# Tagged Questions

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### Is there any interactive spline fitting software?

I'd like to know if there's any software (freeware) for interactive data interpolation. What I want is to be able to visualize my data on an XY plot and drag the points to see how it affects the ...
27 views

### How can missing data be organised or classified (Interpolation vs Approximation)?

I'm looking for a way to distinguish between the various types of missing data techniques? Can someone help to clarify or organize these categories in sub-sections or indicate similarities or ...
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### Calculating a cubic spline goes wrong

I am trying to solve a old exam and really stuck at the cubic splines. We have the function $f(x) = \cos^2(\frac{x}{2})$ and the points $x_0 = \frac{\pi}{2}$, $x_1=0$ and $x_2 = \frac{\pi}{2}$. ...
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### How to calculate the length of a cubic hermite spline between two points

I am using the following equation to create a cubic hermite spline: $$p_n(t) = a_nt^3+b_nt^2+c_nt+d_n$$ $$1\geq t\geq 0$$ $p_n(t)$ is the unit interval interpolation equation for dimension n. $t$ is ...
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### How to calculate a bezier curve given derivative of endpoints, location of endpoints, and points on the curve?

I know how to calculate a hermite spline, which has known derivatives and locations for each point, and I know how to calculate bezier curves which go through certain points, but I need to be able to ...
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### How can I generate a spline with a maximum second derivative without specifying first derivative for mid points?

I've done interpolation before with bezier splines and cubic splines, but I need to find a way to limit the second derivative throughout the curve so that there is a limit to how sharp the corner can ...
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### NURBS surface fitting for a closed region on mesh

I'm developing a tool that allows users to select a closed boundary (a polygon) on the triangle mesh and then from this boundary, generate a NURBS surface fitting the original mesh surface. My idea ...
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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 ...
3k 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 ...
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### How do I interpolate the derivative of a catmull-rom spline?

I am creating an implementation of a cubic hermite spline in Python. One feature I would like to add is a method to compute the slope (IE the derivative) for a given T value. Currently, I can do it ...
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### Catmull-Rom blending functions

I have a non-uniform Catmull-Rom spline (so the $t_i$ parameter values are not uniformly distributed). Is there a simple way to calculate the blending functions of the control points? So the spline ...
635 views

### How to calculate cubic spline coefficients from end slopes

I want to know how to calculate cubic spline interpolation coefficients, which uses end point slope constraint. There are $N$ points $(x_0,y_0),(x_1,y_1),\dots,(x_{N-1},y_{N-1}) \in \mathbb{R}^2$ ...
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### How to find B-Spline represenation of an Akima spline?

Given points $t_i$ and values $y_i$, I'd like to use Akima interpolation to interpolate to a different set of locations $x_j$. This means I need to calculate the cubic polynomials $A_{3,t}(x)$. Given ...
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### Piecewise interpolation with derivatives that is also twice differentiable

This question regards the issue of interpolation of one dimension real functions. If one has a finite set of function values and its corresponding derivatives, one could find unique continuous ...
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### Implemented Cubic Spline is not smooth

I want to implement cubic spline, so I found and implemented this discription and this method for solving tridiagonal system. I'd like to draw without using any math libraries, so cubic spline is ...
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### Spline interpolation that is non-decreasing when given non-decreasing sequence

How can I achieve a spline interpolation such that when given non-decreasing sequence of points the resulting spline will also be a non-decreasing function (and vice-versa, when given non-increasing ...
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### What do quadratic smoothing splines minimize?

Cubic smoothing splines minimize a combination of Interpolation cost and Smoothness (roughness) cost: $\qquad$ min Icost + $\lambda$ Scost where $\qquad$ Icost $\equiv \sum (Y_i - \mu(x_i))^2$ ...
531 views

### Spline interpolation versus polynomial interpolation

What is the difference, if any, between spline interpolation and piecewise polynomial interpolation?
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### What is the maximum overshoot of interpolating splines in $d$ dimensions?

