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.