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Shortest Rotation Between Two Quaternions

Discussion in 'Scripting' started by imchrissharp, Jan 19, 2020.

  1. imchrissharp

    imchrissharp

    Joined:
    May 2, 2018
    Posts:
    15
    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. Kurt-Dekker

    Kurt-Dekker

    Joined:
    Mar 16, 2013
    Posts:
    38,656
    I think the Slerp operation is what you want:

    https://en.wikipedia.org/wiki/Slerp

    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. SparrowGS

    SparrowGS

    Joined:
    Apr 6, 2017
    Posts:
    2,536
    can you maybe check if the rotation of c is over 180/pie and if so just flip it?
     
  4. imchrissharp

    imchrissharp

    Joined:
    May 2, 2018
    Posts:
    15
    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 -


      public static Quaternion ShortestRotation(Quaternion a, Quaternion b)
    {
    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);
    }
     
  5. Antistone

    Antistone

    Joined:
    Feb 22, 2014
    Posts:
    2,836
    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. SparrowGS

    SparrowGS

    Joined:
    Apr 6, 2017
    Posts:
    2,536
    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. :confused:
     
  7. walaber_entertainment

    walaber_entertainment

    Joined:
    Jul 10, 2017
    Posts:
    30
    This is exactly what I was looking for today. Thanks for sharing Guadinman!