Generating all points of grid from given vectors of vertical and horizontal coordinates - MATLAB

Question

I have a square grid of 10 by 10 points. v1 is the vector of horizontal coordinates and v2 is the vector that contains the vertical coordinates. From these two vectors, I want to construct all the 100 points. Here is a 2 by 2 example:

v1 = [1 2];
v2 = [3 4];

Then the 4 points I want to generate are:

p(1,:) = [1,3]
p(2,:) = [1,4]
p(3,:) = [2,3]
p(4,:) = [2,4]

How can this be done in MATLAB?

Answer 1

You will want to use meshgrid or even better: ndgrid . The concept of both functions is the same, but ndgrid is more general and has a sorting of the output that is often more useful.

x = [1,2];
y = [3,4];
[X, Y] = ndgrid(x, y);
P = [X(:), Y(:)];

The call to ndgrid will generate two matrices X and Y which will have the structure of the mesh you want, and the values X(i,j) and Y(i,j) correspond to each other. So to get the points P , you just need to reshape those arrays to column vectors and concatenate them.

Answer 2

If you have the Neural Network Toolbox you are looking for the combvec function, which creates all combinations from 2 vectors.

Example:

v1=[1 2] 

v2=[3 4]

V = combvec(v1,v2)

which outputs:

V =

     1     2     1     2
     3     3     4     4