Variant pairing

[nyyssont]

Hi,

the variant pairing histogram shows the variant pairs with respect to variant 1. Does it translate V2-VX to accommodate this sort of pairing or does the histogram only show those pairs where V1 really is a member?

-Tuomo

[nyyssont]

Maybe this is a better way to generate the V1-V24 list:

function [groupIds] = generateGroupIds()
% parent symmetry
cs_fcc = crystalSymmetry('m-3m', [3.6599 3.6599 3.6599], 'mineral', 'Iron fcc');

% child symmetry
cs_bcc = crystalSymmetry('m-3m', [2.866 2.866 2.866], 'mineral', 'Iron bcc');

% generate variants
varInt = variants(orientation.KurdjumovSachs(cs_fcc,cs_bcc),orientation.cube(cs_fcc,1));

% Generate misorientations between all variants
allMisos = inv(varInt)*varInt;

for l = 1:24
    % Compare the misorientations on each row to the first row (where
    % ordering is correct)
    [~,ind] = min(angle(allMisos(1,l),allMisos)/degree);
    % Make a list of variant Id pairs:
    groupIds_trial{l} = [1:24;ind]';
end

%Sort
groupIds_trial = cellfun(@(x) sort(x,2),groupIds_trial,'uniformOutput',false);
groupIds_trial = cellfun(@(x) sortrows(x),groupIds_trial,'uniformOutput',false);

%Remove duplicates
z = cell2mat(cellfun(@(x) x(:),groupIds_trial,'uniformOutput',false));
z = z';
z = unique(z,'rows','stable');
zz = num2cell(z,2);

%Back into cell
groupIds_trial = cellfun(@(x) reshape(x,[],2),zz,'uniformOutput',false);

%Remove duplicate rows, ready to be fed to computeGrainPairs
groupIds = cellfun(@(x) unique(x,'rows'),groupIds_trial,'uniformOutput',false);
groupIds = groupIds(2:end);
end

[nyyssont]

After some fiddling, I think it works. The result generated is close but not quite equivalent to when you use the list in Example 10:

vGroupIds = {[1 2],...
    [1 3; 1 5],...
    [1 4],...
    [1 6],...
    [1 7],...
    [1 8],...
    [1 9; 1 19],...
    [1 10; 1 14],...
    [1 11; 1 13],...
    [1 12; 1 20],...
    [1 15; 1 23],...
    [1 16],...
    [1 17],...
    [1 18; 1 22],...
    [1 21],...
    [1 24]};

[frankNiessen]

Hi Tuomo,

sorry for the late reply, I am rather busy these days ...

So I can tell you that ORTools by default returns all the variant pairs:
computeGrainPairs(grains,'variants','plot');

If you want a 1D histogram you will have to make a decision what you want when defining the groups. In a scenario with 6 variants, the grouping
vGroupIds = {[1,1],[1 2],[1,3],[1,4],[1,5],[1,6]} would correspond to your last sugestion: Only the 1-X pairs, no equivalency.

computeGrainPairs(grains,'variant','group',vGroupIds,'plot'); I think what you suggest is what you want in most cases - finding all equivalent misorientations with respect to the V1-Vx misorientation and plot these. I would in your code check for a matching misorientation axis as well.
You should achieve this by defining vGroupIds according to your groupIds_trial variable.

I will see if I can get Azdiar to comment as well, he knows the implementation better than I do.