Optimal multi-degree reduction of Bézier curves with G2-continuity

Authors:
Lizheng Lu;Guozhao Wang
Affiliations:
Institute of Computer Graphics and Image Processing, Department of Mathematics, Zhejiang University, Hangzhou 310027, China;Institute of Computer Graphics and Image Processing, Department of Mathematics, Zhejiang University, Hangzhou 310027, China
Venue:
Computer Aided Geometric Design
Year:
2006

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Abstract

In this paper we present a novel approach to consider the multi-degree reduction of Bezier curves with G^2-continuity in L"2-norm. The optimal approximation is obtained by minimizing the objective function based on the L"2-error between the two curves. In contrast to traditional methods, which typically consider the components of the curve separately, we use geometric information on the curve to generate the degree reduction. So positions, tangents and curvatures are preserved at the two endpoints. For avoiding the singularities at the endpoints, regularization terms are added to the objective function. Finally, numerical examples demonstrate the effectiveness of our algorithms.