# how to calculate the intersection area of two ellipses

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amal Mbarki on 18 Feb 2016
Commented: Image Analyst on 2 Dec 2018
hello, how can i calculte the intersection area of two ellipses, each ellipse is characterized by(x,y,a,b,w).I thought of solving the system of equations of the two ellipses ,then calculate the area bounded by the points found as solution. would you please help me ?

Hongchu Yu on 1 Dec 2018
Had you solved the problem? I have the same problem now. Could you tell me the solution?
Image Analyst on 2 Dec 2018
The only solution I've seen is a numerical one, not an analytical one.

Kevin Claytor on 18 Feb 2016
Here is an arxiv paper on ellipse intersection algorithms.

Image Analyst on 18 Feb 2016
To create an ellipse numerically in 2-D is very easy - just see the FAQ. http://matlab.wikia.com/wiki/FAQ#How_do_I_create_an_ellipse.3F To rotate it, just multiply the coordinates by the rotation matrix [cos(theta), -sin(theta); cos(theta), sin(theta)]. Then just AND the two ellipse images
intersectionArea = ellipsoid1 & ellipsoid2;
pixelArea = sum(intersectionArea (:)); % Compute the area in pixels.