Merge pull request #1249 from LLNL/pr-from-fork/1232

Pr from fork/1232

RELEASE-NOTES.md

@@ -49,6 +49,7 @@ The Axom project release numbers follow [Semantic Versioning](http://semver.org/
 ### Fixed
 - quest's `SamplingShaper` now properly handles material names containing underscores
 - quest's `SamplingShaper` can now be used with an mfem that is configured for (GPU) devices
+- primal's `Polygon` area computation in 3D previously only worked when the polygon was aligned with the XY-plane. It now works for arbitrary polygons.
 
 ## [Version 0.8.1] - Release date 2023-08-16
 

src/axom/core/numerics/Matrix.hpp

@@ -7,6 +7,8 @@
 #include "axom/core/utilities/Utilities.hpp"  // for utilities::swap()
 #include "axom/core/memory_management.hpp"    // for alloc(), free()
 
+#include "axom/fmt.hpp"
+
 // C/C++ includes
 #include <cassert>   // for assert()
 #include <cstring>   // for memcpy()
@@ -1040,4 +1042,9 @@ std::ostream& operator<<(std::ostream& os, const Matrix<T>& M)
 } /* end namespace numerics */
 } /* end namespace axom */
 
+/// Overload to format a numerics::Matrix using fmt
+template <typename T>
+struct axom::fmt::formatter<axom::numerics::Matrix<T>> : ostream_formatter
+{ };
+
 #endif /* AXOM_MATRIX_HPP_ */

src/axom/primal/geometry/Polygon.hpp

@@ -14,6 +14,7 @@
 
 #include "axom/core/Array.hpp"
 #include "axom/primal/geometry/Point.hpp"
+#include "axom/primal/geometry/Vector.hpp"
 
 #include <ostream>
 
@@ -142,27 +143,23 @@ class Polygon
   typename std::enable_if<TDIM == 3, double>::type area() const
   {
     const int nVerts = numVertices();
-    double sum = 0.;
 
     // check for early return
     if(nVerts < 3)
     {
-      return sum;
+      return 0.0;
     }
 
     // Add up areas of triangles connecting polygon edges the vertex average
+    VectorType sum;
     const auto O = vertexMean();  // 'O' for (local) origin
     for(int curr = 0, prev = nVerts - 1; curr < nVerts; prev = curr++)
     {
-      const auto& P = m_vertices[prev];
-      const auto& C = m_vertices[curr];
-      // clang-format off
-      sum += axom::numerics::determinant(P[0] - O[0], C[0] - O[0],
-                                         P[1] - O[1], C[1] - O[1]);
-      // clang-format on
+      sum +=
+        VectorType::cross_product(m_vertices[prev] - O, m_vertices[curr] - O);
     }
 
-    return axom::utilities::abs(0.5 * sum);
+    return 0.5 * axom::utilities::abs(sum.norm());
   }
 
   /**
@@ -257,4 +254,9 @@ std::ostream& operator<<(std::ostream& os, const Polygon<T, NDIMS>& poly)
 }  // namespace primal
 }  // namespace axom
 
+/// Overload to format a primal::Polygon using fmt
+template <typename T, int NDIMS>
+struct axom::fmt::formatter<axom::primal::Polygon<T, NDIMS>> : ostream_formatter
+{ };
+
 #endif  // AXOM_PRIMAL_POLYGON_HPP_

src/axom/primal/tests/primal_polygon.cpp

@@ -10,6 +10,11 @@
 #include <math.h>
 #include "gtest/gtest.h"
 
+namespace
+{
+constexpr double EPS = 1e-8;
+}
+
 //------------------------------------------------------------------------------
 TEST(primal_polygon, empty)
 {
@@ -353,7 +358,7 @@ TEST(primal_polygon, signed_area_2d)
 }
 
 //------------------------------------------------------------------------------
-TEST(primal_polygon, area_2d_3d)
+TEST(primal_polygon, area_2d_3d_axis_aligned)
 {
   using Polygon2D = axom::primal::Polygon<double, 2>;
   using Point2D = axom::primal::Point<double, 2>;
@@ -362,40 +367,260 @@ TEST(primal_polygon, area_2d_3d)
   using Point3D = axom::primal::Point<double, 3>;
 
