Abstract
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 economical computation of bounds for the range of a bivariate polynomial over a given triangle.
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Hungerbühler, R., Garloff, J. Computation of the Bernstein Coefficients on Subdivided Triangles. Reliable Computing 6, 115–121 (2000). https://doi.org/10.1023/A:1009909004274
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DOI: https://doi.org/10.1023/A:1009909004274