symtropy-math

N-dimensional geometric algebra for game physics. Stack-allocated, zero-heap, const-generic.

use symtropy_math::{Point, Bivector, Rotor};

// 3D rotation in the xy plane by 90°
let plane = Bivector::<3>::unit_plane(0, 1);
let r = Rotor::from_plane_angle(&plane, std::f64::consts::FRAC_PI_2);
let p = Point::<3>::new([1.0, 0.0, 0.0]);
let rotated = r.rotate_point(&p); // → (0, 1, 0)

// Works in 4D too
let tesseract_rotation = Bivector::<4>::unit_plane(0, 3);
let r4d = Rotor::from_plane_angle(&tesseract_rotation, 0.5);

Features

• Point<D>, Bivector<D>, Rotor<D>, Transform<D> — all const-generic
• Shape<D> trait with GJK-compatible support function
• Sphere<D>, ConvexHull<D>, Hyperplane<D> colliders
• Stack-allocated via nalgebra::SVector — zero heap in hot paths
• Works in 2D, 3D, 4D, or any dimension
• WASM compatible

Why Bivectors Instead of Quaternions?

Quaternions only work in 3D. Bivectors (oriented planes) generalize rotations to any dimension. A rotation happens in a plane, not around an axis. In 4D there are 6 rotation planes — bivectors handle this naturally.

Part of the Symtropy consciousness-physics engine.