   // test a simple right triangle
-  // use same xy-data in 2D and 3D
-  {
-    Polygon2D poly2D({Point2D {0, 0}, Point2D {1, 0}, Point2D {1, 1}});
-    EXPECT_DOUBLE_EQ(.5, poly2D.area());
+  Polygon2D poly2D({Point2D {0, 0}, Point2D {1, 0}, Point2D {1, 1}});
+  EXPECT_DOUBLE_EQ(.5, poly2D.area());
 
-    Polygon3D poly3Da({Point3D {0, 0, 0}, Point3D {1, 0, 0}, Point3D {1, 1, 0}});
-    EXPECT_DOUBLE_EQ(.5, poly3Da.area());
+  // in xy-plane
+  Polygon3D poly3Da({Point3D {0, 0, 0}, Point3D {1, 0, 0}, Point3D {1, 1, 0}});
+  EXPECT_DOUBLE_EQ(.5, poly3Da.area());
 
-    Polygon3D poly3Db({Point3D {0, 0, 1}, Point3D {1, 0, 1}, Point3D {1, 1, 1}});
-    EXPECT_DOUBLE_EQ(.5, poly3Db.area());
-  }
+  // in xz-plane
+  Polygon3D poly3Db({Point3D {0, 0, 0}, Point3D {1, 0, 0}, Point3D {1, 0, 1}});
+  EXPECT_DOUBLE_EQ(.5, poly3Db.area());
 
-  // test regular polygons
-  // use same xy-data in 2D and 3D
-  for(int nSides = 3; nSides < 10; ++nSides)
-  {
-    Polygon2D poly2D(nSides);
-    Polygon3D poly3D(nSides);
+  // in yz-plane
+  Polygon3D poly3Dc({Point3D {0, 0, 0}, Point3D {0, 1, 0}, Point3D {0, 1, 1}});
+  EXPECT_DOUBLE_EQ(.5, poly3Dc.area());
+}
+
+//------------------------------------------------------------------------------
+TEST(primal_polygon, area_2d_3d_affine_transforms)
+{
+  using Polygon2D = axom::primal::Polygon<double, 2>;
+  using Point2D = axom::primal::Point<double, 2>;
+
+  using Polygon3D = axom::primal::Polygon<double, 3>;
+  using Point3D = axom::primal::Point<double, 3>;
+  using Vector3D = axom::primal::Vector<double, 3>;
+
+  using TransformMatrix = axom::numerics::Matrix<double>;
 
-    // choose an arbitrary z_offset for 3D polygon
-    const double z_offset = 5.;
+  // lambda to generate a regular n-sided 2D polygon centered around origin
+  auto generateNSidedPolygon = [](int nSides) {
+    Polygon2D polygon(nSides);
 
     for(int i = 0; i < nSides; ++i)
     {
       const double angle = 2. * M_PI * i / nSides;
-      poly2D.addVertex(Point2D {cos(angle), sin(angle)});
-      poly3D.addVertex(Point3D {cos(angle), sin(angle), z_offset});
+      polygon.addVertex(Point2D {cos(angle), sin(angle)});
     }
 
