area of intersection between a circle and polygon

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.

Answer 1

[Akira Agata]

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]

Thank you sir. But I would like to know what will be the units of the answer calculated?

[Akira Agata]

It depends on the units of x and y. If you assume the unit of x and y are [m] (meter), then the units of area(poly2) will be [m^2] (square meter).

[Ananya Malik]

Thank you sir.

[Adam Fleetwood]

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?