A better data structure for `VMobject`s

[Darylgolden]

Enhancement proposal

Currently, Manim stores the point data for VMobjects as a flat list of points. This is not representative at all of how VMobjects are actually structured, i.e. as composite bezier curves. In fact, every four points (three for OpenGL) form the points defining a cubic/bezier curve, yet they are currently not explicitly grouped together. Furthermore, the data of which points form what paths is not stored, and Manim instead spends a significant amount of time every frame checking whether for each pair of consecutive bezier curves, their end and start points are close enough to be considered part of the same path. This is of course extremely inefficient. I'm not exactly sure on how to resolve these problems, but a good data structure should have the following properties:

• Explicitly groups the data for each bezier curve together
• Explicitly groups the data for each subpath together
• Does not cause a significant performance loss when pointwise functions (functions acting on each point of the VMobject) are applied (perhaps grouping the points might cause overhead in this respect)
• Works with current animations (if paths are explicitly grouped, how do we implement a transformation of a VMobject to another VMobject with a different amount of paths?)
• Easily extendible to support different path components (like arcs and lines)

Additional comments

[Darylgolden]

A possible approach is to have a Bezier dataclass, then having the points array be an array of these dataclasses. This easily extends to allow different path components. If they are made immutable, it will help with caching. However, this might cause overhead when operating on points (I think it would be perfect, if not for that problem).

[Darylgolden]

One possible approach is to have components be subclasses of numpy arrays. Pointwise functions can still be applied directly with numpy through apply_along_axis. This could retain speed while semantically splitting up data. Needs more investigation.