Fixes armature deformation bug when Preserve Volume is enabled and deforming bones are both rotated and scaled.
The bug happens because Preserve Volume uses Quaternion to interpolate rotations. A bone has 3 parts of data describing its deformation: Quaternion(w,x,y,z) rotation (`quat`), Translation(w,x,y,z) (`trans`), and Scaling(4x4 matrix) (`scale`). To calculate deformed position of a vertex `r`, it will be firstly scaled by `scale`, then rotated and translated by `quat & trans`.
The 4x4 scaling matrix `scale` has a 3x3 part `S33` about scaling and shearing along 3 axes, and a vector part `ST3` that further translate the scaled position. i.e. `scale@r = S33@r + ST3`. This enables scaling about an arbitrary "pivot" (a point `r0` satisfies `scale@r0 = r0`).
However, when blending influence of multiple bones, different bones have different scaling pivot (their head position). Since quaternion rotation and translation/scaling are not commutative operations, this is what I believe causing this bug.
How this is fixed:
Note that the translational part `ST3` of the scaling matrix is redundant in functionality with Translational part `trans` in deformation data. There exists an equivalence transformation that simultaneously change `trans` and `ST3`, while keeping the deformation unchanged.
I applied this equivalence transformation to move the pivot to the vertex that the bones are deforming, before blending multiple bone transformations. Note that now the vertex is the pivot, so scaling transformations will not change its position. Further blending/applying of scaling matrices can be avoided.
Pull Request: https://projects.blender.org/blender/blender/pulls/108134
f12e9f32b5