Distance Between Skew Lines

Problem

Compute the distance between two lines in 3D: L1 = p1 + t*d1 and L2 = p2 + s*d2.

Use the common perpendicular direction n = d1 x d2:

dist = |(p2 - p1) . n| / ||n||

Return None if n is (nearly) zero, meaning the directions are parallel.

Hint

The shortest segment joining two skew lines is parallel to their cross product.

case 1

in: [[0,0,0],[1,0,0],[0,1,0],[0,0,1]]

expected: 1

case 2

in: [[0,0,0],[1,0,0],[0,1,0],[2,0,0]]

expected: null

case 3

in: [[1,0,0],[0,1,0],[0,1,1],[1,0,0]]

expected: 1

case 4

in: [[0,0,0],[1,0,0],[0,0,0],[0,1,0]]

expected: 0

case 5

in: [[1,1,1],[1,1,0],[0,0,2],[0,1,1]]

expected: 0.5773502691896258

Starter codePython

def distance_skew_lines(p1, d1, p2, d2):
    # Your code here
    pass

5 test cases · run your code against them in the editor