points lying in the intersection of 2 circles

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Ananya Malik 2016-8-26

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https://ww2.mathworks.cn/matlabcentral/answers/300944-points-lying-in-the-intersection-of-2-circles

编辑： KSSV 2016-8-26

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.

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KSSV 2016-8-26

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 2016-8-26

All the points within the oval.

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Answer 1

KSSV 2016-8-26

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https://ww2.mathworks.cn/matlabcentral/answers/300944-points-lying-in-the-intersection-of-2-circles#answer_232817

编辑：KSSV 2016-8-26

在 MATLAB Online 中打开

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') ;