function millerind
% MILLERIND Cubic Miller Indices Explanation GUI
%
% millerind() is a graphical user interface that gives a simple method to
% view and understand the underlying princples behind the Miller indices of
% a cubic crystal.
%
% By entering a desired plane and pressing "Plot", the desired plane along
% with its orthogonal vector is displayed on the crystal cube, and all
% possible plane equivalents are shown. You can choose any of these planes
% to have them being shown on the axes, or you can rotate the cube manually
% and find out which equivalent plane results.
%
% To launch, simply type 'millerind' in your command window.
% Alternatively, you can choose run from this editor window, or press 'F5'.
%
% Created with MATLAB R2008b (7.7), but should work on earlier versions.
%
% numandina@gmail.com Jordan 2009
%
global C til pl tl mp lp sp
figure('color',[1,1,1],...
'menubar','none',...
'numbertit','off',...
'name','Miller Indices')
uipanel('un','n',...
'pos',[.01 .05 .275 .925],...
'backgroundc',[1,1,1])
uipanel('un','n',...
'pos',[.285 .775 .675 .2],...
'backgroundc',[1,1,1])
uipanel('un','n',...
'pos',[.285 .05 .675 .725],...
'backgroundc',[1,1,1])
axes('un','n',...
'pos',[0 -.1 1.2 1])
uicontrol('sty','tex',...
'un','n',...
'pos',[.05 .8 .2 .05],...
'backgroundc',[1,1,1],...
'string','Enter Plane Index')
e1 = uicontrol('sty','ed',...
'un','n',...
'pos',[.05 .77 .2 .05],...
'backgroundc',[1,1,1],...
'string','',...
'fontn','courier',...
'fonts',12,...
'fontw','b');
uicontrol('sty','pushbutton',...
'un','n',...
'pos',[.1 .7 .1 .05],...
'backgroundc',[1,1,1],...
'string','Plot',...
'callback',@main)
r1r = uicontrol('sty','pushbutton',...
'un','n',...
'pos',[.3 .9 .2 .05],...
'backgroundc',[1,1,1],...
'string','Rotate about x',...
'callback',@r1,...
'visible','off');
r2r = uicontrol('sty','pushbutton',...
'un','n',...
'pos',[.525 .9 .2 .05],...
'backgroundc',[1,1,1],...
'string','Rotate about y',...
'callback',@r2,...
'visible','off');
r3r = uicontrol('sty','pushbutton',...
'un','n',...
'pos',[.75 .9 .2 .05],...
'backgroundc',[1,1,1],...
'string','Rotate about z',...
'callback',@r3,...
'visible','off');
r1r2 = uicontrol('sty','pushbutton',...
'un','n',...
'pos',[.3 .8 .2 .05],...
'backgroundc',[1,1,1],...
'string','Rotate about -x',...
'callback',@r4,...
'visible','off');
r2r2 = uicontrol('sty','pushbutton',...
'un','n',...
'pos',[.525 .8 .2 .05],...
'backgroundc',[1,1,1],...
'string','Rotate about -y',...
'callback',@r5,...
'visible','off');
r3r2 = uicontrol('sty','pushbutton',...
'un','n',...
'pos',[.75 .8 .2 .05],...
'backgroundc',[1,1,1],...
'string','Rotate about -z',...
'callback',@r6,...
'visible','off');
t1 = uicontrol('sty','text',...
'un','n',...
'pos',[.05 .6 .2 .05],...
'backgroundc',[1,1,1],...
'string','X Planes Found',...
'foregroundc',[0,.5,0],...
'fontw','b',...
'visible','off');
uicontrol('sty','text',...
'un','n',...
'pos',[.05 .56 .2 .05],...
'backgroundc',[1,1,1],...
'string','Animation Speed',...
'foregroundc',[0,0,0],...
'fontw','b');
l1 = uicontrol('sty','listbox',...
'un','n',...
'pos',[.025 .1 .25 .4],...
'backgroundc',[1,1,1],...
'fontname','courier',...
