Comments on: Decomposing Matrices

By: Vitaly

Vitaly — Tue, 12 Apr 2011 13:20:22 +0000

The tricks are great, but math is all wrong from the very beginning. 1) Correct rotation matrices (common rotation direction is assumed): 1 0 0 0 cosx -sinx 0 sinx cosx

cosy 0 siny 0 1 0 -siny 0 cosy

cosz -sinz 0 sinz cosz 0 0 0 1

2) If you rotate around X, then around Y and then around Z, you should multiply Rz by Ry and then by Rx: R = (RzRy)Rx. Correct final rotation matrix is given here http://en.wikipedia.org/wiki/Rotation_matrix#General_rotations phi is x, theta is y and psi is z

By: Tim

Tim — Mon, 09 Aug 2010 10:53:21 +0000

Thank you. That helps. I kept trying to somehow make _23 and _33 equal each other. What you're saying makes perfect sense.

Again, great article!

By: Administrator

Administrator — Mon, 09 Aug 2010 04:11:30 +0000

Hi Tim!

I hope I've clarified a bit how I arrived at this - basically, I'm solving a system with two unknowns for one of them, taking advantage of common terms between them

By: Tim

Tim — Sun, 08 Aug 2010 18:27:01 +0000

Hey Rachel - this is great. Thank you. The one think I'm stumped on is your statement:

"We find a nice pair of values in row 2&3, column 3: Sin(x).Cos(y) and Cos(x).Cos(y). If we divide those two, we get Sin(x)/Cos(x) = Tan(x)"

I don't understand what allows us to divide m23 by m33. They are just two different values in two cells. How did you determine you could divide?

I'm sure I'm missing something obvious.

Thanks

By: Rachel 'Groby' Blum

Rachel 'Groby' Blum — Wed, 24 Jun 2009 12:25:10 +0000

Hey Aaron – you are perfectly right. It’s amazing how many typos one can add transcribing math

By: Aaron

Aaron — Fri, 19 Jun 2009 23:01:38 +0000

I think there’s a mistake: rotation.y=asin( matrix._13 ) I think should be rotation.y=asin( -matrix._13 )

By: Andy Geers

Andy Geers — Sat, 09 May 2009 11:40:58 +0000

Assuming the description of how to apply the scaling is correct, then I think there's an error in your code: rotation.x = atan2( matrix._23scale.x, matrix._33 ); rotation.z = atan2( matrix._12scale.y, matrix._11 );

should really read as follows: rotation.x = atan2( matrix._23scale.z, matrix._33 ); rotation.z = atan2( matrix._12scale.x, matrix._11 );

... since you said you want to divide matrix._11 by scale.x and matrix._33 by scale.z

By: cb

cb — Thu, 16 Apr 2009 19:13:00 +0000

Are we there yet? Not quite! What if Cos(y) is zero?

Is there any way you could add code for this case, as well? Thanks!

By: Administrator

Administrator — Tue, 03 Jun 2008 14:05:06 +0000

@Bill: Indeed. Great catch. I’ve updated it

By: Administrator

Administrator — Tue, 03 Jun 2008 04:24:05 +0000

Thanks, Bill. Updated the article.