"Mark M. Wilson" wrote:

> I have a couple of questions, actually.  The second is dependent on the
> first.
> 1) It's been a LOOONNNNGGGGGG time since high school geometry, but it
> seems to me it should be possible to scribe a circle given any three
> (coplanar) points.  Am I right?
>
> 2) if the premise in #1 is correct, does anyone know of any macros for
> Povray that will calculate the coordinates of  the center of such a
> circle?
>
> TIA,
> Mark M. Wilson

Here is a macro I created using the Law of Sines.

#macro Center(a,b,c)
  #local d = (a+b)/2;
  #local e = (b+c)/2;
  #local v0 = vnormalize(vcross((b-c),(b-a)));
  #local v1 = vnormalize(vcross(d-b,v0));
  #local v2 = vnormalize(vcross(v0,e-b));
  #local a1 = (acos(vdot(d-e,v2)/vlength(d-e)*vlength(v2)));
  #local a2 = (acos(vdot(e-d,v1)/vlength(e-d)*vlength(v1)));
  #local a3 = pi-a1-a2;
  #local l = (sin(a1)/sin(a3))*vlength(e-d);
  #local f = d + vnormalize(v1)*l;
  #local t1 = vlength(f-a);
  #local t2 = vlength(f-b);
  #local t3 = vlength(f-c);
  #if ((t1!=t2)|(t2!=t3)|(t1!=t3))
    #render "help"
    #local f =Center(a,c,b);
  #end
  f
#end

The only problem with it is that I have to check that the point it finds
is equidistant to all three points. I think it has to do with the
orientation of the points, since the correction only requires a reversal
of orientation to fix the problem.





--
Josh English
eng### [at] spiritonecom
The POV-Ray Cyclopedia http://www.spiritone.com/~english/cyclopedia/

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