Abstract: Systems and methods pertaining to nearness calculations of points in n-space. Among the embodiments is associating points of interest with point records in a data store, and efficient retrieval of subsets of those point records which meet arbitrary criteria. Criteria can limit retrieval to neighbors of a reference point (i.e., point records associated with points of interest whose home cells that share at least one interface with another designated home cell). Computationally expensive, at-retrieval range calculations are avoided by performing complimentary calculations at-storage and saving them with related records. The invention is appropriate for use with data storage mechanisms which limit inequality or range operations, or for which such operations result in inefficiencies. When used to model neighboring points on a planetary surface in 3-space, the invention does not suffer from polar distortion (where spherical coordinate systems have difficulty).

Abstract: Systems and methods pertaining to nearness calculations of points in n-space. Among the embodiments is associating points of interest with point records in a data store, and efficient retrieval of subsets of those point records which meet arbitrary criteria. Criteria can limit retrieval to neighbors of a reference point (i.e., point records associated with points of interest whose home cells that share at least one interface with another designated home cell. Computationally expensive, at-retrieval range calculations are avoided by performing complimentary calculations at-storage and saving them with related records. The invention is appropriate for use with data storage mechanisms which limit inequality or range operations, or for which such operations result in inefficiencies. When used to model neighboring points on a planetary surface in 3-space, the invention does not suffer from polar distortion (where spherical coordinate systems have difficulty).

Abstract: Provided are: 1) storage in a data store of points of interest in n-space along with arbitrary related information; and 2) efficient retrieval of subsets of those points meeting arbitrary criteria. Criteria can limit retrieval to neighbors of a reference point (i.e., points that are within a specified distance of that reference point). The method may be used to retrieve subsets from data stores which limit inequality or range operations. When used to model neighboring points on a planetary surface in 3-space, the method does not suffer from polar distortion (where spherical coordinate systems have difficulty).