8.2 Stationary points of curvature of free-form parametric surfaces

For simplicity, the underlying surface is assumed to be an integral Bézier patch (polynomial patch) defined over of degrees and in and , respectively. Extension to rational Bézier patch and rational B-spline patch, although tedious does not present conceptual difficulties. We also assume that the surface is regular. In the rest of this chapter we employ convention (b) (see Fig. 3.7 (b) and Table 3.2) such that the normal curvature of a surface at point is positive when the center of curvature is on the opposite direction of the unit normal vector of the surface. More details for obtaining stationary points of curvature of free-form parametric surfaces are given in [255].