demorotdefinition.m

这是几何代数的matlab工具包

     disp('>> % | ');
     % | 
     disp('>> % |   ROTATION DEFINITION');
     % |   ROTATION DEFINITION
     disp('>> % |');
     % |
     x = unit(e1-e2/3); %/
     I = e1^e2; %/
     angle = pi/6; %/
     Rx = gexp(-I*angle)*x; %/
     xper = x*I; %/
     Iper = I/I3; %/
     clf; %/
     draw(x,'r'); GAtext(1.1*x+0.1*Iper,'x','r'); %/
     draw(I*pi*norm(x)*norm(x),'y'); %/
     axis off; %/
     disp('>> % | ');
     % | 
     disp('>> % |   A vector x and a plane I containing it');
     % |   A vector x and a plane I containing it
     disp('>> % |');
     % |
     GAprompt; %/
     %GAview([0 90]); %/
     draw(xper,'b'); GAtext(1.1*xper+0.1*Iper,'x_\perp = x {\fontname{times}I}','b'); %/
     disp('>> % |');
     % |
     disp('>> % |   The perpendicular to x in that plane (its dual)');
     % |   The perpendicular to x in that plane (its dual)
     disp('>> % |');
     % |
     GAprompt; %/
     draw(Rx,'r'); GAtext(1.1*Rx+0.1*Iper,'Rx','r'); %/
     DrawPolyline({(Rx^x)/x,Rx,inner(Rx,x)/x},'m'); %/
     disp('>> % |');
     % |
     disp('>> % |   The rotated x can be composed from these, ');
     % |   The rotated x can be composed from these, 
     disp('>> % |   in a coordinate-free manner.');
     % |   in a coordinate-free manner.
     disp('>> % |');
     % |
     title('Rx = (cos \phi) x + (sin \phi) (x {\fontname{times}I}) = x (cos \phi + {\fontname{times}I} sin \phi) = x e^{{\fontname{times}I}\phi}'); %/
     disp('>> ');