We solve algorithmic geometrical problems in real 3-space or the real plane arising from applications in the area of CAD, computer vision, and motion planning. The problems include parallel and central projection problems, shade and cast shadow problems, reconstruction of objects from images, offsets of objects, Voronoi diagrams of a finite families of objects, and collision of moving objects. Our tools are real elimination algorithms implemented in the REDUCE package REDLOG. In many cases the problems can be solved uniformly in unspecified parameters. The power of the method is illustrated by examples many of which have been outside the scope of real elimination methods so far.
Ulrike Peiker, Martin Griebl