Hybrid Bézier patches on sphere-like surfaces

We develop a method for interpolating scattered data on sphere-like based on a local triangular patch which is constructed from a blend of certain spherical Bernstein-Bézier polynomials introduced recently by Alfeld, Neamtu and Schumaker (1996). The method produces a C1 interpolant which matches values and derivatives, and is a natural analog of a planar method of Foley and Opitz (1992) and Goodman and Said (1991). We also show how the same approach can be used to construct a C2 quintic hybrid patch matching second derivative information as an analog of a planar method of Chang and Said (1995).