Small MATLAB script
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function PoleFigureAngles(varargin) hs=varargin{1}; qs=varargin{2}; rotation=0; if length(varargin)>2 filename=varargin{3}; if length(varargin)==4 rotation=varargin{4}; end end if size(hs,1)==size(qs,1) for j=1:size(hs,1) % for each plane and substrate pair calculate the alpha and beta angles h=hs(j,:); % find all permutations of measurement plane qperm=perms(qs(j,:)); % calculate the all permutations with both plus and minus sign signperm=[1,1,1;unique(perms([-1,1,1]),'rows');unique(perms([-1,-1,1]),'rows');-1,-1,-1]; allperm=zeros(size(qperm,1)*size(signperm,1),3); k=size(qperm,1); for i =1: size(signperm,1) allperm((i-1)*k+1:i*k,:)= qperm.*signperm(i,:); end % Find all unique permutations uniqperm=unique(allperm,'rows'); alpha=zeros(length(uniqperm),1); onplane=zeros(size(uniqperm)); %Calculate alpha angles and their projection on the plane for i=1:length(uniqperm) alpha(i)=90-acosd(h*uniqperm(i,:)'/(norm(h)*norm(uniqperm(i,:)))); onplane(i,:) = uniqperm(i,:)-h*uniqperm(i,:)'/norm(h)^2*h; end % Calculate beta angles from the first vector in onplane beta=zeros(size(onplane,1),1); betat=zeros(size(onplane,1),3); for i=2:size(onplane,1) betat(i,:)=cross(onplane(1,:),onplane(i,:)); if betat(i,:)*h'<0 beta(i)=360-atan2d(norm(cross(onplane(1,:),onplane(i,:))),... dot(onplane(1,:),onplane(i,:))); else beta(i)=atan2d(norm(cross(onplane(1,:),onplane(i,:))),... dot(onplane(1,:),onplane(i,:))); end end % sort angles acorting to alpha and print to console [A,I]=sort(alpha); index=I(A>0); angles=[alpha(index),beta(index)]; str=strcat(sprintf('alpha\t beta'),sprintf('\n%3.2f\t %3.2f',angles')); disp(str); % Plot angles on polar figure if j==1 scat=figure; else figure(scat) hold on end polarscatter(beta(index)*pi/180,90-alpha(index)) pax=gca; pax.ThetaZeroLocation = 'top'; rlim([0 90]) rticks([0 30 60 90]) rticklabels({'90','60','30','0'}); % If a data set from 3D explore is given, overlay the angles on the % data if exist('filename','var') if j==1 cont=figure; hold on axis square axis off polefig=importdata(filename,'\t',14); sizes=textscan(polefig.textdata{14},'%[# number of data :] %f %f'); x=reshape((90-polefig.data(:,1)).*sind(polefig.data(:,2)-rotation)... ,[sizes{2},sizes{3}]); y=reshape((90-polefig.data(:,1)).*cosd(polefig.data(:,2)-rotation)... ,[sizes{2},sizes{3}]); z=reshape(log10(polefig.data(:,3)),[sizes{2},sizes{3}]); z(z==-inf)=-1; contourf(x,y,z,'linestyle','none') colorbar caxis([-1,max(max(z))]) colormap('jet') else figure(cont) hold on end xa=(90-alpha(index)).*sind(beta(index)); ya=(90-alpha(index)).*cosd(beta(index)); scatter(xa,ya,'LineWidth',1,'MarkerEdgeColor','k') end end end