PolyChopper: a Polyhedron Splitting Scheme

Abstract

We introduce and implement a novel scheme, called \textit{PolyChopper}, for splitting a convex polyhedron into a finite set of disjoint convex sub-polyhedra. The algorithm cuts the polyhedron with a plane, which can either be prescribed as an external constraint or automatically determined from the inertia tensor. The resulting intersection vertices are then adjusted to control the complexity and quality of the generated elements, introducing additional ``notch wedges'', tetrahedra and pyramids, according to a user-defined quality parameter. Experimental results demonstrate that the proposed approach is robust and consistently produces sub-polyhedra that are both simpler and of higher quality than the original polyhedron. Furthermore, recursively applying the algorithm generates a hierarchy of polyhedral subdivisions with progressively smaller elements, all guaranteed to remain convex and predominantly tetrahedral.