A MATLAB script to create 2D line patterns inspired by far-field high energy x-ray diffraction.

moving_diffraction_patterns.m

%% Moving diffraction patterns
% A MATLAB-based program to generate high energy x-ray diffraction inspired
% line art.
%
%% USAGE
% Enter various parameters in the INPUT section. The meaning of each
% parameter is described below. Then run this script. It will produce a
% plot with the line patterns.
%
% The basic concept behind the pattern generation is this -
% We start with a few spots in a plne, much like an area diffraction
% pattern generated during synchrotron-based far-field x-ray diffraction.
% Then we move the detector. There are several degrees of freedom possible
% - translation perpendicular to the detector plane, rotation along the
% detector plane normal, translation along the detector width and height.
% Additionally, a purturbation can be applied to the ngular and radial
% position of a spot.
% This can produce a rich variety of line patterns. You can run the script
% with the default values to see an example. For many parameters, a few
% examples are given.
%
%% Inputs
number_of_spots           = 200;            % Number of spots. More = denser pattern
seed_distribution         = 1;              % 0 = rand, 1 = uniform
d_seed                    = 0.1;            % Start detector distance (normalized units)
detector_angular_velocity = 0.0;            % angular velo (normalized units)
detector_normal_velocity  = 4;              % velo normal to detctor plane (normalized units)
detector_x_velocity       = @(x, y, s) 0;   % detector speed along X axis
                                            % Examples:
                                            % 3.5*sin(x/300*pi/2);
detector_y_velocity       = @(x, y, s) 5;   % detector speed along y axis
                                            % Examples:
                                            % 2*sin((x)/300*pi/2.1);
total_time                = 10;             % Total time for movement
time_steps                = 300;            % Steps
plot_line_width           = 8;              % Width of a line in the plot
debug_mode                = 0;              % 1 = display debug info
% dev functions: purturbe the angles or the radial diatance of each spot
angular_dev_function      = @(x, y, s) sin(x/time_steps*pi*10)*0.1; 
% Examples
% sign(mod(floor(x/50), 2) - 2)*tan(mod(x, 50)/55*pi/2.2)*0.1;
normal_dev_function       = @(x, y, s) 0;
% Examples
% @(x, y, s) tan(x/time_steps*pi/2.03)*0.4;
% @(x, y, s) sin(20*s)*0.4;
% @(x, y, s) sawtooth(20*s, 0.5)*1.6*x/time_steps;
% @(x, y, s) min(abs(tan(20*s)*1.6*x/time_steps), 5);
%
% END of inputs
%
if(seed_distribution == 0)
    eta_seed = rand(number_of_spots,1)*2.0*pi;     % Start angular positions for spots (rad)
elseif(seed_distribution == 1)
    eta_seed = [0:(2*pi/number_of_spots):(2*pi)]';
end
spot_location_seed = [d_seed*cos(eta_seed) d_seed*sin(eta_seed)];   % X, Y coordinates for starting spot positions
%
spot_location = zeros(size(spot_location_seed, 1), time_steps, 2);
eta = zeros(size(eta_seed, 1), 1);
% Loop over time steps
for i = 1:time_steps
    d = d_seed + total_time/time_steps*detector_normal_velocity*i;
    for j = 1:size(eta_seed, 1)
        eta(j) = eta_seed(j) + total_time/time_steps*detector_angular_velocity*i + angular_dev_function(i, j, d);
        % Update coordinates of the spot
        spot_location(j, i, :) = [(d + normal_dev_function(i, j, eta(j)))*cos(eta(j)) + detector_x_velocity(i, j, eta(j))*total_time/time_steps*i
                                  (d + normal_dev_function(i, j, eta(j)))*sin(eta(j)) + detector_y_velocity(i, j, eta(j))*total_time/time_steps*i];
        if(debug_mode)
            disp([d normal_dev_function(i, j, d)])
        end
    end
end
%
% Plot
f = figure;
set(f, 'Units', 'Normalized')
set(f, 'Position', [0.1, 0.1, 0.8, 0.8]);
hold on;
spot_color = rand(size(eta_seed, 1), 3); %hsv(size(eta_seed, 1));
for i = 1:size(eta_seed, 1)
    plot(squeeze(spot_location(i, :, 1)), squeeze(spot_location(i, :, 2)), 'LineWidth', plot_line_width, 'Color', spot_color(i, :))
end
hold off;
axis equal;
axis off;
%