How to Calculate a 3x3 Rotation Matrix around a Given Axis?

[yanyin]

Hi, if i want to find a 3x3 matrix R which represents a rotation of Pi/6 around the axis of rotation v(vector)={1, 2, 3}. how can i find it?

 

[Janitor]

Are you saying that your axis is along a vector that starts at the origin of the coordinate system and has its tip at the point (x,y,z)=(1,2,3)? And is your rotation direction clockwise or counterclockwise as viewed from the perspective of (0,0,0)?

 

[yanyin]

Originally posted by Janitor
Are you saying that your axis is along a vector that starts at the origin of the coordinate system and has its tip at the point (x,y,z)=(1,2,3)? And is your rotation direction clockwise or counterclockwise as viewed from the perspective of (0,0,0)?

Thanks. it's a vector from origin to (1, 2, 3). which direction? i am not sure yet. let say clockwise.

 

[NateTG]

Start by figuring out what the result of rotating
[0,0,1]
[0,1,0]
and
[1,0,0]
are.

Once you've done that, you shouldn't have any trouble making hte matrix.

 

[Janitor]

This link may or may not help:

http://en.wikipedia.org/wiki/3D_projection

 

[Janitor]

Another

http://mathworld.wolfram.com/RotationMatrix.html