# Tag Info

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### How to define a custom 2/3D graphic primitive like built-in?

If my answer for the 2D case lacks detail, it's because TypesetMakeBoxes is an internal, undocumented function. That makes it hard to say anything authoritative ...
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### 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 ...
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### 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 ...

### 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] ...
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### 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 ...
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### How to calculate the control points of a Bézier curve?

Here is my approach: ...
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### 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 ...

### Implementation of tensor product formula

Update Fully compiling the code to C makes it as fast as the built-in: ...
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### How to generate a closed B-spline curve?

The following works for your curve: ...

### 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 ...

### Why does BezierFunction not follow BezierCurve at npts>4?

BezierCurve normally gives a composition of local 4point-Bezierfunctions. You get equal curves by setting ...

### What do the arguments of a generated BSplineFunction mean?

Mimicking the spelunking in How to splice together several instances of InterpolatingFunction? We find ...

### 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: ...
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### 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. ...

### 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 ...

### 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 ...
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### 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: ...

### Extracting polynomials from a cubic spline function

I've finally decided to write a "modern" re-implementation of the old SplineFit[] routine from NumericalMathSplineFit`. In the ...

### 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 - ...
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### 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: ...
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### 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 ...

### 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 ...
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### 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 ...
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### 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: ...

### 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 ...