# 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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### What is the relationship between cubic B-splines and cubic splines?

What is the relationship between cubic B-splines and cubic splines?
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### Implementation of Monotone Cubic Interpolation

I'm in need to implement Monotone Cubic Interpolation for interpolate a sequence of points. The information I have about the points are x,y and timestamp. I'm much more an IT guy rather than a ...
31k views

### How to calculate interpolating splines in 3D space?

I'm trying to model a smooth path between several control points in three dimensions, the problem is that there doesn't appear to be an explanation on how to use splines to achieve this. Are splines a ...
3k views

### Motivation of Splines

What is the motivation of splines, in particular cubic splines. For example, why does it matter that they have any type of smoothness at the knots.
360 views

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### Linear Spline Interpolation

Can someone explain to me how linear splines work and what formulas are used. I can only seem to find information on cubic splines. Which I don't really understand either Specifically, if I were ...
1k views

### Physical significance of knot vector in B-spline.

A B-spline blending curve formulation is: $P(u)=\sum_{k=0}^np_k B_{k,d}(u)$ Given $n+1$ control points, B-spline blending functions are polynomials of degree $d-1$, $(1<d<=n+1)$. ...
2k views

### Program to find closest function to fit arbitrary data

I've wanted this for years, but have never come across anything; a program for Windows to find the closest function to fit arbitrary data. The data I feed it is simple: A table with two columns ...
876 views

### How can I fit a spline curve through points in the plane with constraints on the curvature?

If I have a number of points in the plane (say I have some points $(x_n, y_n),\ n = 0,1,\ldots, N$) and I would like to fit a parametrised curve through them: $(x(t), y(t))$ where $t$ is some ...
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### How to calculate a spline for points in general position?

I want to find a curve passing through (or near) $n$ points in the plane. The catch is that the curve need not be a function. That is, a vertical line might pass through the curve in more than one ...
Let be given a set of measurements $\left\{(x_1,y_1), (x_2,y_2),\ldots, (x_n,y_n)\right\}$. For these points, we further are given the slopes $y'_i$ measured at the support points $x_i$ for $i \in \{1,... 1answer 337 views ### Spline interpolation degrees of freedom When using cubic spline interpolation, we have to solve$n-1$equations with$n+2$unknowns. What we can do is set$z_0 = z_n = 0$, which gives the natural cubic spline. But could we also set some ... 2answers 1k views ### spline derivation Assume the following representation for cubic splines with$T$interior knots is given. Let$g(Y)=\sum_{j=0}^3 \alpha_j Y_j+\sum_{t=1}^T \gamma_t (Y-\zeta_t)_{+}^{3}$where$(Y-\zeta_t)_{+}:= max\{0,...
I am dealing with spline interpolation and what I do is basically interpolating $6$th order ($7$ control points) spline through some discrete points. Curve-based part of my algorithm is done, however, ...