Abstract: Techniques and systems for processing within-distance queries are provided. A query for geometry objects within a query distance of a query geometry is received. An in-memory R-tree (IMR-tree) is generated for the query geometry. The IMR-tree includes nodes corresponding to edges of the query geometry. An R-tree index for a plurality of candidate geometries is accessed. At least one node of the R-tree index is processed by: generating an expanded bounding geometry based on the query distance, and using the IMR-tree to determine a topological relationship between the expanded bounding geometry and the query geometry. When the expanded bounding geometry intersects the query geometry, if at least one within-distance test is satisfied, the candidate geometries associated with the selected node are added to a result set. Otherwise, if the selected node is a non-leaf node of the R-tree index, child nodes of the selected node are processed.

Abstract: A method and apparatus for querying a database table containing point spatial data and without indexes is provided. A request for point spatial data in the table includes a query window provided by the user and describing an area of interest in which the user desires the point spatial data contained therein. The query window is tiled to create interior tiles and boundary tiles. A first query is formed to determine the point spatial data contained in the interior tiles. A second query is formed to determine the point spatial data contained within the boundary tiles and also within the query window. The second query includes a function that tests to determine whether the point spatial data within a boundary tile also lies within the query window. The first and second queries are executed in part on an enhanced data storage device and the results joined and returned to the user in answer to the request.

Abstract: Techniques and systems for processing within-distance queries are provided. A query for geometry objects within a query distance of a query geometry is received. An in-memory R-tree (IMR-tree) is generated for the query geometry. The IMR-tree includes nodes corresponding to edges of the query geometry. An R-tree index for a plurality of candidate geometries is accessed. At least one node of the R-tree index is processed by: generating an expanded bounding geometry based on the query distance, and using the IMR-tree to determine a topological relationship between the expanded bounding geometry and the query geometry. When the expanded bounding geometry intersects the query geometry, if at least one within-distance test is satisfied, the candidate geometries associated with the selected node are added to a result set. Otherwise, if the selected node is a non-leaf node of the R-tree index, child nodes of the selected node are processed.

Abstract: A method and apparatus for querying a database table containing point spatial data and without indexes is provided. A request for point spatial data in the table includes a query window provided by the user and describing an area of interest in which the user desires the point spatial data contained therein. The query window is tiled to create interior tiles and boundary tiles. A first query is formed to determine the point spatial data contained in the interior tiles. A second query is formed to determine the point spatial data contained within the boundary tiles and also within the query window. The second query includes a function that tests to determine whether the point spatial data within a boundary tile also lies within the query window. The first and second queries are executed in part on an enhanced data storage device and the results joined and returned to the user in answer to the request.

Abstract: A method for determining positional relationships among objects represented in a database. A plurality of tiles are defined. A distribution of objects with respect to the tiles is determined. The distribution of objects is compared with respect to the tiles to identify objects fulfilling a primary filter condition related to an interaction of the objects with respect to the tiles. Objects are identified that fulfill a secondary filter condition related to an interaction of the geometries of the objects by analyzing the distribution of objects that fulfill the primary filter condition with respect to the tiles. Objects are identified that fulfill the secondary filter condition by comparing geometries of objects that fulfill the primary filter condition that the analysis does not identify as fulfilling the secondary filter condition.

Abstract: A method for evaluating a spatial query comprises receiving a spatial query defining a query window including a void, identifying an interior circle for the query window, wherein the interior circle includes a void, and processing the spatial query by either (1) modifying the at least one interior circle to exclude the void, and using the modified interior circle to evaluate the spatial query by checking whether a data MBR is inside the modified interior circle and when it does, including the data item in the query result set, or (2) by checking whether a data MBR is inside the interior circle and when it does, checking whether the data MBR intersects the MBRs of any of the voids, and including the data item in the query result set when there is no intersection.

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: 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: Quicker and more efficient processing of spatial queries is provided when the query window has holes. A method for evaluating a spatial query comprises receiving a spatial query defining a query window including a void, identifying an interior circle for the query window, wherein the interior circle includes a void, and processing the spatial query efficiently in one of the following two alternate ways: (1) modifying the at least one interior circle to exclude the void, and using the modified interior circle to evaluate the spatial query by checking if a data mbr is inside the modified interior circle and if it does, including the data item in the query result set. Or (2) by checking for a data MBR is inside the interior circle and if so, checking if the data MBR intersects the MBRs of any of the voids, and including the data item in the query result set if there is no intersection.

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.