Circle from two points and a sweep angle

from math import *

def VSum(*VectorArgs):
  if len(VectorArgs) == 1:
    Vectors = VectorArgs[0]
  else:
    Vectors = VectorArgs
  Result = tuple(Vectors[0])
  for i in range(1, len(Vectors)):
    Result = tuple(a + b for a, b in zip(Result, Vectors[i]))
  return Result

def VDiff(A, B):
  return tuple(x - y for x, y in zip(A, B))

def VLengthSquared(A):
  return sum(x * x for x in A)

def VLength(A):
  return sqrt(VLengthSquared(A))

def VScaled(A, Scale):
  return tuple(x * Scale for x in A)

def VPerp(A):
  return (-A[1], A[0])


def CentredArcFromArcSweep(P1, P2, SweepAngle):

  circle = 2.0 * pi

  Diff = VDiff(P2, P1)
  Dist = VLength(Diff)
  s = sin(0.5 * SweepAngle)
  Radius = Dist / (2.0 * s)

  M = VScaled(VSum(P1, P2), 0.5)
  t = tan(0.5 * SweepAngle)
  Centre = VSum(M, VPerp(VScaled(Diff, 0.5 / t)))

  R1 = VDiff(P1, Centre)
  StartAngle = atan2(R1[1], R1[0])
  EndAngle = StartAngle + SweepAngle
  EndAngle = ((EndAngle + pi) % circle) - pi

  return Centre, Radius, StartAngle, EndAngle

def Main():

  P1 = (0.7071, 2.0 - 0.7071)
  P2 = (0.7071, 2.0 + 0.7071)
  Angle = radians(90.0)

  print "Start point, end point and (signed) sweep angle:"
  print P1, P2, degrees(Angle)

  Centre, Radius, StartAngle, EndAngle = CentredArcFromArcSweep(P1, P2, Angle)

  print "Centre, radius and start and end angles:"
  print Centre, Radius, degrees(StartAngle), degrees(EndAngle)


Main()