Geometric computing and uniform grid technique

Abstract

If computational geometry should play an important role in the professional environment (e.g. graphics and robotics), the data structures it advocates should be readily implemented and the algorithms efficient. In the paper, the uniform grid and a diverse set of geometric algorithms that are all based on it, are reviewed. The technique, invented by the second author, is a flat, and thus non-hierarchical, grid whose resolution adapts to the data. It is especially suitable for telling efficiently which pairs of a large number of short edges intersect. Several of the algorithms presented here exist as working programs (among which is a visible surface program for polyhedra) and can handle large data sets (i.e. many thousands of geometric objects). Furthermore, the uniform grid is appropriate for parallel processing; the parallel implementation presented gives very good speed-up results. © 1989.