Complex conforming Delaunay triangulation

Abstract

A novel algorithm of conforming Delaunay triangulation for curved geometry is presented in the paper. A progress has been made for the problem puzzled Delaunay refinement where curved constraints cannot be accepted as input directly. The algorithm is based on a new sufficient condition for the existence of constraints in triangulation. It requires computing only the intersection between constraints and Voronoi edges or faces instead of the circum-sphere of curved constraint. For the termination of the algorithm when small input angles exist in constraints, a weighted method is applied to ensure that the algorithm can terminate under any input. Some two-dimensional and three-dimensional results are also presented. It is shown that the algorithm has the capability of dealing with both linear and nonlinear constraints in a consistent way, without the need of maintaining triangular meshes on face constraints.