Curvature from sliding

We introduce a novel interpretation of the curvature over discrete surfaces that allows to compute a multi scale measure of principal directions and values of curvature and which is robust with regards to tessellation degeneracies and geometric and topological noise. The key observation is that there is a direct relation between the way a portion of surface can rotationally slide over a surface and the directions of principal curvature. We exploit such relation to setup a optimization problem that we use to actually compute the curvature values in a novel way.