerateTris(), 0); + EXPECT_EQ(extrusion.Genus(), 502); } #endif