Functional Granularity

The method presented in this paper aims to reduce the computational costs of some kinds of navigation in a world with obstacles. We give algorithms to capture the logical structure of an object given a polygonal representation of it. Then these algorithms are used in conjunction with the notion of functional granularity to handle navigation of a moving object. 1 Framework The class of problems we are interested in deals with physical interactions among a set of objects. Several works (often labelled \Qualitative Spatial Rea-soning") choose a local approach of the problem: an object is not located with regard to an origin (with a coordinate system for instance). The position of an object is rather determined with its spatial relations to other objects. A set of objects is then described by a list of qualitative relations among them. Providing objects have only limited spatial innuence, local relations are often suucient to a complete description, a good choice of relations thus providing a quite short description. 2 Precision of the representation Depending on the studied relations, the precision of the representation of the objects has to be adapted. For instance, the representation of an object can be as simple as a point (a town in a country located with respect to other cities), or very complex (the same town with regard to a car navigating in the town). Two opposite technics can then be envisaged: The maximal needed precision is predictable. Each object can then be represented at the given precision. It is very eecient if the targeted application only use relations that need little diierent precision level. At the opposite, if two of the used relations need very diierent precisions, the one that needs only simple representation could be limited in its eeciency, handling to complex representations. The previous condition is not possible (or not wanted). The grain of the representation must be adapted for each relation. Such a system could then handle relations with quite diierent level of precision in the representation of objects. We choose to take an interest in the last option, and present in this framework the notion of functional granularity. 3 Matching granularity and functionality of a relation By studying a set of objects and a type of relation on this set, the characteristics of the objects needed to apply the relation can be determined. If we focused on qualitative spatial relations, the following classiication …