Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

3D Rotations using complex numbers

  1. Oct 25, 2013 #1
    I was thinking that if you could use quaternions to rotate an object using quaternion algebra that there might be a way to rotate an object using complex numbers in some fashion. I was looking at quaternion rotation of a vector and the amount of operations seemed to be a lot. Of course it levels out or even out performs matrices with linear interpolation and concatenation of rotations. But anyhow what i decided to do was rotate a vector (x ,y , z) = x + yi + zj

    with the rotation complex numbers
    (a + bi)
    (a + bj)

    a = cos

    b = sin

    Following this algorithm
    (a + bi)(x + yi) = x' + y'i
    (a + bj)(y' + zj) = y'' + z'j

    the new rotated vector is x' + y''i + z'j;
    This works, it rotates the object and preserves the magnitude of the vector.

    What I don't understand is how it is rotating the object.

    When I put in 90 degrees v(1,0,0) goes to v(0,0,1) to (0,-1,0) back to (1,0,0)

    When I put in 90 degrees v(1,1,1) goes to v(-1,-1,1) to (1, -1, -1) to (1,1,1)

    My question is: Is it rotating around an axis? Can it be changed? Is it Euler angles in disguise?

    Why is it the first time it rotates by 90 degrees when I put in 90?

    Then it rotates 180 when I still have 90 degrees in?
     
  2. jcsd
  3. Oct 25, 2013 #2

    UltrafastPED

    User Avatar
    Science Advisor
    Gold Member

    Sure ... complex numbers are natural for 2D rotations, just as quaternions are natural for 3D rotations.

    But you can also do rotations with matrices; see SO(3).

    The question which you have found, what is the axis of rotation, is to be found in the construction of the above systems.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: 3D Rotations using complex numbers
  1. Rotating circles in 3D (Replies: 2)

  2. Complex numbers (Replies: 5)

Loading...