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Aregular grid is atessellation ofn-dimensionalEuclidean space bycongruentparallelotopes (e.g.bricks).^[1] Its opposite isirregular grid.

Grids of this type appear ongraph paper and may be used infinite element analysis,finite volume methods,finite difference methods, and in general for discretization of parameter spaces. Since the derivatives of field variables can be conveniently expressed as finite differences,^[2] structured grids mainly appear in finite difference methods.Unstructured grids offer more flexibility than structured grids and hence are very useful in finite element and finite volume methods.

Each cell in the grid can be addressed by index (i, j) in twodimensions or (i, j, k) in three dimensions, and eachvertex hascoordinates${\displaystyle (i\cdot dx,j\cdot dy)}$ in 2D or${\displaystyle (i\cdot dx,j\cdot dy,k\cdot dz)}$ in 3D for some real numbersdx,dy, anddz representing the grid spacing.

ACartesian grid is a special case where the elements areunit squares orunit cubes, and the vertices arepoints on theinteger lattice.

Arectilinear grid is a tessellation byrectangles orrectangular cuboids (also known asrectangular parallelepipeds) that are not, in general, allcongruent 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 onlogarithmic scalegraph paper.

Askewed grid is a tessellation ofparallelograms orparallelepipeds. (If the unit lengths are all equal, it is a tessellation ofrhombi orrhombohedra.)

Acurvilinear grid orstructured grid is a grid with the same combinatorial structure as a regular grid, in which the cells arequadrilaterals or[general] cuboids, rather than rectangles or rectangular cuboids.

• Cartesian coordinate system – Most common coordinate system (geometry)
• Integer lattice – Lattice group in Euclidean space whose points are integer n-tuples
• Unstructured grid – Unstructured (or irregular) grid is a tessellation of a part of the Euclidean plane
• Discretization – Conversion of continuous functions into discrete counterparts

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