Given 2 vectors in 3 dimensions and the angle between them (theta), determine the rotations required to get from v1 to v2.
3D Rotation
Rotation is applied on the x axis first, then y, then z, e.i. in the order x, y, z.
Rotating the x-axis rotates no other axes.
Rotating the y-axis rotates the axis of rotation of the x axis (see below).
Rotating the z-axis rotates the axis of rotation of the x and y axis (see below).
The z axis is never rotated
More background
Since the axis of rotation on which to rotate v1 to v2 theta radians, is the cross product of v1 and v2, an idealistic scenario would be to rotate some vector (I suspect would be (1,0,0), not sure) on the y and z axis so it is equal to the cross product vector, from which it can act as the rotational axis, on which the x rotation of theta can be applied; thus giving us the rotational (x,y,z) set. Given that the solution fits these constraints, there should be only one solution.
I suspect that the solution is ambiguous, e.i. there are multiple different rotation sets (x,y,z) that would result in the same vector result (from v1 to v2).
Rotating vectors
Problem:
Given 2 vectors in 3 dimensions and the angle between them (theta), determine the rotations required to get from v1 to v2.
3D Rotation
More background
Since the axis of rotation on which to rotate v1 to v2
thetaradians, is the cross product of v1 and v2, an idealistic scenario would be to rotate some vector (I suspect would be (1,0,0), not sure) on the y and z axis so it is equal to the cross product vector, from which it can act as the rotational axis, on which the x rotation of theta can be applied; thus giving us the rotational (x,y,z) set. Given that the solution fits these constraints, there should be only one solution.I suspect that the solution is ambiguous, e.i. there are multiple different rotation sets (x,y,z) that would result in the same vector result (from v1 to v2).