How does "Shear" work in transform/edit/polyextrud?

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Does anyone understand and can explain how this damn "Shear" works? To get the right shift, I rotate the pivot every time, try to enter values ​​in different axes. Sometimes I manage to get the right shear, sometimes not, even after trying all the pivot turns.
X, Y, Z carry some unknown function, completely unrelated to the world X, Y, Z.
Even a year later, I have not managed to figure out the principle of choosing the "Shear" direction. Are there people who understand this? Write, please!
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shear 1 adds s1 * y to x
shear 2 adds s2 * z to x
shear 3 adds s3 * z to y

There are other shears, but only 3 are possible with the transform sop.
Enable output attribute "xform" and observe the values in the resulting matrix to see the direct effect on a single cell that a shear has.
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Might need to take a deep dive into linear algebra, but this is a simple case
|1 1|  X  |x|=|x·1+y·1|=|x+y|
|0 1|     |y|=|x·0+y·1|  |y|
This is shear: another element's value contribute to this element's position on this element's axis
Like sitting on an empy box and causing it its top to move horizontally first and then collapsed


I have this problem when I use edit tool and use scaling to tweak positions of two joints.
Then although the skeleton looks normal and even in rigvis node it is normal, when I plugin the skeleton into an IK chain node
the whole system explodes, joints start rotating to very wired angles.

What I did is to use skeleton tool to tweak position of joints.

Perhaps you could share a hip file containing the minimum system?
Edited by goose7 - 2024年8月22日 08:24:19
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