//
// SPDX-License-Identifier: BSD-3-Clause
// Copyright Contributors to the OpenEXR Project.
//
//
// A 3D line class template
//
#ifndef INCLUDED_IMATHLINE_H
#define INCLUDED_IMATHLINE_H
#include "ImathMatrix.h"
#include "ImathNamespace.h"
#include "ImathVec.h"
IMATH_INTERNAL_NAMESPACE_HEADER_ENTER
///
/// The `Line3` class represents a 3D line, defined by a point and a
/// direction vector.
///
template <class T> class Line3
{
public:
/// @{
/// @name Direct access to member fields
/// A point on the line
Vec3<T> pos;
/// The direction of the line
Vec3<T> dir;
/// @}
/// @{
/// @name Constructors
/// Uninitialized by default
IMATH_HOSTDEVICE constexpr Line3() IMATH_NOEXCEPT {}
/// Initialize with two points. The direction is the difference
/// between the points.
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 Line3 (const Vec3<T>& point1, const Vec3<T>& point2) IMATH_NOEXCEPT;
/// @}
/// @{
/// @name Manipulation
/// Set the line defined by two points. The direction is the difference
/// between the points.
IMATH_HOSTDEVICE void set (const Vec3<T>& point1, const Vec3<T>& point2) IMATH_NOEXCEPT;
/// @}
/// @{
/// @name Utility Methods
/// Return the point on the line at the given parameter value,
/// e.g. L(t)
IMATH_HOSTDEVICE constexpr Vec3<T> operator() (T parameter) const IMATH_NOEXCEPT;
/// Return the distance to the given point
IMATH_HOSTDEVICE constexpr T distanceTo (const Vec3<T>& point) const IMATH_NOEXCEPT;
/// Return the distance to the given line
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 T distanceTo (const Line3<T>& line) const IMATH_NOEXCEPT;
/// Return the point on the line closest to the given point
IMATH_HOSTDEVICE constexpr Vec3<T> closestPointTo (const Vec3<T>& point) const IMATH_NOEXCEPT;
/// Return the point on the line closest to the given line
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 Vec3<T> closestPointTo (const Line3<T>& line) const IMATH_NOEXCEPT;
/// @}
};
/// Line of type float
typedef Line3<float> Line3f;
/// Line of type double
typedef Line3<double> Line3d;
template <class T> IMATH_CONSTEXPR14 inline Line3<T>::Line3 (const Vec3<T>& p0, const Vec3<T>& p1) IMATH_NOEXCEPT
{
set (p0, p1);
}
template <class T>
inline void
Line3<T>::set (const Vec3<T>& p0, const Vec3<T>& p1) IMATH_NOEXCEPT
{
pos = p0;
dir = p1 - p0;
dir.normalize();
}
template <class T>
constexpr inline Vec3<T>
Line3<T>::operator() (T parameter) const IMATH_NOEXCEPT
{
return pos + dir * parameter;
}
template <class T>
constexpr inline T
Line3<T>::distanceTo (const Vec3<T>& point) const IMATH_NOEXCEPT
{
return (closestPointTo (point) - point).length();
}
template <class T>
constexpr inline Vec3<T>
Line3<T>::closestPointTo (const Vec3<T>& point) const IMATH_NOEXCEPT
{
return ((point - pos) ^ dir) * dir + pos;
}
template <class T>
IMATH_CONSTEXPR14 inline T
Line3<T>::distanceTo (const Line3<T>& line) const IMATH_NOEXCEPT
{
T d = (dir % line.dir) ^ (line.pos - pos);
return (d >= 0) ? d : -d;
}
template <class T>
IMATH_CONSTEXPR14 inline Vec3<T>
Line3<T>::closestPointTo (const Line3<T>& line) const IMATH_NOEXCEPT
{
// Assumes the lines are normalized
Vec3<T> posLpos = pos - line.pos;
T c = dir ^ posLpos;
T a = line.dir ^ dir;
T f = line.dir ^ posLpos;
T num = c - a * f;
T denom = a * a - 1;
T absDenom = ((denom >= 0) ? denom : -denom);
if (absDenom < 1)
{
T absNum = ((num >= 0) ? num : -num);
if (absNum >= absDenom * std::numeric_limits<T>::max())
return pos;
}
return pos + dir * (num / denom);
}
/// Stream output, as "(pos dir)"
template <class T>
std::ostream&
operator<< (std::ostream& o, const Line3<T>& line)
{
return o << "(" << line.pos << ", " << line.dir << ")";
}
/// Transform a line by a matrix
template <class S, class T>
constexpr inline Line3<S>
operator* (const Line3<S>& line, const Matrix44<T>& M) IMATH_NOEXCEPT
{
return Line3<S> (line.pos * M, (line.pos + line.dir) * M);
}
IMATH_INTERNAL_NAMESPACE_HEADER_EXIT
#endif // INCLUDED_IMATHLINE_H
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