Shortest Rotation Between Two Quaternions

Unity Engine
,
1

I am needing to get the shortest rotation path between two quaternions.

Quaternion a;
Quaternion b;

var c = a * Quaternion.Inverse(b);

c is usually the shortest path, but there are instances where it is the significantly longer rotation.

Is there an easy way to guarantee that c is always the absolute shortest rotation between a and b?

2

I think the Slerp operation is what you want:

The reason I think this is that article mentions “great circle arc,” which is of course what airliners do to get the shortest distance between distant airports.

3

can you maybe check if the rotation of c is over 180/pie and if so just flip it?

4

Hey Kurt good find, I was able to extract what I needed out of this. Here is the fix for anyone else running into this -

{
if (Quaternion.Dot(a, b) < 0)
{
return a * Quaternion.Inverse(Multiply(b, -1));
}
else return a * Quaternion.Inverse(b);
}

public static Quaternion Multiply(Quaternion input, float scalar)
{
return new Quaternion(input.x * scalar, input.y * scalar, input.z * scalar, input.w * scalar);
}```
8 Likes
5

I think you are imagining that c is a float representing the angle between two vectors. In the example c is a Quaternion representing the rotation to get from one orientation to another.

6

sorta but not really, just look if that rotation(c) is looking over 180 degrees from “0” rotation…?

I guess quaternion doesn’t work anything like that eh?
lucky there’s all of those functions, haha. :face_with_spiral_eyes:

7

This is exactly what I was looking for today. Thanks for sharing Guadinman!