Ordered sets are used as a computational model for motion planning in which figures on the plane may be moved along a ray emanating from a light source. The resulting obstructions give rise to ordered sets which, in turn, are precisely the (truncated) spherical orders. We show too, that there is a linear-time algorithm to recognize such ordered sets. This paper is inspired by an article of Rival and Urrutia [5] in which a computational model for motion planning is introduced based on ordered sets. According to this model, robots are idealized by convex figures on the plane and their motion on the plane is studied by assigning to each a direction along which it may be moved with some velocity. The objective may be to separate these robots efficiently or, perhaps, to relay messages among them.
Let F be a family of closed connected plane figures and x a point on the plane not contained in any element of F. For figures A and B we say that B obstructs A if there exists a point b in B such that the line segment joining x to b intersects A. We write A-B. More generally, we say that B blocks A, and write A < B, if there is a sequence A = Al+ AZ+ * * -+Ak = B. This relation < is transitive, and it is called a blocking relation. If the blocking relation has no directed cycles then it is antisymmetric too. In that case the blocking relation < is a (strict) order on the set of these figures. (See Fig. 1.)
An order P has a light source representation if there is a (reference) point x, a