geometry – Add and Removing Elements on the Circumference of a Circle

I’m attempting to spawn entities on the circumference of a circle.

These entities could also be eliminated at any time, together with all of them being eliminated.

Periodically I wish to add a component on the circle on the furthest distance from all different entities, however I can’t work out the maths.

The fundamentals is so as to add an entity on the midpoint between the 2 neighbors which have the best distance between them.

My pseudo code is –

positions = []
radius = 40
max_angle = 0
if positions.measurement() == 0:
  positions.append( {x: radius, y: 0} )
elif positions.measurement() == 1:
  positions.append( {x: -positions[0].x, y: -positions[0].y })
elif positions.measurement() > 1:
  for i in [0 to positions.size()]:
    p1 = positions[i]
    p2 = positions[i + 1 % positions.size()]
    angle = atan2(p2.y - p1.y, p2.x - p1.x)
    if angle > max_angle:
      temp = {x: cos(angle/2) * radius, y: sin(angle/2) * radius}
  positions.append(temp)

Everything breaks down in my for loop when attempting to calculate the third level. This is as a result of the angle after 2 iterations is 0, and ends in a nasty spawn.

My information of geometry will not be actually adequate for me to determine what I must be doing right here.

I’ve some work arounds which might contain including static factors on the circle, or redistributing factors alongside the circle on a brand new spawn, however it will be fairly cool if I might get this perform capable of robotically discover the proper mid level.

Any assist or route is appreciated.