Find the intersection of a line with a plane

Find the intersection of a line with a plane is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Finding the intersection of an infinite ray with a plane in 3D is an important topic in collision detection.

Task

Find the point of intersection for the infinite ray with direction (0,-1,-1) passing through position (0, 0, 10) with the infinite plane with a normal vector of (0, 0, 1) and which passes through [0, 0, 5].

Python

Based on the approach at geomalgorithms.com

<lang python>#!/bin/python from __future__ import print_function import numpy as np

def LinePlaneCollision(planeNormal, planePoint, rayDirection, rayPoint, epsilon=1e-6):

ndotu = planeNormal.dot(rayDirection) if abs(ndotu) < epsilon: raise RuntimeError("no intersection or line is within plane")

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

if __name__=="__main__": #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

Psi = LinePlaneCollision(planeNormal, planePoint, rayDirection, rayPoint) print ("intersection at", Psi)</lang>

Output:

intersection at [ 0 -5  5]