# A Seed Placement Strategy for Conforming Voronoi Meshing

Ahmed Abdelkader,
Chandrajit Bajaj,
Mohamed Ebeida,
Scott Mitchell

July 2017

### Abstract

We show how to place a set of seed points such that a given piecewise linear complex is the union of some faces in the resulting Voronoi diagram. The seeds are placed on sufficiently small spheres centered at input vertices and are arranged into little circles around each half-edge where every seed is mirrored across the associated triangle. The Voronoi faces common to the seeds of such arrangements yield a mesh conforming to the input complex. If the input contains sharp angles, then additional seeds are needed, analogous to nonobtuse refinement. Finally, we propose local optimizations to reduce the number of seeds and output facets.

Publication

In *Canadian Conference on Computational Geometry*