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ImathSphere.h

///////////////////////////////////////////////////////////////////////////
//
// Copyright (c) 2002, Industrial Light & Magic, a division of Lucas
// Digital Ltd. LLC
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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 = 2.0 * (line.dir ^ v);
    T C = (v ^ v) - (radius * radius);

    // compute discriminant
    // if negative, there is no intersection

    T discr = B*B - 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) * 0.5;

      if (t < 0.0)
      {
          // no intersection, try t1: (-B + sqrt(B^2 - 4AC)) / 2A  (A = 1)

          t = (-B + sqroot) * 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

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