A library for doing Euclidean Plane-Based Geometric Algebra (basically, "Projective Geometric Algebra") in Unity, based on the bivector.net library. It includes operator overloading and conversion between Unity-style objects and PGA-style objects, i.e. Unity quaternions and vectors and PGA points, directions, rotors and motors.
- Copy the .cs file into your project folder alongside your other .cs files
- Put the line
using static PGA3D;at the top of any file you want to use PGA in, and you're good to go!
I can recommend the Bivector Discord. You can ask any question, from the most basic to the most advanced, and there should be someone there to help you!
- There may be a problem with the minus signs of the join and projections. It is very unlikely to affect anyone. This is ongoing research in my opinion
- Conversion to Matrix4x4. This should be easy, I just don't have time.
- Dedicated Dual Quaternion, Bivector, point, plane classes. Add in flector and now we're more typed I guess?
- Perhaps you should even just be able to use unity planes as- is. Not vectors though, there's unavoidable ambiguity about directions vs positions in there
- Arbitrary distance and angle formulae
- Overload some operator to do sandwiching
- More compatibility with FABRIK
- I might be being paranoid to have (~X) rather than just ~X
- I have some visualizations of the objects you get in this library, which you can see in this video: https://www.youtube.com/watch?v=KY9SzXLmBQI and it miiiight be worth putting these in?
hamish.todd1 at google's email service, or hamish_todd on twitter
Aside from writing (the code that generated) the initial version of this library, I am heavily indebted to Steven De Keninck! Indebted too to others who helped me including Pontus Granström, Chris Doran, Anthony John Bell, Charles Gunn, Hugo Hadfield, Eric Lengyel, and Martin Roelfs
This library was developed at Imagination Technologies. If, like Houdini/Maya, you want nice skinning by running the Dual Quaternion exp and log on your GPU, make sure you use an ifdef to look out for our "sinc" function, which enables you to write it in a much more performant way!