Connected and Manifold Sierpinski Polyhedra

Abstract

In this paper, we present a subdivision-inspired scheme to construct generalized Sierpinski polyhedron. Unlike usual Sierpinski polyhedra construction schemes, which create either an infinite set of disconnected tetrahedra or a non-manifold polyhedron, our robust construction scheme creates one connected and manifold polyhedron. Moreover, unlike the original schemes, this new scheme can be applied to any manifold polyhedral mesh and based on the shape of this initial polyhedra a large variety of Sierpinski polyhedra can be obtained.Our basic scheme can be viewed as applying simplest subdivision scheme [23] to an input polyhedron, but retaining old vertices. The porous structure is then obtained by removing the refined facets of the simplest subdivision.