# Questions tagged [splines]

Splines and their properties and applications. A spline is a function defined piecewise by polynomials, and is typically used in interpolating problems.

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### Which data structure should I use for hierarchical T-meshes and PHT-splines?

Recently, I'm working on something about polynomial splines over hierarchical T-meshes, which is basically a rectangular grid that allows T-junctions. I want to do some numerical experiments but I don'...
566 views

### Once differentiable, piecewise degree three polynomials on triangulated planar domains

Here is an easily described, but very difficult, problem that I (and a number of other people) really would like to see solved during our life times. The basic problem is to compute the dimension of ...
272 views

### Cubic spline smoothing question

I came across this link when searching for an algorithm for spline smoothing. Though I understand basically what I have to do, I need further clarifications on the formula chosen for curvature ...
326 views

### Finding 3 dimensional B-spline control points from given array of points from spline solution?

Wa are talking about Non-uniform rational B-spline. We have some simple 3 dimensional array like {1,1,1} {1,2,3} {1,3,3} {2,4,5} {2,5,6} {4,4,4} Which are ...
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### Interpolation splines of bounded curvature

Given $n$ points $p_i=(x_i,y_i)$ on the [Euclidean] plane, and a positive real number $\rho$. Can we have a polynomial spline (e.g., natural cubic spline) passing through all these points, such that: (...
The Fourier series of a function (B-spline) is given by: $$s(x)=\sum_{j=-\infty}^{\infty}\operatorname{sinc}\Bigl[\pi\frac{j}{K}\Bigr]^{p}\exp[2\pi ijx]$$ But the B-spline has only finite support. How ...
So, I am aware of how to (both iteratively and using a linear equation) compute the cubic spline of a one-variable function with $m$ control points. However, I am not sure how to do any type of spline ...