0
votes
0answers
6 views

Maple Cubic Spline Interpolation

Need help on this one... Using the strategy of the second derivative, solve the interpolation problem with cubic spline for a problem of $n+1$ points. In order to do this, two Maple procedures will ...
0
votes
1answer
12 views

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 ...
0
votes
0answers
15 views

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 ...
0
votes
0answers
23 views

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 ...
0
votes
0answers
22 views

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 ...
2
votes
1answer
34 views

Can you interpolate a function $f: \mathbb{R} \rightarrow \mathbb{R}^2$ piecewise (by two interpolations)?

I am currently trying to improve on-line handwriting recognition. On-line means in this case that I have the information how the symbols are written as a list of $n$ tuples of coordinates $(x(t_i), ...
0
votes
0answers
22 views

Approximate function algorithm using a polynomial and Boor splines

I have a defined function and a set of points with equal distance between them. The problem is that I have to approximate the graphic of that function using a polynomial function of 3rd degree and a ...
0
votes
1answer
36 views

Defined matrix in Catmull Spline Curve

I am trying to use Catmull spline curve in my program , I am trying to understand it but why we only use below given Matrix , because the examples I saw I only found the below one In Catmull spline ...
0
votes
0answers
10 views

Interpolating on the borders of differently-resolved images

I'm creating a three-dimensional model of the earth based on SRTM height data. The data set is pretty huge, so only a small fraction of the data is available at any given time. The height data is ...
0
votes
0answers
25 views

Possibility of 3D interpolation without decouple axis

I am wondering if it is possible to do 3d spline interpolation without decoupling the axis. Such as creating a spline function on x then a different one on y and another on z. Then for any given ...
0
votes
2answers
98 views

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 ...
0
votes
1answer
23 views

Using the TPS to interpolate between points

I have implemented the Thin Plate Spline interpolation. I successfully plotted surfaces which go through all my 3D data points. What I want to do is calculate a few points which lie between my known ...
1
vote
2answers
241 views

Is there a cubic spline interpolation with minimal curvature?

I came across the term "cubic spline with minimal curvature". However, I am not able to find any documentations/explaination on its computation method. Can anyone help me by advising how I can go ...
0
votes
1answer
449 views

Cubic Spline Interpolation practice

Going over practice problems for our final exam. I'm stuck on a problem involving cubic splines. In fact, I don't even know where to begin. I need to find the natural cubic spline $S(t)$ at $t_0=0, ...
1
vote
1answer
105 views

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 ...
3
votes
2answers
2k 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 ...
0
votes
1answer
184 views

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 ...
0
votes
0answers
38 views

Spline interpolation problem akin to Bezier spline

Given three pairwise distinct points $p_1, p_2, p_3 \in \mathbb{R}^2$, I'd like to find a function $f: \mathbb{R} \to \mathbb{R}^2$ with at least $f \in C^1$ such that $f(0) = p_1, f(1) = p_3, f'(1) ...
0
votes
0answers
42 views

Tile a spline with bricks

I have a series of identically sized virtual Lego bricks. I need to "tile" these bricks along the length of a Hermite spline to create a curved road. The spline is two-dimensional. E.g. the curve only ...
0
votes
1answer
101 views

Cubic splines on a grid

I trying to work out how to interpolate on a grid with cubic splines. Let the point at which I'm trying to interpolate be at {xp,yp}. At the moment I am fitting splines across the rows and then ...
-1
votes
1answer
37 views

Cant understand how we got this equation

I was going through a tutorial that introduces cubic splines. A snapshot of the tutorial is as follows : Image begins: Image End: Now I dont understand how we got: $y_1''=6a_1(x_1-x_1)+2b_1=0 + ...
1
vote
1answer
92 views

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 ...
0
votes
1answer
573 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 $(x_0,y_0),(x_1,y_1),\dots,(x_{N-1},y_{N-1}) \in \mathbb{R}^2$ ...
0
votes
1answer
217 views

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 ...
1
vote
2answers
333 views

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 ...
0
votes
1answer
228 views

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 ...
2
votes
1answer
138 views

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 ...
1
vote
0answers
68 views

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 $\equiv \sum (Y_i - \mu(x_i))^2$ ...
3
votes
2answers
460 views

Spline interpolation versus polynomial interpolation

What is the difference, if any, between spline interpolation and piecewise polynomial interpolation?
4
votes
0answers
256 views

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 ...
0
votes
1answer
329 views

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 ...
1
vote
2answers
146 views

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 ...
2
votes
1answer
205 views

About Generalized Hermite interpolation

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\\ ...
1
vote
1answer
230 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 ...
1
vote
2answers
144 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 ...
1
vote
2answers
354 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 ...
2
votes
0answers
155 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 ...
1
vote
1answer
165 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 ...
1
vote
1answer
148 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 ...
0
votes
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 ...
2
votes
1answer
505 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 ...
0
votes
1answer
332 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 ...
0
votes
1answer
213 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 ...
0
votes
1answer
93 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 ...
0
votes
1answer
1k views

Need to understand question about not-a-knot spline

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 ...
5
votes
1answer
2k views

Natural cubic splines vs. Piecewise Hermite Splines

Recently, I was reading about a "Natural Piecewise Hermite Spline" in Game Programming Gems 5 (under the Spline-Based Time Control for Animation). This particular spline is used for generating a C2 ...