Convexity Preserving Interpolatory Subdivision Schemes

摘要

The authors construct local subdivison schemes which interpolate functionalunivariate data and which preserve convexity. The resulting limiting function of these schemes is continuous and convex for arbitrary convex data. One unique subdivision scheme is constructed that generates a limiting function that is convex and continuously differentiable for strictly convex data. The approximation order of this scheme is four. Some generalizations, such as tension control and piecewise convexity preservation, are briefly discussed.