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Computing signed distances between free-form objects

Given two sculptured objects, described by a collection of rational Bezier patches, we propose an algorithm that provides the distance between them if the objects are not intersecting, or a measure of penetration otherwise. The algorithm extends the upper-lower bound subdivision approach to the computation of the nearest points by considering the relative orientations between the subdivided patches. All required geometric constructions can be described as rational Bezier patches so that their control points can be precomputed from those of the original patches. Additional operations have been designed to exhibit linear complexity with the total number of involved control points.