Implement Godot methods for Quat

[Demindiro]

No description provided.

[Demindiro]

glam's from_quat method calls this internally:

    #[inline]
    fn from_quaternion(rotation: XYZW<T>) -> Self {
        glam_assert!(rotation.is_normalized());
        let x2 = rotation.x + rotation.x;
        let y2 = rotation.y + rotation.y;
        let z2 = rotation.z + rotation.z;
        let xx = rotation.x * x2;
        let xy = rotation.x * y2;
        let xz = rotation.x * z2;
        let yy = rotation.y * y2;
        let yz = rotation.y * z2;
        let zz = rotation.z * z2;
        let wx = rotation.w * x2;
        let wy = rotation.w * y2;
        let wz = rotation.w * z2;

        Self::from_cols(
            V3::new(T::ONE - (yy + zz), xy + wz, xz - wy),
            V3::new(xy - wz, T::ONE - (xx + zz), yz + wx),
            V3::new(xz + wy, yz - wx, T::ONE - (xx + yy)),
        )
    }

Godot's Basis constructor uses set_quat internally and looks like this:

void Basis::set_quat(const Quat &p_quat) {

        real_t d = p_quat.length_squared();
        real_t s = 2.0 / d;
        real_t xs = p_quat.x * s, ys = p_quat.y * s, zs = p_quat.z * s;
        real_t wx = p_quat.w * xs, wy = p_quat.w * ys, wz = p_quat.w * zs;
        real_t xx = p_quat.x * xs, xy = p_quat.x * ys, xz = p_quat.x * zs;
        real_t yy = p_quat.y * ys, yz = p_quat.y * zs, zz = p_quat.z * zs;
        set(1.0 - (yy + zz), xy - wz, xz + wy,
                xy + wz, 1.0 - (xx + zz), yz - wx,
                xz - wy, yz + wx, 1.0 - (xx + yy));
}

The implementations are different, which could be the cause of the inaccuracy. Then again, the to_basis test does pass...

[Bromeon]

Thanks a lot for the contribution! 🙂
I left some comments.

[Bromeon]

Looks mostly good, added a last few cosmetic remarks.
In my opinion this can be merged afterwards 🙂

[Bromeon]

Missed your comments at first. Hope I got them all now 🙂

[Bromeon]

bors try

[bors]

try

Merge conflict.

[Bromeon]

Thanks for the quick adaptation! I'm waiting for @setzer22's feedback (who is a big user of quaternions), after that we can merge 🙂

bors try

[bors]

try

Build failed:

• ci

[Bromeon]

bors try

[bors]

try

Build succeeded:

• ci

[Bromeon]

bors r+

[bors]

Build succeeded:

• ci

[Bromeon]

Thanks a lot for the work @Demindiro and for the (off-site) feedback @setzer22!