function eangles
% EANGLES Graphical Display of Euler Angle Characteristics
%
% eangles() opens a graphical user interface which gives the user two
% options. The first (forward) takes values for angles alpha, beta and gamma
% (in radians) and gives the output of the 3x3 rotation matrix R.
%
% The second option (backward) takes the inputted 3x3 rotation matrix R and
% gives the values (in radians) for the three euler angles alpha, beta and
% gamma.
%
% In both cases, one of the twelve conventions for Euler Angles needs to be
% given (for example zyz), and a small animation showing these rotations
% (according to the specified convention) will be ran.
%
% Created on MATLAB R2007a (7.4)
% Husam Aldahiyat, Jordan, 2009
%
% create main figure
figure('units','normalized','position',[.2 .2 .7 .7],'color','w','menubar','non','numbertitle','off',...
'name','Euler Angles')
% create main axes
am = axes('position',[.5 -.025 .55 .55]);
view(3)
ame = axes('position',[.5 .3 .55 .55]);
view(3)
amf = axes('position',[.5 .625 .55 .55]);
view(3)
% create an edit and text boxe for the rotation matrix
eR = uicontrol('style','edit','max',2,'un','n','pos',[.05 .6 .35 .25],'fonts',8,'fontn','courier',...
'backgroundcol',[1,1,1]);
uicontrol('sty','te','un','n','pos',[.05 .85 .35 .07],'string','Rotation Matrix','fonts',20,'fontweig','b',...
'backgroundcol','w')
% three edits for the angles
ea = uicontrol('sty','ed','un','n','pos',[.1 .45 .1 .1],'backgroundc','w','fonts',18,'string','20');
eb = uicontrol('sty','ed','un','n','pos',[.1 .3 .1 .1],'backgroundc','w','fonts',18,'string','30');
eg = uicontrol('sty','ed','un','n','pos',[.1 .15 .1 .1],'backgroundc','w','fonts',18,'string','60');
% create three small axes to the left of each angle edit box,
% then put a nice looking text in each axes
axes('position',[0 .45 .1 .1]);
axis off
text('position',[0.3 .6],'string','\alpha','fontsize',50)
axes('position',[0 .3 .1 .1]);
axis off
text('position',[0.3 .6],'string','\beta','fontsize',50)
axes('position',[0 .15 .1 .1]);
axis off
text('position',[0.4 .7],'string','\gamma','fontsize',50)
% create the button group at the bottom of the figure (backward/forward)
hg = uibuttongroup('unit','no','pos',[.05 .025 .4 .1],'backgroundc','w');
h1 = uicontrol('style','radiobutton','parent',hg,'un','n','pos',[0,0,.5,1],'background','w','string','Forward','fonts',20);
h2 = uicontrol('style','radiobutton','parent',hg,'un','n','pos',[0.5,0,.5,1],'background','w','string','Backward','fonts',20);
% pushbutton uicontrol
uicontrol('un','n','pos',[.25 .15 .1 .1],'sty','pu','string','Go','fonts',20,'backgroundc','w','callback',@go1)
% create convntion edit and text boxes
uicontrol('un','n','pos',[.25 .5 .2 .1],'sty','te','string','Convention','fonts',20,'backgroundc','w')
ce = uicontrol('un','n','pos',[.25 .45 .2 .1],'sty','e','string','xyz','fonts',20,'backgroundc','w');
% revert back to main axes for future plots
axes(am)
rotate3d
hold on
% draw the three coloured frame lines
Lx = line([0 1],[0,0],[0,0],'color',[1,0,0]);
Ly = line([0 0],[0,1],[0,0],'color',[0,1,0]);
Lz = line([0 0],[0,0],[0,1],'color',[0,0,1]);
set([Lx,Ly,Lz],'linewidth',3)
% draw the three base frame axis lines
line([0 1.5],[0,0],[0,0],'color',[0,0,0],'linewidth',2);
line([0 0],[0,1.5],[0,0],'color',[0,0,0],'linewidth',2);
line([0 0],[0,0],[0,1.5],'color',[0,0,0],'linewidth',2);
text('position',[1.3 0 .1],'string','x_0','fontw','b');
