Degree reduction of Bezier simplexes

Suresh Kumar Lodha; Joe D. Warren

doi:10.1117/12.131731

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1 November 1992 Degree reduction of Bezier simplexes

Suresh Kumar Lodha, Joe D. Warren

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Proceedings Volume 1830, Curves and Surfaces in Computer Vision and Graphics III; (1992) https://doi.org/10.1117/12.131731
Event: Applications in Optical Science and Engineering, 1992, Boston, MA, United States

Abstract

This work describes a degree reduction method for Bezier simplexes with the following properties: (1) Symmetry: The degree reduction method is symmetric with respect to the corner points of the Bezier simplex. (2) Restriction: The degree reduction method restricted to the boundary of a Bezier simplex yields the same result as the boundary of the degree-reduced Bezier simplex. (3) Interpolation: The degree-reduced simplex of degree e interpolates the value and the first [e-1/2] derivatives at the corner points of the original Bezier simplex. (4) Optimal order of approximation: The order of approximation of the given simplex by the degree-reduced simplex is O(he+1), (where h is the diameter of the domain simplex), which is optimal for functional approximation. The method, restricted to Bezier surface, yields a new technique for degree reduction, which is easy to implement.

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Suresh Kumar Lodha and Joe D. Warren "Degree reduction of Bezier simplexes", Proc. SPIE 1830, Curves and Surfaces in Computer Vision and Graphics III, (1 November 1992); https://doi.org/10.1117/12.131731

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