6
votes
Accepted
Minimize distance between curves
Let's assume you have a set of abscissas $x_i$ and two sets of function values on these grid points $f_i, g_i$ representing the functions $f$ and $g$.
As mentioned in the comments, you'll need a model ...
- 3,042
6
votes
Accepted
Parametrized spline - oscilating second derivative
Your choice of parameterization is creating problems. Instead of spanning one in $t$ between points, span an amount proportional to the line segment between the two points in $(x,y)$ space.
I've ...
- 1,223
3
votes
in Finite Element, which approximation requires less number of unknowns: B-splines vs Shape functions vs Spectral Elements
Based on the comments below your post you may reach the conclusion that # DOFs and speed have no correlation whatsoever - this is not true. Keeping all other things fixed and increasing the number of ...
- 1,271
3
votes
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Fitting a monotonically increasing spline function
A smoothing spline might be good enough in your case. For example, scipy.interpolate.UnivariateSpline implements this.
You can use it in the following way:
...
- 459
3
votes
Accepted
What are the various methods in adding an additional constraint to the quadratic spline interpolation problem
End slope for quadratic splines is a generalization of the natural quadratic spline condition: $p'_0(x_0) = v_0$. Alternatively, you could specify instead $p'_n(x_{n+1}) = v_{n+1}$. Since $\mathcal{C}...
- 2,391
3
votes
Accepted
Is a B-spline curve uniquely defined by one set of coefficients?
No, it's not completely unique. Like @origimbo said, a straight line can have many different representations that describe the same curve. Less trivially, splines can be degree-elevated and have ...
- 383
2
votes
Accepted
B-Splines Matlab Package
You may use Curve fitting toolbox which is provided by MATLAB.
The function you need is spcol.
- 56
2
votes
Minimize distance between curves
Here is a simple solution.
Find the curve $(x_m, y_m)$ with the largest domain $x$. In your case it is (x2, y2).
Assign it to be the main curve and shift all other ...
1
vote
Minimize distance between curves
Taking a function as reference $f_r$ the scale-translation transformations for each remaining functions can be handled by minimizing
$$
E(a,b,r) = \sum_{k\ne r}^{m}\sum_{j=1}^n \left(f_k(j)a_k+b_k - ...
- 166
1
vote
Spline regularization
As your problem is a local regression problem, I would not use a spline fit, but LO(W)ESS. This estimates $f(x)$ at a sample point $x$ by a weighted least squares fit to the points $x_i$ that are the $...
- 481
1
vote
Accelerating Conjugate Gradients fitting for small localized kernel (like cubic B-spline)
You certainly can try using Gauss-Seidel based preconditioning that is relatively easy to construct and is cheap enough (by my assessment) to give it a try.
Other choices of algebraic preconditioners ...
- 8,602
1
vote
Integrating/Implementing NURBS-related calculations
I think that you should take a look to OpenCascade. It provides with Spline surfaces, and NURBS particularly. It is written in C++ and it is released under LGPL license.
Regarding FreeCAD, I don't ...
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How to interpolate a set of points with a continuous closed B-spline curve?
The classic book in B-Splines is de Boor, C. (1978). A Practical Guide to Splines. New York: Springer-Verlag, but I spent many weeks on it and was not able to make his algorithms work. The algorithm ...
- 161
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How to connect two fitted B-spline curve?
Fitting together B-splines with a given continuity is a hard problem. This was actually the motivation behind developing a generalization of NURBS called T-splines. There are many articles on T-...
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