   Rotation about arbitrary axes
  I have a problem with one formula which I don''t understand.I want to rotate vector v around vector n.I understand the global process of doing that but I don''t understand one formula in it. First some symbol explanation:v_ means v perpendicular, v,, means v paralell, @ means theta.I understand that v = v,, + v_ and I understand that vector w (which is perpendicular to v,, and v_) is  w = n x v_Next formula I don''t understand and that is:v''_ = cos@v_ + sin@wv''_ is a portion of v'' perpendicular to n.v'' is rotated vector v.Can someone explain me how that formula is derived and what does it mean? 
  Consider 2D polar coordinates:x = cos(theta);y = sin(theta);And in 3D about an arbitrary axis:x = perpendicular component in 3D arbitrary axisy = crossproduct between vector being rotated and vector to rotate aboutThe two are equivalent.The parallel component is only added afterwards, and doesn't get changed during the rotation.[edited by - Shadow12345 on February 12, 2004 11:56:44 AM]