Fit a circle to (x,y) datapoints?

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3 total messages Started by Patrick Haggard Tue, 26 Jan 1993 14:14

#843

Author: Patrick Haggard
Date: Tue, 26 Jan 1993 14:14

9 lines
788 bytes

I have 40 (x,y) datapoints which I hypothesise form the arc of a 
circle of unknown origin and radius.  I want to find an estimate
of the radius of the circle.  The preferred platform is SAS:
I imagine proc nlin; would do it, but what is the neatest way
to specify y in terms of x.  Any suggestions on how to tackle this.
Thanks

Patrick Haggard

Re: Fit a circle to (x,y) datapoints?

#846

Author: William B Dwinnell
Date: Tue, 26 Jan 1993 19:20

7 lines
784 bytes

I don't know much about SAS, nor how much coding you could do in it,
but fitting a circle to a set of data points would be trivial for a
genetic algorithm. Frankly, I don't understand why GA's aren't used
more often, especially as they are limited by the weaknesses of 
least-squared error systems. Anyway, I'd specify the circle as
x and y of the center, and r, the radius.

Re: Fit a circle to (x,y) datapoints?

#863

Author: Clint Cummins
Date: Tue, 26 Jan 1993 22:44

9 lines
953 bytes

You can't specify y in terms of x, because a circle is not a function
(one x can map to 2 different values of y).  Instead, use a "fake" dependent
variable with the value zero, and on the right hand side, write the function
to be minimized (when squared).  This approach will work for any nonlinear
least squares package.  In your case, let's say the circle's origin is
(A,B) with radius R.  Dependent variable:  ZERO=0;
Function for PROC NLIN:  ZERO = R - SQRT((X-A)**2 + (Y-B)**2)

Clint Cummins

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