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Is the inverse of an orthonormal basis always equal to the transpose?

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Indeed. This is one of the many optimizations you can employ when working with 3x3 rotation matrices (or a 4x4 transformation matrix, as long as you handle the rotation and translation components separately).

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That's nifty. I saw how gluLookAt worked and wondered why they constructed the matrix that way.

Which is a better coordinate system, left-handed or right-handed? Which is more popular?

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Quote:
 Original post by BoderThat's nifty. I saw how gluLookAt worked and wondered why they constructed the matrix that way.
Note that the gluLookAt() implementation is based not only on the inverse-transpose equivalency, but also on the property (AB)^-1 = B^-1*A^-1.
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 Which is a better coordinate system, left-handed or right-handed? Which is more popular?
That's sort of unrelated, but basically:

1. DirectX is LH but offers RH versions of most functions
2. OpenGL is RH, but can probably be coerced into being LH by constructing your own matrices
3. I think most math and physics references assume a RH system
4. I don't know what the various modelling programs use, but google will probably tell you

Once you understand the underlying math, switching back and forth between the two when necessary isn't too hard.

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Quote:
 Original post by BoderWhich is a better coordinate system, left-handed or right-handed?

Neither is better. The question is akin to "which is better, clockwise or anticlockwise?"

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Are eigenvectors and eigenvalues used in 3D graphics?

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Yes :).

One example use is helping fit Oriented Bounding Boxes (OBBs) to geometry.

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