Complex conforming Delaunay triangulation

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.