Is there any way of producing a 4d plot from a matrix which has 4 columns (coordinates + value)?

I'm trying to produce a volume plot from a matrix that has 4 columns: x_coordinate, y_coordinate, z_coordinate and the value of the variable I'm working with.

It's something like this, assuming that my volume is 3x3x3:

x | y | z | value
0   0   0
0   0   1
0   0   2
0   1   0
0   1   1
0   1   2
0   2   0
0   2   1
0   2   2
1   0   0
1   0   1
1   0   2
1   1   0
1   1   1
1   1   2
1   2   0
1   2   1
1   2   2
2   0   0
2   0   1
2   0   2
2   1   0
2   1   1
2   1   2
2   2   0
2   2   1
2   2   2

At this moment, I'm trying to use 'surf' to do that, but I don't have any idea of how to build my code to convert the coordinates system I have into vectors that can be used without losing my 'value' information. I wanted to know if there's any function that can deal with information organized this way or maybe some simple idea of how to build the code.

Thanks, David

Answer 1

[W. Owen Brimijoin]

It's generally difficult to provide an intuitive graphical representation of high dimensional data. But, and mind you I say this without seeing your dataset, you could try using:

scatter3(x,y,z,S,'filled')

Where S (the size of the markers) is the vector of values* from your fourth column. This will result in a 3D grid of points of different sizes, so you could rotate this plot and see regions in your 3D space that had larger values associated with them.

. .

*You will probably need S to actually be some function of those values, because I believe the units in S are specified as number of pixels, rather than in axis coordinates.

[David Vicente]

I'm assuming you're telling me to use each column as an input vector for the 'scatter3'.

I tried and I get the following error:

scatter3(data(:,1),data(:,2),data(:,3),data(:,4),'filled')
Error using patch
Value must be finite and greater than zero

Error in specgraph.scattergroup/refresh (line 136)
        p = patch('Parent',double(this),...

Error in specgraph.scattergroup/schema>LdoDirtyAction (line 145)
  refresh(h);

Warning: Error occurred while evaluating listener callback. 
> In scatter3 at 90

The data I'm working with was obtained with the use of other software. I have a comma separated .txt file that I load to Matlab, so I can't define my values as a function.

I think what I might need is to convert this 2D matrix to a 3D matrix in which each entry corresponds to a voxel and has a 'value' from the fourth column.

[W. Owen Brimijoin]

No I simply meant that the numbers in data(:,4) might be negative (which from the error you are getting might be the case), or might have a dynamic range that wouldn't work well for specifying the size of a dot. So you might have to make another variable, say,

dot_sizes = data(:,4) - min(data(:,4)) %getting rid of the -values
scatter3(data(:,1),data(:,2),data(:,3),dot_sizes,'filled')

Then if the resulting dots are either way too big, or way to small you might have to scale them somehow:

scatter3(data(:,1),data(:,2),data(:,3),dot_sizes*scale_value,'filled')

I don't know what your data is like, you might have a value of 10,000 in there somewhere and that'd be a really big dot on a graph.