Delaunay triangulations of polyhedral surfaces, a discrete Laplace-Beltrami operator and applications
Alexander I. Bobenko · 2008
A simplicial surface provides its carrier with a natural triangulation whose vertex set includes the cone points and the corners of the boundary. However, this triangulation is not intrinsically distinguished from other triangulations with the same vertex set, it is not preserved under isometric deformations of the surface. Delaunay tessellations of polyhedral surfaces are defined intrinsically in terms of empty discs on surfaces. The edges of Delaunay tessellations are geodesics on the original polyhedral surface (and not necessarily straight edges in the 3-space). For any polyhedral surface there exists a unique Delaunay tessellation. It is not necessarily strongly regular, i.e. the intersection of two closed cells may not be a single closed cell.