Pole figures are two dimensional representations of orientations. To illustrate this we define a random orientation with trigonal crystal symmetry
cs = crystalSymmetry('321')
ori = orientation.rand(cs)
cs = crystalSymmetry
symmetry : 321
elements : 6
a, b, c : 1, 1, 1
reference frame: X||a*, Y||b, Z||c*
ori = orientation (321 → xyz)
Bunge Euler angles in degree
phi1 Phi phi2
0.572564 61.1121 197.428
Starting point is a fixed crystal direction h
, e.g.,
% the fixed crystal directions (100)
h = Miller({1,0,0},cs);
Next the specimen directions corresponding to all crystal directions symmetrically equivalent to h
are computed
r = ori * h.symmetrise
r = vector3d
size: 1 x 6
x y z
-1.09997 -0.178076 -0.302808
-0.854083 0.368866 0.683969
0.854083 -0.368866 -0.683969
1.09997 0.178076 0.302808
0.245885 0.546942 0.986777
-0.245885 -0.546942 -0.986777
and ploted in a spherical projection
plot(r)
![](images/OrientationPoleFigure_01.png)
Since the trigonal symmetry group has six symmetry elements the orientation appears at six possitions.
A shortcut for the above computations is the command
% a pole figure plot
plotPDF(ori,Miller({1,0,-1,0},{0,0,0,1},{1,1,-2,1},ori.CS))
![](images/OrientationPoleFigure_02.png)
We observe, that for some crystal directions only the upper hemisphere is plotted while for other upper and lower hemisphere are plotted. The reason is that if h
and -h
are symmetrically equivalent the upper and lower hemisphere of the pole figure are symmetric as well.
Contour plots
plotPDF(ori,Miller({1,0,-1,0},{0,0,0,1},{1,1,-2,1},ori.CS),'contourf')
mtexColorbar
![](images/OrientationPoleFigure_03.png)