Advertisement Jump to content
Sign in to follow this  

affine decomp

This topic is 4374 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

If you intended to correct an error in the post then please contact us.

Recommended Posts

This has prob been asked before... If i have: M = ScaleMatrix * RotationMatrix * TranslationMatrix (Left Handed) How can i extract the scale vector, rotation quat? (translation vector is obvious)

Share this post

Link to post
Share on other sites
The scaling factors are the sizes of the heterogeneous vectors constituting the top-left 3x3 block. Dividing these vectors so that each is unitary, you're left with a rotation matrix. For (a column-vector) example:

The rotation-scaling-translation matrix:
a11 a12 a13 a14
a21 a22 a23 a24
a31 a32 a33 a34
0 0 0 1
Translation vector = (a14, a24, a34)

The rotation-scaling matrix:
a11 a12 a13 0
a21 a22 a23 0
a31 a32 a33 0
0 0 0 1
XScale = sqrt(a11² + a12² + a13²)
YScale = sqrt(a21² + a22² + a23²)
ZScale = sqrt(a31² + a32² + a33²)

The rotation matrix:
a11/XScale a12/XScale a13/XScale 0
a21/YScale a22/YScale a23/YScale 0
a31/ZScale a32/ZScale a33/ZScale 0
0 0 0 1
Now, calculating the rotation quaternion is a little more involved, so I'll link you to this FAQ.


Share this post

Link to post
Share on other sites
Sign in to follow this  

  • Advertisement

Important Information

By using, you agree to our community Guidelines, Terms of Use, and Privacy Policy. is your game development community. Create an account for your GameDev Portfolio and participate in the largest developer community in the games industry.

Sign me up!