Re: Best fit ellipse given vertice and a few points

"Conrad Andrew" <conrad7@xxxxxxx> wrote in message <gdpo05$gn3$1@xxxxxxxxxxxxxxxxxx>...


I would have thought that if one quadrant of an ellipse can be approximated, then it must be possible to get the coordonates of the whole ellipse. Does any of you experts out there have a solution that I could use?


The problem is that you there is no assurance that
the part of an ellipse that falls in the first quadrant
will actually be only one quadrant of an ellipse.
You may find that fully half the ellipse falls in the
first quadrant, or you may find the entire ellipse
does so, depending on the orientation and the
center of the ellipse.

You ask for an expert who will give you a magic
solution. While I might qualify as an expert, the
solution is probably just hard work. To be solved,
this will require an optimization with 5 unknowns.
You need reasonably good starting values, since
it is easy to get trapped in a spurious local
minimum of the sum of squares objective (as
you have clearly found.) And, since you want to
find a solution that solves for a total least squares
solution (allowing errors in both variables) you
will not find any easy way out.

Sorry, but merely wanting something badly
enough only works if you are wearing a pair of
ruby slippers. Close your eyes, click your heels
together three times, ... ;-)

John
.

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