So I'm working on multiple gaussian splat rendering in VRChatGaussianSplatting (via combining transformed splats into 1 texture).
One of the questions I have to everyone interested, is if shearing transforms of splats are necessary?
Because it actually makes it quite a lot more complex mathematically - I need to use SVD matrix decomposition to get the splat quaternion+scale back (or move to a symmetric 3x3 matrix representation for splats internally)
Another issue is that SVD introduces slight imprecision with the transform, and it looks slightly worse, so generally I'd do 3x3 symmetric, but that a quite a different rendering approach compared to native quat+scale.