Tiling the sphere with rational bezier patches

One of the fundamental problems in Computer Aided Geometric Design (CAGD) is the representation of shapes. Two representation schemes that have proved useful for modeling free-form shapes are parametric Bezier and B-spline surfaces [2,8]. In fact the Bezier patch is a special case of the B-spline surface. Therefore remarks below about B-spline surfaces apply as well to Bezier patches. For some modeling systems the B-spline or Bezier representation is the base upon which other shape descriptions rest. For example, the Unisurf system [2] uses Bezier patches, and the Alpha_l system relies on B-splines. For such a modeling system it is necessary to provide adequate representation of simple shapes (e.g. spheres, ellipsoids, and cones) in terms of the more general scheme. One would like the underlying representation to be exact, with accuracy limited only by the numeric representation within the computer, not by the choice of representation. Furthermore, this representation should avoid degeneracies that would impair the robustness of the modeling system.