g3

Rust crate for plane-based projective geometric-algebra for 3D aka the Clifford Algebra with signature P(R*_3,0,1).

API

Plane

Point

Line

Meet Operation ^

Join Operator &

Inner Product |

Geometric Product *

a*b = a|b + a^b

Sandwich Product a(b)

Dual Operator !

Get Started

This software uses some of Rust experimental feautures like fn_traits so make sure to compile using the nightly release.

bash rustup update -- nightly

bash cargo +nightly build

Build Doc

RUSTDOCFLAGS="--html-in-header src/doc.html" cargo doc --open

Run example

cargo +nightly run --example elements --features="mirror"

Awesome Links

• Bivector, community site with more info on geometric algebra including videos, software and a discrord server.
• Videos:
  • Siggraph2019 Geometric Algebra, Talk explaining the why and a bit of the how of GA.
• Software:
  • Klein is a similar project in C++ as was the inspiration for g3.
  • ganja.js, JavaScript library for geometric algebra of arbitrary signature.
• Articles:
  • Geometric Algebra - Duality and the Cross Product
  • Geometric Algebra Tutorial
  • https://mattferraro.dev/posts/geometric-algebra
• Cheat Sheet
• May the forque be with you: Rigid body dynamics in PGA
• The Geometry of 3DPGA products
• PGA Easy
• Automatic differentiation
• Paper with CGA
• New Developments in Projective Geometric Algebra
• Flectors
• Space & Antispace
• Rational trigonometry via projective geometric algebra
• Alan Macdonald videos
• Geometric Calculus Talk
• Lecture playlist
• TensorFlow-based framework for Geometric Algebra

https://enki.ws/ganja.js/examples/coffeeshop.html#ydDtaGu0a