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question on skinning with 'relative deformations'

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Okay. So I perfectly understand the usual skinning system. You have an initial bone matrix B[sub]i[/sub] which gives the initial bone-to-mesh transformation. Then you have a current bone-to-mesh matrix B[sub]f. [/sub]To compute the shift from initial(bind) pose to current pose, you are interested in the transformation T such that T*B[sub]i[/sub] = B[sub]f[/sub] so solving gives T = B[sub]f[/sub] B[sub]i[/sub] [sup](-1)[/sup] (Order of multiplication may need to be reversed depending on what system you're using, but same elements)

Okay thats fine. However! In the graphics package I am currently using, skin deformations also inherit from parent deformations. So the deformations from a bone are relative to other deformations. Call the initial/final parent deformations A[sub]i[/sub] and A[sub]f[/sub] respectively.

I am extremely puzzled because the transformation the example code uses is: A[sub]i[/sub]A[sub]f[/sub][sup](-1)[/sup]B[sub]f [/sub]B[sub]i[/sub] [sup](-1)[/sup][sup] [/sup] Notice it uses the inverse of the final matrix. I would have expected the inverse of the initial to come first.

I guess its worth mentioning that the complete transformation is carrried out in a particular node's space with transformation M so the total transformation formula is:

But that matrix M is not time dependant so I don't think this matters much.

Its also worth mentioning that the documentation did not give a very clear explanation on exactly how deformations are inherrited. So if anyone has a good hypothesis on that, for which the given formula makes sense, I'd love to hear it!

(edit) So I came up with a HAZY idea of what might be happening. Assume there is no bone shift (B[sub]f[/sub] = B[sub]i[/sub]) so the transformation is just A[sub]i[/sub]A[sub]f[/sub][sup](-1)[/sup]and consider the following diagram:


On one hand, this can be interpretted as the coordinate system 'A' shifting to the right. But if the coordinate system is viewed as the point of reference, then the mesh is actually shifting to the left. This would explain the reverse order shift from A[sub]f [/sub]to A[sub]i[/sub]

The exact story is still very blurry to me though. Anyone that can offer some insight here would be very much appreciated! Edited by mv348

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