demoinvertible.m

这是几何代数的matlab工具包

     disp('>> % |    INVERTIBILITY OF GEOMETRIC PRODUCT');
     % |    INVERTIBILITY OF GEOMETRIC PRODUCT
     disp('>> % |');
     % |
     clf; %/
     a=e1; %/
     x = 2*e1+e2; %/
     ip = inner(x,a); %/
     proj=ip/a; %/
     rej = (x^a)/a; %/
     urej = unit(rej); %/
     aplane = unit(a)*I3; %/
     perp = -urej/aplane; %/
     draw(a,'r'); GAtext(a/2-0.1*urej+0.1*perp,'a','r'); %/
     axis off; %/
     gaview([-15,60]); %/
     axis([-1 4 -1.5 1.5 -1.5 1.5]); %/
     disp('>> % |    Given a and a.x, what is x?');
     % |    Given a and a.x, what is x?
     disp('>> % |');
     % |
     title('Given a and x \bullet a, what is x?'); %/
     GAprompt; %/
     s = 1.5*norm(rej); %/
     DrawPolygon({proj+s*(urej+perp),proj+s*(urej-perp),proj+s*(-urej-perp),proj+s*(-urej+perp)},'w'); %/
     GAtext(proj-(s+0.1)*urej,'x \bullet a - plane','r'); %/
     gaview([-15,60]); %/
     axis([-1 4 -1.5 1.5 -1.5 1.5]); %/
     disp('>> % |    Somewhere in the x.a-plane...');
     % |    Somewhere in the x.a-plane...
     disp('>> % |');
     % |
     title('Somewhere in the x \bullet a - plane...'); %/
     GAprompt; %/
     disp('>> clf;');
     clf;
     draw(a,'r'); GAtext(a/2-0.1*urej+0.1*perp,'a','r'); %/
     axis off; %/
     gaview([-15,60]); %/
     axis([-1 4 -1.5 1.5 -1.5 1.5]); %/
     disp('>> % |    Given a and x^a, what is x?');
     % |    Given a and x^a, what is x?
     disp('>> % |');
     % |
     title('Given a and x \wedge a, what is x?'); %/
     GAprompt; %/
     y = x; %/
     DrawPolygon({0,a,a+y,y},'y'); %/
     y = x-2*a; %/
     DrawPolygon({0,a,a+y,y},'y'); %/
     DrawPolyline({x-3*a,x+2*a},'r'); %/
     GAtext(x+2.2*a,'x \wedge a - line','r'); %/
     axis([-1 4 -1.5 1.5 -1.5 1.5]); %/
     disp('>> % |    Somewhere on the x^a-line...');
     % |    Somewhere on the x^a-line...
     disp('>> % |');
     % |
     title('Somewhere on the x \wedge a - line...'); %/
     GAprompt; %/
     DrawPolygon({proj+s*(urej+perp),proj+s*(urej-perp),proj+s*(-urej-perp),proj+s*(-urej+perp)},'w'); %/
     GAtext(proj-(s+0.1)*urej,'x \bullet a - plane','r'); %/
     disp('>> % |    Now combine these to the invertible geometric product');
     % |    Now combine these to the invertible geometric product
     disp('>> % |');
     % |
     title('Combine in the geometric product:  x a = x \bullet a + x \wedge a'); %/
     axis([-1 4 -1.5 1.5 -1.5 1.5]); %/
     GAprompt; %/
     disp('>> % |    And solve!');
     % |    And solve!
     disp('>> % |');
     % |
     title('Solve as:  x = (x \bullet a)/a + (x \wedge a)/a'); %/
     draw(x,'k'); GAtext(2*x/3-0.1*urej+0.1*perp,'x','k'); %/
     draw(proj,'b'); GAtext(1.1*proj,'(x \bullet a)/a','b'); %/
     draw(rej,'b'); GAtext(1.3*rej+0.1*perp,'(x \wedge a)/a','b'); %/
     axis([-1 4 -1.5 1.5 -1.5 1.5]); %/