Support Function Representation for Curvature Dependent Surface Sampling

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 B´ezier spline surfaces have quite simple support functions, we approximate any given free-form surface by a quadratic triangular B´ezier spline surface. Then the corresponding approximate SF representation can be efficiently exploited to produce a curvature dependent sampling of the approximated surface.