OffsetCrust: Variable-Radius Offset Approximation with Power Diagrams

Introduction

This is the official implementation of our paper "OffsetCrust: Variable-Radius Offset Approximation with Power Diagrams."

OffsetCrust is a novel framework that efficiently addresses the variable-radius offsetting problem by computing a power diagram. Please refer to our paper for more details.

Getting Started

The results presented in our paper were obtained on the following platform:

• Windows 11
• Intel i9-13900K CPU
• 64GB memory

We recommend using different package managers depending on your operating system:

• Windows: We recommend using vcpkg to install the required packages
• macOS: We recommend using Homebrew (brew) to install the required packages

Dependencies

The following libraries are required for this project:

• CGAL
• Eigen3
• libigl
• cli11
• PQP
• Intel TBB
• OpenMP
• nanoflann

Build On Windows

Step 1: Install Dependencies

vcpkg install cgal:x64-windows
vcpkg install eigen3:x64-windows
vcpkg install nanoflann:x64-windows
vcpkg install tbb:x64-windows

Step 2: Configure CMake

1. Change toolchainFile in CmakePresets.json to your vcpkg.cmake path (e.g.E:/vcpkg/scripts/buildsystems/vcpkg.cmake)

Step 3: Build with Visual Studio

1. In Visual Studio, open File > Open > Folder > ./OffsetCrust, and wait until CMake generation finished.
2. In Visual Studio, select x64 Release, Build -> Rebuild All. Then in folder ./out/build/x64-release/, we have folders with corresponding generated .exe file in: constant3d, variable3dand evaluation.

Build On MacOS

Step 1: Install Dependencies

brew install cgal
brew install eigen
brew install nanoflann
brew install tbb
brew install libomp
brew install llvm

Step 2: Configure Environment and Build

Note: The following steps must be executed in the same terminal session.

1. Open terminal and navigate to the project folder

2. Set environment variables:

   export CC=/opt/homebrew/opt/llvm/bin/clang
   export CXX=/opt/homebrew/opt/llvm/bin/clang++
   export LDFLAGS="-L/opt/homebrew/opt/llvm/lib"
   export CPPFLAGS="-I/opt/homebrew/opt/llvm/include"

3. Build project in the same terminal:

   mkdir build
   cd build
   cmake ..
   make

Usage

Note: To ensure the quality of results, the input triangle mesh needs to be of high quality (manifold, closed, free of self-intersections, with evenly sized dense triangles, and without narrow triangles). It is better to preprocess it using TetWild.

We have prepared pre-compiled .exe files in the data folder, along with some input meshes referenced in certain sections of our paper. Below, we provide the commands to run the corresponding offset.

Example Usage

The code provides necessary data files. Assuming the data folder path is <data_folder>, here's an example command:

./3DVer_variable --input <data_folder>/6_freeform/67855_sf.obj --outdir "<data_folder>/6_freeform/" --dis "<data_folder>/6_freeform/chair.txt" --sphere <data_folder>/sphere.obj --diag

Command Format

./3DVer_variable [OPTIONS]

Required Parameters

• --input TEXT Path to the input mesh file

Offset Parameters

• -d FLOAT Offset distance (relative to model size), default: 2%
• --diag Use offset distance relative to model bounding box diagonal
• --dis TEXT User-defined distance file for variable offset distances Format: Each line contains "vertex_id distance" Note: Consider the norm of the gradient
• --inside Perform inside offset instead of outside offset
• --sphere TEXT Input discrete spherical surface file

Output Parameters

• --outdir TEXT Output directory for results
• --poly Output polygon mesh results

Sampling Parameters

• --blue INT Number of blue noise samples, default: 70000
• --centroid Use triangle centroids instead of blue noise sampling (Recommended for dense meshes)
• --slerp INT Number of spherical interpolation steps, default: 10

Feature Preservation

• --corner FLOAT Protection radius for non-smooth regions, default: 0.05
• --sharp Preserve all sharp features in offset
• --diheral FLOAT Dihedral angle threshold (radians) for detecting sharp features, default: 0.2

Optimization Parameters

• --lambda FLOAT Optimization parameter for surface reconstruction, default: 0.01

Performance

• -t INT Number of threads to use, default: 33

Reproducing Paper Results

Note: For the following examples, we assume the main executable has been moved to the data folder. Otherwise, you will need to modify the file paths accordingly.

