| Computer Aided Design & Computer Graphics |
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| Constrained multi-degree reduction of rational Bézier curves using reparameterization |
| CAI Hong-jie, WANG Guo-jin |
| Institute of Computer Images and Graphics, State Key Laboratory of CAD & CG, Zhejiang University, Hangzhou 310027, China |
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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 Bézier curves. The idea is introducing two criteria, variance criterion and ratio criterion, for reparameterization of rational Bézier curves, which are used to make uniform the weights of the rational Bézier 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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Received: 13 December 2006
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