Function circle_circle_intersection

numericals.py:481–504

Returns a pair of Points as intersections of c1 and c2.

(c1: Circle, c2: Circle)

def circle_circle_intersection(c1: Circle, c2: Circle) -> tuple[Point, Point]:
  """Returns a pair of Points as intersections of c1 and c2."""
  # circle 1: (x0, y0), radius r0
  # circle 2: (x1, y1), radius r1
  x0, y0, r0 = c1.a, c1.b, c1.radius
  x1, y1, r1 = c2.a, c2.b, c2.radius

  d = math.sqrt((x1 - x0) ** 2 + (y1 - y0) ** 2)
  if d == 0:
    raise InvalidQuadSolveError()

  a = (r0**2 - r1**2 + d**2) / (2 * d)
  h = r0**2 - a**2
  if h < 0:
    raise InvalidQuadSolveError()
  h = np.sqrt(h)
  x2 = x0 + a * (x1 - x0) / d
  y2 = y0 + a * (y1 - y0) / d
  x3 = x2 + h * (y1 - y0) / d
  y3 = y2 - h * (x1 - x0) / d
  x4 = x2 - h * (y1 - y0) / d
  y4 = y2 + h * (x1 - x0) / d

  return Point(x3, y3), Point(x4, y4)


class InvalidQuadSolveError(Exception):