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We present a procedure for computing the coefficients of the expansion of a bivariate polynomial into Bernstein polynomials over subtriangles. These triangles are generated by partitioning the unit triangle. The coefficients are computed directly from the coefficients on the subdivided triangle from the preceding subdivision level. This allows a recursive computation of the coefficients and facilitates...
The problem of finding an enclosure for the range of a bivariate polynomial p over the unit triangle is considered. The polynomial p is expanded into Bernstein polynomials. If p has only real coefficients the coefficients of this expansion, the so-called Bernstein coefficients, provide lower and upper bounds for the range. In the case that p has complex coefficients the convex hull of the Bernstein...