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Do all 2D affine transformations become a shear operation in 3D?


I'm genuinely in awe of homogenous coordinates' power. I'm curious on why haven't I never seen it in other places. It seems to be extremely powerful as we can theoretically bump up the dimensions to be always 1 higher than what we are dealing with. Does it have its limitations?


Is it ever useful to go in the other direction, turning a linear transformation in 3D into an affine transformation in 2D?