//
// SPDX-License-Identifier: BSD-3-Clause
// Copyright Contributors to the OpenEXR Project.
//
//
// A 3D sphere class template
//
#ifndef INCLUDED_IMATHSPHERE_H
#define INCLUDED_IMATHSPHERE_H
#include "ImathExport.h"
#include "ImathNamespace.h"
#include "ImathBox.h"
#include "ImathLine.h"
#include "ImathVec.h"
IMATH_INTERNAL_NAMESPACE_HEADER_ENTER
///
/// A 3D sphere
///
template <class T> class IMATH_EXPORT_TEMPLATE_TYPE Sphere3
{
public:
/// @{
/// @name Direct access to member fields
/// Center
Vec3<T> center;
/// Radius
T radius;
/// @}
/// @{
/// @name Constructors
/// Default is center at (0,0,0) and radius of 0.
IMATH_HOSTDEVICE constexpr Sphere3() : center (0, 0, 0), radius (0) {}
/// Initialize to a given center and radius
IMATH_HOSTDEVICE constexpr Sphere3 (const Vec3<T>& c, T r) : center (c), radius (r) {}
/// @}
/// @{
/// @name Manipulation
/// Set the center and radius of the sphere so that it tightly
/// encloses Box b.
IMATH_HOSTDEVICE void circumscribe (const Box<Vec3<T>>& box);
/// @}
/// @{
/// @name Utility Methods
/// If the sphere and line `l` intersect, then compute the
/// smallest `t` with `t>=0` so that `l(t)` is a point on the sphere.
///
/// @param[in] l The line
/// @param[out] intersection The point of intersection
/// @return True if the sphere and line intersect, false if they
/// do not.
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 bool
intersect (const Line3<T>& l, Vec3<T>& intersection) const;
/// If the sphere and line `l` intersect, then compute the
/// smallest `t` with `t>=0` so that `l(t)` is a point on the sphere.
///
/// @param[in] l The line
/// @param[out] t The parameter of the line at the intersection point
/// @return True if the sphere and line intersect, false if they
/// do not.
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 bool intersectT (const Line3<T>& l, T& t) const;
/// @}
};
/// Sphere of type float
typedef Sphere3<float> Sphere3f;
/// Sphere of type double
typedef Sphere3<double> Sphere3d;
//---------------
// Implementation
//---------------
template <class T>
inline 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>
IMATH_CONSTEXPR14 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 = std::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>
IMATH_CONSTEXPR14 bool
Sphere3<T>::intersect (const Line3<T>& line, Vec3<T>& intersection) const
{
T t (0);
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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