Degree reduction of Bezier simplexes

Suresh Kumar Lodha; Joe D. Warren

doi:10.1117/12.131731

1 November 1992 Degree reduction of Bezier simplexes

Suresh Kumar Lodha, Joe D. Warren

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.

Citation Download Citation

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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