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The Bernstein–Fourier algorithm for the evaluation of polynomial curves is extended for the evaluation of polynomial tensor product surfaces. Under a natural hypothesis, accurate evaluation of Bézier curves and surfaces through several algorithms is discussed. Numerical experiments comparing the accuracy of the corresponding Horner, de Casteljau, VS and Bernstein–Fourier algorithms are presented. [ABSTRACT FROM AUTHOR]

Abstract: Given four polynomial or rational Bézier curves defining a curvilinear rectangle, we consider the problem of constructing polynomial or rational tensor-product Bézier patches bounded by these curves, such that they are geodesics of the constructed surface. The existence conditions and interpolation scheme, developed in a general context in earlier studies, are adapted herein to ensure that the geodesic-bounded surface patches are compatible with the usual polynomial/rational representation schemes of CAD systems. Precise conditions for four Bézier curves to constitute geodesic boundaries of a polynomial or rational surface patch are identified, and an interpolation scheme for the construction of such surfaces is presented when these conditions are satisfied. The method is illustrated with several computed examples. [Copyright &y& Elsevier]