Symmetric algorithms for curves and surfaces

Hans-Peter Seidel

doi:10.1117/12.19727

Abstract

Using the concept of synmietric algorithms, 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 3-parameter family of knots. If the knots in each family coincide, we obtain the Bezier representation of a hivariate polynomial over a triangle. Therefore B-patches are a generalization of Bezier 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 simpy inserting a sequence of knots into the corresponding polar form. B-patches can be joined smoothly and they have an algorithm for knot insertion that is completely similar to Boehm's algorithm for curves.

Citation Download Citation

Hans-Peter Seidel, Hans-Peter Seidel, } "Symmetric algorithms for curves and surfaces", Proc. SPIE 1251, Curves and Surfaces in Computer Vision and Graphics, (1 August 1990); doi: 10.1117/12.19727; https://doi.org/10.1117/12.19727

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