Function form

[C,R] =meshgrid(c, r)

Preliminary explanation

The first thing to be clear is that the parameters c and r are both row vectors. This function transforms the domain specified by the row vectors c and r into arrays C and R. These 2 arrays can be used to indicate a function with 2 variables and a three-dimensional graph .
Each row of the output array C is a row vector c, and each column of the output array R is a row vector r. For example, we need to form a two-dimensional function whose elements are the sum of the squares of the coordinate variables x and y. That is, the form f(x,y) = x^2 +y^2. The variables x = 0,1,2 and y = 0,1. Trivially list all coordinate pairs:
(x,y) = (0,0) (0,1)
(1,0) (1,1)
(2,0) (2,1)
In matlab, what we need is such data, and then substitute the coordinate pair into the function to get the result.

[C,R] = meshgrid([0,1],[0,1,2])
%%%%%%%%%result%%%%%%%%%
C =

     0     1
     0     1
     0     1


R =

     0     0
     1     1
     2     2
%%%%%%%%%%%%


% f(1,1)  =  R(1,1).^2 +C(1,1).^2
f = R.^2 + C.^2

If you carefully observe the above results, you will find that the two-dimensional array of R specifies the row label (component) of x, and the two-dimensional array of C specifies the column label (component) of y.

Deepen understanding

Give another example, mainly to deepen the understanding of the meshgrid function, such as implementing f(x,y) = A*sin(u0*x+v0*y), where x = 0,1,2,...,M-1; y=0,1,2,….,N-1.
In addition, it should be noted that the constants of M, N, A, u0, v0 are all given by themselves.
First give a general implementation, but the rate is very slow.

for r =1:M
    u0x = u0*(r-1)
    for c=1：N
        v0y =v0*(c-1)
        f(r,c) = A*sin(u0x+v0y)
    end
end

Use the meshgrid function to achieve, according to the conditions given above, explain that x = [0,1,..,M-1] and y=[0,1,...,N-1], so we will determine c and r these two row vectors. Then generate the corresponding two-dimensional arrays C and R of row and column labels.

r = 1：M-1;
c = 1: N-1;
[C,R] =meshgrid(c,r);

g = A*sin(u0*R +v0*C);

g = mat2gray(g);
imshow(g)