Patent ID: 7239989

Claim:
A method for determining a within-distance relationship between a first geometry object and a second geometry object, the method comprising: receiving a query; and providing the query to a first filter configured to: define an exterior approximation of the first geometry and the second geometry; compute a distance between the exterior approximations; compare the computed distance with a first predetermined distance to determine whether the second geometry satisfies a first filter condition with respect to the first geometry, and if the first filter condition is satisfied, providing the second geometry to a query result set, otherwise, defining an interior approximation of the first geometry; expanding the interior approximation by a second predetermined distance; and comparing the expanded interior approximation with the second geometry to determine if the second geometry satisfies the first filter condition with respect to the first geometry; and if the first filter condition is satisfied, providing the second geometry to a query result set, otherwise, providing the first geometry and the second geometry to a second filter configured to perform an exact mathematical comparison of the first geometry and the second geometry to determine whether the second geometry satisfies a second filter condition with respect to the first geometry; and if the second filter condition is satisfied, providing the second geometry to the query result set, otherwise, excluding the second geometry from the query result set, wherein the result set specifies that the within-distance relationship between the first geometry object and the second geometry object is satisfied.