gadmeetlineplane.m

这是几何代数的matlab工具包

%% slight cheat, since I set J = I3 explicilty
%% so merely for illustration of the principle
%% should actually allow line to in plane as well
% |
% |   MEET AND JOIN OF LINE AND PLANE 
% |
clf; %/
A = e1+e3; %/
A=A/norm(A); %/
B = (e1+e2)^(e2+e3); %/
B =B/norm(B); %/
draw(A,'m'); GAtext(1.1*A,'A'); %/
draw(B,'c'); GAtext(0.45*(e2+e3),'B'); %/
axis off; %/
axis([-0.7 0.7 -0.7 0.7 -0.75 0.75]); %/
% |
% |   The line A and plane B.
% |
GAprompt; %/
GAorbiter(40,5); %/
GAprompt; %/
J = I3; %/
draw(J,'y'); GAtext(0.5*(e1-e2)+0.05*I3,'J \equiv A \cup B = I_3'); %/
axis([-0.7 0.7 -0.7 0.7 -0.75 0.75]); %/
% |
% |  Their join is the trivector I3.
% | 
GAprompt; %/
M = inner((B/J),A) %/
DrawPoint({0},'r',20); %/
GAtext(0.1*e1,'M \equiv A \cap B = scalar'); %/
axis([-0.7 0.7 -0.7 0.7 -0.75 0.75]); %/
% |
% |  Their Meet is a scalar, representing the point at the origin.
% |
GAprompt; %/
GAorbiter(-30,5); %/