Computing the width of a three-dimensional point set: an experimental study

We describe a robust, exact, and efficient implementation of an algorithm that computes the width of a three-dimensional point set. The algorithm is based on efficient solutions to problems that are at the heart of computational geometry: three-dimensional convex hulls, point location in planar graphs, and computing intersections between line segments. The latter two problems have to be solved for planar graphs and segments on the unit sphere, rather than in the two-dimensional plane. The implementation is based on LEDA, and the geometric objects are represented using exact rational arithmetic. (orig.)SIGLEAvailable from TIB Hannover: RR 4485(1998,18) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Protecting facets in layered manufacturing

In Layered Manufacturing, a three-dimensional polyhedral object is built by slicing its (virtual) CAD model, and manufacturing the slices successively. During this process, support structures are used to prop up overhangs. An important issue is choosing the build direction, as it affects, among other things, the location of support structures on the part, which in turn impacts process speed and part finish. Algorithms are given here that (i) compute a description of all build directions for which a prescribed facet is not in contact with supports, and (ii) compute a description of all build directions for which the total area of all facets that are not in contact with supports is minimum. The first algorithm is worst-case optimal. A simplified version of the first algorithm has been implemented, and test results on models obtained form industry are given. (orig.)SIGLEAvailable from TIB Hannover: RR 4485(1999,10) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman