Constrained polynomial degree reduction in the L2-norm equals best weighted Euclidean approximation of Bézier coefficients

Authors:
Young Joon Ahn;Byung-Gook Lee;Yunbeom Park;Jaechil Yoo
Affiliations:
Department of Mathematics Education, Chosun University, Gwangju, 501-759, South Korea;Division of Internet Engineering, Dongseo University, Busan, 617-716, South Korea;Department of Mathematics Education, Seowon University, Cheongju, 361-742, South Korea;Department of Mathematics, Dongeui University, Busan, 614-714, South Korea
Venue:
Computer Aided Geometric Design
Year:
2004

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Abstract

In this paper we show that the best constrained degree reduction of a given Bézier curve f of degree from n to m with Cα-1-continuity at the boundary in L2-norm is equivalent to the best weighted Euclidean approximation of the vector of Bernstein-Bézier (BB) coefficients of f from the vector of degree raised BB coefficients of polynomials of degree m with Cα-1-continuity at the boundary.