Build a combinatorial matrix from two vectors

Question

I want to define a matrix of values with a very simple pattern. I've achieved it with the code below but it's ugly - very difficult to read (I find) and surely not as optimal, in terms of performance, as it could be. The former is really what I'm trying to address here. I feel this can be done much more elegantly and would love some guidance from the community.

Here is an example of what I am hoping to achieve, from x and y I want to get points:

y =
 10 30 50 70
x =
 10 30 50
points =
 10 10
 30 10
 50 10
 10 30
 30 30
 50 30
 10 50
 30 50
 50 50
 10 70
 30 70
 50 70

x and y are, of course, no always those exact vectors. They are, however, very simply created. Something like so:

scale = 20;
max_x = 85;
max_y = 62;
y_count = floor(max_x / scale);
x_count = floor(max_y / scale);
y = ((1:y_count) * scale) - scale / 2;
x = ((1:x_count) * scale) - scale / 2;

Here's my brute force approach:

y = repmat(y, x_count, 1);
y = reshape(y, 1, size(y, 1) * size(y, 2));
y = y';
x = repmat(x, y_count, 1);
x = x';
x = reshape(x, 1, size(x, 1) * size(x, 2));
x = x';
points = [x y];

It works, but it isn't very elegant.

Answer 1

It's called Cartesian product and you can do that easily:

Here's one way:

y = [10 30 50 70]
x = [10 30 50]
[X,Y] = meshgrid(y,x);
result = [Y(:) X(:)];

Result:

10 10
30 10
50 10
10 30
30 30
50 30
10 50
30 50
50 50
10 70
30 70
50 70