Is there a way to plot (4D) such that x, y, and z are in the linear scale but the fourth dimension is logarithmic?

I am having problems plotting a 243,082 row, 4 column data set. I want to display some amplitude values at specific times. I have x coordinates on the x axis, y coordinates on the y axis, time on the z axis, and want amplitude displayed by color at each time. I have been trying to use the scatter3 command to display the data, and everything displays correctly except for the amplitude (all the amplitudes are blue). I think part of the problem may be the fact that the amplitudes range from 10^-27 to 10^-6 and so MATLAB is just rounding each value to zero. Is there a way to make the amplitude display in the logarithmic scale? And will that fix the problem?

Here is my code:

file=uigetfile;

x_coordinate=xlsread(file,'a2:a243082');

y_coordinate=xlsread(file,'b2:b243082');

time=xlsread(file,'c2:c243082');

amplitude=xlsread(file,'d2:d243082');

figure

scatter3(x_coordinate,y_coordinate,time,amplitude)

caxis([10^(-27) 10^(-6)])

colorbar

Answer 1

[John Barber]

Deven,

As far as I know, the color axis cannot be directly set to log-scale, unlike the three coordinate axes. However, you can log-transform the color data yourself and get the same result with a bit of work. To get the colorbar to work out, one approach is to first log-transform the data, then rescale the transformed data to fit the same range as the original data. You can then set the colorbar to use log-scaling, and the result will be log-scaled coloring, with the correct scale shown on the colorbar.

Here is some sample code:

% Get the min and max of the unscaled data
minC = min(C(:));
maxC = max(C(:));

% Log-transform and scale the data
Cscaled = minC + (maxC-menC)*(log10(C) - log10(minC))/(log10(maxC/minC));

% (plot using the scaled data)

% Make a log-scaled colorbar
hCbar = colorbar;
set(hCbar,'Yscale','log');

You can also take a look at the code in my File Exchange program logzplot: http://www.mathworks.com/matlabcentral/fileexchange/29317.

- John

[Deven V]

Thanks for your help