Animate a line in polar coordinates

I want to animate a Lemniscate of Bernoulli in polar system. When I addpoints, system display:

Error using animatedline

Argument Y cannot be complex.

My code is under here:

clc, clear, close all;
theta = 0:0.001:2*pi;
r = sqrt(cos(2*theta));
figure;
polarplot(theta, r, 'r', 'LineWidth',1.5);
figure;
h = animatedline(polaraxes,theta,r);
figure;
for k = 1:length(theta)
    addpoints(h,theta(k),r1(k));
    drawnow
end

Answer 1

[Sarvesh Kale]

Hi ロン,

You are trying to animate the Lemniscate of Bernoulli, here is an example in rectangular co-ordinate system

clear
clc;
h=animatedline;
xlim([-1.5 1.5]);
ylim([-1.5 1.5]);
h.LineWidth=1.5;

% parametric representation of Lemniscate of Bernoulli
t = linspace(-4,4,10000);
x = cos(t)./(1+(sin(t).^2));
y = (sin(t).*cos(t))./(1+(sin(t).^2));

for k = 1:10000
addpoints(h,x(k),y(k))
drawnow
end

the above is simple cartesian representation however while doing the polar representation you have to take care of angles as negative quantities cannot be present inside the square root sign as they would lead to complex number so your angles should be constrained, the representation in polar co-ordinates you require is given below

clear;
figure;
h = animatedline(polaraxes);
rlim([0 1]);
h.LineWidth = 1.5;
h.Color=[1 0 0] ;
theta = -pi/4:0.001:pi/4; % cosine of 2*theta will be positive for this range 
n= length(theta);

% first half animation 
r = -sqrt(cos(2*theta));
for k = 1:length(theta)
    addpoints(h,theta(k),r(k))
    drawnow 
end

% second half animation 
r = sqrt(cos(2*theta)); % the negative sign covers second half 
theta = pi/4:-0.001:-pi/4;
for k = 1:length(theta)
    addpoints(h,theta(k),r(k))
    drawnow
end

I hope the above two code snippets achieve your end goal, please accept the answer if the query is answered. Thank you

[ロン]

Thank you very much. It works! The negative part in square root makes trouble a lot. But your code solve it well.

Answer 2

[KSSV]

In your case r is comlex number which is not allowed. You need to get r as shown below.

theta = 0:0.001:2*pi;
R = 1 ; 
x = R*cos(theta) ; y = R*sin(theta) ; 
r = sqrt(x.^2+y.^2) ; ;
figure;
polarplot(theta, r, 'r', 'LineWidth',1.5);
figure;
h = animatedline(polaraxes,theta,r);
figure;
for k = 1:length(theta)
    addpoints(h,theta(k),r(k));
    drawnow
end

[ロン]

Thanks for your help. It seems like that your code is a circle and the part in the sqrt() is always positive. So there isn't complex number. But the Lemniscate of Bernoulli have some negative quantities inside the square root sign.