3b1b/manim ? reverse-engineered prompt

I want you to build me an animation engine for making explanatory math videos, heavily inspired by the style of the 3Blue1Brown YouTube channel. It should be a Python library that lets me create animations programmatically by writing code.

I'll need to be able to define scenes with different shapes, text, and especially complex mathematical formulas using LaTeX. The main feature is being able to animate these objects with code—things like morphing one shape into another, moving objects along a path, fading them in and out, or plotting functions.

The end goal is to run a Python script from my command line and have it render a high-quality video file of the animation. You'll likely need to integrate it with something like OpenGL for rendering the graphics and FFmpeg for creating the final video file. I should also be able to save a single high-resolution frame as an image.