Points on a circle

Hello everyone!

how can i get a random point on the min and max circles on these:

format short
A = load('C:\Users\Stefan\Desktop\MatiValjasMatLAb/vruut.txt')
nurgad=A(:,1)
kaugused=A(:,2)
%polarplot(nurgad,kaugused,'o')

%Joonise järgi võiks lähendada ringjoonega
%Arvandmete järgi võiks ka eeldada, et saab lähendada ringjoonega
%sest raadiused ei kõigu palju.

%joonised
x = kaugused.*cos(nurgad); y = kaugused.*sin(nurgad); 
plot(x,y,'.')
axis equal
hold on
c = [x y ones(length(x),1)]\-(x.^2+y.^2); %vähim ruutude meetod
xhat = -c(1)/2;
yhat = -c(2)/2;
raadius = sqrt(xhat^2+yhat^2-c(3));
plot(raadius*cos(nurgad)+xhat,raadius*sin(nurgad)+yhat,...
    'g','linewidth',1) %parim ring(best fit circle)
hold on
ax = gca;
ax.XAxisLocation = 'origin';
ax.YAxisLocation = 'origin';
raadius
kesk=[xhat, yhat]
plot(xhat,yhat,'O')
hold on
B=max(kaugused);
C=min(kaugused);

theta=0:0.01:2*pi;
xmax=B*cos(theta)+xhat;
ymax=B*sin(theta)+yhat;
plot(xmax,ymax)
hold on

hold on
xmin=C*cos(theta)+xhat;
ymin=C*sin(theta)+yhat;
plot(xmin,ymin)
hold on

hold off

The plot looks like this :

Answer 1

[Adam Danz]

These lines define your circle for each point theta

xmax=B*cos(theta)+xhat;

ymax=B*sin(theta)+yhat;

All you need to do is define theta as random values between 0 and 2pi to plot random points on the circle.

B = 5; 
xhat = 3; 
yhat = -2;
theta = linspace(-pi,pi,500);
xmax=B*cos(theta)+xhat;
ymax=B*sin(theta)+yhat;
plot(xmax,ymax)
axis equal


n = 20;  % number of random points
rng('default')
thetaRand = rand(1,n) * 2*pi;
xp=B*cos(thetaRand)+xhat;
yp=B*sin(thetaRand)+yhat;
hold on
plot(xp,yp,'o')