MATLAB: Points too close XY space

distancepdist2Statistics and Machine Learning Toolbox

Hello,
I have a set of N points with coordinates (x1,y1)…(xN, yN). I would like to find the pairs that are closer than DX in X and closer than DY in Y, avoiding for-loops. Thanks in advance for any help!

Best Answer

Here is a solution that shows you all pairs of points where delta x is less than 0.2:
clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 20;
% Define number of points.
N = 50;
% Get random x,y coordinates for those points.
x = rand(N, 1);
y = rand(N, 1);
subplot(2, 2, 1);
plot(x, y, 'b.', 'MarkerSize', 18);
grid on;
% Get distance of every point to every other point.
distances = pdist2(x, x);
% Find points closer than some specified distance to each other.
closestAllowableDistance = 0.02;
closePairs = distances < closestAllowableDistance;
subplot(2, 2, 2);
imshow(closePairs, []);
axis on;
xlabel('Column Index');
ylabel('Row Index');
% Show circles around pairs that are close

subplot(2, 2, 3);
plot(x, y, 'b.', 'MarkerSize', 18);
grid on;
hold on;
% Set up figure properties:
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0 0 1 1]);
% Get rid of tool bar and pulldown menus that are along top of figure.
set(gcf, 'Toolbar', 'none', 'Menu', 'none');
% Give a name to the title bar.
set(gcf, 'Name', 'Demo by ImageAnalyst', 'NumberTitle', 'Off') 
drawnow;
% Show circles around pairs that are close
hPair = plot(0, 0); % Initialize so we have something to delete the first time though the loop.
for col = 1 : N
  for row = 1 : col-1
    % Plot this point
    if closePairs(row, col)
      % The pair is close, so plot it.
      x1 = x(row);
      y1 = y(row);
      x2 = x(col);
      y2 = y(col);
      % Delete old point
      delete(hPair);
      % Plot next point.
      hPair = plot([x1, x2], [y1, y2], 'ro', 'MarkerSize', 13, 'LineWidth', 2);
      % Tell them how far apart they are, and ask them if they want to continue.
      promptMessage = sprintf('This pair is separated by %f\n\nDo you want to Continue processing,\nor Quit processing?',...
        distances(row, col));
      titleBarCaption = 'Continue?';
      buttonText = questdlg(promptMessage, titleBarCaption, 'Continue', 'Quit', 'Continue');
      if strcmpi(buttonText, 'Quit')
        return;
      end      
    end
  end
end
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