RATIONAL PATCHES ON QUADRIC SURFACES

The paper discusses rational curve segments and surface patches on qua dric surfaces. Detailed constructions of rational Bezier patches from given boundaries on a unit sphere and on a hyperbolic paraboloid are p resented based on a generalization of the stereographic projection. Th e method is applied to interpolation with rational curves on quadrics. The results are extended to rational B-spline representations by disc ussion of products of B-spline functions. Finally, the generalization of the constructions to arbitrary nondegenerated quadric surfaces is o utlined.