Computing strategy for applications involving offsets, sweeps, and Minkowski operations

Abstract

Offsets, sweeps, and Minkowski operations (M-ops) are easy to define in the existential (representation-free) mathematics of point sets, but computing `values for offset, swept, and M-summed entities is thought to he difficult by many. This article argues that such computations may be easy if (1) they are cast in specific application contexts, and (2) relevant mathematical definitions are discretized and implemented directly. The argument is based on 10 years of research on a range of motional, process-modeling, and visualization problems that involved offsetting, sweeping, and M-ops; the solution paradigm common to all was direct approximation of mathematical definitions, using ray representations and parallel computation as primary media. This article presents no new results; it merely summarizes a body of well documented research that illustrates an approach to problem solving, whose primary tenets are: compute only what you need to solve the problem at hand, and do that as directly as possible.