Code of SIGGRAPH Asia 2022 Paper SurfaceVoronoi: Efficiently Computing Voronoi Diagrams over Mesh Surfaces with Arbitrary Distance Solvers.

Abs: In this paper, we propose to compute Voronoi diagrams over mesh surfaces driven by an arbitrary geodesic distance solver, assuming that the input is a triangle mesh as well as a collection of sites $\mathbf{P}={p_i}_{i=1}^m$ on the surface. We propose two key techniques to solve this problem. First, as the partition is determined by minimizing the $m$ distance fields, each of which rooted at a source site,we suggest keeping one or more distance triples, for each triangle, that may help determine the Voronoi bisectors when one uses a mark-and-sweep geodesic algorithm to predict the multi-source distance field. Second, rather than keep the distance itself at a mesh vertex, we use the squared distance to characterize the linear change of distance field restricted in a triangle, which is proved to induce an exact VD when the base surface reduces to a planar triangle mesh.Specially, our algorithm also supports the Euclidean distance, which can handle thin-sheet models (e.g. leaf) and runs fasterthan the traditional restricted Voronoi diagram (RVD) algorithm. It is very extensible to deal with various variants of surface-based Voronoi diagrams including(1) surface-based power diagram, (2) constrained Voronoi diagram with curve-type breaklines,and (3) curve-type generators. We conduct extensive experimental results to validate the ability to approximate the exact VD in different distance-driven scenarios.

Paper link: https://arxiv.org/abs/2212.09029 Doi: https://dl.acm.org/doi/abs/10.1145/3550454.3555453

• CGAL

• Eigen3

• Boost

Before using the core calculation code 'GVD_RVD\GVD_RVD.hpp', you need to compile the lib file for 'Model3D' and 'Geodesic'. These codes are given together in this repository.

At the same time, we have also given two compiled lib files in the 'lib' folder. If you want to use these two lib files, please run them in 'Visual Studio 2022 Release x64' mode.

'RVD_RVD/main.cpp' shows how to use the surfaceVoronoi calculation.

• Windows 10
• Visual Studio 2022
• AMD Ryzen 5950X
• 32GB Momery

If you use our code, please consider citing our work:

@article{xin2022surfacevoronoi,
  title={SurfaceVoronoi: Efficiently Computing Voronoi Diagrams Over Mesh Surfaces with Arbitrary Distance Solvers},
  author={Xin, Shiqing and Wang, Pengfei and Xu, Rui and Yan, Dongming and Chen, Shuangmin and Wang, Wenping and Zhang, Caiming and Tu, Changhe},
  journal={ACM Transactions on Graphics (TOG)},
  volume={41},
  number={6},
  pages={1--12},
  year={2022},
  booktitle = {ACM SIGGRAPH Asia 2022 Papers},
  publisher={ACM New York, NY, USA}
}