Abstract
Bivariate polynomials over triangular domains are widely in use for the definition of surfaces that are continuously differentiable across a set of triangles. A description is given of how explicit formulas for the coefficients of bivariate nonic polynomials can be found with the help of a computer algebra system. A linear system with 55 equations and 45 nonzero right hand sides must be solved algebraically. The interpolant is twice differentiable across triangle sides and based on function values and partial derivatives up to fourth order at the nodes. Horner's scheme for evaluating polynomials can be applied directly, leading to optimal efficiency during the evaluation phase (54 additions and multiplications for one point). Starting with transformed nodal data, the calculation of one set of coefficients takes about 350 additions, the same number of multiplications, and 30 divisions.— Author's Abstract
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