# area of intersection between a circle and polygon

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Ananya Malik on 3 Sep 2018
Commented: Adam Fleetwood on 6 Dec 2020
x = 0;y = 0; r = 0.5;
th = 0:pi/50:2*pi;
xunit = r * cos(th) + x;
yunit = r * sin(th) + y;
h = plot(xunit, yunit);
poly1 = polyshape([0 0 1 1],[1 0 0 1]);
plot(poly1)
I want to find the area of intersection (in units) between a circle and polygon as given above. Any help would be greatly appreciated. TIA.

Akira Agata on 3 Sep 2018
One possible way is generating intersection by intersect function, and calculate it's area by area function. The following is an example.
x = 0; y = 0; r = 0.5;
th = 0:pi/50:2*pi;
xunit = r * cos(th) + x;
yunit = r * sin(th) + y;
poly0 = polyshape(xunit(1:end-1),yunit(1:end-1));
poly1 = polyshape([0 0 1 1],[1 0 0 1]);
poly2 = intersect(poly0,poly1);
area(poly2)
The result is:
>> area(poly2)
ans =
0.1962
Ananya Malik on 3 Sep 2018
Thank you sir.
Adam Fleetwood on 6 Dec 2020
I have tried using something similar for a project, but am getting an error that states, "unable to use a value of type polyshape as an index'. I tried using this exact code shown above, and still got that error. Any idea why?

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