surf for n-dimensional cartesian matrix

This is the dimension of my matrix: 1001,1201,1201 The first dimension is z, the second x and the third is y.

My question is: How can I show this matrix using surf function? or, how can I convert this matrix to a 2 dimensional matrix with dimesnions 1001, 1201 (z,r)?

Thank you

[Stephen23]

Perhaps one of these:

https://www.mathworks.com/help/images/ref/sliceviewer.html

https://www.mathworks.com/help/images/ref/volshow.html

https://www.mathworks.com/help/matlab/ref/slice.html

[Ali Momennezhad]

Thank you for your help. I used volshow and managed to show the volume. But I am wondering if I can put axis x,y and z on the viewer3d? At the moment my target shape is in the middle of a large space.

Answer 1

[John D'Errico]

You cannot do so. That makes no sense at all, sorry.

You actually have a FOUR dimensional problem, thus W(x,y,z). This is because your matrix contains a 4th variable. And surf cannot handle that case, no matter what you do.

Ok, you can fix Z at any level, then taking a slice of the matrix. The result is now something surf can handle. But it is only one tiny piece of the matrix. The analogy here is lie the blind (but wise) men looking at an elephant. One feels a leg, and decides the elephant is like a giant tree. Another feels the tail, and decides the elephant is like a rope. Another feels the trunk, and thinks the elephant is a giant snake. Another feels the body, and decides it is like a huge wall. A final one feels an ear, and thinks it is like a floppy sheet, perhaps a wing.

Could you plot many slices of the matrix in the same plot? Yes. That may be your only real option. Color each surface with a different color, then label the slices using a legend. In the end, your plot will very possibly look confusing.

Is here any alternative? Well, possibly. You can plot an iso-surface. So the set of all (x,y,z), such that W takes on a specific value. This is essentially a contour plot, but with three independent variables. (help isosurface).

[Ali Momennezhad]

For more clarification:

depth=-4:0.01:6;

r=-6:0.01:6;

x=-6:0.01:6;

y=-6:0.01:6;

matrix=ones(1001,1201,1201); % the values for the real matrix are different

surf(r,depth,matrix)

[Ali Momennezhad]

Matrix is comprised of (z,x,y)

So,how can I create a matrix of (z,r) where r is sqrt(x.^2+y.^2) ?

[John D'Errico]

Hint: Can you use meshgrid? Or ndgrid? Once you have x and y as matrices, can you compute r? Do you have a formula for that?

Of course, generating an array that large seems a bit silly, thus of size 1001x1201x1201, will require

1001*1201*1201*8/1024^3

ans = 10.7575

So close to 11 Gigabytes of RAM just to store one array. But you will be generating 3 such matrices, x,y, and z. So you need 33 GB of RAM.

And MATLAB will require contiguous ram. This is not your hard disk space, but RAM. On top of that, if you will do ANY computations on an array that large, now you will need at least twice that available space, if not 3 times. So you probably need at least 96 GB of RAM just to work with arrays of that size.

I would suggest you either get a big computer, way bigger than most laptops have for RM, or learn to work on smaller problems.