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CLC number: TP391.72; O29
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Received: 2006-12-13
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Constrained multi-degree reduction of rational Bézier curves using reparameterization
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CAI Hong-jie, WANG Guo-jin. Constrained multi-degree reduction of rational Bézier curves using reparameterization[J]. Journal of Zhejiang University Science A, 2007, 8(10): 1650-1656.
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author="CAI Hong-jie, WANG Guo-jin",
journal="Journal of Zhejiang University Science A",
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pages="1650-1656",
year="2007",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2007.A1650"
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A1 - WANG Guo-jin
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PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.2007.A1650
Abstract: Applying homogeneous coordinates, we extend a newly appeared algorithm of best constrained multi-degree reduction for polynomial Bézier curves to the algorithms of constrained multi-degree reduction for rational Bé;zier curves. The idea is introducing two criteria, variance criterion and ratio criterion, for reparameterization of rational Bé;zier curves, which are used to make uniform the weights of the rational Bé;zier curves as accordant as possible, and then do multi-degree reduction for each component in homogeneous coordinates. Compared with the two traditional algorithms of “cancelling the best linear common divisor” and “shifted Chebyshev polynomial”, the two new algorithms presented here using reparameterization have advantages of simplicity and fast computing, being able to preserve high degrees continuity at the end points of the curves, do multi-degree reduction at one time, and have good approximating effect.
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