Quaternion Slerp honors closest distance.

[nitrix]

Hello,

This is a fix to the quaternion spherical linear interpolation to make it choose the shortest linear path which is the intended behavior in graphical animations.

• This is glTF's tutorial by Khronos with a reference Slerp implementation (glTF trying to be the standard for 3D model):
  https://github.com/KhronosGroup/glTF-Tutorials/blob/master/gltfTutorial/gltfTutorial_007_Animations.md#linear

//make sure we take the shortest path in case dot Product is negative
if(dotProduct < 0.0)
    nextQuat = -nextQuat
    dotProduct = -dotProduct

• This is the cglm library (GLM being used by practically every 3D engine out there).
  https://github.com/recp/cglm/blob/master/include/cglm/quat.h#L701-L704

if (cosTheta < 0.0f) {
    glm_vec4_negate(q1);
    cosTheta = -cosTheta;
}

You'll find that my changes are in the same spirit as them. Added a test too.

// Make sure we take the shortest path in case dot product is negative.
if dot < 0.0 {
    q2 = q2.Scale(-1)
    dot = -dot
}

This is a very well known problem. Wikipedia documents it here in detail:
https://en.wikipedia.org/wiki/Slerp#Quaternion_Slerp

However, because the covering is double (q and −q map to the same rotation), the rotation path may turn either the "short way" (less than 180°) or the "long way" (more than 180°). Long paths can be prevented by negating one end if the dot product, cos Ω, is negative, thus ensuring that −90° ≤ Ω ≤ 90°.

I ran into this corner case using mathgl, my fork will stay up until the changes can get upstream:
https://github.com/nitrix/mathgl/tree/fix/quat-slerp-closest

Cheers,
Alex.

[dmitshur]

LGTM. Thanks.

This change makes sense and looks right to me. I plan to merge later this week, to give a chance for additional comments.