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From: Conor on 17 May 2010 12:19
Hello,

I was wondering if it is possile to do the following, and if so where should I start looking.

I have a set of maybe ten random x,y coords close together, and I want to fit a circle of known radius around them (not fit a curve through them). There could be infinite possibilities when you just use one circle, but my ultimate goal is to have an aggregate shape consisting of 4 circles - (with fixed, known offsets from each other - imagine a cross with a circle on each end) - and have 4 sets of ten xy points on the one plot and try and get the best fit when you take into account all 4 points.

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From: Matt J on 17 May 2010 13:24


So everything about this 4-circle shape is known a priori except for its translational position (x0,y0) ? And you want to select (x0,y0) to maximize the number of points falling within the circles?
From: ImageAnalyst on 17 May 2010 15:18
(This may not be what you want, but...) To get the circle that fits
around them all, use the convex hull function in base MATLAB,
convhull().
Then use the vertices returned from the convhull() to get the formula
for a circle:
http://en.wikipedia.org/wiki/Circumcircle

I'm don't understand your "four circles" explanation. I don't know
how you'd find the "best" four circles to fit the shape of your
points. Maybe you want to use alpha shapes or restricted convex hull
or morphological closing or something???? Forgetting for the moment
your proposed solution of having 4 circles, what are you REALLY after?
From: Conor on 18 May 2010 07:33
Thanks for the quick replies.

Yes, everything about the four circles will be known before hand, offset , size, rotation etc -even its x,y coordinate (further down the line this will be 3d but not for now).

To explain further - The random sets of 10 points are individual x,y points on a target (the four circles) and quite few in number. What Im hoping to find out is how close will the best fit of the shape be in MATLAB to the very accurate surveyed value that I have for it.

The shapes don't need to be circles, and there can be more or less than four. I chose four because one left too much uncertainty, and i thought that by implementing a fixed shape of four, you would have a cross checking method that would help you narrow down the possibilities. Ive tested it in manually in CAD, it seemed to work ok.
From: Matt J on 18 May 2010 09:48
"Conor " <remove.this-con20or(a)gmail.com> wrote in message <hstttg$6vb$1(a)fred.mathworks.com>...
> Thanks for the quick replies.
>
> Yes, everything about the four circles will be known before hand, offset , size, rotation etc -even its x,y coordinate (further down the line this will be 3d but not for now).
==================

If, as you say, everything about the circle configuration is known a priori, what shape parameter are you fitting? There doesn't seem to be anything left...
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