'string',{'2 3 4';'3 2 1'},...
'fonts',15,...
'visible','off',...
'callback',@liz);
sd = uicontrol('style','slider',...
'un','n',...
'pos',[.0225 .525 .25 .05],...
'min',10,...
'max',210,...
'value',120,...
'sliderstep',[1/20,1/5],...
'callback',@ups);
axis off
hold on
function ups(varargin)
sp = 220 - get(sd,'value');
end
function r1(varargin)
rot(1,[1,0,0])
end
function r2(varargin)
rot(1,[0,1,0])
end
function r3(varargin)
rot(-1,[0,0,1])
end
function r4(varargin)
rot(-1,[1,0,0])
end
function r5(varargin)
rot(-1,[0,1,0])
end
function r6(varargin)
rot(1,[0,0,1])
end
function rot(s,az)
delete(findobj('type','text'));
rotate([pl,tl,mp,lp],az,s*90,[0.5,0.5,0.5])
p1 = str2num(get(e1,'string')); %#ok;
x = get(tl,'xdata');
y = get(tl,'ydata');
z = get(tl,'zdata');
v1 = [x(2)-x(1),y(2)-y(1),z(2)-z(1)];
v1 = round(v1(~~v1)*abs(prod(p1(~~p1))));
v1(end+1:3) = 0;
v1 = round(v1/gcd(gcd(v1(1),v1(2)),v1(3)));
X = v1(1);
Y = v1(2);
Z = v1(3);
tlt = text('string',[' Plane (',num2str(X),' ',num2str(Y),...
' ',num2str(Z),')'],'position',[1,.5,1.5]);
set(tlt,'fontsize',12,'fontw','b')
rotate([pl,tl,mp,lp],az,-s*90,[0.5,0.5,0.5])
for t = 1:sp
rotate([pl,tl,mp,lp],az,s*90/sp,[0.5,0.5,0.5])
drawnow
end
end
function liz(varargin)
cla
a = [0 0 0;...
1 0 0;...
1 1 0;...
0 1 0;...
0 0 1;...
1 0 1;...
1 1 1;...
0 1 1];
b=[1 2 6 5;2 3 7 6;3 4 8 7;4 1 5 8;1 2 3 4;5 6 7 8];
mp = patch('vertices',a,...
'faces',b,...
'edgecolor',[0,0,0],...
'facecolor',[.24 .24 .24]+.6,...
'linewidth',2,...
'facealpha',.5,...
'linestyle','-');
p1 = str2num(get(e1,'string')); %#ok;
[kkk,lll] = unique(round(C*10000),'rows','first');
if isequal((sort(abs(p1))),[0,1,1])
lll = lll(7:12);
end
[rr1,rr2,rr3] = ind2sub([4,4,4],(lll));
rr3=rr3-1;
rr2=rr2-1;
rr1=rr1-1;
rr3(rr3 == 4) = 0;
rr1(rr2 == 4) = 0;
rr2(rr2 == 4) = 0;
v = get(l1,'value');
tlt = plot(0,0,'.','markersize',.0001);
for kj = v:v
delete(tlt)
tlt = text('string',[' Plane (',num2str(til(kj,:)*1),')'],...
'position',[1,.5,1.5]);
set(tlt,'fontsize',12,'fontw','b')
if sum(~~p1) == 3
a = [0 0 1/p1(3);1/p1(1) 0 0;0 1/p1(2) 0];
b=[1,2,3];
elseif sum(~~p1) == 2
if ~p1(3)
a = ([0 1/p1(2) 1;1/p1(1) 0 1;1/p1(1) 0 0;0 1/p1(2) 0]);
elseif ~p1(2)
a = [0 0 1/(p1(3));1/p1(1) 0 0;1/p1(1) 1 0;0 1 1/(p1(3))];
elseif ~p1(1)
a = ([0 0 1/p1(3);0 1/p1(2) 0;1 1/p1(2) 0;1 0 1/p1(3)]);
end
b=[1,2,3,4];
else
a = [0 0 0;...
1 0 0;...
