Interpolating Unit Quaternions

• To interpolate two orientations
  • Could use linear interpolation on all entries of quaternion (i.e. treat as four-dimensional vector)
  • Unfortunately, intermediate quaternions would not have unit norm
  • Angular velocity would not be constant even if renormalized
• Solution: spherical linear interpolation, or the slerp.
  • Consider the quaternions as vectors
  • Find the angle between them:

    

  • Given parameter , the slerp interpolated value is

    

  • Numerical difficulties when .

    Replace the slerp with a lerp.

  • Also a problem with ;

    Should probably be flagged with an error and/or a request for more keyframes.