Keep constant number of visible circles in 3D animation

Coding
1

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).

enter image description here

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.dx = speed * np.sin(-phi_rad - theta_rad) / frameRate
      circle.dy = -speed * np.cos(phi_rad + theta_rad) / frameRate
      circle.dz = -speed * np.cos(theta_rad) / frameRate

  • Then, in the loop that plays the animation, and updates the position of each circle:

         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

enter image description here

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