Grid (spatial index): Difference between revisions

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{{Short description|Partition of a surface into contiguous cells}}

In the context of a [[spatial index]], a '''grid''' (a.k.a. "mesh", also "global grid" if it covers the entire surface of the [[Globe]]) is a regular tessellation of a [[manifold]] or 2-D surface that divides it into a series of contiguous cells, which can then be assigned unique identifiers and used for spatial indexing purposes. A wide variety of such grids have been proposed or are currently in use, including grids based on "square" or "rectangular" cells, triangular grids or meshes, hexagonal grids, grids based on diamond-shaped cells, and possibly more.

{{Refimprove|date=September 2018}}

In the context of a [[spatial index]], a '''grid''' (a.k.a.or "'''mesh",''' alsois "globala grid"regular{{fact|reason=What ifabout itirregular coversgrids?|date=October the entire surface of the2023}} [[Globetessellation]]) is a regular tessellation of a [[manifold]] or [[Surface (topology)|2-D surface]] that [[Space partitioning|divides it]] into a series of contiguous cells, which can then be assigned unique identifiers and used for spatial indexing purposes. A wide variety of such grids have been proposed or are currently in use, including grids based on "[[Square tiling|square]]" or "rectangular" cells, [[Triangular tiling|triangular grids]] or meshes, [[Hexagonal tiling|hexagonal grids]], and grids based on diamond-shaped cells,. andA possibly"[[discrete moreglobal grid|global grid]]" is a kind of grid that covers the entire surface of the [[globe]].

==Types of grids==

[[File:Geodesic Grid (ISEA3H) illustrated.png|right | 500px]]

"'''Square'''" or "'''rectangular'''" grids are frequently theused simplestfor inpurposes use,such i.e. foras translating spatial information expressed in Cartesian coordinates ([[latitude]] and [[longitude]]) into and out of the grid system. Such grids may or may not be aligned with the gridlinesgrid lines of latitude and longitude; for example, [[Marsden Square|Marsden squares]]s, [[World Meteorological Organization squares]], [[c-squares]] and others are aligned, while [[Universal Transverse Mercator coordinate system|UTM]], and various national (=local) grid based systems such as the [[British national grid reference system]] are not. In general, these grids fall into two classes, those"''equal angle''" or "''[[equal-area map|equal area]]''". Grids that are "''equal angle''", that have cell sizes that are constant in degrees of latitude and longitude but are unequal in area (particularly with varying latitude), or. thoseGrids that are "''equal area''" ([[statistical grid]]s), that have cell sizes that are constant in distance on the ground (e.g. 100  km, 10  km) but not in degrees of longitude, in particular.

TheA mostcommonly influentialused '''triangular''' grid is that entitledthe "Quaternary Triangular Mesh" or (QTM), thatwhich was developed by Geoffrey Dutton in the early 1980s. It eventually resulted in a thesis entitled "A Hierarchical Coordinate System for Geoprocessing and Cartography" that was published in 1999 (see publications list on.<ref>Geoffrey Dutton's .
[http://www.spatial-effects.com/SE-papers1.html "Spatial&nbsp; Effects: Research Papers and Data"] website){{Webarchive|url=https://web.archive.org/web/20070219054353/http://www.spatial-effects.com/SE-papers1.html |date=2007-02-19 }}.</ref>
This grid was also employed as the basis of the rotatable globe that forms part of the Microsoft [[Encarta]] product.

Hexagonal grids may also be used. In general, triangular and hexagonal grids are constructed so as to better approach the goals of equal-area (or nearly so) plus more seamless coverage across the poles, which tends to be a problem area for square or rectangular grids since in these cases, the cell width diminishes to nothing at the pole and those cells adjacent to the pole then become 3- rather than 4-sided. Criteria for optimal discrete global gridding have been proposed by both Goodchild and Kimerling<ref>[http://www.ncgia.ucsb.edu/globalgrids-book/comparison Criteria and Measures for the Comparison of Global Geocoding Systems, Keith C. Clarke, University of California] {{webarchive|url=https://web.archive.org/web/20100623002915/http://www.ncgia.ucsb.edu/globalgrids-book/comparison/ |date=2010-06-23 }}</ref> in which equal area cells are deemed of prime importance.

