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Non-Convex Coordinate Transform Problem Rotating Frame

  1. May 28, 2014 #1
    I am sure this is not the best description of the problem, so let me know how I can clarify.

    Say there are 2 coordinate systems, with one orbiting around the other. Call one fixed ƒ and the other rotating ρ. The goal is to find the transform between the two frames.

    What's known is
    1) A set of 3D points at a given time τ in frame ρ
    2) The angle θ which frame ρ is subsequently rotated about the z-axis of frame ƒ between time τ and τ+1
    3) New 3D points at time τ+1 in frame ρ, and so forth.
    4) All points from all views lie in a single plane in frame ƒ (this does not mean the points at time τ and time τ+1 are the same, just that they are coplanar)

    I want to set up the problem to use the plane equation in frame ƒ to solve an overdetermined system, but I run into the problem that I do not know the plane normal η and distance d in frame ƒ.

    Is there any way this can be solved (even approximately)? Thanks
  2. jcsd
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