Finite piecewise polynomial parametrization of plane rational algebraic curves
Finite piecewise polynomial parametrization of plane rational algebraic curves
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DOI：
10.1007/s00200-006-0029-2
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发表时间：
2007-01
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影响因子：
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通讯作者：
S. Pérez-Díaz;J. Sendra;Carlos Villarino
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文献类型：
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作者：
S. Pérez-Díaz;J. Sendra;Carlos Villarino
本文提出了一种算法，它具有如下特点：给定平面曲线和公差的一个真实的非多项式有理参数化，将其分解为多个区间的并集，并且对于划分的每一个区间，除了某些孤立的区间外，该算法生成一个多项式参数化。此外，作为选项，也可以输入自然数N，然后算法返回次数小于或等于N的多项式参数化。此外，我们还进行了误差分析，证明了曲线段最多在距离的偏移区域内，反之亦然。
We present an algorithm with the following characteristics: given a real non-polynomial rational parametrizationof a plane curve and a tolerance,is decomposed as union of finitely many intervals, and for each intervalIof the partition, with the exception of some isolating intervals, the algorithm generates a polynomial parametrization. Moreover, as an option, one may also input a natural numberNand then the algorithm returns polynomial parametrizations with degrees smaller or equal toN. In addition, we present an error analysis where we prove that the curve pieceis in the offset region ofat distance at most, and conversely.