Maximum scaling resolution of colormap for colorbar to be correct

I am experimenting with a function for using several colormaps in the same surface plot - e.g one colormap scaling for values < 0, another one for values between 0 and 1 and a third for values > 1.

I have used the following code as a proof of concept:

clear
clf('reset')
[x, y, z] = peaks(30);
surface(x, y, z);

n1 = 512;
n2 = 512;

cbar_mapping = [spring(n1); bone(n2)];

colormap(cbar_mapping);
colorbar

The function above generates the following figure.

In the final function I will set the values of variables n1, n2, ... , so that the relative contribution of each colormap will be assigned to the different regions of z, as described above. The higher the total value of n1 + n2+ ..., the better the range for each colormap will be pinpointed. However, if for instance I set n1 = 1024, n2 = 1024 in the code snippet above the colorbar will be faulty:

Questions: 1) Is this a bug, or a limitation implemented on purpose to fulfill another constraint?

2) Can the maximal sum of values n1 + n2 + ... be determined?

[David Goodmanson]

Hello Hannes, I tried n1 = n2 = 1024 on my PC with Matlab R2016b and it works. So did n1 = n2 = 10000, although the plot of course looked the same. I tried a couple of other things to verify the 20k example and it looks like whatever the upper limit is, it is going to be high enough for most practical purposes.

[Hannes Mogensen]

Thanks David! I also run R2016b on a PC (Windows 10). I guess for most practical purposes n_total = 1024 will work (as in my first example), I was more curious whether the behavior was deterministic and, if it was, the maximum working value could be calculated.

[Adam]

This also works fine for me, although I also added in

caxis( [-1 1] .* max( abs( z(:) ) ) )

to centre the colourmap correctly.

512 is already more variations in colour than can possibly be perceived by the human eye anyway though unless your colourmap is one that jumps around to very different colours for every consecutive element on the colourmap, in which case it would be incomprehensible anyway!

[David Goodmanson]

Hello Hannes, Did you find out why your colorbar was not working correctly?

[Image Analyst]

It also works fine for me with 1024 with Windows 10 and R2016b, and I didn't even have to mess with caxis() like Adam did. My colorbar looks like Hannes top colorbar, not the bottom gray one.

[Adam]

Yes, mine also looks like the top one. The caxis stuff is just to centre 0 which was something mentioned in the original question as having the colourmaps join at an essentially arbitrary value is misleading.

[Hannes Mogensen]

@David Goodmanson: No, I haven't figured out why it sometimes looks as in the bottom figure. The maximum value that works sometimes differ for a single computer, depending on change in some parameters I have not pinpointed yet. If I figure out I will post here.

[David Goodmanson]

Thanks Hannes. I and several other folks will be interested to know what is going on once you find out.