This library provides Proper Geometry Algorithms, for doing geometry in 3D as the math-gods intended.
Psst ... if you're a math-person, this library implements Projective
Geometric Algebra in 3D (i.e. ℝ(3, 0, 1)), so that intersections and
joins etc. are super easy to implement, and benefit from all the
nicities of this algebra. But I don't want to scare our users, so we provide
an API that normal humans can actually understand.
Experimental and work in progress. I dug into this to see if it's something we could use in pygfx. I'm not sure yet. This state matches my progress (and understanding) so far.
- Small size (once we have the algebra set up, all conversions, intersections etc. are one-liners).
- Transformations (translation + rotations) can be composed with minimal loss of precision (in contrast to composing multiple 4x4 matrices).
- Transformations are "linear", in that you can multiply them, e.g. to get smooth interpolation.
- Less need for checks and exceptions: intersecting two parallel lines? Fine! The result is a point at infinity (a direction)!
- No implicit design decisions like right-handed vs left-handed.
This lib attempts to provide a way to use a very cool/advanced/new mathematical tool (3D PGA) without having to know about it.
If you do want to learn more about (projective) geometric algebra, here are some resources that I found useful. Prepare for your mind being blown:
- Probably a good start: https://www.youtube.com/watch?v=tX4H_ctggYo
- General resources: https://bivector.net
- Cheat sheet: https://bivector.net/3DPGA.pdf
- PGA explained for devs: https://observablehq.com/@enkimute/understanding-pga-1
- Geometric algebra in JS, with interactive demos: https://github.com/enkimute/ganja.js
- C++ implementation of 3D PGA: https://github.com/jeremyong/Klein