SurfaceVoronoi

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