Let them fall where they may: capture regions of curved 3D objects

When an object is placed on a supporting plane, gravitational forces move it to one of a finite set of stable poses. For each stable pose, there is a region in configuration space (a capture region) from which the object is guaranteed to converge to that pose. The problem of computing maximal capture regions for an object with a smooth convex hull is analyzed assuming only that its dynamics are dissipative; the precise equations governing the system are unnecessary. As examples from an implemented algorithm demonstrate, calculating these regions from a geometric model is computationally practical