Parting directions for mould and die design

Abstract

On the basis, of the condition for demouldability, two levels of visibility, complete and partial visibility, are defined. The viewing directions from which a surface is completely visible can be represented as a convex region on the unit sphere called the visibility map of the surface. Algorithms are given for dividing a given object into pockets, for which visibility and demouldability can be determined independently, for constructing visibility maps, and for selecting an optimal pair of parting directions for a mould that minimizes the number of cores. An example illustrates the algorithms.

Geometric algorithms for automated design of multi-piece permanent molds

“…Definition [1]: If a surface S on an object O is completely and globally ray-accessible from a direction d, the mold face forming S can be translated to infinity in the direction d, without intersecting the interior of O.…”

“…All the facets on the part other than convex-hull facets are called non-convex-hull facets. Connected sets of non-convex-hull facets form concave regions (pockets in [1]). …”

“…The global accessibility cone of a convex-hull facet is a hemisphere generated using the direction normal of the facet as its pole [1].…”

“…A non-convex-hull facet can be blocked only by a non-convex-hull facet present in the same concave region [1]. A ray emanating from a point in a concave region will either intersect a facet in the same concave region or go to infinity.…”

The Min-Max Voronoi Diagram of Polygons and Applications in VLSI Manufacturing

“…clockwise) list of its vertices. An alternative representation can be obtained by the Gaussian Map [3] of S, for short GMap(S), onto the unit circle. In the Gaussian Map every mM-hull edge e i is mapped to a point ν(e i ) on the circumference of a unit circle K o as obtained by the outward pointing unit normal.…”