Discretise a domain into a grid of uniform volume size

Given a domain say in how do I split/discretise the domain into a grid of uniform volume/ fixed number of grid points?

For example given how can I discretise this domain into a grid points? For some given . The linspace function has not been helpful for me.

Answer 1

[Sargondjani]

Why is linspace not helpful?

x1 = linspace(0,1,M);

x2 = linspace(0,1,M);

[X1,X2] = ndgrid(x1,x2);

[daniel adams]

Because the grid points arnt exactly the center of the volume bins ( e.g the end points )

[Sargondjani]

Ok, so with linspace and ndgrid you get rectangles with equal area. So you only need to find the middle points of each segment? This would be the mean in each dimension.

dx1 = x1(2) - x1(1);%linspace results in equal distances between gridpoints

x1_mid = x1(1:end-1)+dx1;

And the same for x2. You now have a vector x1_mid and x2_mid which are the midpoints of the rectangular areas.