Example of regular grid.

Example of Cartesian grid.

Example of rectilinear grid.

Example of Curvilinear grid.

A regular grid is a tesselation of the Euclidean plane by congruent rectangles or a space-filling tessellation of rectilinear parallelepipeds. Grids of this type appear on graph paper and may be used in finite element analysis. A tessellated plane A tessellation of the plane is a collection of plane figures that fill the plane with no overlaps and no gaps. ... In mathematics and astronomy, Euclidean space is a generalization of the 2- and 3-dimensional spaces studied by Euclid. ... Graph paper is paper that is printed with fine lines making up a grid. ... The introduction to this article is too long. ...

Each cell in the grid can be addressed by index (i, j) in two dimensions or (i, j, k) in three dimensions, and each vertex has coordinates in 2D or in 3D for some real numbers dx, dy, and dz representing the grid spacing. :For other senses of this word, see dimension (disambiguation). ... In geometry, a vertex (Latin: whirl, whirlpool; plural vertices) is a corner of a polygon (where two sides meet) or of a polyhedron (where three or more faces and an equal number of edges meet). ... See Cartesian coordinate system or Coordinates (elementary mathematics) for a more elementary introduction to this topic. ...

Related grids

A Cartesian grid is a special case where the elements are unit squares or unit cubes, and the vertices are integer points. The unit square in a Cartesian coordinate system with coordinates (x,y) is defined as the square consisting of the points where both x and y lie in the unit interval from 0 to 1. ... A unit cube is a 3-dimensional geometric figure that consists of a cube in which all of its dimensions are 1 unit long. ... In mathematics, The n-dimensional integer lattice, or cubic lattice, denoted Zn, is the lattice in the standard n-dimensional real inner product space, where the inner product is the dot product, and where the lattice points are n-tuples of integers. ...

A rectilinear grid is a tesselation by rectangles or parallelepipeds that are not all congruent to each other. The cells may still be indexed by integers as above, but the mapping from indexes to vertex coordinates is less uniform than in a regular grid. An example of a rectilinear grid that is not regular appears on logarithmic scale graph paper. A logarithmic scale is a scale of measurement that uses the logarithm of a physical quantity instead of the quantity itself. ... Graph paper is paper that is printed with fine lines making up a grid. ...

A curvilinear grid or structured grid is a grid with the same combinatorial structure as a regular grid, in which the cells are quadrilaterals or cuboids rather than rectangles or rectangular parallelepipeds.

See also

• Cartesian coordinate system
• Integer point
• Unstructured grid