text('position',[ 0 1.3 .1],'string','y_0','fontw','b');
text('position',[.05 0.05 1.3],'string','z_0','fontw','b');
% text for x,y and z for each frame line
tX = text('position',[.7 0 .1],'string','x','fontw','b');
tY = text('position',[ 0 .7 .1],'string','y','fontw','b');
tZ = text('position',[.05 0.05 .7],'string','z','fontw','b');
% create our sphere and plot it
[xx,yy,zz]=sphere;
pp = surf(xx.*.34,yy.*.34,zz.*.34);
colormap bone
% plot origin point
plot3(0,0,0,'.','markersize',20,'color','k')
% more axes options (changing axis properties)
axis square
axis equal
axis off
% wR stands for "what to rotate"
wR = [tX,tZ,tY,Lx,Ly,Lz,pp];
% pushbutton callback
function go1(varargin)
axes(am)
% delete everything (start over)
delete(wR)
% create new lines and sphere
[xx,yy,zz]=sphere;
pp = surf(xx.*.34,yy.*.34,zz.*.34);
colormap bone
Lx = line([0 1],[0,0],[0,0],'color',[1,0,0]);
Ly = line([0 0],[0,1],[0,0],'color',[0,1,0]);
Lz = line([0 0],[0,0],[0,1],'color',[0,0,1]);
set([Lx,Ly,Lz],'linewidth',3)
tX = text('position',[.7 0 .1],'string','x','fontw','b');
tY = text('position',[ 0 .7 .1],'string','y','fontw','b');
tZ = text('position',[.05 0.05 .7],'string','z','fontw','b');
wR = [tX,tZ,tY,Lx,Ly,Lz,pp];
% get the value of the button group (forward or backward)
v = get(hg,'selectedobject');
% get value for convention
conv = get(ce,'string');
switch v
% forward
case h1
% get angles values
a = str2double(get(ea,'string'))/180*pi;
b = str2double(get(eb,'string'))/180*pi;
g = str2double(get(eg,'string'))/180*pi;
% obtain rotation matrix
s = eulfor(a,b,g,conv);
% display rotation matrix
set(eR,'string',num2str(s,5))
% backward
case h2
% get rotation matrix and use eul() to obtain three angles
s = eul(str2num(get(eR,'string')),conv); %#ok
% display three angles
set(ea,'string',num2str(s.a*180/pi));
set(eb,'string',num2str(s.b*180/pi));
set(eg,'string',num2str(s.g*180/pi));
end
% get Euler angles
a = str2double(get(ea,'string'))/180*pi;
b = str2double(get(eb,'string'))/180*pi;
g = str2double(get(eg,'string'))/180*pi;
% rotate first time
for k = 20:20
if strcmp(conv(1),'x')
rotate(wR,[1,0,0],rad2deg(a),[0,0,0])
elseif strcmp(conv(1),'y')
rotate(wR,[0,1,0],rad2deg(a),[0,0,0])
elseif strcmp(conv(1),'z')
rotate(wR,[0,0,1],rad2deg(a),[0,0,0])
end
% pause(.05)
end
% get new vectors for x,y and z (for next rotation)
pxx = eval(['get(L',conv(2),',','''xdata''',')']);
pyy = eval(['get(L',conv(2),',','''ydata''',')']);
pzz = eval(['get(L',conv(2),',','''zdata''',')']);
% rotate second time
for k = 20:20
rotate(wR,[pxx(2)-pxx(1),pyy(2)-pyy(1),pzz(2)-pzz(1)],rad2deg(b),[0,0,0])
% pause(.05)
end
pxx2 = eval(['get(L',conv(3),',','''xdata''',')']);
pyy2 = eval(['get(L',conv(3),',','''ydata''',')']);
pzz2 = eval(['get(L',conv(3),',','''zdata''',')']);
% rotate third time
for k = 20:20
rotate(wR,[pxx2(2)-pxx2(1),pyy2(2)-pyy2(1),pzz2(2)-pzz2(1)],rad2deg(g),[0,0,0])
% pause(.05)
end
axes(ame)
% delete everything (start over)
delete(wRe)
% create new lines and sphere
[xx,yy,zz]=sphere;
pp = surf(xx.*.34,yy.*.34,zz.*.34);
colormap bone
Lx = line([0 1],[0,0],[0,0],'color',[1,0,0]);
Ly = line([0 0],[0,1],[0,0],'color',[0,1,0]);
Lz = line([0 0],[0,0],[0,1],'color',[0,0,1]);
set([Lx,Ly,Lz],'linewidth',3)
tX = text('position',[.7 0 .1],'string','x','fontw','b');
tY = text('position',[ 0 .7 .1],'string','y','fontw','b');
tZ = text('position',[.05 0.05 .7],'string','z','fontw','b');
wRe = [tX,tZ,tY,Lx,Ly,Lz,pp];
