def intersection(line1, line2):
x1, y1, x2, y2 = line1
x3, y3, x4, y4 = line2
a, b = x2 - x1, y2 - y1
c, d = x3 - x1, y3 - y1
e, f = x4 - x1, y4 - y1
t1 = c * b - a * d
t2 = e * b - a * f
if t1 * t2 >= 0:
return 0
g, h = x4 - x2, y4 - y2
i, j = x4 - x3, y4 - y3
t1 = e * j - i * f
t2 = g * j - i * h
if t1 * t2 >= 0:
return 0
denom = a * j - b * i
ynum = b * c * j + a * j * y1 - b * i * y3
xnum = a * (c * j - d * i) + x1 * denom
g = pef.ggcd((denom, ynum, xnum))
return (ynum/g, xnum/g, denom/g)
def rgen(m, n):
"""
Using co-prime pairs to generate primitive Eisenstein triplets.
See https://en.wikipedia.org/wiki/Integer_triangle
"""
if m > 2 * n:
a, b = 2*m*n - n*n, m*m - n*n
else:
a, b = m*m - n*n, 2*m*n - n*n
g = pef.ggcd((a, b, m*m - m*n + n*n))
return g, sqrt(3) / 2 * (m-n) * n / g