Arbitrarily precise computation of Gauss maps and visibility sets for freeform surfaces

Abstract

The need to compute visibility and accessibility surfaces occurs in a broad range of applications from computer aided design and manufacturing to computer graphics and vision. Surface-surface intersection is an essential task in modeling systems that support boolean operations. Recently, Gauss maps and visibility sets were shown [3, 4, 20, 21] to be helpful in robustly solving the above problems. This paper presents a symbolic based method to both compute and exploit the Gauss map of a freeform surface or a model consists of several, possibly trimmed, freeform surfaces. Unlike other approaches to the computation of the Gauss map, the method presented here can be made arbitrarily precise for piecewise polynomial and rational surfaces. The Gauss map is then employed to compute the set of views from which a freeform surface is completely locally visible.