?? gablock.m
字號:
function GAblock(GAn)%GAblock: run sample code in tutorial.tryif ( GAn == 1 ) GAps = 'GAblock >> '; disp('>> % ORTHOGONALIZATION'); % ORTHOGONALIZATION disp('>> clf;'); clf; disp('>> u = e1+e2;'); u = e1+e2; disp('>> v = 0.3*e1 + 0.6*e2 - 0.8*e3;'); v = 0.3*e1 + 0.6*e2 - 0.8*e3; disp('>> w = e1 -0.2*e2 + 0.5*e3;'); w = e1 -0.2*e2 + 0.5*e3; disp('>> up = u;'); up = u; disp('>> vp = (v^up)/up;'); vp = (v^up)/up; disp('>> wp = (w^up^vp)/(up^vp);'); wp = (w^up^vp)/(up^vp); disp('>> draw(u); draw(v); draw(w); %% The original vectors ...'); draw(u); draw(v); draw(w); %% The original vectors ... GAprompt; disp('>> draw(up,''r''); draw(vp,''r''); draw(wp,''r''); %% ... and orthognalized'); draw(up,'r'); draw(vp,'r'); draw(wp,'r'); %% ... and orthognalized GAprompt; disp('>> GAorbiter'); GAorbiter disp(' '); disp('End of GAblock sequence. Returning to Matlab.');elseif ( GAn == 2 ) GAps = 'GAblock >> '; disp('>> % ROTATION EXERCISE'); % ROTATION EXERCISE disp('>> clf;'); clf; disp('>> R1 = gexp(-I3*e1*pi/2/2);'); R1 = gexp(-I3*e1*pi/2/2); disp('>> R2 = gexp(-I3*e2*pi/2/2);'); R2 = gexp(-I3*e2*pi/2/2); disp('>> R = R2*R1;'); R = R2*R1; disp('>> a = e1+e2;'); a = e1+e2; disp('>> Ra = R*a/R;'); Ra = R*a/R; disp('>> RRa = R*Ra/R;'); RRa = R*Ra/R; disp('>> draw(a); draw(Ra,''m''); draw(RRa,''r''); %% Draw the objects'); draw(a); draw(Ra,'m'); draw(RRa,'r'); %% Draw the objects GAprompt; disp('>> axisR = unit( -GAZ(sLog(R))/I3 );'); axisR = unit( -GAZ(sLog(R))/I3 ); disp('>> draw(axisR,''g''); % Draw the axis of rotation'); draw(axisR,'g'); % Draw the axis of rotation GAps = 'Refer to the tutorial before continuing >> '; disp(' '); GAprompt; GAps = 'GAblock >> '; disp('>> draw(dual(axisR),''g'');'); draw(dual(axisR),'g'); disp(' '); disp('End of GAblock sequence. Returning to Matlab.');elseif ( GAn == 3 ) GAps = 'GAblock >> '; disp('>> % INTERPOLATION OF ORIENTATIONS'); % INTERPOLATION OF ORIENTATIONS disp('>> clf;'); clf; disp('>> RA = gexp(-I3*e1*pi/2/2);'); RA = gexp(-I3*e1*pi/2/2); disp('>> RB = gexp(-I3*e2*pi/2/2);'); RB = gexp(-I3*e2*pi/2/2); disp('>> Rtot = RB/RA'); Rtot = RB/RA disp('>> n = 8; % we rotate in 8 steps'); n = 8; % we rotate in 8 steps disp('>> R = gexp(sLog(Rtot)/n);'); R = gexp(sLog(Rtot)/n); GAps = 'Refer to the tutorial before continuing >> '; disp(' '); GAprompt; GAps = 'GAblock >> '; disp('>> u = e1+e2-e3;'); u = e1+e2-e3; disp('>> v = e1+e3;'); v = e1+e3; disp('>> view = [-0.6 2.5 -1 1.16 -2 1.1]; % select the view'); view = [-0.6 2.5 -1 1.16 -2 1.1]; % select the view disp('>> % === initial orientation:'); % === initial orientation: disp('>> DrawBivector(RA*u/RA,RA*v/RA,''b''); axis(view); GAview([30 30]); %%'); DrawBivector(RA*u/RA,RA*v/RA,'b'); axis(view); GAview([30 30]); %% GAprompt; disp('>> % === final orientation:'); % === final orientation: disp('>> DrawBivector(RB*u/RB,RB*v/RB,''g''); axis(view); %%'); DrawBivector(RB*u/RB,RB*v/RB,'g'); axis(view); %% GAprompt; disp('>> axisR = unit(GAZ(-sLog(R)/I3)); % reorientation axis: '); axisR = unit(GAZ(-sLog(R)/I3)); % reorientation axis: disp('>> draw(axisR,''r''); %% displayed for visualization '); draw(axisR,'r'); %% displayed for visualization GAprompt; disp('>> % === display of the 7 intermediate orientations '); % === display of the 7 intermediate orientations disp('>> Ri = RA;'); Ri = RA; for i=1:n-1 disp('>> for i=1:n-1'); disp(['i = ', num2str(i)]) disp('>> Ri = R*Ri;'); Ri = R*Ri; disp('>> ui = Ri*u/Ri;'); ui = Ri*u/Ri; disp('>> vi = Ri*v/Ri;'); vi = Ri*v/Ri; disp('>> DrawBivector(ui,vi);'); DrawBivector(ui,vi); disp('>> drawnow;'); drawnow; disp('>> end'); end disp('>> GAorbiter(125);'); GAorbiter(125); disp(' '); disp('End of GAblock sequence. Returning to Matlab.');elseif ( GAn == 4 ) GAps = 'GAblock >> '; disp('>> % LINE INTERSECTS LINE'); % LINE INTERSECTS LINE disp('>> p = e2; u = 0.2*e2 + e1;'); p = e2; u = 0.2*e2 + e1; disp('>> q = e1; v = e2-2*e1;'); q = e1; v = e2-2*e1; disp('>> clf; '); clf; disp('>> draw(p); GAview([0 90]);'); draw(p); GAview([0 90]); disp('>> DrawPolyline({p-2*u,p+2*u});'); DrawPolyline({p-2*u,p+2*u}); disp('>> draw(q,''g''); DrawPolyline({q-v,q+2*v},''g'');'); draw(q,'g'); DrawPolyline({q-v,q+2*v},'g'); GAps = 'Refer to the tutorial before continuing >> '; disp(' '); GAprompt; GAps = 'GAblock >> '; disp('>> U = (q^v/(u^v)) * u'); U = (q^v/(u^v)) * u disp('>> V = (p^u/(v^u)) * v'); V = (p^u/(v^u)) * v disp('>> draw(U,''m'') %% Draw U'); draw(U,'m') %% Draw U GAprompt; disp('>> draw(V, ''m'') %% Draw V'); draw(V, 'm') %% Draw V GAprompt; disp('>> draw(U+V, ''r'' ) % Draw U+V'); draw(U+V, 'r' ) % Draw U+V disp(' '); disp('End of GAblock sequence. Returning to Matlab.');elseif ( GAn == 5 ) GAps = 'GAblock >> '; disp('>> % PROJECTION, REJECTION'); % PROJECTION, REJECTION disp('>> x = e1 + e2/2+e3;'); x = e1 + e2/2+e3; disp('>> A = e2 + e3/3; % a linear subspace'); A = e2 + e3/3; % a linear subspace disp('>> xA = geoall(x,A);'); xA = geoall(x,A); disp('>> clf; draw(x,''b''); draw(A,''g''); %% Draw A and x'); clf; draw(x,'b'); draw(A,'g'); %% Draw A and x GAprompt; disp('>> DrawPolyline({xA.rej,xA.rej+xA.proj,xA.proj},''k'');'); DrawPolyline({xA.rej,xA.rej+xA.proj,xA.proj},'k'); disp('>> draw(xA.rej,''m''); draw(xA.proj,''m''); %% Draw rej and proj'); draw(xA.rej,'m'); draw(xA.proj,'m'); %% Draw rej and proj GAprompt; disp('>> distxA = norm(xA.rej)'); distxA = norm(xA.rej) disp('>> tanglexA = xA.rej/xA.proj'); tanglexA = xA.rej/xA.proj disp('>> anglexA = atan(norm(tanglexA))*180/pi %%'); anglexA = atan(norm(tanglexA))*180/pi %% GAprompt; disp('>> B = e1^A; % A planar subspace (containing A)'); B = e1^A; % A planar subspace (containing A) disp('>> xB = geoall(x,B); '); xB = geoall(x,B); disp('>> draw(B,''y''); %%'); draw(B,'y'); %% GAprompt; disp('>> DrawPolyline({xB.rej,xB.rej+xB.proj,xB.proj},''k'');'); DrawPolyline({xB.rej,xB.rej+xB.proj,xB.proj},'k'); disp('>> draw(xB.rej,''r''); draw(xB.proj,''r''); %% rej and proj for B'); draw(xB.rej,'r'); draw(xB.proj,'r'); %% rej and proj for B GAprompt; disp('>> distxB = norm(xB.rej)'); distxB = norm(xB.rej) disp('>> tanglexB = xB.rej/xB.proj'); tanglexB = xB.rej/xB.proj disp('>> anglexB = atan(norm(tanglexB))*180/pi'); anglexB = atan(norm(tanglexB))*180/pi disp('>> side = sign((x^B)/I3)'); side = sign((x^B)/I3) disp(' '); disp('End of GAblock sequence. Returning to Matlab.');elseif ( GAn == 6 ) GAps = 'GAblock >> '; disp('>> % MEET, JOIN '); % MEET, JOIN disp('>> A = e2^(e1+e3);'); A = e2^(e1+e3); disp('>> B = e1^(e2+e3/2);'); B = e1^(e2+e3/2); disp('>> cAB = inner(A,B); pAB = cAB/B; rAB = A - pAB;'); cAB = inner(A,B); pAB = cAB/B; rAB = A - pAB; disp('>> clf; draw(A,''b''); draw(B,''g''); %%'); clf; draw(A,'b'); draw(B,'g'); %% GAprompt; disp('>> draw(cAB,''r''); draw(pAB,''c''); draw(rAB,''m'');'); draw(cAB,'r'); draw(pAB,'c'); draw(rAB,'m'); GAps = 'Refer to the tutorial before continuing >> '; disp(' '); GAprompt; GAps = 'GAblock >> '; disp('>> mAB = meet(A,B)'); mAB = meet(A,B) disp('>> clf; draw(A,''b''); draw(B,''g''); draw(mAB,''y'');'); clf; draw(A,'b'); draw(B,'g'); draw(mAB,'y'); GAps = 'Refer to the tutorial before continuing >> '; disp(' '); GAprompt; GAps = 'GAblock >> '; disp('>> jAB = join(A,B)'); jAB = join(A,B) disp('>> draw(jAB,''k'');'); draw(jAB,'k'); disp(' '); disp('End of GAblock sequence. Returning to Matlab.');elseif ( GAn == 7 ) GAps = 'GAblock >> '; disp('>> % MEET AND JOIN DECOMPOSED');?? 快捷鍵說明
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