De Boor’s algorithm is a generalization of de Casteljau’s and univariate B-splines are a generalization of Bernstein polynomials. Analogously, it is possible to generalize de Casteljau’s algorithm for multivariate polynomials to multivariate splines. The underlying basis functions of this generalized algorithm are simplex splines forming a partition of unity. These simplex splines are proper generalizations of the univariate B-splines and many properties of the univariate B-splines also hold for these multivariate simplex splines.
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