I'm using the Douglas peucker (DP) algorithm to simplify some (2d) closed paths forming a shape. This works pretty good, but not so much for closed paths that have some symmetry. Take for example a pyramid like shape, with the slopes essentially being staircases. Depending where you define the start for DP it will (obviously) result in different simplified shapes.
Does anyone know of some sort of generic symmetry preserving simplification algorithm? In the case of (a top up) pyramid you could force this manually by having DP run from the end vertice of the top line to the first vertice of the bottom line, and another run from the end vertice of the bottom line to the first vertice of the top line. but this is of course very specific to the symmetry of this particular pyramid.