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Math Help - Rotation matrix from vectors to cone

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    Rotation matrix from vectors to cone

    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
    Last edited by barcafan; August 11th 2011 at 05:43 PM.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Re: Rotation matrix from vectors to cone

    Quote Originally Posted by barcafan View Post
    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
    Could you explain this a little more?
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  3. #3
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    Re: Rotation matrix from vectors to cone

    Quote Originally Posted by Drexel28 View Post
    Could you explain this a little more?
    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.
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