EVALUATION AND APPROXIMATE EVALUATION OF THE MULTIVARIATE BERNSTEIN-BEZIER FORM ON A REGULARLY PARTITIONED SIMPLEX

Polynomials of total degree d in m variables have a geometrically intu itive representation in the Bernstein-Bezier form defined over an m-di mensional simplex. The two algorithms given in this article evaluate t he Bernstein-Bezier form on a large number of points corresponding to a regular partition of the simplicial domain. The first algorithm is a n adaptation of isoparametric evaluation. The second is a subdivision algorithm. In contrast to de Casteljau's algorithm, both algorithms ha ve a cost of evaluation per point that is linear in the degree regardl ess of the number of variables. To demonstrate practicality, implement ations of both algorithms on a triangular domain are compared with gen eric implementations of six algorithms in the literature.