Abstract
Polynomials of the total degree d in m variables have a geometrically intuitive representation in the Bernstein-Be´zier form defined over an m -dimensional simplex. The two algorithms given in this article evaluate the Bernstein-Be´zier form on a large number of points corresponding to a regular partition of the simplicial domain. The first algorithm is an adaptation of isoparametric evaluation. The second is a subdivision algorithm. In contrast to de Casteljau's algorithm, both algorithms have a cost of evaluation per point that is linear in the degree regardless of the number of variables. To demonstrate practicality, implementations of both algorithms on a triangular domain are compared with generic implementations of six algorithms in the literature.
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