Line of intersection between two planes

by

The equation of the plane is ax + by + cz + d = 0, where (a,b,c) is the plane’s normal, and d is the distance to the origin. This means that every point (x,y,z) that satisfies that equation is a member of the plane.

Given two planes:

P1: a1x + b1y + c1z + d1 = 0
P2: a2x + b2y + c2z + d2 = 0

The intersection between the two is the set of points that verifies both equations. To find points along this line, you can simply pick a value for x, any value, and then solve the equations for y and z.

y = (-c1z -a1x -d1) / b1
z = ((b2/b1)*(a1x+d1) -a2x -d2)/(c2 - c1*b2/b1)

If you make x=0, this gets simpler:

y = (-c1z -d1) / b1
z = ((b2/b1)*d1 -d2)/(c2 - c1*b2/b1)

More Related Contents:

  1. Is floating point math broken?
  2. Understanding “randomness”
  3. Projecting 3D points to 2D plane [closed]
  4. What types of numbers are representable in binary floating-point?
  5. Why does floating-point arithmetic not give exact results when adding decimal fractions?
  6. Why can’t decimal numbers be represented exactly in binary?
  7. How can i produce multi point linear interpolation? [closed]
  8. How to determine if a list of polygon points are in clockwise order?
  9. Turning a cylinder into a sphere without pinching at the poles
  10. How to convert latitude or longitude to meters?
  11. How do I combine complex polygons?
  12. Smart design of a math parser?
  13. Using atan2 to find angle between two vectors
  14. Need help in mod 1000000007 questions
  15. What does the ^ (XOR) operator do? [duplicate]
  16. How to test randomness (case in point – Shuffling)
  17. Puzzle: Find largest rectangle (maximal rectangle problem)
  18. How to distribute points evenly on the surface of hyperspheres in higher dimensions?
  19. How to calculate Tangent and Binormal?
  20. Can a IEEE 754 real number “cover” all integers within its range?
  21. The Sieve of Atkin
  22. Calculating bounding box a certain distance away from a lat/long coordinate in Java
  23. Plotting a point on the edge of a sphere
  24. How to find pair with kth largest sum?
  25. Finding the coordinates of points from distance matrix
  26. Should we compare floating point numbers for equality against a *relative* error?
  27. Handling errors in math functions
  28. How to calculate an RGB colour by specifying an alpha blending amount?
  29. Do not want scientific notation on plot axis
  30. OpenGL Math – Projecting Screen space to World space coords

Leave a Comment