Conversions between a Rotor3 and quaternions

[expenses]

Ultraviolet is awesome and I love using rotors, but it's tricky to integrate it with other geometry crates such as ncollide3d because you have to convert Rotor3s by going though Rotor3 -> Mat3 -> array -> other matrix type -> quaternion type. It would be lovely to have two conversion functions like:

fn from_quaternion_array(quaterion: [f32; 4]) -> Self;
fn to_quaternion_array(&self) -> [f32; 4];

I'm happy to implement this, but I've been unable to find out the maths to do this thus far.

[thenlevy]

According to paragraph 3.8 of this article writing those functions should be quite easy: one just need to swap the first and third component of the imaginary part. For example r.to_quaternion_array() = [q.s, q.bv.yz, q.bv.xz, q.bv.xy]

[expenses]

@thenlevy awesome, thanks! From experimenting, I'm pretty sure you have to invert the i and j (here x and z) parts of the quaternion, but I haven't worked out why:

fn na_quaterion_to_rotor(quaternion: ncollide3d::na::geometry::Quaternion<f32>) -> Rotor3 {
    Rotor3::new(quaternion.coords.w, ultraviolet::Bivec3::new(-quaternion.coords.z, quaternion.coords.y, -quaternion.coords.x))
}

[fu5ha]

The i/j (x/z) components need to be inverted because ultraviolet currently uses the xz basis vector rather than the zx basis vector (i.e. pointed the opposite direction), which is common in other literature/implementations.