Abstract: Some embodiments provide a non-transitory machine-readable medium that stores a program. The program receives, from a client device, a percentage value for a set of points. The program further determines a triangulation based on the set of points. The program also determines an alpha value based on the triangulation and the percentage value. The program further determines an alpha shape based on the alpha value. The program also provides the client device the alpha shape.

Abstract: Some embodiments provide a non-transitory machine-readable medium that stores a program. The program receives, from a client device, a percentage value for a set of points. The program further determines a triangulation based on the set of points. The program also determines an alpha value based on the triangulation and the percentage value. The program further determines an alpha shape based on the alpha value. The program also provides the client device the alpha shape.

Abstract: Some embodiments provide a non-transitory machine-readable medium that stores a program. The program receives, from a client device, a percentage value for a set of points. The program further determines a triangulation based on the set of points. The program also determines an alpha value based on the triangulation and the percentage value. The program further determines an alpha shape based on the alpha value. The program also provides the client device the alpha shape.

Abstract: A data set of spatial data having a plurality of dimensions and including linestrings can be processing by decomposing each linestring of the plurality of linestrings into a plurality of line segments. Each coordinate dimension appears in at least one line segment of the plurality of line segments can be listed in one of a plurality of dimensional dictionaries that each correspond to a dimension of the plurality of dimensions. A linestring of the plurality of linestrings can be represented as a set of the line segments using the plurality of dimensional dictionaries.

Abstract: Some embodiments provide a non-transitory machine-readable medium that stores a program. The program receives, from a client device, a percentage value for a set of points. The program further determines a triangulation based on the set of points. The program also determines an alpha value based on the triangulation and the percentage value. The program further determines an alpha shape based on the alpha value. The program also provides the client device the alpha shape.

Abstract: Some embodiments provide a non-transitory machine-readable medium that stores a program. The program receives, from a client device, a percentage value for a set of points. The program further determines a triangulation based on the set of points. The program also determines an alpha value based on the triangulation and the percentage value. The program further determines an alpha shape based on the alpha value. The program also provides the client device the alpha shape.

Abstract: Some embodiments provide a non-transitory machine-readable medium that stores a program. The program receives, from a client device, a percentage value for a set of points. The program further determines a triangulation based on the set of points. The program also determines an alpha value based on the triangulation and the percentage value. The program further determines an alpha shape based on the alpha value. The program also provides the client device the alpha shape.

Abstract: A query of spatial data is received by a database comprising a columnar data store storing data in a column-oriented structure. Thereafter, a minimal bounding rectangle associated with the query is identified using a grid order scanning technique. The spatial data set corresponding to the received query is then mapped to physical storage in the database using the identified minimal bounding rectangle so that the spatial data set can be retrieved. Related apparatus, systems, techniques and articles are also described.

Abstract: DBSCAN clustering analyses can be improved by pre-processing of a data set using a Hilbert curve to intelligently identify the centers for initial partitional analysis by a partitional clustering algorithm such as CLARANS. Partitions output by the partitional clustering algorithm can be process by DBSCAN running in parallel before intermediate cluster results are merged.

Abstract: A data set of spatial data having a plurality of dimensions and including linestrings can be processing by decomposing each linestring of the plurality of linestrings into a plurality of line segments. Each coordinate dimension appears in at least one line segment of the plurality of line segments can be listed in one of a plurality of dimensional dictionaries that each correspond to a dimension of the plurality of dimensions. A linestring of the plurality of linestrings can be represented as a set of the line segments using the plurality of dimensional dictionaries.

Abstract: DBSCAN clustering analyses can be improved by pre-processing of a data set using a Hilbert curve to intelligently identify the centers for initial partitional analysis by a partitional clustering algorithm such as CLARANS. Partitions output by the partitional clustering algorithm can be process by DBSCAN running in parallel before intermediate cluster results are merged.

Abstract: A data set of spatial data having a plurality of dimensions and including linestrings can be processing by decomposing each linestring of the plurality of linestrings into a plurality of line segments. Each coordinate dimension appears in at least one line segment of the plurality of line segments can be listed in one of a plurality of dimensional dictionaries that each correspond to a dimension of the plurality of dimensions. A linestring of the plurality of linestrings can be represented as a set of the line segments using the plurality of dimensional dictionaries.

Abstract: A query of spatial data is received by a database comprising a columnar data store storing data in a column-oriented structure. Thereafter, a minimal bounding rectangle associated with the query is identified using a grid order scanning technique. The spatial data set corresponding to the received query is then mapped to physical storage in the database using the identified minimal bounding rectangle so that the spatial data set can be retrieved. Related apparatus, systems, techniques and articles are also described.

Abstract: Polygons can be simplified from an original, higher resolution to a simplified, lower resolution such that the simplified versions of the polygons do not introduce errors and also do not render boundaries shared with other polygons invalid.

Abstract: DBSCAN clustering analyses can be improved by pre-processing of a data set using a Hilbert curve to intelligently identify the centers for initial partitional analysis by a partitional clustering algorithm such as CLARANS. Partitions output by the partitional clustering algorithm can be process by DBSCAN running in parallel before intermediate cluster results are merged.

Abstract: A query of spatial data is received by a database comprising a columnar data store storing data in a column-oriented structure. Thereafter, a minimal bounding rectangle associated with the query is identified using a tree-order scanning technique. A spatial data set that corresponds to the received query is then mapped to the physical storage in the database using the identified minimal bounding rectangle. Next, the spatial data set is then retrieved. Related apparatus, systems, techniques and articles are also described.

Abstract: Using index clusters to approximate coordinate values for vertices of compressed simplexes of a spatial data set, valid subspaces can be identified and used to identify other simplexes that may intersect a first simplex. Such approaches can be used for filtering, refining, etc. analysis of intersections between areas, lines, volumes, etc. within spatial data sets.

Abstract: Cluster analysis of data points in a data set can be optimized by identification of a preferred cluster analysis method. This identification can be based on indexing the data using a Hilbert curve and determining whether the data points are predominantly in spherical or non-spherical clusters. Methods, systems, and articles of manufacture are described.

Abstract: Polygons can be simplified from an original, higher resolution to a simplified, lower resolution such that the simplified versions of the polygons do not introduce errors and also do not render boundaries shared with other polygons invalid.

Abstract: DBSCAN clustering analyses can be improved by pre-processing of a data set using a Hilbert curve to intelligently identify the centers for initial partitional analysis by a partitional clustering algorithm such as CLARANS. Partitions output by the partitional clustering algorithm can be process by DBSCAN running in parallel before intermediate cluster results are merged.