On Some Geometric Optimization Problems in Layered Manufacturing

Abstract

Efficient geometric algorithms are given for optimization problems arising in layered manufacturing, where a 3D object is built by slicing its CAD model into layers and manufacturing the layers successively. The problems considered include minimi7,ing the degree of stair-stepping on the surfaces of the manufactured object, minimizing the volume of the so-called support structures used, and minimizing the contact area between the supports and the manufactured object- all of which are factors that affect the speed and accuracy of the process. The stair-step minimization algorithm is valid for any polyhedron, while the support minimization algorithms are applicable t.o convex polyhedra only. Algorithms arc a1so given for optimizing supports for non-convex, simple polygons. The techniques used to obtain these results include construction and searching of certain arrangements on the sphere, 3D convex hulls, balfplanc range searching, ray-shooting, visibility, and constrained optimization.