Boost中的c ++ Hermite插值算法 [英] c++ Hermite interpolation algorithm in Boost
问题描述
我正在尝试使用Boost c ++库进行Hermite插值，但是没有充分的文档记录，我也不了解.
I'm trying to use Boost c++ library for Hermite interpolation, but it's not well documented and I'm not well understand.
我的情况是从以下数据点计算x位置的y值:
My case is to calculate y values at some x position from data points such as:
X: 0.9, 1.7, 2.55, 3.39...
Y: 0.9, 0.8, 0.85, 0.84...
并获得相等的x间隔(x间隔0.5)的结果:
And get result with equal x spaces (x space 0.5):
X: 0.5, 1.00, 1.5, 2.00, 2.5, 3.0,...
Y: 0.8, 0.95, 0.8, 0.85, 0.9, 0.9,...
提升对我有帮助吗?我在Web中找到了Hermite的更多实现，但是示例和结果输出不是我想要的.我认为那是因为我不了解它是如何工作的.当我读到Hermite时，我坚信该算法应该询问一些点，间距值以及可能很少的其他输入值，然后计算并返回新的点，但是我错了，现在迷路了.
Can boost be helpful for me? I had found more implementations of Hermite in web, but examples and it's result output was not what I'm looking for. I think thats because I don't understand how it works. When I read about Hermite I tought that algorithm should ask for some points, spacing value and might few other input values and then calculate and return new points, but I was wrong and now lost..
也许有人有使用Hermite的经验并且有类似的案例?
Maybe someone has experience using Hermite and had similar case?
推荐答案
首先，Hermite是一位多产的数学家，所以 Hermite多项式(正交族)与
Well, first of all, Hermite was a prolific mathematician, so Hermite polynomials (an orthogonal family) are unrelated to Hermite interpolating polynomials that arise in the interpolation method.
第二，当您具有前几个函数导数的值以及每个点的函数值时，将应用Hermite内插法，因此它不适用于您的情况.
Second, Hermite interpolation is applied when you have values of first few function derivatives as well as function values at each point, so it's not really applicable in your case.
In Boost specifically, I could find only this algorithm for non-uniform interpolation: http://www.boost.org/doc/libs/1_65_0/libs/math/doc/html/math_toolkit/interpolate/barycentric.html —hopefully it is good enough for your purposes.
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