gtMisorientation : very simple function to compute the misorientation angle...

gtMisorientation : very simple function to compute the misorientation angle and axis between two r_vectors, by given symmetry operators and lattice parameters.

Signed-off-by: Laura Nervo <laura.nervo@esrf.fr>

zUtil_Maths/gtMisorientation.m

+function [mis_angle, mis_axis, Gsymm] = gtMisorientation(r_vector1, r_vector2, symm, latticepar)
+% GTMISORIENTATION  Easy function to calculate the misorientation angle and axis
+%                   between two R_vectors
+%
+%     [mis_angle, mis_axis, Gsymm] = gtMisorientation(r_vector1, r_vector2, symm, [latticepar])
+%     -----------------------------------------------------------------------------------------
+%     INPUT:
+%       r_vector1  = <double>          R_vector for grain 1 (1x3)
+%       r_vector2  = <double>          R_vector for grain 2 (1x3)
+%       symm       = <struct array>    symmetry operators list from gtCrystGetSymmetryOperators
+%       latticepar = <double>          lattice parameters in case of hexagonal
+%                                      crystals (1x6)
+%
+%     OUTPUT:
+%       mis_angle = <double>           misorientation angle between the grains
+%       mis_axis  = <double>           misorientation axis (1x4 if hexagonal)
+%                                      notation)
+%       Gsymm     = <struct>           misorientation matrices, angles and axes
+%                                      using symm (extra info)
+%
+%     The result has been checkes and confirmed with the same calculation from the 
+%     xfab package in fable.
+%
+%
+%     Version 002 04-06-2013 by LNervo
+%       Simplified function and optimized speed
+
+
+if isempty(r_vector1) || isempty(r_vector2)
+    gtError('gtMisorientation:missingArgument','One r_vector is empty...please give two valid r_vectors.');
+end
+if ~exist('symm', 'var') || isempty(symm)
+    gtError('gtMisorientation:missingArgument','Symmetry operators are missing... Use gtCrystGetSymmetryOperators to calculate them')  
+end
+
+if size(r_vector1,2) == 4
+    r_vector1 = r_vector1(2:4);
+end
+if size(r_vector2,2) == 4
+    r_vector2 = r_vector2(2:4);
+end
+
+% orientation matrices : Vc = g*Vs
+g1 = gtMathsRod2OriMat(r_vector1');
+g2 = gtMathsRod2OriMat(r_vector2');
+
+% net rotation : g2 * symm().g3 * (inv(g1))
+netGs = arrayfun(@(num) g2*(symm(num).g3*g1'), 1:length(symm), 'UniformOutput', false);
+% calculate the misorientation angle and axis between these grains
+mis_angles = arrayfun(@(num) acosd((trace(netGs{num})-1)/2), 1:length(symm));
+
+%calculate eigen-vectors to find misorientation axis
+[eigVecs, eigVals] = arrayfun(@(num) eig(netGs{num}), 1:length(symm), 'UniformOutput', false);
+% choose the only one real
+misorientation_axes = arrayfun(@(num2) eigVecs{num2}(:,arrayfun(@(num) isreal(eigVecs{num2}(:,num)), 1:3))', 1:length(symm), 'UniformOutput', false);
+eigVals = arrayfun(@(num2) eigVals{num2}( arrayfun(@(num) isreal(eigVecs{num2}(:,num)),1:3), arrayfun(@(num) isreal(eigVecs{num2}(:,num)),1:3) ), 1:length(symm) );
+
+% choose the minimum mis_angle
+dummy = find(min(mis_angles));
+
+mis_angle = mis_angles(dummy);
+
+if nargout > 1
+    mis_axis = misorientation_axes{dummy};
+  
+    if exist('latticepar', 'var') && ~isempty(latticepar)
+        mis_axis = gtCart2Hex(mis_axis, latticepar);
+    end
+
+    if nargout > 2
+        Gsymm.r1 = r_vector1;
+        Gsymm.r2 = r_vector2;
+        Gsymm.g1 = g1;
+        Gsymm.g2 = g2;
+
+        for ii=1:length(symm)
+            symm(ii).netG      = netGs{ii};
+            symm(ii).mis_angle = mis_angles(ii);
+            symm(ii).mis_axis  = misorientation_axes{ii};
+        end
+
+        Gsymm.symm = symm;
+    end
+
+end % end of function