WIAS Preprint No. 1329, (2008)

The existence of triangulations of non-convex polyhedra without new vertices


Authors

  • Si, Hang

2010 Mathematics Subject Classification

  • 52B55 65D18

Keywords

  • non-convex polyhedron, regular subdivision, triangulation, Steiner points

DOI

10.20347/WIAS.PREPRINT.1329

Abstract

It is well known that a simple three-dimensional non-convex polyhedron may not be triangulated without using new vertices (so-called it Steiner points). In this paper, we prove a condition that guarantees the existence of a triangulation of a non-convex polyhedron (of any dimension) without Steiner points. We briefly discuss algorithms for efficiently triangulating three-dimensional polyhedra.

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