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.
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.
Data within the interior of such cells can be computed by trilinear interpolation from the boundary values at the 8 corners, 12 edges, and 6 faces.
In the special case of all pillars being vertical, the top and bottom face of each corner-point cell are described by bilinear surfaces and the side faces are planes.
Corner-point grids are supported by most reservoir simulation software, and has become an industry standard.
Degeneracy
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.
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).
