Bézier nets, convexity and subdivision on higher-dimensional simplices Original Research Article

Explicit necessary and sufficient conditions for the convexity of a multivariate Bézier 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 Bézier points on a regular subdivision of a simplex in higher dimensions. This subdivision process preserves the convexity of the Bézier net.