论文标题
理性毕达哥拉斯式曲线曲线的部分分数分解
Partial Fraction Decomposition for Rational Pythagorean Hodograph Curves
论文作者
论文摘要
所有具有规定多项式切线方向的有理参数曲线构成矢量空间。通过具有合理规范的切线方向，其中包括理性毕达哥拉斯曲线曲线的重要情况。我们研究通过固定分母多项式来定义的矢量子空间，并描述为它们的规范底座的构建。我们还显示（类似于理性函数的分数分解）表明，矢量空间的任何元素都可以作为有限的曲线总和，该曲线在分母处具有单根。我们的结果洞悉了这些空间的结构，阐明了它们多项式和真正理性（非多项式）曲线的作用，并提出了用于插值问题的应用。
All rational parametric curves with prescribed polynomial tangent direction form a vector space. Via tangent directions with rational norm, this includes the important case of rational Pythagorean hodograph curves. We study vector subspaces defined by fixing the denominator polynomial and describe the construction of canonical bases for them. We also show (as an analogy to the fraction decomposition of rational functions) that any element of the vector space can be obtained as a finite sum of curves with single roots at the denominator. Our results give insight into the structure of these spaces, clarify the role of their polynomial and truly rational (non-polynomial) curves, and suggest applications to interpolation problems.
