Generation of lunes on the Ewald sphere
Matlab code 

% Program to generate lunes 

% Uses an adaptation of the function platonic_solid, see 

% https://ch.mathworks.com/matlabcentral/fileexchange/28213-platonic_solid 

% Courtesy Kevin Moerman 

 

clear; close all;

 

prompt = 'Rotation of crystal around z-axis in degrees [default = 0]: ';

theta = input(prompt);

if isempty(theta)

    theta = 0;

end

 

fileName = 'lunes.mp4'; % Name of file depends on type of crystal sample

vid = VideoWriter(fileName,'MPEG-4');

vid.Quality = 100;

vid.FrameRate = 30;

open(vid);

figure('units','pixels','position',[0 0 1920 1080],'ToolBar','none');

set(0,'defaultfigurecolor',[1 1 1]);

set(gca,'linewidth',7);

set(gca, 'Projection','perspective');

lp = [-1 -2 0.7];

myBlue = [0.55 0.61 0.89]; 

myBlue2 = [0.31 0.37 0.64]; 

myGold = [0.7969 0.6406 0.2383]; 

LL = 1.1; 

delk = 0.01; 

 

 

[a,b,c] = sphere(70); 

 

for phi = 0:0.25:89.8 

    phi 

    newplot

    hold off

    xlim([-LL LL]);

    ylim([-LL LL]);

    zlim([-LL LL]);

    

    axis equal

    axis square

    axis off

    

    for hh = -1:0.02:1

        for kk = -1:0.02:1

            for ll = -1:0.02:1

                % Calculate new absolute h k l after rotation

                hhnew = hh*cosd(phi) + ll*sind(phi);

                kknew = kk;

                llnew = ll*cosd(phi) - hh*sind(phi);

                hhnew2 = hhnew*cosd(theta) + kknew*sind(theta);

                kknew2 = kknew*cosd(theta) - hhnew*sind(theta);

                llnew2 = llnew;

                

                radNow = ((hhnew2-0.5)^2+kknew2^2+llnew2^2)^0.5;

                if (radNow <= 0.5+delk/2.5) && (radNow >= 0.5-delk/2.5)

                    [V,F] = platonic_solid(2,delk/2); % Cube

                    V(:,1) = V(:,1)+hhnew2;

                    V(:,2) = V(:,2)+kknew2;

                    V(:,3) = V(:,3)+llnew2;

                    ps = patch('Faces',F,'Vertices',V,'FaceColor',myGold,'FaceAlpha',1, ...

                        'EdgeColor','none','FaceLighting','flat','DiffuseStrength',1);

                    direction = [0 1 0];

                    rotate(ps,direction,phi,[hhnew2 kknew2 llnew2])

                    hold on                  

                end

            end

        end

    end

 

    xlim([-0.1 LL]);

    ylim([-LL LL]/1.1);

    zlim([-LL LL]/1.1); 

    % Ewald sphere 

    surf(0.5*a+0.5,0.5*b,0.5*c,'FaceAlpha',0.55,'FaceColor',...

        myBlue2,'LineStyle','none','FaceLighting','gouraud','DiffuseStrength',0.25); 

    % Dummy sphere to stop small changes in FOV 

    surf(0.52*a+0.5,0.52*b,0.52*c,'FaceAlpha',0.0001,'FaceColor',...

        myBlue,'LineStyle','none','FaceLighting','gouraud','DiffuseStrength',1);

    axis equal

    axis off

    axis tight 

    set(gca, 'Projection','perspective');

    set(gca,'View',[-30,32]);

    light('Position',lp,'Style','infinite');

    frame = getframe(gcf);

    writeVideo(vid,frame);

    hold off    

end

 

% Output the movie as an mpg file

close(vid);