A computing strategy for applications involving offsets, sweeps, and Minkowski operations

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 be difficu lt by many. This article argues that such computations may be easy if (1) t hey are cast in specific application contexts, and (2) relevant mathematica l definitions are discretized and implemented directly. The argument is bas ed on 10 years of research on a range of motional, process-modeling, and vi sualization problems that involved offsetting, sweeping, and M-ops; the sol ution paradigm common to all was direct approximation of mathematical defin itions, 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 han d, and do that as directly as possible. (C) 1999 Elsevier Science Ltd. All rights reserved.