Abstract
Using the concept of a symmetric recursive algorithm, we construct a new patch representation for bivariate polynomials: the B-patch. B-patches share many properties with B-spline segments: they are characterized by their control points and by a three-parameter family of knots. If the knots in each family coincide, we obtain the Bézier representation of a bivariate polynomial over a triangle. Therefore B-patches are a generalization of Bézier patches. B-patches have a de Boor-like evaluation algorithm, and, as in the case of B-spline curves, the control points of a B-patch can be expressed by simply inserting a sequence of knots into the corresponding polar form. In particular, this implies linear independence of the blending functions. B-patches can be joined smoothly and they have an algorithm for knot insertion that is completely similar to Boehm's algorithm for curves.
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Communicated by Carl de Boor.
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Seidel, HP. Symmetric recursive algorithms for surfaces: B-patches and the de boor algorithm for polynomials over triangles. Constr. Approx 7, 257–279 (1991). https://doi.org/10.1007/BF01888157
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DOI: https://doi.org/10.1007/BF01888157