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In geometry, a corner-point grid is a tessellation of a Euclidean 3D volume where the base cell has 6 faces.
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 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 {\displaystyle } , where the k {\displaystyle k} coordinate runs along the pillars, and i {\displaystyle i} and j {\displaystyle j} span each layer. The cells are ordered naturally, where the index i {\displaystyle i} runs the fastest and k {\displaystyle k} 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.