Vector Space Traits

A collection of traits for generic vector math in Rust. Provides VectorSpace, DotProduct, InnerSpace (with normalize, project, reject, reflect, angle, etc.), and free functions like distance and interpolate.

Designed for custom vector types (2D, 3D, Geometric Algebra, etc.). Implement once, get dozens of methods for free. Works with no_std.

Features

• Efficiency: Inline defaults, no allocations
• Useful trait methods for inner space: magnitude(), normalize(), project(), reject(), reflect(), angle(), etc.
• Flexible for multivectors: Provides OuterProduct and DotProduct traits
• Free functions: distance(), distance2(), interpolate()
• no_std: Full support (libm for floats)
• Heterogeneous operations: Vector.dot(Rotor) → Rotor (GA-friendly)

Geometric Algebra Example

use vector_space::{VectorSpace, InnerSpace, DotProduct};

// Assume your GA types: Vector, Bivector, Rotor
impl VectorSpace for Vector<f32> { type Scalar = f32; }
impl InnerSpace for Vector<f32> {
    fn scalar(&self, other: &Self) -> f32 { /* dot */ }
}
impl DotProduct<Bivector<f32>> for Vector<f32> {
    type Output = Vector<f32>;  // Geometric product grade filter
    fn dot(self, biv: Bivector<f32>) -> Vector<f32> { /* impl */ }
}