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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).

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?