CGAL users discussion list

["Thomas Zangl - Home" <>]

Dear List,

I need to implement a Sphere-Line intersection which returns the
intersection points.

Is there anything exact already in CGAL hidden, which I am not able to
find? :-)

If no, does somebody have such a construction which does not use any
sqrt or at least computes the sqrt using exact arithmetic?

I already have an implementation. However, look at this fragment:

   if (i>0)
   {
      // first intersection
      mu = (-b + sqrt(to_double(b*b - 4*a*c ))) / (2*a);
      x = x1 + mu*(x2-x1);
      y = y1 + mu*(y2-y1);
      z = z1 + mu*(z2-z1);
      vIntersections.push_back(Point(x,y,z));

      // second intersection
      mu = (-b - sqrt(to_double(b*b - 4*a*c ))) / (2*a);
      x = x1 + mu*(x2-x1);
      y = y1 + mu*(y2-y1);
      z = z1 + mu*(z2-z1);
      vIntersections.push_back(Point(x,y,z));
      return;
   }

As you can see, it requires the sqrt of the term "(b*b - 4*a*c )"
which introduces some inaccuracy. Can I get rid of it? The intersection
routine is based on
http://ozviz.wasp.uwa.edu.au/~pbourke/geometry/sphereline/.

Has anybody something better? TIA!  

Best regards,
-- 
,yours Thomas Zangl, Bakk.rer.soc.oec. - 

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