% wR = wRe;
% get the value of the button group (forward or backward)
v = get(hg,'selectedobject');
% get value for convention
conv = get(ce,'string');
switch v
% forward
case h1
% get angles values
a = str2double(get(ea,'string'))/180*pi;
b = str2double(get(eb,'string'))/180*pi;
g = str2double(get(eg,'string'))/180*pi;
% obtain rotation matrix
s = eulfor(a,b,g,conv);
% display rotation matrix
set(eR,'string',num2str(s,5))
% backward
case h2
% get rotation matrix and use eul() to obtain three angles
s = eul(str2num(get(eR,'string')),conv); %#ok
% display three angles
set(ea,'string',num2str(s.a*180/pi));
set(eb,'string',num2str(s.b*180/pi));
set(eg,'string',num2str(s.g*180/pi));
end
% get Euler angles
a = str2double(get(ea,'string'))/180*pi;
b = str2double(get(eb,'string'))/180*pi;
g = str2double(get(eg,'string'))/180*pi;
% rotate first time
for k = 1:20
if strcmp(conv(1),'x')
rotate(wRe,[1,0,0],rad2deg(a/20),[0,0,0])
elseif strcmp(conv(1),'y')
rotate(wRe,[0,1,0],rad2deg(a/20),[0,0,0])
elseif strcmp(conv(1),'z')
rotate(wRe,[0,0,1],rad2deg(a/20),[0,0,0])
end
pause(.05)
end
% get new vectors for x,y and z (for next rotation)
pxx = eval(['get(L',conv(2),',','''xdata''',')']);
pyy = eval(['get(L',conv(2),',','''ydata''',')']);
pzz = eval(['get(L',conv(2),',','''zdata''',')']);
% rotate second time
for k = 1:20
rotate(wRe,[pxx(2)-pxx(1),pyy(2)-pyy(1),pzz(2)-pzz(1)],rad2deg(b/20),[0,0,0])
pause(.05)
end
pxx2 = eval(['get(L',conv(3),',','''xdata''',')']);
pyy2 = eval(['get(L',conv(3),',','''ydata''',')']);
pzz2 = eval(['get(L',conv(3),',','''zdata''',')']);
% rotate third time
for k = 1:20
rotate(wRe,[pxx2(2)-pxx2(1),pyy2(2)-pyy2(1),pzz2(2)-pzz2(1)],rad2deg(g/20),[0,0,0])
pause(.05)
end
axes(amf)
% delete everything (start over)
delete(wRf)
% create new lines and sphere
[xx,yy,zz]=sphere;
pp = surf(xx.*.34,yy.*.34,zz.*.34);
colormap bone
Lx = line([0 1],[0,0],[0,0],'color',[1,0,0]);
Ly = line([0 0],[0,1],[0,0],'color',[0,1,0]);
Lz = line([0 0],[0,0],[0,1],'color',[0,0,1]);
set([Lx,Ly,Lz],'linewidth',3)
tX = text('position',[.7 0 .1],'string','x','fontw','b');
tY = text('position',[ 0 .7 .1],'string','y','fontw','b');
tZ = text('position',[.05 0.05 .7],'string','z','fontw','b');
wRf = [tX,tZ,tY,Lx,Ly,Lz,pp];
% wR = wRf;
% get the value of the button group (forward or backward)
v = get(hg,'selectedobject');
% get value for convention
conv = get(ce,'string');
switch v
% forward
case h1
% get angles values
a = str2double(get(ea,'string'))/180*pi;
b = str2double(get(eb,'string'))/180*pi;
g = str2double(get(eg,'string'))/180*pi;
% obtain rotation matrix
s = eulfor(a,b,g,conv);
% display rotation matrix
set(eR,'string',num2str(s,5))
% backward
case h2
% get rotation matrix and use eul() to obtain three angles
s = eul(str2num(get(eR,'string')),conv); %#ok
% display three angles
set(ea,'string',num2str(s.a*180/pi));
set(eb,'string',num2str(s.b*180/pi));
set(eg,'string',num2str(s.g*180/pi));
end
% get Euler angles
a = str2double(get(ea,'string'))/180*pi;
b = str2double(get(eb,'string'))/180*pi;
g = str2double(get(eg,'string'))/180*pi;
% rotate first time
for k = 1:20
if strcmp(conv(3),'x')
rotate(wRf,[1,0,0],rad2deg(g/20),[0,0,0])
elseif strcmp(conv(3),'y')
rotate(wRf,[0,1,0],rad2deg(g/20),[0,0,0])
elseif strcmp(conv(3),'z')
rotate(wRf,[0,0,1],rad2deg(g/20),[0,0,0])
end
pause(.05)
end
%
% % get new vectors for x,y and z (for next rotation)