For a discussion of '''hexagonal''' and other grids (including diamond-shaped), the paper of Sahr ''et al''. (2003)<ref>[http://www.sou.edu/cs/sahr/dgg/pubs/gdggs03.pdf#search=%22hexagonal%20grid%20kimerling%22 Kevin Sahr, Denis White, and A. Jon Kimerling. 2003. Geodesic Discrete Global Grid Systems. Cartography and Geographic Information Science, 30(2), 121-134.]</ref> is recommended reading.

'''[[Quadtree|Quadtrees]]'''s are a specialised form of grid in which the resolution of the grid is varied according to the nature and/or complexity of the data to be fitted, across the 2-d space. Polar grids utilize the [[polar coordinate system]], andusing arecircles consideredof separatelya underprescribed radius that headingare divided into sectors of a certain angle. Coordinates are given as the radius and angle from the center of the grid.

In general, triangular and hexagonal grids are constructed so as to better approach the goals of equal-area (or nearly so) plus more seamless coverage across the poles, which tends to be a problem area for square or rectangular grids since in these cases, the cell width diminishes to nothing at the pole and those cells adjacent to the pole then become 3- rather than 4-sided.

'''[[Quadtree|Quadtrees]]''' are a specialised form of grid in which the resolution of the grid is varied according to the nature and/or complexity of the data to be fitted, across the 2-d space, and are considered separately under that heading.

==Grid-based spatial indexing==

In practice, construction of grid-based spatial indexesindices entails allocation of relevant objects to their position or positions in the grid, then creating an index of object identifiers vs. grid cell identifiers for rapid access. This is an example of a "space-driven" or data independent method, as opposed to "data-driven" or data dependent method, as discussed further in Rigaux et al. (2002)).<ref>Rigaux, P., Scholl, M., and Voisard, A. 2002. Spatial Databases - with application to GIS. Morgan Kaufmann, San Francisco, 410pp.</ref>. A grid-based spatial index has the advantage that the structure of the index can be created first, and data added on an ongoing basis without requiring any change to the index structure; indeed, if a common grid is used by disparate data collecting and indexing activities, such indexesindices can easily be merged from a variety of sources. On the other hand, data driven structures such as [[R-tree|R-trees]]s can be more efficient for data storage and speed at search execution time, though they are generally tied to the internal structure of a given data storage system.

The use of such spatial indexesindices is not limited to digital data; the "index" section of any global or street atlas commonly contains a list of named features (towns, streets, etc.) with associated grid square identifiers, and may be considered a perfectly acceptable example of a spatial index (in this case, typically organised by feature name, though the reverse is conceptually also possible).

==Other uses==

The individual cells of a grid system can also be useful as units of aggregation, for example as a precursor to data analysis, presentation, mapping, etc. For some applications (e.g., statistical analysis), equal-area cells may be preferred, although for others this may not be a prime consideration.

In computer science, one often needs to find out all cells a ray is passing through in a grid (for raytracing or collision detection); this is called "grid traversal".

==References==

<references/>

*[http://matlabdatamining.blogspot.com/2008/04/generating-hexagonal-grids-for-fun-and.html Generating Hexagonal Grids] A brief article on hexagonal grids including MATLAB source code.

*[http://www.star.le.ac.uk/~cgp/ag/skyindex.html Indexing the Sky - Clive Page] - Grid indexes for astronomy

==See also==

*[[Discrete global grid]]

*[[Euclidean tilings by convex regular polygons]]

*[[Geodesic grid]]

*[[Digital Earth reference model]]

*[[Spatial index]]

* [[Grid plan]]

*[[Grid reference]]

*[[Geocode]]

* [[hex map]]

*[[quadrilateralized spherical cube]]

*[[Quadtree]]

*[[R-tree]]

*[[Alpha-numeric grid]]

*[[Hierarchical Triangular Mesh]]

*[[Utility pole#Coordinates on pole tags]] (some based on rectangular grids)

*[[HEALPix]]

==References==

<references/>

*[http://www.star.le.ac.uk/~cgp/ag/skyindex.html Indexing the Sky - Clive Page] - Grid indexesindices for astronomy

== External links ==

*[https://web.archive.org/web/20090724075851/http://www.gamerendering.com/2009/07/20/grid-traversal/ Grid Traversal implementation details and applet demonstration]

*[http://www.pyxisinnovation.com/pyxwiki/index.php?title=How_PYXIS_Works PYXIS Discrete Global Grid System using the ISEA3H Grid]

{{DEFAULTSORT:Grid (Spatial Index)}}

[[Category:Geocodes]]

[[Category:Geographic coordinate systems]]

[[Category:Database index techniques]]