Distance Calculation Between a Point and a NURBS Surface

In this paper, we consider the computation of an Euclidean shortest path between a point and a modelled curve or surface in three-dimensional space, which is one of the fundamental problems in robotics and many other areas. A new accurate algorithm for the distance-calculation between a point and a NURBS curve and its extension to the case of a point and a NURBS surface is presented. The algorithm consists of two steps, and is crucially based on appropriate projections and subdivision techniques. To solve a nonlinear polynomial system derived from the classical formulation of the distance problem, the well-known Newton-type algorithms or subdivision-based techniques first considered by Sherbrooke and Patrikalakis are used. Their modifications in conjunction with a low subdivision depth in the presented algorithms yield a verified enclosure of the solution. Presented at Intl. Conference on Curves and Surfaces (4th). Held in St. Malo, France, 1-7 Jul 1999. Publ. in Proceedings, v1, Curve and Surface Design, p55-62. This article is from ADA399461 International Conference on Curves and Surfaces (4th), Saint-Malo, France, 1-7 July 1999. Proceedings, Volume 1. Curve and Surface Design