meshgrid

Create 2-D grid coordinates with x-coordinates defined by the vector x and y-coordinates defined by the vector y.

x = 1:3;
y = 1:5;
[X,Y] = meshgrid(x,y)

X = 5×3

     1     2     3
     1     2     3
     1     2     3
     1     2     3
     1     2     3

Y = 5×3

     1     1     1
     2     2     2
     3     3     3
     4     4     4
     5     5     5

Evaluate the expression $$x^2+y^2$$ over the 2-D grid.

X.^2 + Y.^2

ans = 5×3

     2     5    10
     5     8    13
    10    13    18
    17    20    25
    26    29    34

Create a 2-D grid with uniformly spaced x-coordinates and y-coordinates in the interval [-2,2].

x = -2:0.25:2;
y = x;
[X,Y] = meshgrid(x);

Evaluate and plot the function $$f(x,y)=x{e}^{-x^2-y^2}$$ over the 2-D grid.

F = X.*exp(-X.^2-Y.^2);
surf(X,Y,F)

Starting in R2016b, it is not always necessary to create the grid before operating over it. For example, computing the expression $$x{e}^{-x^2-y^2}$$ implicitly expands the vectors x and y. For more information on implicit expansion, see Array vs. Matrix Operations.

surf(x,y,x.*exp(-x.^2-(y').^2))

Create 3-D grid coordinates from x-, y-, and z-coordinates defined in the interval [0,6], and evaluate the expression $$x^2+y^2+z^2$$.

x = 0:2:6;
y = 0:1:6;
z = 0:3:6;
[X,Y,Z] = meshgrid(x,y,z);
F = X.^2 + Y.^2 + Z.^2;

Determine the size of the grid. The three coordinate vectors have different lengths, forming a rectangular box of grid points.

gridsize = size(F)

gridsize = 1×3

     7     4     3

Use the single-input syntax to generate a uniformly spaced 3-D grid based on the coordinates defined in x. The new grid forms a cube of grid points.

[X,Y,Z] = meshgrid(x);
G = X.^2 + Y.^2 + Z.^2;
gridsize = size(G)

gridsize = 1×3

     4     4     4