On the smoothness of real-valued functions generated by subdivision schemes using nonlinear binary averaging

Our main result is that two point interpolatory subdivision schemes using C nonlinear averaging rules on pairs of real numbers generate real-valued functions that are also C. The significance of this result is the following consequence: Suppose that S is a subdivision algorithm operating on sequences of real numbers using linear binary averaging that generates C real-valued functions and S is the same subdivision procedure where linear binary averaging is replaced everywhere in the algorithm by a C nonlinear binary averaging rule on pairs of real numbers; then the functions generated by the nonlinear subdivision scheme S are C , where k = min(m, n). Classification: CCScat{I.3.5}{Computer Graphics}{Curve, surface, and solid representations}