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<div>{{unreferenced|date=August 2012}}<br />
[[Image:TwoCells.png|thumb|A trivial example of a Corner-point grid with only two cells.]]<br />
In [[geometry]], a '''corner-point grid''' is a [[tessellation]] an [[Euclidean space|Euclidean]] 3D volume where the base cell has 6 [[Face (geometry)|faces]] ([[hexahedron]]).<br />
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A set of straight lines defined by their end points define the ''pillars'' of the corner-point grid. The pillars have a lexicographical ordering that determines neighbouring pillars. On each pillar, a constant number of nodes (corner-points) is defined. A corner-point cell is now the volume between 4 neighbouring pillars and two neighbouring points on each pillar. <br />
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Each cell can be identified by integer coordinates <math>(i,j,k)</math>, where the <math>k</math> coordinate runs along the pillars, and <math>i</math> and <math>j</math> span each layer. The cells are ordered naturally, where the index <math>i</math> runs the fastest and <math>k</math> the slowest.<br />
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In the special case of all pillars being vertical, the top and bottom face of each corner-point cell are described by [[Bilinear interpolation|bilinear surfaces]] and the side faces are [[plane (geometry)|plane]]s.<br />
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Corner-point grids are supported by most [[reservoir simulation]] software, and has become an industry standard.<br />
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==Degeneracy==<br />
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A main feature of the format is the ability to define [[erosion]] surfaces in [[geological modelling]], effectively done by collapsing nodes along each pillar. This means that the corner-point cells degenerate and may have less than 6 faces.<br />
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For the corner-point grids non-neighboring connections are supported, meaning that grid cells that are not neighboring in ijk-space can be defined as neighboring. This feature allows for representation of faults with significant throw/displacement. Moreover, the neighboring grid cells do not need to have matching cell faces (just overlap).<br />
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[[Category:Tessellation]]<br />
[[Category:Geometry]]<br />
[[Category:Petroleum production]]<br />
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