decomposition is useful when you need to reverse the operation, and that you need to calculate the inverse of the transformation matrix. If you can decompose the operation nicely, every inverse matrix is easy and all you need to do is multiply the simple inverse matrices, therefore save a lot of computational cost.
MrRockefeller
but for decomposing regarding to interpolation, i think the useful part is to enhance user experience when they are, for example 3d rotating a CAD object. If you can parametrize the the interpolation with a t to make it tA+(1-t)A', it will save a lot of computational costs and the user can see a smoother transformation when they try to drag and look around the CAD object.
decomposition is useful when you need to reverse the operation, and that you need to calculate the inverse of the transformation matrix. If you can decompose the operation nicely, every inverse matrix is easy and all you need to do is multiply the simple inverse matrices, therefore save a lot of computational cost.
but for decomposing regarding to interpolation, i think the useful part is to enhance user experience when they are, for example 3d rotating a CAD object. If you can parametrize the the interpolation with a t to make it tA+(1-t)A', it will save a lot of computational costs and the user can see a smoother transformation when they try to drag and look around the CAD object.