Find total area of all circles

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Elysi Cochin
Elysi Cochin on 17 Jan 2023
Edited: Elysi Cochin on 18 Jan 2023
How can we calculate the total area covered by all the circles together using Monte Carlo method?
Image Analyst
Image Analyst on 17 Jan 2023
Did you see my Answer below?
Why would you want to compute the area of overlap? If you did, how do you think you'd handle it? Remove the break, right? What else?

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Accepted Answer

Image Analyst
Image Analyst on 17 Jan 2023
You need to generate an (x,y) point, like in an outer loop. Then in the inner loop you need to loop over all the known circles. If the point is inside a circle, increment the count, and skip checking the rest of the circles by calling "break" so that you don't count a point twice if it's in two circles. Here's a start, assuming xc and yc is a list of the circle center coordinates, and radii is a list of the corresponding radii.
numPoints = 100000; % Whatever
count = 0;
for k = 1 : numPoints
x = whatever, get random number in the range.
y = whatever
for c = 1 : numCircles
if sqrt(x - xc(c)).^ 2 + (y - yc(c))^2) < radii(c)
% Then it's inside this circle
count = count + 1
break; % Skip checking the rest of the circles.
percentArea = count / numPoints

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