Algebraic Methods for Geometric Reasoning
Bruno Buchberger, George Ernest Collins, Bernhard Kutzler · Annual Review of Computer Science · 1988
In recent years, it has been widely recognized that geometric reasoning is one of the most promising areas of computer science. An extrapolation of market trends shows that worldwide the CAD/CAM/CAE industry, which is heavily based on geometric reasoning, expects an expansion from $5 billion in 1985 to $20 billion in 1990 and, hence, is one of the fastest growing industries. This is the practical reason for the challenge inherent in geometric reasoning. On the other hand, the algorithmic problems occurring in geometric reasoning have also an enormous scientific appeal. In the past few years, geometric reasoning problems have provoked a whole spectrum of new algorithmic techniques. Still, many of the more advanced geometric reasoning problems are far from a satisfactory solu tion, and the pertinent mathematical investigations have hardly scratched the surface. Thus, in the immediate future, we expect to see an enormous expansion of basic and applied research in geometric reasoning. The present survey reviews recent algebraic approaches to the algo-