I would like to open a discussion on future improvements for Corrective smooth modifier.
On August 2021, a new study was published on Direct Delta Mush Skinning Compression.
This study centers on improving rigging workflow by trying to remove unneccessary manual rigging that is needed on animating a humanoid.
The first study to Delta Mush was introduced in 2014 and was implemented in 2015 as Corrective smooth modifier
As the July 2019 study says on page 113:4 :
“The core idea of Direct Delta Mush schemes. The accumulated affect of iterated Laplacian smoothing is captured in a per-vertex weight mask (column Bi , red color gradient) that if applied to the undeformed geometry produces the equivalent of the iteratively smoothed result (inner blue geometry). These weights are used to solve for the local coordinate transformation Γi which is defined as the best rigid transformation to align the local patch (red regions) from the rest pose to the LBS deformed pose,
a.k.a. a form of Weighted Procrustes problem. The delta between ui and ̃ui is also transformed and added to the smoothed deformed position ̃vi ,producing the final vertex position xi .”
The continued studies to this subjects were introduced in July 2019:
And the newest was released in August 2021:
For reference on different type of skinning methods, kindly check the following:
The study also shows that the vertice positions can be calculated using matrix.
I wanted to bring this forward as someone who is interested in new studies for improved workflow on Blender.