Support Function Representation for Curvature Dependent Surface Sampling

Abstract

In many applications it is required to have a curvature-dependent surface sampling, based on a local shape analysis. In this work we show how this can be achieved by using the support function (SF) representation of a surface. This representation, a classical tool in Convex Geometry, has been recently considered in CAD problems for computing surface offsets and for analyzing curvatures. Starting from the observation that triangular Bézier spline surfaces have quite simple support functions, we approximate any given free-form surface by a quadratic triangular Bézier spline surface. Then the corresponding approximate SF representation can be efficiently exploited to produce a curvature dependent sampling of the approximated surface.