Consider cubic splines $s( x, y )$ which interpolate values $y = \{ y_0, y_1, \dots,y_n \}$, on the uniform grid $\{ 0, 1,\dots, n \}$. Fix $s''(0) = s''(n) = 0$ (natural splines). How big can ...
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### Spline Interpolation

I have four questions about splines. Any help would be greatly appreciated. 1) Boundary conditions for cubic spline interpolation to a set of data $a=x{}_{1}<x2<...<x_{m} ,$ like for ...
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### What's the best way to calculate all of the points for a curve given only a few points?

I've been reading up on curves, polynomials, splines, knots, etc., and I could definitely use some help. (I'm writing open source code, if that makes a difference.) Given two end points and any ...
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I am currently studying numerical method. I understand that the regular way of cubic Hermite interpolation on arbitrary interval $[a,b]$ is: $p(u)=\left( \begin{array}{c} 2t^3-3t^3+1\\ t^3-2t^2+t\\ ... 1answer 238 views ### B-Spline Interpolation/Approximation I've got a couple of probably very simple questions, yet some googling didn't bring up what I was looking for. First what I want to do: I have a grid, and the gridpoints are function values. I want to ... 2answers 151 views ### Finding a simple spline-like interpolating function I am looking for a continuous function$y=f(x,\alpha)$for the interval$0\le x \le 1$such that$0\le y \le 1$and$y(0,\alpha)=0$and$y(1,\alpha) = 1$and$y(\alpha,\alpha) = 1-\alpha$and ... 2answers 367 views ### Cubic spline interpolation not producing an interpolant with continuous first derivative consistently I have coded a nice cubic spline interpolator following the basic methods laid out here http://people.math.sfu.ca/~stockie/teaching/macm316/notes/splines.pdf . My program reproduces the example laid ... 0answers 159 views ### B-Spline Definition I'm currently working on my master's project. For this, I rely on one PhD-thesis in which I found a statement I do not understand. Unfortunately, the author hasn't answered to my mails yet, so I have ... 1answer 177 views ### 3D Numerical differentiation with spline approximation I have three 3D matrices X, Y, and Z that define a matrix V of the same size over some region. The matrices are regularly spaced. I'm trying to compute the gradient of V. I have read that ... 1answer 156 views ### Knot placement for a natural cubic spline I am trying to approximate a function via a natural cubic spline. Suppose I sample the function on a grid i.e. I know the value of the function at a fixed number of equidistant points, say on 200 ... 2answers 2k views ### Eigen library: spline interpolation vs spline smoothing The C++ library Eigen provides an "unsupported" splines module which is giving me troubles. The task is typical: a data-acquisition device provides me with a time series that is sort-of regular and ... 1answer 524 views ### Akima spline interpolation I want to use Akima interpolation on series of points. I have those points in 3D [x, y, z]. But in all resources, I found, there is only f(x) and x (so [x,y]). In Natrual Cubic Spline I am using this ... 1answer 348 views ### Resolve a thin plate spline function I am trying to keep the outline of an object in a video. So I have the coordinate of the outline of the object in the image$t$and after computing the optical flow I have the coordinate in the image ... 1answer 241 views ### Spline with varing tension, selection of tension factor I need to perform a special interpolation, using that kind of basis : $$\varphi_{i,j}(x) = a_i + b_ix + c_i(\cosh(\tau\ x) - 1) + d_i(\sinh(\tau\ x) - \tau\ x)$$ where the$a_i$,$b_i$,$c_i$and ... 1answer 98 views ### Fixing end derivatives up to the second order when interpolating points I would like to interpolate a set of points in the real plane$(x_i,y_i), \ 1\leq i \leq n$with specified end derivatives up to the second order. That is finding$f \in ...
I am having some trouble understanding what the question below is asking. What does the given polynomial $P(x)$ have to do with deriving the not-a-knot spline interpolant for $S(x)$? Also, since ...