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Lecture 4: Transforms (44)

in this case is translation still accounted? Since S is diagonal, how can the translation happen here even with homogenous coordinates?


This decomp works with any matrix.

If you do it on a non-homogenized matrix then A = QSR' means that anything that non-homogenized matrix does (which excludes translation and perspective because it's non-homogenized) can be broken down into rotation-scale-rotation.

If you use a homogenized matrix then everything include translation and perspective can be expressed as rotation-scale-rotation, which sounds crazy but remember you are now in n+1 dimensions because of the added W coordinate. So translation in 3D is rotation-scale-rotation in 4D...

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