COMPUTATION OF STATIONARY-POINTS OF DISTANCE FUNCTIONS

This paper presents an algorithm for computation of the stationary points of the squared distance functions between two point sets. One point set consists of a single space point, a rational B-spline curve, or a rational B-spline surface. The problem is reformulated in terms of solution of n poly-nomial equations with n variables expressed in the tensor product Bernstein basis. The solution method is based on subdivision relying on the convex hull propel ty of the n-dimensional Bernstein basis and minimization techniques. We also cover classification of the stationary points of these distance functions, and include a method for tracing curves of stationary points in case the solution set is not zero-dimensional. The distance computation problem is shown to be equivalent to the geometrically intuitive problem of computing collinear normal points. Finally, examples illustrate the applicability of the method