I have a set of given vectors, I want to find a rotation matrix to convert them to vectors belong to surface of a cone with vertex is origin(vectors with the same slant angle but different tilt angles). Is there any body know what is the solution?
Thanks
Thank for caring my problem. my problem is that: originally, there is a set of vectors, which in 3D co-ordiante have the same slant angle but different tilt angles (Li=(ai*sin(s)*cos(ti),ai*sin(s)*sin(ti),ai*cos(s) );i=1:n). Here s is slant angle, ti is the tilt angle. After a rotation matrix conversion R (R*Li), it becomes a set of vectors (Vi, i=1:N). it mean that R*Li=Vi with i=1:N. The question is that: I am given set of Vi, all I have to find are R matrix and Li with i=1:N.
I think that for each i, R*Li=Vi make 3 equations, for i=1:N, it makes 3*N equation. Rotation matrix equavalent to 3 variables, Li (i=1:N) has N+1 variables (since slant angle s is the same). Logically, there is more number of equations than number of varialbes, then there is solution to find Li and R from Vi with i=1:N. But I can not do that.