How to plot 3D data values in a 2D map?

Hello,

For a project I am working on, I have a truckload of data. For a few hundred thousand points in a room, I have x-, y- and z-coordinates and a value of the amount of radiation there. Here, y is the height and x and z are the width and breadth of the room. I want to plot this in a top-view, so adding all y-values for a certain (x,z) together, and then plotting the resulting values in a heat map to show where there is a lot of radiation and where you're fairly safe.

My data is of the format (x, y, z, value):

1   1   1   v1
1   1   2   v2
1   1   3   v3
1   1   4   v4
1   2   1   v5
1   2   2   v6
1   2   3   v7
1   2   4   v8
2   1   1   v9
etc.

I already have variables for the unique number of x-, y- and z-points. Let's say I sampled 5 x-, 4 y- and 3 z-locations. I would like to write a loop that automates the addition of, in this scenario, v1, v4, v7 and v10 (the row increases by the number of z-points and the number of values that are added together are the number of sampled y-points), and then of v2, v5, v8, v11, etc. Is there any easier way than three nested for-loops? For now, that is all I can come up with, but I hope there's a more straightforward way of getting the plot I want.

Answer 1

[Jack]

 a = your_data;
 b = reshape(b, n_x, n_y, n_z, 4); %n_i is the size of the ith grid direction

 c = sum(b,2); %sum in the y direction

 [X,Z] = meshgrid(1:n_x, 1:n_z);
 d = [X(:),Z(:),c(:)];

Takes ~0.1s for a 100x100x100 data set

[Erik den Boer]

Hi Jack, I posted a comment last week but for some reason it didn't go through, I see now. Internet can be a bit spotty here, maybe that was it.

Anyway, thanks for your reply. The reshape command does what I want it too indeed, except I now have a 271x3x246x4 matrix. The first three sizes seem correct, but why is the 4 required? I would interpret that as the number of 'results', and expected it to be 1 since each xyz location of course has just a single value?

In any case the code works, until I get to the concatenating for variable d. My X and Z are 246x271, but my c is 271x1x246x4, so Matlab is complaining that the dimensions aren't consistent. Do you have any ideas how I can fix this?

[Jack]

Hi Erik, I don't know why I put a 4 before. Looking at my code:

tic
% generate random values
n_x=100;
n_y=100;
n_z=100;
[Z,Y,X] = ndgrid(1:n_z,1:n_y,1:n_x);
a=[X(:),Y(:),Z(:)];
a(:,4)=randi([0,100],n_x*n_y*n_z,1);

% run reshape
b = a(:,4); %values
b = reshape(b, n_x, n_y, n_z, 1);
c = sum(b,2);
[X,Z] = meshgrid(1:n_x, 1:n_z);
d = [X(:),Z(:),c(:)];
toc

There is no 4, so I guess it was a typo.

Thanks, Jack

[Erik den Boer]

Ah I thought it might be indeed, but swapping it for a 1 still made things crash, and since I didn't really know what it was doing, I couldn't fix it. This code does give me a plot tho, so thanks for the help!