Robust construction of 3-d conforming delaunay meshes using arbitrary-precision arithmetic

Abstract

An algorithm for the construction of 3-D conforming Delaunay tetrahe-dralizations is presented. The boundary of the meshed domain is contained within Voronoï cells of the boundary vertices of the resulting mesh. The algorithm is explained heuristically. It has been implemented. The problem of numerical precision is shown to be a major obstacle to robust implementation of the algorithm. The Automatic Arbitrary-Precision Arithmetic Library is introduced to solve this problem. The resulting program is intended to be applicable to any mathematically correct input. It has performed successfully on a number of test cases, including a known difficult case for tetrahedral meshing. It is available on the Internet. The Arithmetic Library may be useful for resolving numerical precision problems in any application, and as a base for experimenting with new meshing strategies. © 2005 Springer-Verlag Berlin Heidelberg.