Misorientation angle plots as percentage

[DavidMainprice]

For example for two phase case

plotAngleDistribution(ebsd('Olivine').CS,ebsd('Antigorite').CS,'fundamentalRegion','percent')

If you code your own plot ...

%**************************************************************************
%% uniform distributions - Angles & axes:  Olivine - Antigorite
%**************************************************************************
% direct calculation - uniform distributions of angles
[density,omega] = calcAngleDistribution(ebsd('Olivine').CS,ebsd('Antigorite').CS);
omega_deg = omega./degree;
frequency_percent = 100 * density ./sum(density);
[max_frequency findex]  = max(frequency_percent);
omega_at_max_ol_atg = omega_deg(findex)
frequency_at_max_ol_atg = frequency_percent(findex)
close all
figure
plot(omega_deg,frequency_percent,'b','LineWidth',2)
axis tight
xlabel('Misorientation angle in degrees','FontSize',18)
ylabel('Frequency in percent','FontSize',18)
% plot title
title('Uniform misorientation angle distribution: Olivine - Antigorite','FontSize',18)
saveFigure('987_Y_Uniform_Misorientation_angles_ol_atg.png')

So the MTEX

plotAngleDistribution(ebsd('Olivine').CS,ebsd('Antigorite').CS,'fundamentalRegion','percent')

frequency should be divided by some factor

all the best David

[ralfHielscher]

Hi David,

I would think the MTEX output is correct. The point is that in your code you divide by sum(density) but you should divide by mean(density).

Ralf.

[zmichels]

But the plot David showed as an example of the MTEX approach gives frequency (%) values >250%. Is that reasonable?

[ralfHielscher]

I think so. Ask yourself: which frequency would get a uniform distribution. I would say 100 percent.

[kilir]

So, in a uniform mdf/odf, the angle distribution both times is:

cs=crystalSymmetry('321')
plotAngleDistribution(uniformODF(cs,cs),'fundamentalRegion','percent')

and

plotAngleDistribution(uniformODF(cs),'fundamentalRegion','percent')

So can there be actually a uniform mdf?

I think maybe calling it 'percent' in the angle distribution might be misleading as it seems to be the density relative to a uniform odf, but the uniform mdf does not have a uniform angle distribution. (?)

[zmichels]

Yeah. I agree that 'percent' is misleading (for me at least). I am not used to seeing a plot where the frequency (%) goes above 100% frequency. I still am not sure what that would mean for the angle distribution plot... more than 100% of the time you can expect to observe a specific angle? The plots in the mtex documentation (attached example) are like those I am used to seeing (i.e., don't go above 100%).

[ralfHielscher]

You may like to think about the angle distribution as an histogram with infinitely small bins. However, if you in an histogram increase the number of bin you see that them height of the bins decreases indirectly proportional with the number of bins.

If the continuous angle distribution is plotted on top of an histogram MTEX automatically scales it such that it fits to the histogram. However, if there is no histogram, one scaling has to be fixed. In statistics density distributions are always scaled such that the integral is 1. If given in percent this means that the mean value is 100.

Note also that percent is not the default scaling in MTEX.

Ralf.

[DavidMainprice]

Dear Ralf,

Many people use the normalisation with line integral of one, for uniform distribution line or uncorrelated line, but also the sum of histogram bins has to be one as well. However a plot that has percent scale with values greater than 100 does not make much sense to me.

If you want to remove the ‘percent’ option or encourage MTEX users to use the default option of times uniform distribution, that is not ‘percent’ that is fine. The percent scale is used by many of the commercial EBSD packages and I find it useful to compare with results published by other people using different softwares.

all the best David

Le 25 mars 2016 à 07:40, Ralf Hielscher notifications@github.com a écrit :

You may like to think about the angle distribution as an histogram with infinitely small bins. However, if you in an histogram increase the number of bin you see that them height of the bins decreases indirectly proportional with the number of bins.

If the continuous angle distribution is plotted on top of an histogram MTEX automatically scales it such that it fits to the histogram. However, if there is no histogram, one scaling has to be fixed. In statistics density distributions are always scaled such that the integral is 1. If given in percent this means that the mean value is 100.

Note also that percent is not the default scaling in MTEX.

Ralf.

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