Methodology of Spatial Reasoning and Planning

Given a set of relative qualitative spatial relationships represented using theformalisms of Chapter 4 (e.g., the length and orientation of a link), two problems are of particular interest. First, how can one infer other new spatial relationships? Secondly, how can one synthesize a sequence of spatial configurations from an initial state to a goal state for a planar object which not only comply with the existing known geometric constraints but also satisfy some optimality criteria?