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 minimizing 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 to convex polyhedra only. Algorithms are also given for optimizing supports for non-convex, simple polygons. The techniques used include construction and searching of certain arrangements on the sphere, 3D convex hulls, halfplane range searching, ray-shooting, visibility, and constrained optimization.

JM's and RJ's work supported, in part, by a Grant-in-Aid of Research from the Graduate School of the Univ. of Minnesota. MS's work done, in part, while at the Dept. of Computer Science, King's College London, UK. PG's work done, in part, while at MPI-Informatik, Saarbrücken, Germany and at the Univ. of Minnesota.