orientation matrix #473

samjliu · 2020-04-13T01:52:55Z

samjliu
Apr 13, 2020

I notice some discrepancy between the orientation matrix I get from an Orientation object by MTEX and that I calculate by equation in textbooks (please see below the function I wrote based on the equations). For example,

% using MTEX
   ori = orientation.goss;
   gmatrix = ori.matrix;
  gmatrix = 
   1.0000   -0.0000    0.0000
    0.0000    0.7071   -0.7071
    0.0000    0.7071    0.7071. 
% Using the function below euler2matrix
   eul = ori.Euler;
   euld = eul/degree;
   gmatrix = euler2matrix(euld(1),euld(2),euld(3));
   gmatrix =
    1.0000         0         0
         0    0.7071    0.7071
         0   -0.7071    0.7071

**Could you please help check which one is correct? Thank you. **

        function f = euler2matrix(varphi1d,Phid,phi2d)
            % Convert three eular angles to a grain orientation matrix
            varphi1 = deg2rad(varphi1d);
            Phi = deg2rad(Phid);
            varphi2 = deg2rad(phi2d);
            g11 = cos(varphi1) .* cos(varphi2) - sin(varphi1) .* sin(varphi2) .* cos(Phi);
            g12 = sin(varphi1) .* cos(varphi2) + cos(varphi1) .* sin(varphi2) .* cos(Phi);
            g13 = sin(varphi2) .* sin(Phi);
            g21 = -cos(varphi1) .* sin(varphi2) - sin(varphi1) .* cos(varphi2) .* cos(Phi);
            g22 = -sin(varphi1) .* sin(varphi2) + cos(varphi1) .* cos(varphi2) .* cos(Phi);
            g23 = cos(varphi2) .* sin(Phi);
            g31 = sin(varphi1) .* sin(Phi);
            g32 = -cos(varphi1) .* sin(Phi);
            g33 = cos(Phi);
            f(1,1,:) = g11;
            f(1,2,:) = g12;
            f(1,3,:) = g13;
            f(2,1,:) = g21;
            f(2,2,:) = g22;
            f(2,3,:) = g23;
            f(3,1,:) = g31;
            f(3,2,:) = g32;
            f(3,3,:) = g33;
        end