Computing the Distance Between Two Surfaces via Line Geometry

This paper presents an algorithm for computing the distance between two free-form surfaces. Using line geometry, the distance computation is reformulated as a simple instance of a surface-surface intersection problem, which leads to a low-dimensional root finding in a system of equations. This approach produces an efficient algorithm for computing the distance between two ellipsoids, where the problem is reduced to finding a specific solution in a system of two equations in two variables. Similar algorithms can be designed for computing the distance between an ellipsoid and a simple surface (such as cylinder, cone, and torus). In an experimental implementation (on a 500 MHz Windows PC), the distance between two ellipsoids was computed in less than 0.3 msec on average; and the distance between an ellipsoid and a simple convex surface was computed in less than 0.15 msec on average.