%% Exercise 1
%
% a) Consider cubic crystal symmetry. Find crystal directions with
% multiplicty 1, 2, 3 and 4.
%
%%
% b) Are there symmetry groups with infinitely many crystal directions that
% have multiplity larger then 1?
%

%% Exercise 2
%
% What are the common symmetries of the point groups m-3 and 321 ?
%

%% Exercise 3
% 
% Consider hexagonal symmetry. Which of the setups of the orthogonal
% crystal reference frame are compatible and which not: x||a, x||a*, x||b,
% x||b*,  y||a, x||a*, y||b, y||b*?
%


%% Exercise 4
%
% a) Most fundamental sectors of crystal symmetries are triangles. The
% fundamental sector of which crystal symmetry is a quadrangle? Visualize
% it.
%
% b) In fact the fundamental sector for this symmetry could by replaced by
% a triangle. Which one? Define and visualize it.
%


%% Exercises 5
%
% Define a crystal symmetry such that (110) is not parallel to {110}
%


%% Exercise 6
%
% Consider the following crystal symmetries and find an orientation with
% maximum rotational angle
%
% a) 112
%
%%
% b) 222
%
%%
% c) 432
%

%% Exercise 7
%
% Consider orthorhombic crystal symmetry and inspect the following pole
% figures:

cs = crystalSymmetry('222');

ori = secret('2_5'); % some secret orientations

% plot pole figures
h = Miller({1,0,0},{0,1,0},{0,0,1},cs)
plotPDF(ori,h)

%%
% a) How many orientations are displayed?
%
%%
% b) Determine the orientation(s) approximately.
%
%%
% c) Replace the crystal symmetry by the corresponding Laue group? Plot the
% pole figures. How many poles do you expect and how many do you observe?
% 
%% 
% d) Has the number of orientations changed? Verify you result by
% additional pole figures.

%% Exercise 8
% 
% Consider cubic crystal symmetry and inspect the following inverse pole
% figures:

cs = crystalSymmetry('m-3m')
ori = secret('2_6'); % some secret orientations

plotIPDF(ori,[vector3d.Z,vector3d.X])

%%
% a) Determine approximately the preferred orientation.
%
%%
% b) What is the percentage of orientations within a 5 degree ball around
% the preferrd orientation?
%
%%
% c) Visualize those orientations in 3d Euler angle space, in 3d axis angle
% space in phi2 sections and in sigma sections
% 
%

