Abstract: Systems, methodologies, media, and other embodiments associated with a three dimensional spatial engine in an RDBMS are described. One example system includes logic to receive and store data representing a set of spatial features of a three dimensional geometry object. The example system may also include logic to validate the three dimensional geometry object and to provide a signal concerning the validity of the object.

Abstract: Systems, methods, and other embodiments associated with determining whether a point is located in a polyhedron are described. One example method includes identifying a ray that connects a query point to a second point located outside a minimum bounding volume of a solid polyhedron without intersecting a vertex of the solid polyhedron. The method includes counting crossings of planar faces of the solid polyhedron by the ray. The crossings may be mid-face crossings, edge crossings, and/or coplanar crossings. The crossings are selectively counted based on whether the ray actually crosses a face, grazes a face without crossing it, or runs coplanar with a face without crossing another face. The method includes controlling an automated process based on whether first point is inside the solid polyhedron.

Abstract: Systems, methods, and other embodiments associated with determining whether geometries represented by geometry objects intersect are described. One example method recursively decomposes a higher order geometry (e.g., solid) into a set of lower order geometries (e.g., surfaces) and examines the lower order geometries, continuing the recursion until an intersection decision is reached. The example method includes accessing geometry objects and accessing a spatial index that stores MBVs associated with the geometry objects. The method includes extracting candidate pairs of intersecting features upon determining MBVs associated with the geometry objects intersect and providing the candidate features to a feature-feature logic. The method includes providing an intersection signal based on a features intersection signal provided by the feature-feature logic.

Abstract: Methods and other embodiments associated with performing an in-memory triangulation of a large data set are described. One example method for performing in-memory triangulation of a large data set includes partitioning a large geographical information data set into a set of stripes and generating, in-memory, a set of local triangulated irregular networks (TINs) corresponding to members of the set of stripes. Information associated with triangles associated with the set of local TINs are stored.

Abstract: Methods and other embodiments associated with performing an in-memory triangulation of a large data set are described. One example method for performing in-memory triangulation of a large data set includes partitioning a large geographical information data set into a set of stripes and generating, in-memory, a set of local triangulated irregular networks (TINs) corresponding to members of the set of stripes. Information associated with triangles associated with the set of local TINs are stored.

Abstract: Methods and other embodiments associated with performing an in-memory triangulation of an arbitrarily large data set are described. One example method for performing in-memory triangulation of an arbitrarily large data set includes striping a data set into multiple stripes, selecting a first stripe to triangulate, and then performing an in-memory triangulation on the stripe. The method may also include removing certain triangles from the triangulated irregular network produced by the triangulation, merging another stripe with the leftover data, and repeating the process until the arbitrarily large data set has been triangulated piece-by-piece, with the triangulations occurring in memory.

Abstract: Systems, methods, and other embodiments associated with determining whether a point is located in a polyhedron are described. One example method includes identifying a ray that connects a query point to a second point located outside a minimum bounding volume of a solid polyhedron without intersecting a vertex of the solid polyhedron. The method includes counting crossings of planar faces of the solid polyhedron by the ray. The crossings may be mid-face crossings, edge crossings, and/or coplanar crossings. The crossings are selectively counted based on whether the ray actually crosses a face, grazes a face without crossing it, or runs coplanar with a face without crossing another face. The method includes controlling an automated process based on whether first point is inside the solid polyhedron.

Abstract: Methods and other embodiments associated with performing an in-memory triangulation of an arbitrarily large data set are described. One example method for performing in-memory triangulation of an arbitrarily large data set includes striping a data set into multiple stripes, selecting a first stripe to triangulate, and then performing an in-memory triangulation on the stripe. The method may also include removing certain triangles from the triangulated irregular network produced by the triangulation, merging another stripe with the leftover data, and repeating the process until the arbitrarily large data set has been triangulated piece-by-piece, with the triangulations occurring in memory.

Abstract: Systems, methods, and other embodiments associated with determining whether geometries represented by geometry objects intersect are described. One example method recursively decomposes a higher order geometry (e.g., solid) into a set of lower order geometries (e.g., surfaces) and examines the lower order geometries, continuing the recursion until an intersection decision is reached. The example method includes accessing geometry objects and accessing a spatial index that stores MBVs associated with the geometry objects. The method includes extracting candidate pairs of intersecting features upon determining MBVs associated with the geometry objects intersect and providing the candidate features to a feature-feature logic. The method includes providing an intersection signal based on a features intersection signal provided by the feature-feature logic.

Abstract: Systems, methodologies, media, and other embodiments associated with a three dimensional spatial engine in an RDBMS are described. One example system includes logic to receive and store data representing a set of spatial features of a three dimensional geometry object. The example system may also include logic to validate the three dimensional geometry object and to provide a signal concerning the validity of the object.

Abstract: A system and method for indexing and storing multi-dimensional or multi-attribute data. Data items are recursively sorted in a selected dimension (e.g., the dimension having the greatest variance) and divided until each subdivision fits into a leaf node having a specified fanout. Intermediate nodes and a root node are constructed to complete the index. Each node of the index is stored in a database as a separate object or record and may include a node identifier of the unique, an identifier of a parent and/or a sibling node and an entry for each child of the node, which may be data items or other nodes. Each record entry for a child includes an associated bounding area encompassing descendant data items. Another database table or module may store information about the index, such as the dimensionality of the data, the index fanout and an identifier of a root of the index.

Abstract: Methods are provided for buffering nodes of a hierarchical index (e.g., R-tree, bang file, hB-tree) during operations on multi-dimensional data represented by the index. The methods are particularly suited for query operations, and a different method may be more suitable for one pattern of queries than another. Where queries are distributed in a relatively uniform manner across the domain or dataspace of an index, a node-area buffering method is provided. In this method nodes are cached or buffered in order of their respective areas (e.g., their minimum bounding areas), and a node having a smaller area will be replaced in cache before a node having a larger area. When, however, queries are not uniformly distributed, then a least frequently accessed buffering technique may be applied. According to this method statistics are maintained concerning the frequency with which individual index nodes are accessed. Those accessed less frequently are replaced in cache before those accessed more frequently.

Abstract: A system and method for indexing and storing multi-dimensional or multi-attribute data. Data items are recursively sorted in a selected dimension (e.g., the dimension having the greatest variance) and divided until each subdivision fits into a leaf node having a specified fanout. Intermediate nodes and a root node are constructed to complete the index. Each node of the index is stored in a database as a separate object or record and may include a node identifier of the unique, an identifier of a parent and/or a sibling node and an entry for each child of the node, which may be data items or other nodes. Each record entry for a child includes an associated bounding area encompassing descendant data items. Another database table or module may store information about the index, such as the dimensionality of the data, the index fanout and an identifier of a root of the index.