Construction of Sparse Well-spaced Point Sets for Quality Tetrahedralizations

Summary. We propose a new mesh refinement algorithm for computing quality guaranteed Delaunay triangulations in three dimensions. The refinement relies on new ideas for computing the goodness of the mesh, and a sampling strategy that employs numerically stable Steiner points. We show through experiments that the new algorithm results in sparse well-spaced point sets which in turn leads to tetrahedral meshes with fewer elements than the traditional refinement methods. 1 Introduction We consider the following three dimensional geometric problem: Problem 1. [Quality Steiner Triangulation] Compute a small size tri-angulation of a given three dimensional domain such that all the tetrahedra in the triangulation are of good quality. The quality constraint is motivated by the numerical methods used in manyengineering applications. Among various criteria, the following two are widel