Robust Geometric Computations for Vision and Robotics

A new technique, the hidden variable method, is described for the creation of robust geometric algorithms: algorithms which can be implemented with absolute reliability using rounded nite precision arithmetic. The speciic application given here is an algorithm for computing arrangements of line segments in two dimensions: determining how a set of line segments subdivides the plane into vertices, line segments, and polygons. Using rubber band curves, an implicit representation for the line segments, the algorithm can generate an arrangement with N bits of accuracy using rounded arithmetic with just N + 6 bits of precision. Applications of this algorithm to problems in vision and robotics are discussed.