# Questions tagged [spline]

A smooth piecewise-defined curve formed by joining segments together, end-to-end. The segments are usually described by polynomial or rational functions. Splines are typically used for approximation or data fitting.

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### B-Spline how to create control points for a curve to pass through knot values

I want to create a b-spline curve that will pass through all the (knot) points I give it. How do I construct it? Do I need to find the control points for that curve? And if so - how?
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### Fitting splines to famous curves programmatically

this may be a bit of a naive question. I am looking for a way to input a Cartesian description of a famous curve and map that to some spline say NURBS to make spline paths. Is this at all possible? ...
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### Polynomial representation: Marsden's Identity.

Marsden's Identity states that: For every $\tau$ in $\mathbb{R }$: $(\cdot -\tau)^{k-1}=\sum_j\Psi_{j,k}B_{j,k,t}$ with: $\Psi_{j,k}=(t_j-\tau)\times...\times(t_{j+k-1}-\tau)$ Following de Boor'...
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### Find the natural cubic spline interpolant at the nodes?

Find the natural cubic spline interpolant to $f(x) = e^{x^2}$ at the nodes $\{x_i\}^2_{i=0} = \{−1, 0, 1\}$. Calculate the value of the interpolant at $x = 0.5$. What is the error at this point? S"(a) ...
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### Line intersect spline surface

The intersection of a line with a bi-n surface is the solution of $A+Bt=Cu^nv^n+...$, where A, B, C, etc. are 3-vectors. The first step in solving this system is eliminating to get two bi-n equations ...
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### Linear spline over a polynomial

The Question Suppose that $t$ is a polynomial of degree $n$ or less and satisfies $$t(x_0)=f_0 \; \; \; \; t(x_n)=f_n \; \; \; \; t(x_i)=0 \; \; , \; \; i=1,2,\dots,n-1$$ where \$x_0<x_1<\dots&...