1 1 0;...
0 1 0;...
0 0 1;...
1 0 1;...
1 1 1;...
0 1 1];
B = [2,6,7,3;...
4,8,7,3;...
5:8;...
1,4,8,5;...
1,2,6,5;...
1:4];
c = find(p1);
if p1(c) < 0
c = c + 3;
end
b = B(c,:);
end
for k = 1:3
if any(a(:,k) < 0)
a(:,k) = a(:,k) + 1;
end
end
lx = [0,p1(1)];
ly = [0,p1(2)];
lz = [0,p1(3)];
ml = max(abs([lx,ly,lz]));
lx = lx/ml + (1 - lx(1))*~(sign(p1(1))+1); % + ~sum(lx)*.5;
ly = ly/ml + (1 - ly(1))*~(sign(p1(2))+1); % + ~sum(ly)*.5;
lz = lz/ml + (1 - lz(1))*~(sign(p1(3))+1); % + ~sum(lz)*.5;
tl = line(lx,ly,lz,...
'color',[.25,.9,.5],...
'linewidth',3);
pl = plot3(lx(2),ly(2),lz(2),'.');
set(pl,'color',[.25,.9,.5],...
'markersize',20);
lp = patch('vertices',a,...
'faces',b,...
'edgecolor','k',...
'facecolor',[.94 .24 .24],...
'linewidth',1,...
'facealpha',1,...
'linestyle','-');
drawnow
pause(.5)
for ind = 1:rr3(kj)
for t = 1:sp
if rr3(kj) == 3
rotate([pl,tl,mp,lp],[0,0,1],-90/sp,[0.5,0.5,0.5])
else
rotate([pl,tl,mp,lp],[0,0,1],90/sp,[0.5,0.5,0.5])
end
drawnow
end
if rr3(kj) == 3
break
end
end
for ind = 1:rr2(kj)
for t = 1:sp
if rr2(kj) == 3
rotate([pl,tl,mp,lp],[0,1,0],-90/sp,[0.5,0.5,0.5])
else
rotate([pl,tl,mp,lp],[0,1,0],90/sp,[0.5,0.5,0.5])
end
drawnow
end
if rr2(kj) == 3
break
end
end
for ind = 1:rr1(kj)
for t = 1:sp
if rr1(kj) == 3
rotate([pl,tl,mp,lp],[1,0,0],-90/sp,[0.5,0.5,0.5])
else
rotate([pl,tl,mp,lp],[1,0,0],90/sp,[0.5,0.5,0.5])
end
drawnow
end
if rr1(kj) == 3
break
end
end
end
end
function main(varargin)
cla
sp = 220 - get(sd,'value');
a = [0 0 0;...
1 0 0;...
1 1 0;...
0 1 0;...
0 0 1;...
1 0 1;...
1 1 1;...
0 1 1];
b=[1 2 6 5;2 3 7 6;3 4 8 7;4 1 5 8;1 2 3 4;5 6 7 8];
mp = patch('vertices',a,...
'faces',b,...
'edgecolor','k',...
'facecolor',[.24 .24 .24]+.6,...
'linewidth',2,...
'facealpha',.5,...
'linestyle','-');
view(3)
axis vis3d
axis([-.5 1.5 -.5 1.5 -.5 1.5])
p1 = str2num(get(e1,'string')); %#ok;
if gcd(gcd(p1(1),p1(2)),p1(3)) ~= 1
errordlg(['The greatest common divisor of the the plane''s',...
