Quaternion SLERP

Problem

Spherical linear interpolation between unit quaternions q1 and q2 at parameter t:

If dot(q1, q2) < 0, negate q2 for the shortest path. If the adjusted dot exceeds 0.9995, normalize the linear interpolation; otherwise use theta = acos(dot) and interpolate with sin weights. Return a unit quaternion.

Hint

Negating a quaternion represents the same rotation, so pick the hemisphere closer to q1.

Test cases

case 1

in: [[1,0,0,0],[0,0,0,1],0.5]

expected: [0.7071067811865475,0,0,0.7071067811865475]

case 2

in: [[1,0,0,0],[0,0,0,1],0]

expected: [1,0,0,0]

case 3

in: [[1,0,0,0],[0,0,0,1],1]

expected: [0,0,0,1]

case 4

in: [[0.7071067811865476,0,0,0.7071067811865476],[-0.7071067811865476,0,0,-0.7071067811865476],0.5]

expected: [0.7071067811865476,0,0,0.7071067811865476]

Starter codePython

def quaternion_slerp(q1, q2, t):
    # Your code here
    pass

4 test cases · run your code against them in the editor