def polar_to_cartesian(r, start_angles, end_angles):
 cartesian = (lambda r, alpha: ((r * cos(alpha)), (r * sin(alpha))))
 points = []
 for (r, start, end) in zip(r, start_angles, end_angles):
  points.append(cartesian(r, ((end + start) / 2)))
 return zip(*points)

def polar_to_cartesian ( r , start_angles , end_angles ) : cartesian = ( lambda r , alpha : ( ( r * cos ( alpha ) ) , ( r * sin ( alpha ) ) ) ) points = [ ] for ( r , start , end ) in zip ( r , start_angles , end_angles ) : points . append ( cartesian ( r , ( ( end + start ) / 2 ) ) ) return zip ( * points )
translate polar coordinates to cartesian .