Abstract: A method for locating neighboring data geometries of a query geometry. A minimum bounding rectangle of the query geometry is determined. A minimum bounding rectangle of each data geometry is determined. Candidate data geometries are identified by determining if a distance between the minimum bounding rectangle of the query geometry and the data geometry is less than a threshold distance. A distance between the query geometry and the candidate data geometry is mathematically calculated when a number of candidate data geometries equals a threshold number or when no more data geometries remain.

Abstract: To determine relationships among objects represented in a database at least one interior rectangle lying entirely within a first geometric shape is define. A minimum bounding area for the first geometry and a minimum bounding area for a second geometry are defined and compared with one another to determine if the second geometry fulfills a primary filter condition of an interaction between the first and second geometries. Based on the fulfillment of the primary condition by the second geometry, it is determined whether an intermediate filter condition of interaction between the first and second geometries is fulfilled by analyzing the distribution of the second geometry with respect to at least one interior rectangle within the first geometry. It is determined whether the second geometry fulfills a secondary filter condition by comparing the second geometry with the first geometry if the second geometry fulfills the primary filter condition.

Abstract: A method for locating neighbor objects of a query object in a database. A query tile set is defined including a plurality of tiles that define an initial query radius that the query object is grouped within. Neighbor objects are located within the initial query radius. A number of neighbor objects within the initial query radius is determined. The query radius is expanded beyond the initial query radius by defining an expanded query tile set beyond the query tile set if the number of neighbor objects is less than a target number. Neighbor objects are located within the expanded query radius. It is determined whether a number of neighbor objects within the expanded radius corresponds to a target number. The query radius is expanded and neighbor objects located within the expanded radius until the number of neighbor objects equals or exceeds the target number.

Abstract: A method and software for bulk insertion of data into a spatial or other multidimensional-keyed index are described that includes partially reorganizing the selected portions of the index while inserting data in bulk. In one implementation using an R-Tree, whenever new data are inserted into the entries of a node, potentially overlapping entries of a node can be treated as a big cluster node and reorganized to reduce the overlap of bounding boxes among entries in the big cluster node.

Abstract: 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.

Abstract: A method for determining relationships among data representing regions on a surface of a body. The method includes identifying a center of a first geometry. A minimum distance is identified from the center to a boundary of the first geometry. A first circle is defined on the surface of the body having the minimum distance as its radius and the center of the first geometry as its center. The first circle is compared with a second geometry to determine if the second geometry fulfills a first filter condition with respect to the first geometry.

Abstract: A method for locating neighboring data geometries of a query geometry. A minimum bounding rectangle of the query geometry is determined. A minimum bounding rectangle of each data geometry is determined. Candidate data geometries are identified by determining if a distance between the minimum bounding rectangle of the query geometry and the data geometry is less than a threshold distance. A distance between the query geometry and the candidate data geometry is mathematically calculated when a number of candidate data geometries equals a threshold number or when no more data geometries remain.