How do I do "soft" bends with a mesh

So the simple way of animating a mesh is to have one segment rotate into the other. So if it were a tube, you’d see a sharp bend, but how do I do a soft bend such that I’d see a round corner without having to manipulate each point outside of the shader? In my case I’m storing the mesh as a list of points, and a list sets of 3 indexes for each of the faces. Can it be done such that I have two matrix, one being the position of the original position and the other either being next transformation or the product of that transformation?