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mathgraphics3drotationcomputer-vision

Math: How to convert a left-handed transformation matrix to a right handed one

I have a transformation matrix (rotation + translation) which was constructed in a right-handed coordinate system where X is right, Y is up and Z is into the screen.

If I want to apply this same transformation but in a left-handed coordinate system where X is right, Y is down and Z is out of the screen (is this left handed?) what alterations should I make to the existing transformation matrix.

Thanks

Solution

  • a right-handed coordinate system where X is right, Y is up and Z is into the screen

    Then it's a left-handed coordinate system: X is the thumb, Y is the forefinger, Z is the middle-finger. Your right hand should not be able to do what you describe without breaking a few bones :-p

    a left-handed coordinate system where X is right, Y is down and Z is out of the screen

    This one is indeed a left-handed coordinate system too.

    As for the transformation linking these two, this is a simple 180° rotation around the X axis (beware of the wrist sprain while trying this one), which expresses as the following 3x3 matrix:

    (1  0  0)
(0 -1  0)
(0  0 -1)

    You can pre-multiply your transformation with this one!

    Hope this helps!