Spatial Motion

Generic spatial transforms and movement for Rust, built on geometric algebra traits.

Dimension-agnostic: works with any position, rotor, and bivector types that implement the right traits from the scalars and vector-space ecosystem.

Types

• Transform<P, R> — position (P) + orientation (R), with composition via *
• Movement<V, B> — velocity (V) + spin (B), applied to transforms via +=

Position can be any affine type (Point or Vector). Movement velocity is always a vector. They connect through P + V = P (Point + Vector = Point).

Operations

• Transform composition: transform * transform (requires position to support addition)
• Inverse: transform.inv()
• Apply movement: transform += movement
• Apply to point: transform.apply(point) or Transform::apply_point(&self, point)
• Interpolation: transform.lerp(&other, ratio)

Example

use ga2::{Bivector, Vector, Rotor};
use spatial_motion::{Transform, Movement};
use scalars::{One, Zero};

let mut transform: Transform<Vector<f32>, Rotor<f32>> = Transform::one();

let movement = Movement {
    velocity: Vector::new(1.0, 0.0),
    spin: Bivector::new(0.1),
};

transform += movement;

AI-assisted development

This crate is designed for use with AI coding assistants. Fully generic over position/rotor/bivector types, minimal trait bounds per method, and no implicit behavior. The Exp trait from scalars connects bivectors to rotors, and vector_space::Transform connects rotors to vectors.