| Re: Fitting Circles [message #18086 is a reply to message #18085] |
Wed, 01 December 1999 00:00  |
Struan Gray
Messages: 178
Registered: December 1995
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Senior Member |
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F.N.Hatfield@Leeds.ac.uk writes:
> I am trying to fit a circle to a set of points (x,y), and
> from this determine the centre point (x0,y0) and radius r0.
> It is also very important that I obtain the standard
> deviations or errors in the x0,y0 and r0.
I can see two approaches, depending on what you mean
by *the* s.d..
First, Craig Markwardt's MPFIT and associated routines are
much more useful than curvefit:
http://cow.physics.wisc.edu/~craigm/idl/
This will let you find the circle with the mimimum least
squares error w.r.t. your set of points. You can then
define a suitable region of r0,x0,y0 space and simply
calculate the least squares error for an appropriately dense
set of points. IDL's built in MOMENT routine can then be
used to extract the s.d. for each variable.
Alternately, there is a simple algebraic expression for
the unique circle passing through any three points. If you
calculate it for all permutations (warning: the number of
permutations will explode if you have lots of points) you can
generate arrays of r0, x0, and y0 values. Again, MOMENT can
then be used to extract statisics (or you can roll your own
mean and s.d. calculation).
Struan
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