# circle and point

Ben Bush pythonnew at gmail.com
Sun Nov 13 07:25:55 CET 2005

```On 11/12/05, Robert Kern <robert.kern at gmail.com> wrote:
>
> Ben Bush wrote:
> > is there any code to decide whether a point is located within the circle
> > by three other points?
>
> # Converted from my C++ code.
> # C.f. http://www.ics.uci.edu/~eppstein/junkyard/circumcenter.html
> def circumcenter(x0, y0,
> x1, y1,
> x2, y2):
> x0m2 = x0 - x2
> y1m2 = y1 - y2
> x1m2 = x1 - x2
> y0m2 = y0 - y2
> x0p2 = x0 + x2
> y1p2 = y1 + y2
> x1p2 = x1 + x2
> y0p2 = y0 + y2
>
> D = x0m2*y1m2 - x1m2*y0m2
> # You probably want to test for D being close to 0 here
>
> centerx = (((x0m2*x0p2 + y0m2*y0p2)/2*y1m2)
> - (x1m2*x1p2 + y1m2*y1p2)/2*y0m2) / D
> centery = (((x1m2*x1p2 + y1m2*y1p2)/2*x0m2)
> - (x0m2*x0p2 + y0m2*y0p2)/2*x1m2) / D
>
> return centerx, centery
>
> def incircle(x0, y0,
> x1, y1,
> x2, y2,
> x, y):
> centerx, centery = circumcenter(x0, y0, x1, y1, x2, y2)
> return ((x-centerx)**2 + (y-centery)**2 <=
> (x0-centerx)**2 + (y0-centery)**2)
>
> --
> Robert Kern
> rkern at ucsd.edu
>
> "In the fields of hell where the grass grows high
> Are the graves of dreams allowed to die."
> -- Richard Harter
>
> Thanks!
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