BEZIER NETS, CONVEXITY AND SUBDIVISION ON HIGHER-DIMENSIONAL SIMPLICES

摘要

Explicit necessary and sufficient conditions for the convexity of a multivariate Bezier net are given. These are used to show that the Bernstein polynomial of a function on a simplex preserves a strong form of convexity, that takes the generating directions of the simplex into account. Moreover, an efficient algorithm is presented for computing the Bezier points on a regular subdivision of a simplex in higher dimensions. This subdivision process preserves the convexity of the Bezier net. [References: 13]