Plane-plane intersection in python [closed]

Question

I need to calculate intersection of two planes in form of AX+BY+CZ+D=0 and get a line in form of two (x,y,z) points. I know how to do the math, but I want to avoid inventing a bicycle and use something effective and tested. Is there any library which already implements this? Tried to search opencv and google, but with no success.

Answer 1

my numpy solution:

def plane_intersect(a, b):
    """
    a, b   4-tuples/lists
           Ax + By +Cz + D = 0
           A,B,C,D in order  

    output: 2 points on line of intersection, np.arrays, shape (3,)
    """
    a_vec, b_vec = np.array(a[:3]), np.array(b[:3])

    aXb_vec = np.cross(a_vec, b_vec)

    A = np.array([a_vec, b_vec, aXb_vec])
    d = np.array([-a[3], -b[3], 0.]).reshape(3,1)

# could add np.linalg.det(A) == 0 test to prevent linalg.solve throwing error

    p_inter = np.linalg.solve(A, d).T

    return p_inter[0], (p_inter + aXb_vec)[0]


a, b = (1, -1, 0, 2), (-1, -1, 1, 3)
plane_intersect(a, b)

Out[583]: (array([ 0.,  2., -1.]), array([-1.,  1., -3.]))

a test, subs points back in:

p1, p2 = plane_intersect(a, b)
a_vec, b_vec = np.array(a[:3]), np.array(b[:3])

(np.dot(p1, a_vec), np.dot(p2, a_vec), np.dot(p1, b_vec), np.dot(p2, b_vec))
Out[585]: (-2.0, -2.0, -3.0, -3.0)