Constrained Tetrahedral Subdivision for Arbitrary Polygonal Prismatic Meshes

摘要

We consider the tetrahedral subdivision problem for a polygonal prismatic mesh with prescribed boundary constraints and without Steiner points. We prove the necessary and sufficient conditions for the existence of solutions, and also provide algorithms to compute such a constrained subdivision if there exists one. The result applies to arbitrary k-gonal prismatic meshes and even mixed prismatic meshes, allowing arbitrary topology for the base mesh and arbitrary constraints on the boundary.