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# meshgrid

Rectangular grid in 2-D and 3-D space

## Syntax

[X,Y] = meshgrid(xgv,ygv)
[X,Y,Z] = meshgrid(xgv,ygv,zgv)
[X,Y] = meshgrid(gv)
[X,Y,Z] = meshgrid(gv)

## Description

[X,Y] = meshgrid(xgv,ygv) replicates the grid vectors xgv and ygv to produce a full grid. This grid is represented by the output coordinate arrays X and Y. The output coordinate arrays X and Y contain copies of the grid vectors xgv and ygv respectively. The sizes of the output arrays are determined by the length of the grid vectors. For grid vectors xgv and ygv of length M and N respectively, X and Y will have N rows and M columns.

[X,Y,Z] = meshgrid(xgv,ygv,zgv) produces three-dimensional coordinate arrays. The output coordinate arrays X, Y, and Z contain copies of the grid vectors xgv, ygv, and zgv respectively. The sizes of the output arrays are determined by the length of the grid vectors. For grid vectors xgv, ygv, and zgv of length M, N, and P respectively, X, Y, and Z will have N rows, M columns, and P pages.

[X,Y] = meshgrid(gv) is the same as [X,Y] = meshgrid(gv,gv). In other words, you can reuse the same grid vector in each respective dimension. The dimensionality of the output arrays is determined by the number of output arguments.

[X,Y,Z] = meshgrid(gv) is the same as [X,Y,Z] = meshgrid(gv,gv,gv). Again, the dimensionality of the output arrays is determined by the number of output arguments.

The output coordinate arrays are typically used to evaluate functions of two or three variables. They are also frequently used to create surface and volumetric plots.

## Input Arguments

 xgv,ygv,zgv Grid vectors specifying a series of grid point coordinates in the x, y and z directions, respectively. gv Generic grid vector specifying a series of point coordinates.

## Output Arguments

 X,Y,Z Output arrays that specify the full grid.

## Examples

Create a full grid from two monotonically increasing grid vectors:

```[X,Y] = meshgrid(1:3,10:14)
X =
1     2     3
1     2     3
1     2     3
1     2     3
1     2     3
Y =
10    10    10
11    11    11
12    12    12
13    13    13
14    14    14```

Use meshgrid to create a 3-D surface plot of a function:

```[X,Y] = meshgrid(-2:.2:2, -2:.2:2);
Z = X .* exp(-X.^2 - Y.^2);
surf(X,Y,Z)```