3D Line-Plane Intersection

Question

If given a line (represented by either a vector or two points on the line) how do I find the point at which the line intersects a plane? I\'ve found loads of resources on th

Answer 1

Using numpy and python:

#Based on http://geomalgorithms.com/a05-_intersect-1.html
from __future__ import print_function
import numpy as np

epsilon=1e-6

#Define plane
planeNormal = np.array([0, 0, 1])
planePoint = np.array([0, 0, 5]) #Any point on the plane

#Define ray
rayDirection = np.array([0, -1, -1])
rayPoint = np.array([0, 0, 10]) #Any point along the ray

ndotu = planeNormal.dot(rayDirection) 

if abs(ndotu) < epsilon:
    print ("no intersection or line is within plane")

w = rayPoint - planePoint
si = -planeNormal.dot(w) / ndotu
Psi = w + si * rayDirection + planePoint

print ("intersection at", Psi)