%% Draw circle

[cx, cy] = pol2cart(linspace(0, 2*pi, 100), 1);

plot(cx, cy, 'r')

axis equal

hold on

%% Init particle - You can modify this

[px, py] = pol2cart(rand()*2*pi, rand());

p = [px; py];

plot(px, py, 'o')

v = rand(2, 1);

v = v/norm(v);

%%

R = @(t)[cos(t) -sin(t); sin(t) cos(t)];

P = p;

O = [0; 0];

t = fmincon(@(t)abs(norm(p+t*v) - 1), -1, 1, 0);

p = p+t*v;

for i = 1:10    % iterate 10 times

    p = p + 2*(O - p)'*v*v;

    P = [P p];

    t = atan2(p(2), p(1));

    v = R(t) * diag([-1 1]) * R(-t) * v;

end

plot(P(1,:), P(2,:))