Graphics tutorial solution

plane.py

from itertools import permutations

P1 = (10, 20, 5)
P2 = (15, 10, 10)
P3 = (25, 20, 10)

def crossProduct(v1, v2):
    x = v1[1]*v2[2] - v1[2]*v2[1]
    y = v1[2]*v2[0] - v1[0]*v2[2]
    z = v1[0]*v2[1] - v1[1]*v2[0]
    return x, y, z

def normalise(v):
    min_val = min(map(abs, v))
    return tuple(map(lambda x: x/min_val, v))

def getNormal(p1, p2, p3):
    v1 = tuple(map(lambda i: p2[i]-p1[i], range(3)))
    v2 = tuple(map(lambda i: p3[i]-p1[i], range(3)))
    n_ = crossProduct(v1, v2)
    n = normalise(n_)
    return n

def dotProduct(v1, v2):
    return sum(map(lambda x: x[0]*x[1], zip(v1, v2)))

def getCartesianCoeffs(ps):
    p1, p2, p3 = ps
    n = getNormal(p1, p2, p3)
    a, b, c = n
    d = -dotProduct(n, p1)
    coeffs = a, b, c, d
    if (a < 0):
        return tuple(map(lambda x: -x, coeffs))
    return coeffs

# Check all permutations of P1, P2 and P3 give the same result
tests = list(map(getCartesianCoeffs, permutations((P1, P2, P3))))
assert all(test == tests[0] for test in tests)
print(tests[0])