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Journal of Zhejiang University SCIENCE A 2009 Vol.10 No.4 P.577~582

10.1631/jzus.A0820290


Optimal constrained multi-degree reduction of Bézier curves with explicit expressions based on divide and conquer


Author(s):  Lian ZHOU, Guo-jin WANG

Affiliation(s):  Institute of Computer Graphics and Image Processing, Zhejiang University, Hangzhou 310027, China; more

Corresponding email(s):   zhoulia5729@163.com, wanggj@zju.edu.cn

Key Words:  Bé, zier curves, Multi-degree reduction, Divide and conquer


Lian ZHOU, Guo-jin WANG. Optimal constrained multi-degree reduction of Bézier curves with explicit expressions based on divide and conquer[J]. Journal of Zhejiang University Science A, 2009, 10(4): 577~582.

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T1 - Optimal constrained multi-degree reduction of Bézier curves with explicit expressions based on divide and conquer
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DOI - 10.1631/jzus.A0820290


Abstract: 
We decompose the problem of the optimal multi-degree reduction of ;zier curves with corners constraint into two simpler subproblems, namely making high order interpolations at the two endpoints without degree reduction, and doing optimal degree reduction without making high order interpolations at the two endpoints. Further, we convert the second subproblem into multi-degree reduction of Jacobi polynomials. Then, we can easily derive the optimal solution using orthonormality of Jacobi polynomials and the least square method of unequally accurate measurement. This method of ‘divide and conquer’ has several advantages including maintaining high continuity at the two endpoints of the curve, doing multi-degree reduction only once, using explicit approximation expressions, estimating error in advance, low time cost, and high precision. More importantly, it is not only deduced simply and directly, but also can be easily extended to the degree reduction of surfaces. Finally, we present two examples to demonstrate the effectiveness of our algorithm.

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Reference

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