Rational offset approximation of rational Bézier curves |
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| Authors: | Min Cheng Guo-jin Wang |
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| Institution: | (1) Department of Mathematics, Zhejiang University, Hangzhou, 310027, China;(2) Department of Mathematics, Zhejiang University of Technology, Hangzhou, 310032, China |
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| Abstract: | The problem of parametric speed approximation of a rational curve is raised in this paper. Offset curves are widely used in
various applications. As for the reason that in most cases the offset curves do not preserve the same polynomial or rational
polynomial representations, it arouses difficulty in applications. Thus approximation methods have been introduced to solve
this problem. In this paper, it has been pointed out that the crux of offset curve approximation lies in the approximation
of parametric speed. Based on the Jacobi polynomial approximation theory with endpoints interpolation, an algebraic rational
approximation algorithm of offset curve, which preserves the direction of normal, is presented.
Project supported by the National Basic Research Program (973) of China (No. 2002CB312101) and the National Natural Science
Foundation of China (Nos. 60373033 and 60333010) |
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| Keywords: | Rational Bézier curve Parametric speed Offset Rational approximation |
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