# Keep constant number of visible circles in 3D animation

I have created a 3D animation with a perspective projection of white circles moving randomly in a fake 3D space projected on a 2D computer screen (GIF 1).

Since I need to keep the same number of visible circles, every time a circle disappears from the frame, I have to create a new visible one within the frame. To do so, I have written this piece of code:

• First I created initial coordinates and the two angles of movements (spherical coordinates):

for circle in circles:

circle.position.xy = np.random.uniform(-25, 25, size=2)
z = np.random.uniform(near_z, far_z)

circle.position.z = z
circle.position.x *= z/-50
circle.position.y *= z/-50

circle.theta_deg = np.random.rand(1) * 360
circle.phi_deg = np.random.rand(1) * 360

theta_rad = circle.theta_deg * np.pi / 180
phi_rad = circle.phi_deg* np.pi / 180

circle.dz = -speed * np.cos(theta_rad) / frameRate

• Then, in the loop that plays the animation, and updates the position of each circle, I have put this condition following the same answer that was provided to the same kind of issue here:

max_dist = max(abs(circle.position.x),abs(circle.position.y))
limit_dist = 25 * abs((circle.position.z-near_z) / far_z)

z_rel = np.random.uniform(near_z,far_z)

if max_dist > limit_dist:
circle.position.x = np.random.uniform(-25, 25) * z_rel/far_z
circle.position.y = np.random.uniform(-25, 25) * z_rel/far_z


I got a weird result as shown in GIF 2

What is wrong with my condition and how can I detect a circle that disappears from the frame and recreate one inside the frame?