% pxx = eval(['get(L',conv(2),',','''xdata''',')']);
% pyy = eval(['get(L',conv(2),',','''ydata''',')']);
% pzz = eval(['get(L',conv(2),',','''zdata''',')']);
%
%
% rotate second time
for k = 1:20
if strcmp(conv(2),'x')
rotate(wRf,[1,0,0],rad2deg(b/20),[0,0,0])
elseif strcmp(conv(2),'y')
rotate(wRf,[0,1,0],rad2deg(b/20),[0,0,0])
elseif strcmp(conv(2),'z')
rotate(wRf,[0,0,1],rad2deg(b/20),[0,0,0])
end
pause(.05)
end
%
% pxx2 = eval(['get(L',conv(3),',','''xdata''',')']);
% pyy2 = eval(['get(L',conv(3),',','''ydata''',')']);
% pzz2 = eval(['get(L',conv(3),',','''zdata''',')']);
% rotate third time
for k = 1:20
if strcmp(conv(1),'x')
rotate(wRf,[1,0,0],rad2deg(a/20),[0,0,0])
elseif strcmp(conv(1),'y')
rotate(wRf,[0,1,0],rad2deg(a/20),[0,0,0])
elseif strcmp(conv(1),'z')
rotate(wRf,[0,0,1],rad2deg(a/20),[0,0,0])
end
pause(.05)
end
end
axes(amf)
rotate3d
hold on
% draw the three coloured frame lines
Lx = line([0 1],[0,0],[0,0],'color',[1,0,0]);
Ly = line([0 0],[0,1],[0,0],'color',[0,1,0]);
Lz = line([0 0],[0,0],[0,1],'color',[0,0,1]);
set([Lx,Ly,Lz],'linewidth',3)
% draw the three base frame axis lines
line([0 1.5],[0,0],[0,0],'color',[0,0,0],'linewidth',2);
line([0 0],[0,1.5],[0,0],'color',[0,0,0],'linewidth',2);
line([0 0],[0,0],[0,1.5],'color',[0,0,0],'linewidth',2);
text('position',[1.3 0 .1],'string','x_0','fontw','b');
text('position',[ 0 1.3 .1],'string','y_0','fontw','b');
text('position',[.05 0.05 1.3],'string','z_0','fontw','b');
% text for x,y and z for each frame line
tX = text('position',[.7 0 .1],'string','x','fontw','b');
tY = text('position',[ 0 .7 .1],'string','y','fontw','b');
tZ = text('position',[.05 0.05 .7],'string','z','fontw','b');
% create our sphere and plot it
[xx,yy,zz]=sphere;
pp = surf(xx.*.34,yy.*.34,zz.*.34);
colormap bone
% plot origin point
plot3(0,0,0,'.','markersize',20,'color','k')
% more axes options (changing axis properties)
axis square
axis equal
axis off
% wR stands for "what to rotate"
wRf = [tX,tZ,tY,Lx,Ly,Lz,pp];
axes(ame)
rotate3d
hold on
% draw the three coloured frame lines
Lx = line([0 1],[0,0],[0,0],'color',[1,0,0]);
Ly = line([0 0],[0,1],[0,0],'color',[0,1,0]);
Lz = line([0 0],[0,0],[0,1],'color',[0,0,1]);
set([Lx,Ly,Lz],'linewidth',3)
% draw the three base frame axis lines
line([0 1.5],[0,0],[0,0],'color',[0,0,0],'linewidth',2);
line([0 0],[0,1.5],[0,0],'color',[0,0,0],'linewidth',2);
line([0 0],[0,0],[0,1.5],'color',[0,0,0],'linewidth',2);
text('position',[1.3 0 .1],'string','x_0','fontw','b');
text('position',[ 0 1.3 .1],'string','y_0','fontw','b');
text('position',[.05 0.05 1.3],'string','z_0','fontw','b');
% text for x,y and z for each frame line
tX = text('position',[.7 0 .1],'string','x','fontw','b');
tY = text('position',[ 0 .7 .1],'string','y','fontw','b');
tZ = text('position',[.05 0.05 .7],'string','z','fontw','b');
% create our sphere and plot it
[xx,yy,zz]=sphere;
pp = surf(xx.*.34,yy.*.34,zz.*.34);
colormap bone
% plot origin point
plot3(0,0,0,'.','markersize',20,'color','k')
% more axes options (changing axis properties)
axis square
axis equal
axis off
% wR stands for "what to rotate"
wRe = [tX,tZ,tY,Lx,Ly,Lz,pp];
uicontrol('style','text','units','normalized','pos',[.55 .5 .1 .05],'string','Euler','fontweight','bold',...
'fontsize',15,'backgroundcolor',[1,1,1])
uicontrol('style','text','units','normalized','pos',[.55 .8 .1 .05],'string','Fixed','fontweight','bold',...
'fontsize',15,'backgroundcolor',[1,1,1])
end
