Regular grid

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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.

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 $(i\cdot dx, j\cdot dy)$ in 2D or $(i\cdot dx, j\cdot dy, k\cdot dz)$ in 3D for some real numbers dx, dy, and dz representing the grid spacing.

[edit] Related grids

A Cartesian grid is a special case where the elements are unit squares or unit cubes, and the vertices are integer points.

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 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.