19
votes
Accepted
How to define a custom 2/3D graphic primitive like built-in?
If my answer for the 2D case lacks detail, it's because Typeset`MakeBoxes is an internal, undocumented function. That makes it hard to say anything authoritative ...
- 84.4k
19
votes
Accepted
How to calculate the numerical integral more efficiently?
General
When given an array of integrands NIntegrate is run separately over each array element. That is not necessary though, the core ...
- 37.2k
13
votes
Accepted
12
votes
2D smoothing spline interpolation
Update
Since version 12, this functionality in integrated in Mathematica via the Option FitRegularization
Following on @Ajasja's answer in the spirit of this answer one can in fact provide ...
- 22.5k
12
votes
How to discretize a BezierCurve?
This was solved with help from Shutao Tang, J.M., Sander Huisman and Eric Rimbey.
Why do BezierFunction[pt] and BezierCurve[pt] ...
12
votes
Accepted
Why is DiscretizeGraphics missing points on my curve?
So DiscretizeGraphics seems to always miss the first or last point of a BSplineCurve (it seems to do it with a ...
- 67k
12
votes
Accepted
12
votes
Accepted
12
votes
Accepted
Rendering PNG images to spline curves
Extracting a spline from the image is easiest with ImageMesh. I've used the midpoints of the lines on the mesh boundary for the ...
- 23.1k
11
votes
Implementation of tensor product formula
Update
Fully compiling the code to C makes it as fast as the built-in:
...
- 62.9k
11
votes
Accepted
11
votes
Implementation of smoothing splines function
Here is a (simplified) implementation of Reinsch's smoothing spline, which is effectively equivalent to csaps() in MATLAB's Curve Fitting Toolbox. Fancier methods ...
- 123k
11
votes
Why does BezierFunction not follow BezierCurve at npts>4?
BezierCurve normally gives a composition of local 4point-Bezierfunctions.
You get equal curves by setting ...
- 47.2k
11
votes
What do the arguments of a generated BSplineFunction mean?
Mimicking the spelunking in
How to splice together several instances of InterpolatingFunction?
We find
...
- 62.9k
10
votes
Produce a spline from a set of {{x, y}, z} points and get its parameters/expression
I have done this before in some previous spline-related threads, but here it is again:
...
10
votes
Accepted
How to obtain the function of a plotted Bezier curve?
In the documentation for BezierCurve, under Properties & Relations, it is written that a Bezier curve can be constructed from a sum of Bernstein polynomials. ...
- 69.8k
10
votes
Why is there a discrepancy between JoinedCurve/FilledCurve and the underlying BSplineCurve segments?
1. To get "the black curve (to) completely obscure the red curve"
You can replace BSplineCurves with Lines using ...
- 378k
10
votes
What do the arguments of a generated BSplineFunction mean?
This is the full internal representation of BSplineFunction with all relevant parameters. You can fiddle around with the options, then open the information box and ...
- 18.3k
9
votes
Accepted
smooth spline through airfoil coordinates
After permuting the points so that the cusp is the first point (just like in Gypaets's answer), the methods of this answer can be used:
...
8
votes
Extracting polynomials from a cubic spline function
I've finally decided to write a "modern" re-implementation of the old SplineFit[] routine from NumericalMath`SplineFit`. In the ...
- 123k
8
votes
BSplineFunction derivatives wrong if using weights?
The definition of B-Spline curve
$$\vec{C}(u)=\sum _{i=0}^n N_{i,p}(u) \vec{P}_i
\text{ }\qquad
(0\leq u\leq 1)$$
where, $\vec{P}_i$ is the control point, and the $N_ {i, p} (u)$ are the $p$-th - ...
- 555
8
votes
Accepted
Where is the other half of my fourth degree Bézier curve?
Since there is really something wrong with the BezierCurve, I made this work-around:
...
- 96.6k
8
votes
Accepted
How to integrate a Bézier function?
Since f[t] yields in effect {x[t], y[t]} and the area under a curve (with y[t] > 0) is ...
- 233k
8
votes
Stiff BVP of nonlinear ODE, alternative/ enhancement to shooting method
Edit: I have reorganized my earlier answer and added a significant amount of new material.
Transformed Equations
As suggested in the question, the equations are simpler, if ...
- 60.4k
8
votes
Accepted
Different results using spline interpolation in Wolfram and MATLAB
Is the "Spline" same as splinetx?
No.
If not, is there a function in Wolfram like ...
- 123k
8
votes
Accepted
8
votes
Why is there a discrepancy between JoinedCurve/FilledCurve and the underlying BSplineCurve segments?
To avoid the issue mentioned by kglr where points are repeated, you can just add another layer of list:
...
- 129k
8
votes
Why is there a discrepancy between JoinedCurve/FilledCurve and the underlying BSplineCurve segments?
Additional Problem
In addition to the two problems I mentioned above, there was a third problem that
...
- 1,061
8
votes
Convert interpolating function to a Bezier curve
The function hermiteToBezierPoints[] computes the Bezier control points for BezierCurve from values of the function and its ...
- 233k
7
votes
Why is DiscretizeGraphics missing points on my curve?
An alternate, i suspect faster, way to get your evenly spaced points,
using linepoints from here: https://mathematica.stackexchange.com/a/39457/2079
...
- 38.7k
Only top scored, non community-wiki answers of a minimum length are eligible