1_gallery

• Figure 3 (left): .\3DVer_variable.exe --input "./1_gallery/00009875_086229ea796640d29acd68ff_trimesh_010__sf.obj" --outdir "./1_gallery/" --gallery --diag
• Figure 3 (right): .\3DVer_variable.exe --input "./1_gallery/44234_sf.obj" --outdir "./1_gallery/" --gallery --inside

2_robustness

For model 54725, 280279, 99903, fandisk:

• .\3DVer_constant.exe --input "./2_robustness/fandisk.off" -d 0.02 --diag --outdir "./2_robustness/"
• .\3DVer_constant.exe --input "./2_robustness/fandisk.off" -d 0.02 --inside --diag --outdir "./2_robustness/"

For model bunny, beethoven:

• .\3DVer_constant.exe --input "./2_robustness/bunny_highquality.obj" -d 0.02 --diag --centroid --outdir "./2_robustness/"
• .\3DVer_constant.exe --input "./2_robustness/bunny_highquality.obj" -d 0.02 --inside --diag --centroid --outdir "./2_robustness/"

3_comparisons

• 280279_pos: .\3DVer_constant.exe --input "./3_comparisons/213887_sf.obj" --outdir "./3_comparisons/" -d 0.01 --diag
• 280279_neg: .\3DVer_constant.exe --input "./3_comparisons/213887_sf.obj" --outdir "./3_comparisons/" -d 0.008 --inside --diag

4_ablation

kitten (blue noise)

• Blue noise samples
  • .\3DVer_constant.exe --input "./4_ablation/kitten_smooth.obj" -d 0.04 --diag --outdir "./4_ablation/" --blue 35000 --inside
• Centroids
  • .\3DVer_constant.exe --input "./4_ablation/kitten_smooth.obj" -d 0.04 --diag --outdir "./4_ablation/" --centroid --inside

block (change --corner to change $\rho$)

• .\3DVer_constant.exe --input "./4_ablation/block.obj" -d 0.005 --diag --outdir "./4_ablation/" --corner 0.3 --centroid --inside

block (sphere)

• sphere1 (#V=162)

  • .\3DVer_constant.exe --input "./4_ablation/block.obj" -d 0.04 --diag --outdir "./4_ablation/" --sphere "./4_ablation/spheres/sphere1.obj" --slerp 5 --centroid --inside

• sphere2 (#V=2562)

  • .\3DVer_constant.exe --input "./4_ablation/block.obj" -d 0.04 --diag --outdir "./4_ablation/" --sphere "./4_ablation/spheres/sphere2.obj" --slerp 20 --centroid --inside

5_freeform

sharp mode is not robust for some offsets.

• Offset of (A):
  • sharp: .\3DVer_variable.exe --input "./6_freeform/A__sf.obj" --outdir "./6_freeform/" --gallery --sharp --diheral 0.001
  • round: .\3DVer_variable.exe --input "./6_freeform/A__sf.obj" --outdir "./6_freeform/" --gallery
• User-defined input (67855): .\3DVer_variable.exe --input ./6_freeform/67855_sf.obj --outdir "./6_freeform/" --dis "./6_freeform/chair.txt" --diag

View Output Files

All of our output .obj files can be opened with MeshLab. Files ending with _tri represent unoptimized outputs, while those ending with _tri_optim are optimized outputs. You can follow these steps to view our results:

1. Open this file with MeshLab.
2. Select Fill -> Shading -> Face and Fill -> Back-Face -> Double.