MATLAB: How to discover intersecting circles

concentric circlesintersecting circles

I have two types of intersecting circles in images, created by the Matlab imfindcircles function, which returns a matrix of centroid (x, y) and a vector with the radii of the circles (r):

1- Concentric circles;

2 – Circles intersecting.

I need to identify all of these cases and apply two functions to treat these intersections, one for case 1 (function1) and one for case 2 (function2). These functions will have as parameters a matrix containing the centroides and the radii of the circles in each case. I just need a program that reports the parameters of the two functions and when to call one or the other.

Best Answer

Try this:

% Create sample data.
numCircles = 10;
xy = rand(numCircles, 2);
radii = 0.1 * rand(numCircles, 1) + 0.1;
viscircles(xy, radii);
% Label them so we know what circle is what.
for k = 1 : numCircles
	text(xy(k, 1), xy(k, 2), num2str(k));
end
axis square;
% See if any intersect
for k = 1 : numCircles
	% Compute the distance between centers.
	distances = sqrt((xy(k, 1) - xy(:, 1)).^2 + (xy(k, 2) - xy(:, 2)) .^2);
	sumOfRadii = radii(k) + radii(:);
	intersectingIndexes = distances < sumOfRadii;
	% Don't compare circle to itself.  Of course that one intersects!
	intersectingIndexes(k) = false;
	% Convert to linear indexes
	intersectingIndexes = find(intersectingIndexes);
	for k2 = 1 : length(intersectingIndexes)
		fprintf('Circle %d intersects with circle #%d.\n', k, intersectingIndexes(k2));
	end
end

You see

Circle 1 intersects with circle #2.

Circle 1 intersects with circle #5.

Circle 1 intersects with circle #7.

Circle 2 intersects with circle #1.

Circle 2 intersects with circle #5.

Circle 3 intersects with circle #7.

Circle 3 intersects with circle #9.

Circle 5 intersects with circle #1.

Circle 5 intersects with circle #2.

Circle 6 intersects with circle #10.

Circle 7 intersects with circle #1.

Circle 7 intersects with circle #3.

Circle 8 intersects with circle #9.

Circle 9 intersects with circle #3.

Circle 9 intersects with circle #8.

Circle 10 intersects with circle #6.

and it's trivial to find out if one circle is completely contained within another. See if you can do it.

Related Solutions

MATLAB: Creating multiple circles inside an array

Here is a little demo you might find useful. It determines which, if any, circles overlap/intersect:

% Demo to create some circles with random radii and center locations and look for overlaps.
% Initialization steps.
clc;    % Clear the command window.
fprintf('Beginning to run %s.m ...\n', mfilename);
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 short g;
format compact;
fontSize = 20;
% Create some circles randomly.
% Some might overlap, or possibly none overlap (since it's random).
numCircles = 7;
xy = rand(numCircles, 2); % Randomly located centers.
radii = 0.1 * rand(1, numCircles) + 0.05; % Random radii in the range 0.05 to 0.2
% Draw circles.
viscircles(xy, radii);
xlabel('X', 'FontSize', fontSize);
ylabel('Y', 'FontSize', fontSize);
% Label them so we know which circle is which.
% Put the circle number at the center.  
for k = 1 : numCircles
	text(xy(k, 1), xy(k, 2), num2str(k), 'FontWeight', 'bold');
end
grid on;
axis('equal');
% Get a list of separations center-to-center.
distances = pdist2(xy, xy)
% Determine the sum of the radii.
[r1, r2] = meshgrid(radii, radii)
sumOfRadii = r1 + r2
% If there is an overlap, the sum of the radii will be bigger than the distance between them.
overlapping = sumOfRadii > distances;
% Zero out the diagonal because we don't care that 
% circle 1 overlaps circle 1, circle 2 overlaps circle 2, etc.
overlapping(logical(eye(numCircles))) = false
% Make up information message for plot title and command window:
numberOfOverlaps = sum(any(overlapping, 2));
overlappedIndexes = find(any(overlapping, 2));
if numberOfOverlaps > 0
	caption = sprintf('%d circles are overlapped:', numberOfOverlaps);
	for k = 1 : length(overlappedIndexes)
		caption = sprintf('%s %d', caption, overlappedIndexes(k));
	end
else
	caption = sprintf('%d circles are overlapped', numberOfOverlaps);
end
fprintf('%s.\n', caption); % Print to command line.
title(caption, 'FontSize', fontSize); % Title over the plot.
% Report which circles overlap by determining how many rows have at least one 1 in them.
for row = 1 : numCircles
	% See which other circles overlap with the kth circle.
	overlappedCircleIndexes = find(overlapping(row, :));
	if ~isempty(overlappedCircleIndexes)
		% If any overlap with it, print them out.
		for k2 = 1 : length(overlappedCircleIndexes)
			fprintf('Circle %d overlaps with circle %d.\n', ...
				row, overlappedCircleIndexes(k2));
		end
	end
end

For that random set, I see:

distances =

0 0.30561 0.64619 0.32995 0.25392 0.45259 0.70397

0.30561 0 0.54554 0.19313 0.35021 0.29865 0.39959

0.64619 0.54554 0 0.36275 0.41575 0.24748 0.68878

0.32995 0.19313 0.36275 0 0.21992 0.12872 0.49327

0.25392 0.35021 0.41575 0.21992 0 0.2886 0.70892

0.45259 0.29865 0.24748 0.12872 0.2886 0 0.4981

0.70397 0.39959 0.68878 0.49327 0.70892 0.4981 0

sumOfRadii =

0.2034 0.20737 0.16735 0.2079 0.22118 0.19434 0.23533

0.20737 0.21134 0.17132 0.21188 0.22515 0.19832 0.2393

0.16735 0.17132 0.1313 0.17186 0.18513 0.1583 0.19928

0.2079 0.21188 0.17186 0.21241 0.22569 0.19885 0.23983

0.22118 0.22515 0.18513 0.22569 0.23896 0.21213 0.25311

0.19434 0.19832 0.1583 0.19885 0.21213 0.18529 0.22627

0.23533 0.2393 0.19928 0.23983 0.25311 0.22627 0.26725

overlapping =

7×7 logical array

0 0 0 0 0 0 0

0 0 0 1 0 0 0

0 0 0 0 0 0 0

0 1 0 0 1 1 0

0 0 0 1 0 0 0

0 0 0 0 0 0 0

4 Circles overlap.

Circle 2 overlaps with circle 4.

Circle 4 overlaps with circle 2.

Circle 4 overlaps with circle 5.

Circle 4 overlaps with circle 6.

Circle 5 overlaps with circle 4.

Circle 6 overlaps with circle 4.

MATLAB: How to plot a number of circles with the same radius, but the position of the circles is randomly put

N = 10 ;   % number of circles
r = 0.25 ; % radius of circel
%

C = rand(N,2) ;
%
th = linspace(0,2*pi) ;
x = r*cos(th) ;
y = r*sin(th) ;
% Loop for each circle
for i = 1:N
    xc = C(i,1)+x ;
    yc = C(i,2)+y ;
    hold on
    plot(xc,yc) ;
end
axis equal

Best Answer

Related Solutions

MATLAB: Creating multiple circles inside an array

MATLAB: How to plot a number of circles with the same radius, but the position of the circles is randomly put

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