将B样条写为分段三次 [英] Writing B-spline as Piecewise Cubic

问题描述

我正在使用Scipy的SmoothBivariateSpline类在双变量数据上创建三次B样条.现在，我需要为该样条曲线编写分段多项式表达式.

I'm using Scipy's SmoothBivariateSpline class to create a cubic B-spline on bivariate data. I now need to write the piecewise polynomial expression for this spline curve.

我的数学背景不是很强，所以我无法编写自己的算法来将SmoothBivariateSpline的t，c，k输出转换为多项式表示.如果可行，您能否提供有关如何实现此目标的指示?我注意到Scipy具有interpolate.ppform，但是我找不到关于它的任何文档-这相关吗?

My mathematical background isn't very strong, so I wasn't able to write my own algorithm for transforming from the t, c, k output of the SmoothBivariateSpline to a polynomial representation. If this is feasible, can you provide pointers on how to approach this? I noticed that Scipy has interpolate.ppform, but I can't find any docs for it - is this relevant?

我正在考虑的一种方法是将样条的域分解为每个结处的区域(总区域为(n-1)^2，其中n是结数)，然后对网格上的许多点执行三次回归每个区域的样条曲线，以计算每个区域的数据的三次回归.这是有效的方法吗?

One method I was considering was breaking down the domain of the spline into regions at each knot (with (n-1)^2 total regions, where n is the number of knots), then performing a cubic regression on many points on the spline curve in each region in order to calculate a cubic regression to the data for every region. Is this a valid approach?

前一种方法似乎更加严格，因此我更愿意使用该方法，但是后一种方法也是可以接受的.

The former method seems much more rigorous, so I'd prefer to use that one, but the latter is also acceptable.

推荐答案

B样条可以有效地转换为分段多项式.

B-splines can be converted to piecewise polynomials efficiently.

这可以在具有scipy.interpolate.PPoly.from_spline的Scipy 0.14.0(要在几个月后发布)中轻松完成.

This can be easily done in Scipy 0.14.0 (to be released in a couple of months) which has scipy.interpolate.PPoly.from_spline.

从样条线t, c, k本身计算分段多项式的算法非常简单，因此与此同时，您可以编写自己的函数来计算多项式系数: https://github.com/scipy/scipy/blob/master/scipy/interpolate/interpolate.py#L938

The algorithm of computing piecewise polynomials from the spline t, c, k itself is very simple, so in the meantime you can write your own function that computes the polynomial coefficients: https://github.com/scipy/scipy/blob/master/scipy/interpolate/interpolate.py#L938

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