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We develop a method for interpolating scattered data on sphere-like surfaces based on a local triangular patch which is constructed from a blend of certain spherical Bernstein-Bkzier polynomials introduced recently by Alfeld, Neamtu and Schumaker (I 996). The method produces a C' 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 C2doi:10.1016/0377-0427(96)00041-6 fatcat:tbharweluvaz5obgcb2zbullji