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Non-uniform exponential tension splines

机译:不均匀的指数张力花键

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We describe explicitly each stage of a numerically stable algorithm for calculating with exponential tension B-splines with non-uniform choice of tension parameters. These splines are piecewisely in the kernel of D 2(D 2–p 2), where D stands for ordinary derivative, defined on arbitrary meshes, with a different choice of the tension parameter p on each interval. The algorithm provides values of the associated B-splines and their generalized and ordinary derivatives by performing positive linear combinations of positive quantities, described as lower-order exponential tension splines. We show that nothing else but the knot insertion algorithm and good approximation of a few elementary functions is needed to achieve machine accuracy. The underlying theory is that of splines based on Chebyshev canonical systems which are not smooth enough to be ECC-systems. First, by de Boor algorithm we construct exponential tension spline of class C 1, and then we use quasi-Oslo type algorithms to evaluate classical non-uniform C 2 tension exponential splines.
机译:我们明确描述了数值稳定算法的每个阶段,该算法用于以非均匀选择张力参数的指数张力B样条进行计算。这些样条曲线分段地位于D 2 (D 2 –p 2 )的核中,其中D代表在任意网格上定义的普通导数,并且具有不同的拉伸参数选择每个间隔上的p。该算法通过执行正量的正线性组合(称为低阶指数张力样条)来提供关联的B样条及其通用和普通导数的值。我们表明,除了结插入算法和一些基本功能的良好逼近之外,不需要其他任何方法即可达到机器精度。基本理论是基于Chebyshev规范系统的样条曲线,该系统不够平滑,无法成为ECC系统。首先通过de Boor算法构造C 1 类的指数张力样条,然后使用准Oslo型算法评估经典的非均匀C 2 张力指数样条。

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