' three elements needs to be 1'],'Error')
error('err')
end
lx = [0,p1(1)];
ly = [0,p1(2)];
lz = [0,p1(3)];
ml = max(abs([lx,ly,lz]));
lx = lx/ml + (1 - lx(1))*~(sign(p1(1))+1); % + ~sum(lx)*.5;
ly = ly/ml + (1 - ly(1))*~(sign(p1(2))+1); % + ~sum(ly)*.5;
lz = lz/ml + (1 - lz(1))*~(sign(p1(3))+1); % + ~sum(lz)*.5;
rotate3d on
tl = line(lx,ly,lz,'color',[.25,.9,.5],'linewidth',3);
pl = plot3(lx(2),ly(2),lz(2),'.');
set(pl,'color',[.25,.9,.5],'markersize',20);
hold on
if sum(~~p1) == 3
a = [0 0 1/p1(3);1/p1(1) 0 0;0 1/p1(2) 0];
b=[1,2,3];
elseif sum(~~p1) == 2
if ~p1(3)
a = ([0 1/p1(2) 1;1/p1(1) 0 1;1/p1(1) 0 0;0 1/p1(2) 0]);
elseif ~p1(2)
a = [0 0 1/(p1(3));1/p1(1) 0 0;1/p1(1) 1 0;0 1 1/(p1(3))];
elseif ~p1(1)
a = ([0 0 1/p1(3);0 1/p1(2) 0;1 1/p1(2) 0;1 0 1/p1(3)]);
end
b=[1,2,3,4];
else
a = [0 0 0;...
1 0 0;...
1 1 0;...
0 1 0;...
0 0 1;...
1 0 1;...
1 1 1;...
0 1 1];
B = [2,6,7,3;...
4,8,7,3;...
5:8;...
1,4,8,5;...
1,2,6,5;...
1:4];
c = find(p1);
if p1(c) < 0
c = c + 3;
end
b = B(c,:);
end
for k = 1:3
if any(a(:,k) < 0)
a(:,k) = a(:,k) + 1;
end
end
lp = patch('vertices',a,...
'faces',b,...
'edgecolor','k',...
'facecolor',[.54 .54 .24],...
'linewidth',1,...
'facealpha',1,...
'linestyle','-');
C = zeros(4^3,3);
c = 0;
for ro1 = 1:4
for ro2 = 1:4
for ro3 = 1:4
c = c + 1;
x1 = (get(tl,'xdata')');
x2 = (get(tl,'ydata')');
x3 = (get(tl,'zdata')');
C(c,:) = [x1(2)-x1(1),x2(2)-x2(1),x3(2)-x3(1)];
rotate([pl,tl,mp,lp],[1,0,0],90,[0.5,0.5,0.5])
end
rotate([pl,tl,mp,lp],[0,1,0],90,[0.5,0.5,0.5])
end
rotate([pl,tl,mp,lp],[0,0,1],90,[0.5,0.5,0.5])
end
delete([pl,tl,lp])
lp = patch('vertices',a,...
'faces',b,...
'edgecolor','k',...
'facecolor',[.94 .24 .24],...
'linewidth',1,...
'facealpha',1,...
'linestyle','-');
tl = line(lx,ly,lz,'color',[.25,.9,.5],'linewidth',3);
pl = plot3(lx(2),ly(2),lz(2),'.');
set(pl,'color',[.25,.9,.5],'markersize',20);
C(abs(C) < 1e-5) = 0;
[kkk,lll] = unique(round(C*10000),'rows','first');
if isequal((sort(abs(p1))),[0,1,1])
lll = lll(7:12);
end
til = round(C(lll,:)*10000)/10000;
for klm = 1:size(til,1)
til2 = til(klm,:);
til2 = til2(~~til2)*abs(prod(p1(~~p1)));
til2(length(til2)+1:3) = 0;
til2 = round(til2);
til(klm,:) = round(round(til(klm,:)/gcd(gcd(til2(1),til2(2)),...
til2(3))*abs(prod(p1(~~p1)))*100000)/100000);
end
set(t1,'string',[num2str(size(til,1)),' Planes Found'],'visible','on')
set(l1,'visible','on','string',...
transpose(arrayfun(@(x)num2str(til(x,:)),...
1:size(til,1),'uniformoutput',false)),'value',1)
rotate3d on
tlt = text('string',[' Plane (',num2str(p1*1),')'],...
'position',[1,.5,1.5]);
set(tlt,'fontsize',12,'fontw','b')
set([r1r,r2r,r3r,r1r2,r2r2,r3r2],'visible','on')
end
end
