Some embodiments of the invention provide a method of specifying a cost function that represents the estimated distance between an external state and a set of states in a multi-state space that represents a region of a design layout. The method identifies a polygon that encloses the set of states. It then identifies vectors to project from the vertices of the polygon. Based on the projected vectors, the method identifies a set of distances that includes the distance between the polygon and each point in a set of points in the external state. The method then uses the identified set of distance to specify the cost function.

 
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