polar_add.py

  import math

def polar_add( v1, v2 ):
    dtheta = v2[1]-v1[1]
    r = math.sqrt( v1[0]**2 + v2[0]**2 + 2*v1[0]*v2[0]* math.cos(dtheta) )
    theta = v1[1] + math.atan2( 
        v2[1] * math.sin(dtheta),
        v1[1] + v2[1]*math.cos(dtheta)
    )
    return (r, theta )


inpoints = [
    ( 12, math.pi/6 ),
    ( 23, math.pi/4 )
]

def convert_points( inpts ):
    outpts = [inpts[0]]
    for pt in inpts[1:]:
        outpts.append( polar_add( outpts[-1], pt ) )
    return outpts

print(convert_points(inpoints))