How can I write a program to find nodes that are in the region of two intersecting circles

I have written a script for two equal intersecting circles having the same radius. nodes in blue at the centre of the two circles are stationary, while others are mobile. I also generated a random moving node having different energy and successful transmit probability. The problem now is how can I write a code that will determine the nodes that fall in the intersecting boundary. Thanks

Answer 1

[KSSV]

Get the coordinates of intersection circle (this will form closed region), use inpolygon() to know whether given point lies inside closed region or outside the closed region. You may have a look on the below code:

clc; clear all ;
N1 = 100 ; N2 = 50 ;
th = linspace(0,2*pi,N1)' ;
r1 = 1. ; r2 = 1. ;   % radii of circles 
c1 = [0 0] ;          % center of first cirlce 
c2 = [1.5 0] ;        % center of second circle 
a1 = repmat(c1,[N1 1])+[r1*cos(th)  r1*sin(th)] ;
a2 = repmat(c2,[N1 1])+[r2*cos(th)  r2*sin(th)] ;
%
plot(a1(:,1),a1(:,2),'r') ;
hold on
plot(a2(:,1),a2(:,2),'r') ;
axis equal
%%Get points of fitst circle lying in second circle
in12 = inpolygon(a1(:,1),a1(:,2),a2(:,1),a2(:,2)) ;
P1 = a1(in12,:) ;
plot(a1(in12,1),a1(in12,2),'.b') ;
%%Get points of second circle lying in first circle
in21 = inpolygon(a2(:,1),a2(:,2),a1(:,1),a1(:,2)) ;
P2 = a2(in21,:) ;
plot(a2(in21,1),a2(in21,2),'.b') ;
%%form the oval / intersection boundary 
R = [P1 ;P2] ;
%%Form a suare grid around ovel region 
x = linspace(c1(1),c2(1),N2) ;
y = linspace(-r1,r2,N2) ;
[X,Y] = meshgrid(x,y) ;
XX = X(:) ; YY = Y(:) ;
%%Get the random points  inside the region 
l = 1 ;
ax = min(R(:,1)) ; bx = max(R(:,1)) ;
ay = min(R(:,2)) ; by = max(R(:,2)) ;
while l ==1 
      x = (bx-ax).*rand(1,1) + ax;
      y = (by-ay).*rand(1,1) + ay;
    in = inpolygon(x,y,R(:,1),R(:,2)) ;
    if in 
        plot(x,y,'.g') ;
        drawnow
    end
end

[Akande Oluwole]

I have gone through this and have tried to see how i can determine the region, but the answer is quite different from this particular problem since not all nodes are in the region. What I need is to be able to determine the region of intersection, and pick out those nodes that are in the intersecting region.

[KSSV]

That's what I suggested you already...Get the coordinates of intersection circle (this will form closed region), use inpolygon() to know whether given point lies inside closed region or outside the closed region