from pyx import canvas,path,color
from math import *

rot = [e**(pi*0.4j*i) for i in range(5)]

def orient(p,q):
    return p.real * q.imag - p.imag * q.real

def testx(x):
    p = rot[1].real + 1j * x
    return orient(p - 1, p * rot[3] - 1)

lo,hi = 3,4
while hi - lo > 1e-8:
    mid = (lo+hi)/2.0
    if testx(mid) < 0: hi = mid
    else: lo = mid

c = canvas.canvas()

scale=2.0
def edge(p,q):
    c.stroke(path.line(p.real*scale,p.imag*scale,q.real*scale,q.imag*scale),
             [color.rgb.black])

def point(p):
    c.fill(path.circle(p.real*scale,p.imag*scale,0.08*scale),[color.rgb.red])

for i in range(5):
    p2 = 1 * rot[i-4]
    p3 = (rot[1].real + 1j * mid) * rot[i]
    p4 = p3 * rot[2]
    edge(p3,p4)
    edge(p4,p2)

for i in range(5):
    point(1*rot[i])
    point((rot[1].real + 1j * mid) * rot[i])

c.writePDFfile("Non-Desargues configuration")