How to calculate corners based on min and max

If i have an n-dimensional space contained by straight walls (distinct max and min in each dimension). I need to find the position of the corner points.

For example in 3D I have the min and max values in each dimension in a 2x3 matrix. Is there any good way from that to calculate the cornerpoints of the shape that encloses that volume?

[Adam]

The maxes and mins are the corner points aren't they?

[Mats]

Hi Adam,

Yes, but a good way to combine the coordinates to get each cornerpoint on one row with (x,y,z)

Answer 1

[Jos (10584)]

For the 3D case, try this:

    mm = [0 2 ; 1 3 ; 4 5] % column 1 is minimum, column 2 is maximum, rows are [x y z]
    [px,py,pz] = ndgrid(mm(1,:),mm(2,:),mm(3,:))
    P = [px(:) py(:) pz(:)] % the 8 corners of a 3D cube

Flexible ND case:

    mm = [0 2 ; 1 3 ; 4 5 ; -1 1 ;  10 20] ; % 5D
    nd = size(mm,1) ; % number of dimensions
    mmC = mat2cell(mm,ones(1,nd), 2) ;
    [p{1:nd}] = ndgrid(mmC{:}) ;
    P = reshape(cat(nd,p{:}),[],nd) % the 32 corners of a 5D "cube"

[Guillaume]

To avoid problems if p already exists and is not a cell array (or a larger cell array than required) I'd use:

p = cell(1, nd);
[p{:}] = ndgrid(mmC{:});