Corentin Dumery,
François Protais,
Sébastien Mestrallet,
Christophe Bourcier,
Franck Ledoux
Feel free to reach out if you have questions or suggestions :)
Polycube-maps are used as base-complexes in various fields of computational geometry, including the generation of regular all-hexahedral meshes free of internal singularities. However, the strict alignment constraints behind polycube-based methods make their computation challenging for CAD models used in numerical simulation via Finite Element Method (FEM). We propose a novel approach based on an evolutionary algorithm to robustly compute polycube-maps in this context.
We address the labeling problem, which aims to precompute polycube alignment by assigning one of the base axes to each boundary face on the input. Previous research has described ways to initialize and improve a labeling via greedy local fixes. However, such algorithms lack robustness and often converge to inaccurate solutions for complex geometries. Our proposed framework alleviates this issue by embedding labeling operations in an evolutionary heuristic, defining fitness, crossover, and mutations in the context of labeling optimization. We evaluate our method on a thousand smooth and CAD meshes, showing Evocube converges to valid labelings on a wide range of shapes. The limitations of our method are also discussed thoroughly.
git clone https://github.com/LIHPC-Computational-Geometry/evocube.git
git submodule update --init --recursive
mkdir build
cd build
cmake ..
make -j4 evolabel
To compute a labeling on a triangle mesh and visualize it, simply run:
./evolabel path/to/boundary.obj
Paste for a quick test: ./evolabel ../data/moai.obj
To go further, advanced tools used in our paper are showcased in init_from_folder.cpp.