Conforming Weighted Delaunay Triangulations

Input surface mesh	Result surface mesh	Result tetrahedral mesh (shrink: 0.3)
Result tetrahedral mesh (in-out)	Result tetrahedral mesh (wireframe)	Result tetrahedral mesh (clipping)

This repo is a rearrangement of the code for the work "Conforming Weighted Delaunay Triangulations" by Marc Alexa. The original reference implementation can be found at [source code].

If you use this code in your research, please cite the original work:

@article{10.1145/3414685.3417776,
	author = {Alexa, Marc},
	title = {Conforming weighted delaunay triangulations},
	year = {2020},
	issue_date = {December 2020},
	publisher = {Association for Computing Machinery},
	address = {New York, NY, USA},
	volume = {39},
	number = {6},
	issn = {0730-0301},
	url = {https://doi.org/10.1145/3414685.3417776},
	doi = {10.1145/3414685.3417776},
	journal = {ACM Trans. Graph.},
	month = nov,
	articleno = {248},
	numpages = {16},
	keywords = {simplicial meshes, conforming meshes}
}

💡 What did I do?

• Improved code organization
• Enhanced readability
• Updated CMake build configurations
• Added command line applications

🔗 Requirements / dependencies

• Eigen (version >= 3.4)
• Boost (version >= 1.78.0)
• CGAL (version >= 5.6)
• Gurobi
• libigl
• CLI11 (already included)

Note

The gcc version needs to be compatible with the boost version. It seems that gcc 15.1 is not compatible with boost 1.78.0... 🤔

🏁 Getting started

git clone https://github.com/Canjia-Huang/CWDT.git

🔨 Build

mkdir build
cd build
cmake ..
make

💻 Usage

./CWDT [OPTIONS] input_surface_mesh_path

Options (use --help for more details):

OPTIONS:
  -h,     --help              Print this help message and exit 
          --ns INT            Maximum number of splits (default: 100). 
          --nr INT            Maximum number of rounds (default: 100). 
          --hf FLOAT          Height factor (default: 1.0). 
          --wf FLOAT          Weight factor (default: 1.0). 
          --tol FLOAT         Minimum tolerance (default: 1e-9). 
          --np                Not utilize the winding number to eliminate external tetrahedra 
                              (default: false). 
          --pthr FLOAT        Threshold during the peel operation (default: 0.5), where 
                              tetrahedra with a winding number of their centroids less than 
                              this thr are identified as external. 
          --shrink FLOAT      The shrink factor of each tetrahedron in the result used for 
                              visualization (default: 0.3). 

Example

./CWDT ../data/spot_quadrangulated.obj

The following result files will be generated in the directory of the input surface mesh path upon successful execution:

• result_surface_mesh.off - the surface mesh of the input surface mesh in the resulting tetrahedral mesh
• result_weighted_surface_mesh.off - similar as "result_surface_mesh.off", each vertex contains a weight
• result_tets.obj - the file used for visualizating the resulting tetrahedral mesh
• result_tets.mesh - the resulting tetrahedral mesh (can be opened with Gmsh), in which the tetrahedra inside have a label of "1", while the outside tetrahedra have a label of "2"