Publication Detail

Computational of Stationary Points of Distance Functions

Jingfang Zhou, Evan C. Sherbrooke, Nicholas Patrikalakis
16 pp.
MITSG 94-02J

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 polynomial equations with n variables expressed in the tensor product Bernstein basis. The solution method is based on subdivsion relying on the convex hull property 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.

type: Technical reports

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Parent Project

Project No.: 1991-RA-4-PTI
Title: Geometry Data Representation, Exchange and Inspection IV