Maths - Rotations - Forum Discussion

By: Nobody/Anonymous - nobody
help with rotation angles in 3d  
2006-03-10 12:24

Hi, 
I need help to align a 3d volume (cube). The normal to one of the surfaces of this volume makes an angle 5.33 to the z axis, 94.89 to the y axis and 87.9 to the x axis. these are not the angles of the projections of the normal on each of the axes planes, but instead are the actual angles in 3d space. i need to rotate the volume such that the normal to this surface aligns with the z axis so as to make angle 90 with x and y axes. what angles along the x,y,z axes should i rotate the volume by? i hope the above makes sense...having a difficulty figuring out the angles of rotation. Any help wuold be greatly appreciated. 
Thanks, 
PK

By: Martin Baker - martinbaker
RE: help with rotation angles in 3d  
2006-03-11 00:06

I don't know the answer to this, if anyone knows the answer I would be interested, so that I can put it on the web pages. 
 
Martin

By: Nobody/Anonymous - nobody
RE: help with rotation angles in 3d  
2006-03-27 06:38

Firstly you need to find the normal, of course there isnt a specific normal but we can assume a length of 1 it doesnt matter. 
This will make: 
N = ( 1/Cos(87.9), 1/Cos(94.89), 1/Cos(5.33)) 
Once you have the normal you can find the angle from it to (0, 0, 1), and find the rotation axis by computing the cross product of the normal with (0, 0, 1). 
And we know how to rotate around an axis. 
This will of course work for any vector, not only (0, 0, 1). 
 
I hope I understand the situation correctly. 
 
T.D