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inverse transpose

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i understand the way it works is as thus: from world space : coordinates with the inverse matrix take you to object space. using the original matrix, you can then get back to world space. for normals, from object space you use the inverse transpose matrix to transform the normal to world space. however, does the inverse transpose method still work when the matrix is not just a combination of translations,scales and rotations, but also shears?

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Quote:
Original post by luca-deltodesco
however, does the inverse transpose method still work when the matrix is not just a combination of translations,scales and rotations, but also shears?

No. It doesn't even really work for arbitrary shear-free transformations. The inverse-transpose method relies on orthonormality of rotations and symmetry of scaling.

Unless your world-view matrix is a RST composition it's best to extract the homogeneous part manually. That is, extract the upper-left 3x3 minor and normalise each row (or column, for column-vector setups).

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so if i have my 4x4 matrix containing the full transformation of shears, rotations, axial scales and translations so its in the form;

a b c d
e f g h
i j k l
0 0 0 1

i can just take the first 3x3 minor, normalise the collumns and it would be in a suitable form to take inverse transpose for normals?

[Edited by - luca-deltodesco on December 31, 2007 6:12:31 AM]

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