MATLAB: Generating cicle instances around circumference

circumferencetsp

Hello,
for my work I need to generate instances (set of cooirdinaces xy) that have one point in the circle center and random set around (not necessarily on) circumference – like in the picture attached
Number off point should be parametr – so one can generata how many points is needed
I am trying to writte function to generate this points – but dont know how

Best Answer

th = linspace(0,2*pi)' ; 
R = 1. ;    % main circle radius 
C = [0. 0.] ; % main circle center 
x1 = C(1)+R*cos(th) ; y1 = C(2)+R*sin(th) ; 
%% concetric circles 
r1 = 0.75 ; r2 = 1.25 ; 
x2 = C(1)+r1*cos(th) ; y2 = C(2)+r1*sin(th) ; 
x3 = C(1)+r2*cos(th) ; y3 = C(2)+r2*sin(th) ; 
%
a = max(x3);
b = min(x3);
x = (b-a).*rand(1000,1) + a;
y = (b-a).*rand(1000,1) + a;
% 
%  Remove poinsts out side r2 circle 
idx = inpolygon(x, y,x3, y3) ; 
x(~idx) = [] ; y(~idx) = [] ;
%  Remove poinsts out side r1 circle 
idx = inpolygon(x, y,x2, y2) ; 
x(idx) = [] ; y(idx) = [] ;
% points needed 
N = 100 ; % 25,50 
idx = randperm(length(x),N) ; 
x = x(idx) ; y = y(idx) ; 
plot(x1,y1,'r') ;
hold on
plot(x2,y2,'b') ;
plot(x3,y3,'g') ;
plot(x,y,'.r')
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