A general theory for positioning and orienting 2D polygonal or curved parts using intelligent motion surfaces

We present a new approach to compute quasi-static and dynamic equilibrium positions and orientations (if any) of 2D polygonal or curved parts placed on general shaped 2D force field configurations. On the theoretical side, the novelty of our approach is that it puts into practice a fundamental result of piecewise-linear topology-the simplicial approximation theorem-and suggests an implementation using tools and techniques borrowed from modern computational geometry