METHODS AND APPARATA FOR SHAPING MOVING GEOMETRIC SHAPES

Disclosed are methods for determining the largest subset of points that remains within a set of points S (i.e., shape S) when S is subjected to a motion M. These methods, which are generally designated herein as unsweep (or formalistically unsweep(S,M)), can be implemented (preferably by computer) for a variety of practical purposes, for example mechanical parts design. In this instance, simply by knowing the motion to be experienced by a part and the envelope wherein the part must fit during motion, unsweep can define the largest part that fits within the envelope according to the given motion. While direct part shape output is obtained, no part shape needs to be proposed beforehand, and thus the design process is no longer an iterative process of proposing shapes and correcting them in the case of interference. Further, unsweep is related to the known sweep function and can be used to obtain sweeps as well as unsweeps.