Subdividing Prismatic Meshes by Cutting Flow

Abstract

This paper is motivated by the problem of subdividing a prismatic mesh to a tetrahedral mesh with prescribed boundary conditions and without inserting Steiner points. We show that this 3D subdivision problem can be modeled as a 2D cutting flow problem. Then we propose a complete solution to the cutting flow problem, covering all possible combinations of base domain topology and boundary condition. We not only provide provable sufficient and necessary conditions for existence of solutions, but also provide linear algorithms to compute a solution whenever there is one.