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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"
#include "ImathNamespace.h"
IMATH_INTERNAL_NAMESPACE_HEADER_ENTER
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;
}
}
IMATH_INTERNAL_NAMESPACE_HEADER_EXIT
#endif // INCLUDED_IMATHSPHERE_H
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