Math Is Fun Forum
Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °
You are not logged in.
- Topics: Active | Unanswered
#1 2008-05-09 01:47:42
- rashed_karim
- Member
- Registered: 2008-05-09
- Posts: 2
Transformation of an arbitrary plane in 3D to the z=0 plane
Hi Math whizzes,
I need to find the (affine) transformation matrix which transforms an arbitrary plane in 3D i.e. ax+by+cz = d to the z-plane i.e. z=0
Does anyone know I would go about solving this problem?
Offline
#2 2008-05-10 00:02:11
- JaneFairfax
- Member
- Registered: 2007-02-23
- Posts: 6,868
Re: Transformation of an arbitrary plane in 3D to the z=0 plane
This trasforms any point (x,y.z) to (x,y,0).
Last edited by JaneFairfax (2008-05-10 00:07:18)
Offline
#3 2008-05-10 02:38:35
- mathsyperson
- Moderator
- Registered: 2005-06-22
- Posts: 4,900
Re: Transformation of an arbitrary plane in 3D to the z=0 plane
Would this work with, say, x=0? That would get mapped to a line on the z-plane instead of the z-plane itself. Maybe that doesn't matter, I don't know.
Why did the vector cross the road?
It wanted to be normal.
Offline
#4 2008-05-12 12:02:13
- rashed_karim
- Member
- Registered: 2008-05-09
- Posts: 2
Re: Transformation of an arbitrary plane in 3D to the z=0 plane
I dont think just dropping off the z-variable would make this work. The matrix stated does just that. Any other thoughts on how this transformation can be achieved?
Offline