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ZJUS-A
Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering)  2007, Vol. 8 Issue (10): 1657-1662    DOI: 10.1631/jzus.2007.A1657
Computer Aided Design & Computer Graphics     
A quadratic programming method for optimal degree reduction of Bézier curves with G1-continuity
LU Li-zheng, WANG Guo-zhao
Institute of Computer Graphics and Image Processing, Department of Mathematics, Zhejiang University, Hangzhou 310027, China
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Abstract  This paper presents a quadratic programming method for optimal multi-degree reduction of Bézier curves with G1-continuity. The L2 and l2 measures of distances between the two curves are used as the objective functions. The two additional parameters, available from the coincidence of the oriented tangents, are constrained to be positive so as to satisfy the solvability condition. Finally, degree reduction is changed to solve a quadratic problem of two parameters with linear constraints. Applications of degree reduction of Bézier curves with their parameterizations close to arc-length parameterizations are also discussed.

Key words： Degree reduction      Bézier curves      Optimal approximation      G1-continuity      Quadratic programming     
Received: 22 January 2007     
CLC:  TP391.72  
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LU Li-zheng
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LU Li-zheng, WANG Guo-zhao. A quadratic programming method for optimal degree reduction of Bézier curves with G1-continuity. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2007, 8(10): 1657-1662.

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http://www.zjujournals.com/xueshu/zjus-a/10.1631/jzus.2007.A1657     OR     http://www.zjujournals.com/xueshu/zjus-a/Y2007/V8/I10/1657

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