Interactive Mathematics Program Cookies Answers

Python Matplotlib

https://matplotlib.org/

Although Matplotlib's focus is on data plotting, it has become so featureful that you can generally produce good 2D illustrations with it.

Being written in Python is also a huge plus over domain specific languages like gnuplot.

It must be said that since it's main focus is not illustration, sometimes you have to Google a bit for the solution, but one often exists, or at least a reasonable workaround. And when it doesn't, it is often not hard to code it yourself and submit a patch.

Consider for example this simple educational graph demo I've made:

enter image description here

Source code

Also note that nothing in that demo is mandatory: you could easily rip off the axes or title for example.

It must be said that Matplotlib is not perfect for 3D however, as it does not support an OpenGL backend. As a result, the 3D interface is particularly clumsy and rather incomplete.

But you can get away with sometimes if your requirements are not too strict. For example, here's my attempt at a Bloch sphere illustration that I made for this other answer:

enter image description here

Source code.

In that example, we can see how I was unable to place the little circles above the plot as I would have wanted, showing how 3D is not perfect. But there is even a draft pull request for it.

One advantage of Matplotlib is that it has its own LaTeX subset parser, and thus dispenses a full LaTeX installation for mathematics as mentioned at https://matplotlib.org/3.3.3/tutorials/text/mathtext.html:

Note that you do not need to have TeX installed, since Matplotlib ships its own TeX expression parser, layout engine, and fonts. The layout engine is a fairly direct adaptation of the layout algorithms in Donald Knuth's TeX, so the quality is quite good (matplotlib also provides a usetex option for those who do want to call out to TeX to generate their text

Tested on matplotlib==3.2.2.

3blue1brown's Manim

https://github.com/ManimCommunity/manim/

This is based on the engine that 3blue1brown uses for his amazingly looking videos, which include complex moving graphs and formulas.

I'll let a sample video speak for itself: https://www.youtube.com/watch?v=r6sGWTCMz2k&t=1s

And there's an in-tree demo:

          git clone https://github.com/ManimCommunity/manim/ cd manim git checkout 1b12f076be49a677add97346eed6900e3cf18873 cd example_scenes manim basic.py OpeningManimExample xdg-open ./media/videos/basic/480p15/OpeningManimExample.mp4

enter image description here

Inkscape demos

Inkscape had been previously mentioned at: Software for drawing geometry diagrams but here are some demos that felt relevant.

https://graphicdesign.stackexchange.com/questions/141237/how-to-color-2-circles-intersection-in-different-color-in-draw-io shows how it supports doing intersection of figures (you have to potentially copy objects to merge them):

enter image description here

Intuition behind normal subgroups shows a more free-form block diagram I've put up myself:

enter image description here

Inkscape currently doesn't support constraints however unfortunately: https://gitlab.com/inkscape/inbox/-/issues/1465 e.g. "same widths, parallel, etc.", but you can generally get decent results by just snapping to a grid in the editor. The "Align and Distribute" tool also helps, acting as "one time constraints", but there's no way to make real permanent constraints right now.

There isn't LaTeX math support in an extremely convenient out-of-box way it seems, but there are some possible methods available:

https://tex.stackexchange.com/questions/61274/is-there-any-way-to-type-latex-code-directly-into-the-text-boxes-inkscape
https://graphicdesign.stackexchange.com/questions/88027/where-to-find-latex-formula-in-inkscape

FreeCAD SVG export

This is usually a bit overkill, but it is really cool.

FreeCAD, as a CAD software, actually supports explicit constraints with a constraint solver.

This is a bit along the lines of what Software for drawing geometry diagrams mentioned kseg can do, except that kseg seems a bit abandoned, e.g. last release on SourceForge is from 2011.

FreeCAD is not focused on doing nice looking SVGs, but a possible workflow would be to export a perfect geometry to SVG, and then import the SVG into Inkscape to finish more visual details. This might be a reasonable workaround until the blessed day when Inkscape will implement constraints.

To export to SVG, you have to create a sketch. FreeCAD is a bit intimidating since it does so much more than 2D figures, so just watch this video: https://www.youtube.com/watch?v=sxnij3CkkdU

With that, I obtain a perfectly specified figure, you can see some constraints showing on the FreeCAD GUI, e.g. equality of edges of that triangle:

enter image description here

And then, I export to SVG via:

Select the sketch on the right menu
File
Export
Files of type: Flattned SVG

And then after conversion to PNG for uploading here:

          inkscape -b 'FFF' -z -w 512 eye.svg -e eye.png

I obtain:

enter image description here

TODO: why is it so messed up?

Tested on FreeCAD 0.18.4, Ubuntu 20.04.

MathMod

https://github.com/parisolab/mathmod

Not a huge community as of 2020, but it does seem to be able to produce some really nice 3D parametric/isocurve graphs with OpenGL and customizable shading.

You can use a custom scripting language to automate it (shame not python), and the GUI has widgets to vary parameters, including animations in time.

I got it to run on Ubuntu 20.10 by downloading the 10.1 prebuilt from the official download page on SourceForge (unfortunately). Then just unzip and run with: