This invention provides methods, systems and apparatus for performing fast computation of metric queries. To achieve this, in an example embodiment, the present invention segments metric regions into disjoint primitive atomic shapes. It then represents these primitive atomic shapes and then performs off-line computation of their relevant properties. As a result of the off-line computation, the execution of a query requires a minimal number of on-line calculations resulting in a very fast query. Further optimization occurs via storage of query histories and prioritization of queries with respect to the access frequency of a metric space's primitive atomic shapes.