Bezier normal vector surface and its applications

One of the essential properties of a surface is its normal vector. Many applications, i.e., surface rendering, surface-surface intersection, and offset surface generation, require normal vectors. A normal vector at a point on a tensor product surface is usually obtained by taking a cross product of the two partial derivatives. The paper discusses a Bezier normal vector surface which is a locus of an unnormalized cross product normal vector. It also explains several applications of the Bezier normal vector surface, such as detection and computation of degenerate normal vectors which cannot be calculated by the cross product, and an algorithm to find all critical points which are key points to solve the problems on surface-surface intersection.