class RDS_TrapShapeNestedCircles(common.ulb:TrapShape) {
public:
  import "common.ulb"

  func RDS_TrapShapeNestedCircles(Generic pparent)
    TrapShape.TrapShape(pparent)
  endfunc

  float func Iterate(complex pz)
    TrapShape.Iterate(pz)
    pz = pz * (0,1) ^ 0.5
    float d = cabs(pz) - @p_radius;
    if (d > 0)
      return d
    else
      d = -d
    endif

    complex bottomleft = -@p_radius / sqrt(2.0) + flip(-@p_radius / sqrt(2.0))
    int n = 2
    float cur_radius = @p_radius / 2.0
    int level = 1
    while (level < @p_levels)
      float delta = cur_radius * sqrt(2.0)
      complex circle_pos = bottomleft - (cur_radius / sqrt(2.0) + flip(cur_radius / sqrt(2.0)))
      complex newp = (pz - circle_pos) / delta
      complex newf = newp - trunc(newp)

      ; End if point is outside all circles at this level
      if (real(newp) < 0 || real(newp) > n+1 || imag(newp) < 0 || imag(newp) > n+1)
        return d
      endif

      ; Check bottom left circle
      if (real(newp) > 1 && imag(newp) > 1)
        float newd = abs(delta * cabs(newf) - cur_radius)
        if (newd < d)
          d = newd
        endif
      endif

      ; check bottom right circle
      if (real(newp) < n && imag(newp) > 1)
        float newd = abs(delta * cabs(newf - (1,0)) - cur_radius)
        if (newd < d)
          d = newd
        endif
      endif

      ; check top left circle
      if (real(newp) > 1 && imag(newp) < n)
        float newd = abs(delta * cabs(newf - (0,1)) - cur_radius)
        if (newd < d)
          d = newd
        endif
      endif

      ; check top right circle
      if (real(newp) < n && imag(newp) < n)
        float newd = abs(delta * cabs(newf - (1,1)) - cur_radius)
        if (newd < d)
          d = newd
        endif
      endif

      n = n * 2
      cur_radius = cur_radius / 2.0
      level = level + 1
    endwhile

    return d
  endfunc

default:
	title = "Nested Circles"

	int param v_rds_trapshapenestedcircles
		caption = "Version (RDS_TrapShapeNestedCircles)"
		default = 100
		hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
		visible = @v_rds_trapshapenestedcircles < 100
	endparam

  float param p_radius
    caption = "Radius"
    default = 1.0
    min = 0.1
    hint = "Radius of outer circle"
  endparam

	int param p_levels
		caption = "Levels"
		default = 6
    min = 1
    max = 10
		hint = "How many levels of nesting to use."
	endparam
}