Basis3::from_axis_angle with unnormalized axis -> non-orthogonal matrix

[neuschaefer]

extern crate cgmath;

use cgmath::*;

fn main() {
    let axis = vec3::<f64>(1.0, 0.0, 1.0);
    let a = Basis3::from_axis_angle(&axis, deg(75.0).to_rad());
    let b = Basis3::from_axis_angle(&axis.normalize(), deg(75.0).to_rad());

    println!("a = {:?}", a.as_matrix3());
    println!("b = {:?}", b.as_matrix3());
    println!("Δ = {:?}", a.as_matrix3().sub_m(b.as_matrix3()));
    assert!(a.approx_eq(&b));
}

I see different ways to fix this:

• Document this behaviour in Basis3::from_axis_angle and possibly Rotation3::from_axis_angle. Assert that axis.length2() is approximately 1.0 at entry.
• Normalize all incoming axis vectors. Document that external normalization is not required (just in case someone figures out that the algorithm needs a normalized axis vector).

[kvark]

Optimally, I'd like to have the normalization property enforced by the type system, like nalgebra does. In this case we'd have the axis parameter with type NormalizedVector3 or something.