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Delaunay meshes with bounded circumradius to shortest edge length ratio have been proposed in the past for quality meshing. The only poor quality tetrahedra, called slivers, that can occur in such a mesh can be eliminated by the sliver exudation method. This method has been shown to work for periodic point sets, but not with boundaries. Recently a randomized point-placement strategy has been proposed to remove slivers while conforming to a given boundary. In this paper we present a deterministic algorithm for generating a weighted Delaunay mesh which respects the input boundary and has no poor quality tetrahedron including slivers. As in previous work, we assume that no input angle is acute. Our result is achieved by combining the weight pumping method for sliver exudation and the Delaunay refinement method for boundary conformation.
Cheng et al. (Wed,) studied this question.