US Patent 7219108 Query prunning using exterior tiles in an R-tree index

Determining relationships among objects represented in a database includes defining a plurality of tiles in the approximation of the first geometry by dividing the approximation of the first geometry in a first direction a plurality of times and dividing the approximation of the first geometry in a second direction perpendicular to the first direction a plurality of times. A second geometry is analyzed to determine if it fulfills a first filter condition with respect to any of the tiles defined in the approximation of the first geometry. If the second geometry fulfills the first filter condition with respect to any of the tiles defined in the first geometry carrying out a mathematical comparison of the first geometry and the second geometry.