A new interpolatory subdivision zscheme for surface design is presented. The new scheme is designed for a general triangulation of control points and has a tension parameter that provides design flexibility.The resulting limit surface is C' for a specified range of the tension parameter, with a few exceptions. Application of the butterfly scheme and the role of the tension parameter are demonstrated by several examples.

No abstract

The paper analyses the convergence of sequences of control polygons produced by a binary subdivision scheme of the form . 0,1,2,

No abstract

An explicit representation of a C 1 piecewise rational cubic function is developed which can be used to solve the problem of shape preserving interpolation.It is shown that the interpolation method can be applied to convex and/or monotonic sets of data and an error analysis of the interpolant is given. The scheme includes, as a special case, the monotonic rational quadratic interpolant considered by the authors in [1] and [5]. However, the requirement of convexity necessitates the generalization to the rational cubic form employed here.

No abstract

No abstract

No abstract