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Math Help - Ellipse Centre point calculation

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    Re: Ellipse Centre point calculation

    Quote Originally Posted by Randeep View Post
    Hi,
    I am doing a measurement of a cylindral object with might be standing veticle or tilted. A device shoots a laser and takes measurement of (HA,VA,and length from device to the point) by this process three points are measure along top cylindrical object and so on for bottom. The radius of pile is known, now i want to find center for ellipse with measurements of three points as (x1,y1),(x2,y2),(x3,y3) and radius. how can i achieve that?
    Hi !
    A more accurate method consists in more measurements than three. Do as may measurements as possible. Then a elliptic regression (least squares fitting) will provide an accurate approximation of the center of the ellipse and of the length of axes. Nevertheless, the method works also with three points only.
    A direct method (non iterative) is given page 16 of the paper "Régressions coniques, quadriques,..." :
    Scribd

    Note : In general, at least five points are necessary to fully determine the parameters of an ellipse. If you measure only three points, you need more information. For example if you know the location of the directions of the axes : Then, the general method given in the paper referenced above has to be slightly modified, wich is easy : the matrix will be simpler (size 3x3 instead of 5x5).
    Last edited by JJacquelin; December 17th 2012 at 11:56 PM.
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