Programming animations for mathematical formulas

Question

I'm trying to make animations to explain mathematical concepts in which formulas would play a big role. I'd need text and formulas to do some simple things like fading in and out, moving, rotating, morphing, etc.

As my background is in programming, I figured Iid try to make some sort of automated process:

1. Generate SVG formulas out of LaTeX sources.
2. Animate the text/formulas.
3. Export as a video.

I've already managed to do step 1 with little trouble. Now, I know I could do step 2 with some animation software, but I've been looking for some solution that involves programming instead of WYSIWYG, because I feel more comfortable in that territory. I'm open to any language/library, although it's much preferable if it can run on UNIX-like systems. I've already checked some libraries like Cairo and such, but all seem to have big trouble using vector graphics instead of bitmaps, and although using SVGs is not a requirement for me, I think it'd make the process more simple.

Answer 1

I would strongly recommend trying the Jupyter notebooks environment with one of several plotting libraries that support animation.

This combination lets you combine, on a single notebook page, text formatted with markdown, formulae with latex or mathjax, plots & graphs, etc. nice example here.

Amongst the plotting tools that support animation there are:

• matplotlib has animations and even has an example of saving to .mp4
• plotly supports animations
• holoviews has some animation demonstrations in their showcase
• bokeh has some interesting features but animation looks to be complex
• bqplot is well worth a look
• the VPython kernel can produce fantastic animations

It is well worth having a browse at https://github.com/jupyter/jupyter/wiki/A-gallery-of-interesting-Jupyter-Notebooks#data-visualization-and-plotting to see some of the possibilities.

I would also suggest taking a look at MoviePy which can produce an animation of any code that produces a plot as an image or a numpy image array it brings a lot of this together here with the following being some examples of such animations: