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Math Help - Transformation matrices

  1. #1
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    Transformation matrices

    Using homogeneous coordinates, what is the transformation matrix (one matrix) needed to perform a rotation in 2D about point (2,1)^T and about 60 degrees?
    Last edited by posix_memalign; June 3rd 2010 at 07:15 AM. Reason: Forgot that it should be with homogeneous coordinates.
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  2. #2
    Newbie eigenvex's Avatar
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    If you were just rotating about the origin, the transformation matrix would just be your standard



    But now you have to perform 3 operations:

    1) Make (2;1) the "new" origin by shifting it to be the origin
    2) Rotate normally about the origin
    3) Translate back to the origin of (2;1)

    So your resulting transformation matrix will be the product of these three separate transformation matrices. The second is just the standard rotation matrix above (with theta = 60 degrees in your case).

    The first transformation, using homogeneous coordinates, translating (2;1) to be the new origin, is

    [1 0 -2
    0 1 -1
    0 0 1]

    And the third transformation, translating the origin to (2,1), is

    [1 0 2
    0 1 1
    0 0 1]

    So, multiplying these three matrices together will yield the final transformation matrix.
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