   how to know rotate matrix about arbitrariness axis?
  Is it impossible?   
  Quaternions, they are your friend.This is a bit of a trust me it works style tutorial, but its all I could find on the spotThe above tutorial should get you by, but you should really look up how quaternions work, and how arbitrary rotation via them work.  They are powerfull, and will save you a lot of time.   ;  Hey I wrote the part about arbitrary axis rotation wootI completely forgot about that tutorial (most of it is written by another guy though).   ;  But I heard of it is impossible .There are some solution. for example first move object to orgin and then rotate it and then  move back.Edit: rotate arbitrary axis that do NOT pass through origin ,it is callaffine transform.4x4 matrix can represent it.but I want to know why rotate a arbitrary axis(no through origin) <==> move axis to origin ,rotate,and move back. what theory does it base ?[Edited by - luasitdown on December 9, 2005 3:48:42 AM];Quote:but I want to know why rotate a arbitrary axis(no through origin) <==> move axis to origin ,rotate,and move back. what theory does it base ?This is called a similarity transformation. (linear algebra term)A rotation matrix clearly doesn't depend on your object's world position. A Y-rotation matrix i.e. looks the same whether your object is at the origin or anywhere else. The catch is, that it always rotates around the origin, therefore in the first case you would end up rotating your object around Y *through its own center* while in the other case it would end up doing circles around the origin as you rotated it because the center of rotation would be quite far from the object's center.I hope you see what I mean...Its quite a straightforward approach once you've understood how coordinates' tranformations work.I suggest you google for "similarity transform"   