Computing a flattest, undercut-free parting line for a convex polyhedron, with application to mold design

Abstract

A parting line for a convex polyhedron, P, is a closed curve on the surface of P. It defines the two pieces of P for which mold-halves must be made. An undercut-free parting line is one which does not create recesses or projections in P and thus allows easy de-molding of P. Computing an undercut-free parting line that is as flat as possible is an important problem in mold design. In this paper, an O(n2)-time algorithm is presented to compute such a line, according to a prescribed flatness criterion, where n is the number of vertices in P.