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Rotation matrix

Started by Matheass 2 replies 800+ views
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Matheass
Matheass
I was looking on the math of matrixcalculations of openGL, espesially the calculations of modelview-transformations. I looked at the online version of the Red Book, Appendix F. I can''t understand the calculation of the rotation matrix: - What''s the T? - What''s uu^T? - What''s I-uu^t? Thank you for help!
Brother Bob
Brother Bob
T means transposed; you flip the matrix about the main diagonal. If A=BT, then aij=bji.
u is the normalized axis of rotation.
I is the identity matrix.

Matheass
Matheass
but "u" is a vector and "uu" must be a matrix. I doesn''t undersatand how to get this matrix?
Brother Bob
Brother Bob
It's normal matrix multiplication.

    [x]
u = [y]
    [z]
      [x]             [x*x  x*y  x*z]
uuT = [y] * [x y z] = [y*x  y*y  y*z]
      [z]             [z*x  z*y  z*z]


[edited by - Brother Bob on January 16, 2004 6:38:48 AM]

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