-    const double expected_area = nSides / 2. * sin(2 * M_PI / nSides);
+    return polygon;
+  };
+
+  // lambda to generate an affine transformation matrix for 2D points
+  auto generateTransformMatrix2D =
+    [](const Point2D& scale, const Point2D& translate, double rotation_angle) {
+      // create scaling matrix
+      auto sc_matx = TransformMatrix::identity(3);
+      {
+        sc_matx(0, 0) = scale[0];
+        sc_matx(1, 1) = scale[1];
+      }
+
+      // create rotation matrix
+      auto rot_matx = TransformMatrix::identity(3);
+      {
+        const double sinT = std::sin(rotation_angle);
+        const double cosT = std::cos(rotation_angle);
+
+        rot_matx(0, 0) = cosT;
+        rot_matx(0, 1) = -sinT;
+        rot_matx(1, 0) = sinT;
+        rot_matx(1, 1) = cosT;
+      }
+
+      // create translation matrix
+      auto tr_matx = TransformMatrix::identity(3);
+      {
+        tr_matx(0, 2) = translate[0];
+        tr_matx(1, 2) = translate[1];
+      }
+
+      // multiply them to get the final transform
+      TransformMatrix affine_matx1(3, 3);
+      matrix_multiply(rot_matx, sc_matx, affine_matx1);
+
+      TransformMatrix affine_matx2(3, 3);
+      matrix_multiply(tr_matx, affine_matx1, affine_matx2);
+
+      EXPECT_NEAR(scale[0] * scale[1], determinant(affine_matx2), EPS);
+      return affine_matx2;
+    };
+
+  // lambda to generate an affine transformation matrix for 2D points
+  auto generateTransformMatrix3D = [](const Point3D& scale,
+                                      const Point3D& translate,
+                                      const Vector3D& axis,
+                                      double angle) {
+    // create scaling matrix
+    auto sc_matx = TransformMatrix::identity(4);
+    {
+      sc_matx(0, 0) = scale[0];
+      sc_matx(1, 1) = scale[1];
+      sc_matx(2, 2) = scale[2];
+    }
+
+    // create rotation matrix
+    auto rot_matx = TransformMatrix::zeros(4, 4);
+    {
+      const double sinT = std::sin(angle);
+      const double cosT = std::cos(angle);
+
+      const auto unitAxis = axis.unitVector();
+      const double& ux = unitAxis[0];
+      const double& uy = unitAxis[1];
+      const double& uz = unitAxis[2];
+
+      rot_matx(0, 0) = cosT + ux * ux * (1 - cosT);
+      rot_matx(0, 1) = ux * uy * (1 - cosT) - uz * sinT;
+      rot_matx(0, 2) = ux * uz * (1 - cosT) + uy * sinT;
+      rot_matx(1, 0) = uy * ux * (1 - cosT) + uz * sinT;
+      rot_matx(1, 1) = cosT + uy * uy * (1 - cosT);
+      rot_matx(1, 2) = uy * uz * (1 - cosT) - ux * sinT;
+      rot_matx(2, 0) = uz * ux * (1 - cosT) - uy * sinT;
+      rot_matx(2, 1) = uz * uy * (1 - cosT) + ux * sinT;
+      rot_matx(2, 2) = cosT + uz * uz * (1 - cosT);
+      rot_matx(3, 3) = 1;
+    }
+
+    // create translation matrix
+    auto tr_matx = TransformMatrix::identity(4);
+    {
+      tr_matx(0, 3) = translate[0];
+      tr_matx(1, 3) = translate[1];
+      tr_matx(2, 3) = translate[2];
+    }
+
+    // multiply them to get the final transform
+    TransformMatrix affine_matx1(4, 4);
+    matrix_multiply(rot_matx, sc_matx, affine_matx1);
+    TransformMatrix affine_matx2(4, 4);
+    matrix_multiply(tr_matx, affine_matx1, affine_matx2);
+
+    EXPECT_NEAR(scale[0] * scale[1] * scale[2], determinant(affine_matx2), EPS);
+    return affine_matx2;
+  };
+
+  // lambda to transform a 2D polygon into 2D
+  auto transformedPolygon2d = [](const Polygon2D& poly,
+                                 const TransformMatrix& matx) {
+    Polygon2D xformed(poly.numVertices());
+    for(int i = 0; i < poly.numVertices(); ++i)
+    {
+      const double vec_in[3] = {poly[i][0], poly[i][1], 1.};
+      double vec_out[3] = {0., 0., 0.};
+      axom::numerics::matrix_vector_multiply(matx, vec_in, vec_out);
+      xformed.addVertex(Point2D {vec_out[0], vec_out[1]});
+    }
+    return xformed;
+  };
+
+  // lambda to transform a 2D polygon into 3D
+  auto transformedPolygon3d = [](const Polygon2D& poly,
+                                 const TransformMatrix& matx) {
+    Polygon3D xformed(poly.numVertices());
+    for(int i = 0; i < poly.numVertices(); ++i)
+    {
+      const double vec_in[4] = {poly[i][0], poly[i][1], 0., 1.};
+      double vec_out[4] = {0., 0., 0., 0.};
+      axom::numerics::matrix_vector_multiply(matx, vec_in, vec_out);
+      xformed.addVertex(Point3D {vec_out[0], vec_out[1], vec_out[2]});
+    }
+    return xformed;
+  };
+
+  const auto scales = axom::Array<double>({-3., -1., -.5, 0., 0.01, 1., 42.3});
+  const auto translations = axom::Array<double>({-.5, 0., 1., 42.3});
+  const auto angles = axom::Array<double>({-.57, 0., 2. / 3. * M_PI});
+  const auto axes = axom::Array<Vector3D>({
+    Vector3D {0., 0., 1.},
+    Vector3D {0., 1., 0.},
+    Vector3D {1., 0., 0.},
+    Vector3D {1., 0., 1.},
+    Vector3D {1., 1., 1.},
+    Vector3D {-2., -5., 0.},
+  });
+
+  for(int nSides = 3; nSides < 10; ++nSides)
+  {
+    Polygon2D polygon2d = generateNSidedPolygon(nSides);
+    const double unscaled_area = nSides / 2. * sin(2 * M_PI / nSides);
+    EXPECT_DOUBLE_EQ(unscaled_area, polygon2d.area());
 
