% 	INTERPOLATION OF ORIENTATIONSGAfigure; clc; %/% 	INTERPOLATION OF ORIENTATIONSglobal RA RB u v; %/     clf; %/%	Problem: interpolate two orientations.%% 	An orientation can be characterized %	by a rotation from a standard pose.%	Let the orientations be RA and RB.%u = e1+e2-e3; %/v = e1+e3; %/%% view = [-0.6  2.5  -1    1.16  -2  1.1];  %/view = [-1 2 -1 2 -2 1]; %/%%%%=================================================================% 	Initial orientation RA (applied to a bivector u^v):%.RA = gexp(-I3*e1*pi/2/2);DrawBivector(RA*u/RA,RA*v/RA,'b');  %/%% random = unit(pi*e1 + pi/exp(1)*e2 + exp(1)*e3); %/GAtext(1.1* RA*(u+v)/RA,'" R_A"','b'); %/axis(view); axis off; %/GAview([30 30]); %/GAprompt; %/%%=================================================================% 	Final orientation (applied to u^v):%.RB = gexp(-I3*e2*pi/2/2);DrawBivector(RB*u/RB,RB*v/RB,'g');  axis(view); %/GAtext(1.1* RB*(u+v)/RB,'" R_B"','k'); %/GAprompt; %/%%=================================================================% 	Interpolation through division of total rotor:%.Rtot =  RB/RA %w% which is done through incremental rotor R:%.n = 8;                          %/R = gexp(sLog(Rtot)/n)axisR = unit(GAZ(-sLog(R)/I3));   %/ draw(axisR,'r'); %/%% GAtext(1.1*axisR,'R / I_3','r'); %/ %% text in fact incorrect%%GAtext(1.1*axisR,'log(R_B / R_A) I_3^{-1}','r'); %/title('R = exp( log( R_B/R_A ) / n)','Color','r'); %/draw(-sLog(Rtot)/n,'r'); %/axis(view); %/GAprompt; %/%%=================================================================% 	Execute the interpolations from RA[u^v] to RB[u^v]     Ri = RA;  %/     for i=1:n-1  %/	 disp(['i = ', num2str(i) ':   R' num2str(i) ' = R*R' num2str(i-1)]); %/         Ri = R*Ri; %/         DrawBivector(Ri*u/Ri,Ri*v/Ri); %/         axis(view); %/         drawnow; %/     end %/GAprompt; %/title(''); %/GAorbiter(125,10); %/