splines | Interpolation

I think a good place to start with is using ConvexGeometry. You give it an array of points / Vector3 ( which I see you have created under the variable randomPoints ) as a parameter and it will create a shape for you.

I see you used CatmullRomCurve3, this may be a good tool to create the curves between the points as you mentioned. We can combine both of these ideas to create a somewhat curvier model.

Use an invisible edge:

I programmed the following code based on Russian Wikipedia Article, as I see almost the same description and formulas are located in English Article.

To speed-up computation I used both Numpy and Numba.

To check the correctness of code I made tests with comparison to reference implementation of the natural cubic spline of scipy.interpolate.CubicSpline, you can see np.allclose(...) assertion in my code that proves my formulas are correct.

Also, I did timings:

For non-ascending x splines can be easily computed if you make both x and y functions of another parameter t: x(t), y(t).

In your case you have 5 points so t should be just enumeration of these points, i.e. t = 0, 1, 2, 3, 4 for 5 points.

So if x = [5, 2, 7, 3, 6] then x(t) = x(0) = 5, x(1) = 2, x(2) = 7, x(3) = 3, x(4) = 6. Same for y.

Then compute spline function for both x(t) and y(t). Afterwards compute values of splines in all many intermediate t points. Lastly just use all calculated values x(t) and y(t) as a function y(x).

Once before I implemented cubic spline computation from scratch using Numpy, so I use this code in my example below if you don't mind (it could be useful for you to learn about spline math), replace with your library functions. Also in my code you can see numba lines commented out, if you want you can use these Numba annotations to speed up computation.

You have to look at main() function at the bottom of code, it shows how to compute and use x(t) and y(t).

Try it online!

Here's my recommendation (disclaimer: I don't use processing in python, so I couldn't test run this code and there may be errors):

• Graphviz does not offer edge labels that follow the curve of the edge. There is a request for this feature (https://gitlab.com/graphviz/graphviz/-/issues/2007). You might share your interest.
• your source had a couple of suboptimals
  • G was declared twice - legal but unnecessary
  • edge b->X has an X attribute instead of label. No biggie

Possibilities:

• consider other layout engines. circo and twopi are interesting
• increase nodesep
• try splines=true (this really seems to help)
• match font color to edge color
• consider removing rank=same for X and G (again, this really seems to help)
• for a-f -> X, try taillabel instead of label

Most of these changes are cosmetic, just to make things easier for me to understand.
The one iffy change was changing the G and X ranking. Your call.

As it turns out pyearth is a library for earth science. In other words, pyearth has nothing to do with Multivariate Adaptive Regression Splines (MARS).

The library that has the MARS algorithm is sklearn-contrib-py-earth. This is how you can import it on Google Colab:

You could lapply() smooth layers to add to the plot, whilst simultaneously providing new facet variables.

It's not completely clear to me what your exact expectations are..., but I would use the plotting style with boxxyerror (check help boxxyerror).

Code: