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.

Optimum Part Build Orientation in Additive Manufacturing for Minimizing Part Errors and Support Structures

“…They also tried to minimize the volume of trapped volumes for convex polyhedrons. An extension of this by Majhi et al (Majhi et al, 1998) includes minimization of degree of stair stepping for any part and geometric formulations for optimized support volumes for simple, non-convex parts. Yang et al (Yang, et al, 2003) have used the difference in area of successive layers for a multi-orientation deposition method to minimize the use of support structures.…”

Fractional programming: The sum-of-ratios case

“…These often occur in layered manufacturing [41,42,54], for instance in material layout and cloth manufacturing [3]. For various examples we refer to the survey by Chen et al [14] and the references therein.…”

Computing An Optimal Hatching Direction In Layered Manufacturing

“…Recently, the problem of computing a good orientation has been considered in the computational geometry community. See [1,2,6,7,8,13,14,15].…”