# points lying in the intersection of 2 circles

2 views (last 30 days)
Ananya Malik on 26 Aug 2016
Edited: KSSV on 26 Aug 2016
Suppose i have 2 points (x1, y1) and (x2,y2). I draw circle with radius 'r'. I want to find "all" the points which lie in the intersection region of the 2 circles.
KSSV on 26 Aug 2016
Two circles intersect at two points..you want to get these two points? or the intersection region would be oval in shape, you want to generate points inside this oval?
Ananya Malik on 26 Aug 2016
All the points within the oval.

KSSV on 26 Aug 2016
Edited: KSSV on 26 Aug 2016
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 circle
c2 = [1.5 0] ; % Center of second circle
a1 = repmat(c1,[N1 1])+[r1*cos(th) r1*sin(th)] ; % form circle 1
a2 = repmat(c2,[N1 1])+[r2*cos(th) r2*sin(th)] ; % form circle 2
%
plot(a1(:,1),a1(:,2),'r') ;
hold on
plot(a2(:,1),a2(:,2),'r') ;
axis equal
%%Get points of first 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 points inside the region
in = inpolygon(XX,YY,R(:,1),R(:,2)) ;
plot(XX(in),YY(in),'.k') ;
Can be further refined...

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