text: ///////////////////////////////////////////////////////////////////////////
  //
  // Copyright (c) 2002, Industrial Light & Magic, a division of Lucas
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  ///////////////////////////////////////////////////////////////////////////
  
  
  
  #ifndef INCLUDED_IMATHSPHERE_H
  #define INCLUDED_IMATHSPHERE_H
  
  //-------------------------------------
  //
  //	A 3D sphere class template
  //
  //-------------------------------------
  
  #include "ImathVec.h"
  #include "ImathBox.h"
  #include "ImathLine.h"
  
  namespace Imath {
  
  template <class T>
  class Sphere3
  {
    public:
  
      Vec3<T>	center;
      T           radius;
  
      //---------------
      //	Constructors
      //---------------
  
      Sphere3() : center(0,0,0), radius(0) {}
      Sphere3(const Vec3<T> &c, T r) : center(c), radius(r) {}
  
      //-------------------------------------------------------------------
      //	Utilities:
      //
      //	s.circumscribe(b)	sets center and radius of sphere s
      //				so that the s tightly encloses box b.
      //
      //	s.intersectT (l, t)	If sphere s and line l intersect, then
      //				intersectT() computes the smallest t,
      //				t >= 0, so that l(t) is a point on the
      //				sphere.  intersectT() then returns true.
      //
      //				If s and l do not intersect, intersectT()
      //				returns false.
      //
      //	s.intersect (l, i)	If sphere s and line l intersect, then
      //				intersect() calls s.intersectT(l,t) and
      //				computes i = l(t).
      //
      //				If s and l do not intersect, intersect()
      //				returns false.
      //
      //-------------------------------------------------------------------
  
      void circumscribe(const Box<Vec3<T> > &box);
      bool intersect(const Line3<T> &l, Vec3<T> &intersection) const;
      bool intersectT(const Line3<T> &l, T &t) const;
  };
  
  
  //--------------------
  // Convenient typedefs
  //--------------------
  
  typedef Sphere3<float> Sphere3f;
  typedef Sphere3<double> Sphere3d;
  
  
  //---------------
  // Implementation
  //---------------
  
  template <class T>
  void Sphere3<T>::circumscribe(const Box<Vec3<T> > &box)
  {
      center = T(0.5) * (box.min + box.max);
      radius = (box.max - center).length();
  }
  
  
  template <class T>
  bool Sphere3<T>::intersectT(const Line3<T> &line, T &t) const
  {
      bool doesIntersect = true;
  
      Vec3<T> v = line.pos - center;
      T B = T(2.0) * (line.dir ^ v);
      T C = (v ^ v) - (radius * radius);
  
      // compute discriminant
      // if negative, there is no intersection
  
      T discr = B*B - T(4.0)*C;
  
      if (discr < 0.0)
      {
      // line and Sphere3 do not intersect
  
      doesIntersect = false;
      }
      else
      {
      // t0: (-B - sqrt(B^2 - 4AC)) / 2A  (A = 1)
  
      T sqroot = Math<T>::sqrt(discr);
      t = (-B - sqroot) * T(0.5);
  
      if (t < 0.0)
      {
          // no intersection, try t1: (-B + sqrt(B^2 - 4AC)) / 2A  (A = 1)
  
          t = (-B + sqroot) * T(0.5);
      }
  
      if (t < 0.0)
          doesIntersect = false;
      }
  
      return doesIntersect;
  }
  
  
  template <class T>
  bool Sphere3<T>::intersect(const Line3<T> &line, Vec3<T> &intersection) const
  {
      T t;
  
      if (intersectT (line, t))
      {
      intersection = line(t);
      return true;
      }
      else
      {
      return false;
      }
  }
  
  
  } //namespace Imath
  
  #endif
  