close all;clear all;clc;

% Define Quartions with specific designations
q1to4=[1 2 3 4;2 3 4 1;3 4 1 2;4 1 2 3]; % Right-handed Spin=+1
q5to8=[1 4 3 2;2 1 4 3;3 2 1 4;4 3 2 1]; % Left-handed Spin=-1
q9to12=[1 2 4 3;2 3 1 4;3 4 2 1;4 1 3 2]; % Right flip left Spin=0.5
q13to16=[1 4 2 3;2 1 3 4;3 2 4 1;4 3 1 2]; % Left flip right Spin=0.5
q17to20=[1 3 4 2;2 4 1 3;3 1 2 4;4 2 3 1]; % Flip right flip Spin=0.5
q21to24=[1 3 2 4;2 4 3 1;3 1 4 2;4 2 1 3]; % Flip left flip Spin=0.5
quartions=[q1to4;q5to8;q9to12;q13to16;q17to20;q21to24];

% Define Octions with specific designations; valid pairings of Quartions
o1to4=[1 2;2 3;3 4;1 4];            % Right handed Spin=+1
o5to8=[5 6;6 7;7 8;5 8];            % Left handed Spin=-1
o9to12=[1 6;2 7;3 8;4 5];           % Static flip Static Spin=0
o13to16=[9 14;10 15;11 16;12 13];   % Static flip Static Spin=0 (same as above)
o17to20=[2 5;3 6;4 7;1 8];          % Flip static flip Spin=0
o21to24=[17 22;18 23;19 24;20 21];  % Flip static flip Spin=0 (same as above)
o25to28=[10 13;11 14;12 15;9 16];   % Flip flip flip Spin=0
o29to32=[18 21;19 22;20 23;17 24];  % Flip flip flip Spin=0 (same as above)
o33to36=[9 10;10 11;11 12;9 12];    % Right flip left Spin=0.5
o37to40=[13 14;14 15;15 16;13 16];  % Left flip right Spin=0.5
o41to44=[17 18;18 19;19 20;17 20];  % Flip right flip Spin=0.5
o45to48=[21 22;22 23;23 24;21 24];  % Flip left flip Spin=0.5
octions=[o1to4;o5to8;o9to12;o13to16;o17to20;o21to24;o25to28;o29to32;o33to36;o37to40;o41to44;o45to48];

% Define vectors and colours of the four spatial possibilities
pangles=[0,1,0,90;1,0,0,90;0,1,0,-90;1,0,0,-90];
cols=[218/255 6/255 9/255;255/255 222/255 89/255;0/255 191/255 99/255;56/255 182/255 255/255];

figure('units','normalized','outerposition',[0 0 1 1])
hold on

xo=0;

for on=45:48; % Example Octions 45 through 48
if mod(on,4)==1 xo=xo+2;end;
qpair=[octions(on,:)];

for qn=1:2; % Both pairs of Quartions
quartion=quartions(qpair(qn),:);t=0;
origin=[xo,0,0];

for n=1:length(quartion)*1;nmod=mod(n-1,4)+1;p=quartion(nmod);
unitArrow3d(origin,pangles(p,1:3),pangles(p,4),cols(p,:),qn); % Show unit spatial possibility
unitArrow3d(origin,[1 0 0],180,[0.5 0.5 0.5],1); % Show unit time
label=['O',num2str(on),' (Q',num2str(qpair(1)),' Q',num2str(qpair(2)),')'];
text(origin(1),origin(2),.75,label,'Interpreter','tex','color','white','FontSize',10);
t=t+1;origin(3)=origin(3)-1;end
end;
xo=xo+2.5;
end

axis equal
axis auto
view([30 20])
camroll(0)

set(gca,'visible','off')
set(gca,'xtick',[])
set(gcf, 'Color', 'k'); % Set figure background to black
set(gcf, 'Renderer', 'painters');
exportgraphics(gcf,'vectorfig.pdf','ContentType','vector','BackgroundColor','black')
return

% Function to draw colour-coded unit possibilities;
% a ball at origin with extending cylindrical shaft and cone
% disc applied if pairnum is not 1
function unitArrow3d(origin,direction,rotation,colourRGB,pairnum)
a=(pi/180)*(-90:10:60);z=0.05*sin(a);y=0.05*cos(a);x=a*0;
if pairnum==1 z=[z 0.75 0.75 1];y=[y 0.025 0.07 0];x=[x 0 0 0];
else z=[z 0.498 0.498 0.502 0.502 0.75 0.75 1];y=[y 0.025 0.07 0.07 0.025 0.025 0.07 0];x=[x 0 0 0 0 0 0 0];end
a=0:pi/16:33/16*pi;xm=sin(a)';ym=cos(a)';x=xm*y;y=ym*y;zm=xm./xm;z=zm*z;
x=x+origin(1);y=y+origin(2);z=z+origin(3);
unitArrow3d=surf(x,y,z,'FaceColor',colourRGB,'EdgeColor','none');
rotate(unitArrow3d,direction,rotation,origin);
end