points lying inside a polygon and a circle

How can I find the number of point lies inside both a circle and a polygon (the point should lie in the mutual/overlapping area in between the circle and the polygon) ?

Answer 1

[Matt J]

If the circle is centered at (x0,y0), with radius R and the polygon has vertices xv,yv, you could do,

count = sum(    inpolygon(x,y,xv,yv) & ((x-x0).^2+(y-y0).^2<=R^2)  )

[KalMandy]

what is the output of (x-x0).^2+(y-y0).^2<=R^2) ? does it become 1, if the point is inside the circle?

[Matt J]

Yes.

[KalMandy]

Thanks a lot!

Answer 2

[Image Analyst]

Did you try

count = 0;
if inpolygon(x,y,xCircle,yCircle) && inpolygon(x,y,xPoly,yPoly)
   count = count + 1
end

where you call inpolygon twice, once passing in the circle coordinates and once passing in the polygon coordinates and then ANDing the two results together?

[KalMandy]

can I use inpolygon for a circle as well?

[Image Analyst]

Yes, if you have the coordinates for the perimeter of the circle. If you don't, then see Matt J's formula below. You didn't specify in what form you have information about the circle. You'd put my code in a loop over all (x,y) points that you have.

count = 0;
for k = 1 : length(x)
    if inpolygon(x(k),y(k),xCircle,yCircle) && inpolygon(x(k),y(k),xPoly,yPoly)
       count = count + 1
    end
end

Same for Matt's code - loop over all x,y that you have.

[Matt J]

Same for Matt's code - loop over all x,y that you have.

Neither approach requires a loop over x,y. INPOLYGON is vectorized.

[Image Analyst]

You're right. x and y can be a vector of coordinates. Here's a demo:

% Make circle.
x0 = 20;
y0 = 30;
R = 15;
% Plot circle
pos = [x0-R, y0-R, 2*R, 2*R];
rectangle('Position', pos, 'Curvature',[1 1]);
hold on;
% Make polygon
xv = [10, 30, 30, 10, 10];
yv = [40, 40, 5, 5, 40];
plot(xv, yv, 'b-');
grid on;
% Make 60 points for x and y
numPoints = 60;
x = 70 * rand(1, numPoints);
y = 70 * rand(1, numPoints);
plot(x, y, 'r*');
% Now count how many are in both the circle and the polygon.
count = sum(inpolygon(x,y,xv,yv) & ((x-x0).^2+(y-y0).^2<=R^2))

[KalMandy]

I have the radius and the coordinates of the center of the circle. what is given by xCircle,yCircle? Thanks for your response.

[hanif hamden]

If i put (x,y) in geographical coordinate and I want my radius is 10km. How should I do that?