em2five.m

function [qm,nA] = em2five(e1,e2,e3,m1,m2,m3,epsijk)
arguments
   e1(:,3) double {mustBeReal,mustBeFinite}
   e2(:,3) double {mustBeReal,mustBeFinite}
   e3(:,3) double {mustBeReal,mustBeFinite}
   m1(:,3) double {mustBeReal,mustBeFinite}
   m2(:,3) double {mustBeReal,mustBeFinite}
   m3(:,3) double {mustBeReal,mustBeFinite}
   epsijk(1,1) double = 1
end
%--------------------------------------------------------------------------
% Author(s): Sterling Baird
%
% Date: 2020-08-22
%
% Description: to understand format of B matrix as in B*X = 0
%
% Usage:
%  o = TJ2oct(EAs,norms);
%
% Input:
%  EAs - euler angles in sample frame in in triple junction sets
%
%  norms - boundary plane normals in sample frame in triple junction sets
%
% Output:
%  o - rows of octonions (non-symmetrized)
%
% Dependencies:
%  eu2qu.m
%  eunA2five.m
%  GBfive2oct.m
%
% Notes:
%  GB1 (grain 2 --> grain 3) Boundary normal points from grain 2 towards grain 3
%  GB2 (grain 3 --> grain 1)
%  GB3 (grain 1 --> grain 2)
%
%  example: GB1 of TJ1 is defined by EAs(1,1,:) and norms(1,1,:)
%  example: GB2 of TJ1 is defined by EAs(1,2,:) and norms(1,2,:)
%
%  TJs - triple line direction (sample frame, Cartesian unit vector)
%  e1 - Grain 1 Euler Angles (sample frame, in degrees)
%  e2 - Grain 2 Euler Angles
%  e3 - Grain 3 Euler Angles
%
%  m1 - BP normal from 2 --> 3 (Cartesian unit vector, sample frame)
%  m2 - BP normal from 3 --> 1
%  m3 - BP normal from 1 --> 2
%
% References:
%  [1] Shen, Y. F., Zhong, X., Liu, H., Suter, R. M., Morawiec, A., &
%  Rohrer, G. S. (2019). Determining grain boundary energies from triple
%  junction geometries without discretizing the five-parameter space. Acta
%  Materialia, 166, 126–134. https://doi.org/10.1016/j.actamat.2018.12.022
%
%  [2] https://github.com/sgbaird/TJ2GBE
%
%  [3] https://github.com/Yufeng-shen/TJ2GBE
%
% see also Ni_0131_21520_Cub.mat
%--------------------------------------------------------------------------

%convert euler pairs and BP normal (sample frame) to mis quaternion and BP
%normal (grain A crystal frame)
[qm1,nA1] = eumA2five(e2,e3,m1,epsijk);
[qm2,nA2] = eumA2five(e3,e1,m2,epsijk);
[qm3,nA3] = eumA2five(e1,e2,m3,epsijk);

%% interleave
% so that e.g. qm(1,:) corresponds with B(1,:), resE(1), and X0(1:3+3*1);
% qm(2,:) corresponds with B(2,:), resE(2), and X0(1:3+3*2)

%number of
%--triple junctions
nTJ = size(e1,1);
%--grain boundaries
nGB = nTJ*3;

% initialize
qm = zeros(nGB,4);
nA = zeros(nGB,3);

%IDs for interleaving vectors
%e.g. X = [xi_1^x xi_1^y xi_1^z xi_2^x xi_2^y xi_2^z ... ], see [1]
id1 = 1:3:nGB;
id2 = 2:3:nGB;
id3 = 3:3:nGB;
intIDs = [id1 id2 id3]; %interleaf IDs, i.e. [1 4 7 ... 2 5 8 .. 3 6 9 ... ]

%--misorientation quaternions
qm(intIDs,:) = [qm1; qm2; qm3];
%--boundary plane normals
nA(intIDs,:) = [nA1; nA2; nA3];

end

%-----------------------CODE GRAVEYARD-------------------------------------
%{
%}