-    EXPECT_DOUBLE_EQ(expected_area, poly2D.area());
-    EXPECT_DOUBLE_EQ(expected_area, poly3D.area());
-    EXPECT_DOUBLE_EQ(poly2D.area(), poly3D.area());
+    // check area of 2D polygons after affine transforms
+    for(double sc_x : scales)
+    {
+      for(double sc_y : scales)
+      {
+        for(double tr_x : translations)
+        {
+          for(double tr_y : translations)
+          {
+            for(double theta : angles)
+            {
+              const auto sc = Point2D {sc_x, sc_y};
+              const auto tr = Point2D {tr_x, tr_y};
+              auto affine_matx = generateTransformMatrix2D(sc, tr, theta);
+              auto xformed_polygon = transformedPolygon2d(polygon2d, affine_matx);
+
+              const double expected_area =
+                unscaled_area * determinant(affine_matx);
+              EXPECT_NEAR(expected_area, xformed_polygon.signedArea(), EPS);
+
+              if(nSides == 3)
+              {
+                axom::primal::Triangle<double, 2> tri(xformed_polygon[0],
+                                                      xformed_polygon[1],
+                                                      xformed_polygon[2]);
+                EXPECT_NEAR(xformed_polygon.signedArea(), tri.signedArea(), EPS);
+              }
+            }
+          }
+        }
+      }
+    }
+
+    // check area of 3D polygons after affine transforms
+    for(double sc_x : scales)
+    {
+      for(double sc_y : scales)
+      {
+        for(double tr_x : translations)
+        {
+          for(double tr_y : translations)
+          {
+            for(double tr_z : translations)
+            {
+              for(const auto& axis : axes)
+              {
+                for(double theta : angles)
+                {
+                  const auto sc = Point3D {sc_x, sc_y, 1.};
+                  const auto tr = Point3D {tr_x, tr_y, tr_z};
+                  auto affine_matx =
+                    generateTransformMatrix3D(sc, tr, axis, theta);
+                  auto xformed_polygon =
+                    transformedPolygon3d(polygon2d, affine_matx);
+
+                  const auto expected_area = unscaled_area *
+                    axom::utilities::abs(determinant(affine_matx));
+                  EXPECT_NEAR(expected_area, xformed_polygon.area(), EPS);
+
+                  if(nSides == 3)
+                  {
+                    axom::primal::Triangle<double, 3> tri(xformed_polygon[0],
+                                                          xformed_polygon[1],
+                                                          xformed_polygon[2]);
+                    EXPECT_NEAR(xformed_polygon.area(), tri.area(), EPS);
+                  }
+                }
+              }
+            }
+          }
+        }
+      }
+    }
   }
 }