A mathematical ray in N-dimensional space. More...

#include <Ray.hxx>

Public Member Functions
	~Ray ()=default

	Ray ()=default

	Ray (Ray const &r)

	Ray (Point const &o, Vector const &d)

template<typename = std::enable_if<N == 1>>
	Ray (Real const o, Real const d)

template<typename = std::enable_if<N == 2>>
	Ray (Real const o_x, Real const o_y, Real const d_x, Real const d_y)

template<typename = std::enable_if<N == 3>>
	Ray (Real const o_x, Real const o_y, Real const o_z, Real const d_x, Real const d_y, Real const d_z)

template<typename OtherReal>
	Ray (Ray< OtherReal, N > const &r)

template<typename NewReal>
Ray< NewReal, N >	cast () const

Point &	origin ()

Point const &	origin () const

Vector &	direction ()

Vector const &	direction () const

Ray &	normalize ()

Ray	normalized () const

bool	is_approx (Ray const &r, Real const tol=DUMMY_TOL) const

Ray &	translate (Vector const &t)

Ray	translated (Vector const &t) const

template<typename Transform>
Ray	transformed (Transform const &t) const

template<typename Transform>
Ray &	transform (Transform const &t)

bool	contains (Point const &p, Real tol=DUMMY_TOL) const

bool	intersects (Box< Real, N > const &b, Real tol=DUMMY_TOL) const

bool	intersect (Box< Real, N > const &b, Point &c, Point &f, Real tol=DUMMY_TOL) const

Real	squared_distance (Point const &p, Real tol=DUMMY_TOL) const

Real	squared_distance (Point const &p, Point &c, Real tol=DUMMY_TOL) const

Real	distance (Point const &p, Real tol=DUMMY_TOL) const

Real	distance (Point const &p, Point &c, Real tol=DUMMY_TOL) const

Real	squared_interior_distance (Box< Real, N > const &b, Real tol=DUMMY_TOL) const

Real	squared_interior_distance (Box< Real, N > const &b, Point &p1, Point &p2, Real tol=DUMMY_TOL) const

Real	interior_distance (Box< Real, N > const &b, Real tol=DUMMY_TOL) const

Real	interior_distance (Box< Real, N > const &b, Point &p1, Point &p2, Real tol=DUMMY_TOL) const

Real	squared_exterior_distance (Box< Real, N > const &b, Real tol=DUMMY_TOL) const

Real	squared_exterior_distance (Box< Real, N > const &b, Point &p1, Point &p2, Real tol=DUMMY_TOL) const

Real	exterior_distance (Box< Real, N > const &b, Real tol=DUMMY_TOL) const

Real	exterior_distance (Box< Real, N > const &b, Point &p1, Point &p2, Real tol=DUMMY_TOL) const

void	print (std::ostream &os) const

Private Types
using	Point = AABBtree::Point<Real, N>

using	Vector = AABBtree::Vector<Real, N>

Private Attributes
Point	m_origin

Vector	m_direction

Static Private Attributes
static constexpr Real	EPS {std::numeric_limits<Real>::epsilon()}

static constexpr Real	INF {std::numeric_limits<Real>::infinity()}

static constexpr Real	DUMMY_TOL {EPS*static_cast<Real>(100.0)}

Detailed Description

template<typename Real, Integer N>
class AABBtree::Ray< Real, N >

Forward declaration of the Ray class template.

Template Parameters

Real	Type of the scalar coefficients.
N	Dimension of the ambient space.

This class represents a ray defined by an origin point and a direction vector. The ray extends infinitely in the direction of the vector from the origin point. The class provides functionality for:

Ray transformations (translation, rotation, scaling);
Distance computations to points and boxes;
Intersection tests with axis-aligned bounding boxes;
Normalization and comparison operations.

Template Parameters

Real	Floating-point scalar type (must be float or double).
N	Dimension of the ambient space.

Note: The direction vector is not required to be normalized, but some operations (like distance calculations) may internally normalize it.

Member Typedef Documentation

◆ Point

template<typename Real, Integer N>

using AABBtree::Ray< Real, N >::Point = AABBtree::Point<Real, N>

private

◆ Vector

template<typename Real, Integer N>

using AABBtree::Ray< Real, N >::Vector = AABBtree::Vector<Real, N>

private

Constructor & Destructor Documentation

◆ ~Ray()

template<typename Real, Integer N>

AABBtree::Ray< Real, N >::~Ray ( )

default

Default class destructor.

Note: This destructor is trivial and does not perform any special actions.

◆ Ray() [1/7]

template<typename Real, Integer N>

AABBtree::Ray< Real, N >::Ray ( )

default

Default class constructor.

Default class constructor that creates a ray with null origin and direction.

◆ Ray() [2/7]

template<typename Real, Integer N>

AABBtree::Ray< Real, N >::Ray ( Ray< Real, N > const & r )

inline

Copy constructor

Parameters

[in] r Ray to copy

◆ Ray() [3/7]

template<typename Real, Integer N>

AABBtree::Ray< Real, N >::Ray	(	Point const &	o,
		Vector const &	d )

inline

Class constructor for a ray given an origin and a direction.

Parameters

[in]	o	Origin of the ray.
[in]	d	Direction of the ray.

◆ Ray() [4/7]

template<typename Real, Integer N>

template<typename = std::enable_if<N == 1>>

AABBtree::Ray< Real, N >::Ray	(	Real const	o,
		Real const	d )

inline

Class constructor for the 1D ray.

Parameters

[in]	o	Origin of the ray.
[in]	d	Direction of the ray.

Template Parameters

T	Type of the scalar coefficients.

Note: This constructor is only available for 1D rays.

◆ Ray() [5/7]

template<typename Real, Integer N>

template<typename = std::enable_if<N == 2>>

AABBtree::Ray< Real, N >::Ray	(	Real const	o_x,
		Real const	o_y,
		Real const	d_x,
		Real const	d_y )

inline

Class constructor for the 2D ray.

Parameters

[in]	o_x	Origin \( x \)-axis component.
[in]	o_y	Origin \( y \)-axis component.
[in]	d_x	Direction \( x \)-axis component.
[in]	d_y	Direction \( y \)-axis component.

Template Parameters

T	Type of the scalar coefficients.

Note: This constructor is only available for 2D rays.

◆ Ray() [6/7]

template<typename Real, Integer N>

template<typename = std::enable_if<N == 3>>

AABBtree::Ray< Real, N >::Ray	(	Real const	o_x,
		Real const	o_y,
		Real const	o_z,
		Real const	d_x,
		Real const	d_y,
		Real const	d_z )

inline

Class constructor for the 3D ray.

Parameters

[in]	o_x	Origin \( x \)-axis component.
[in]	o_y	Origin \( y \)-axis component.
[in]	o_z	Origin \( z \)-axis component.
[in]	d_x	Direction \( x \)-axis component.
[in]	d_y	Direction \( y \)-axis component.
[in]	d_z	Direction \( z \)-axis component.

Template Parameters

T	Type of the scalar coefficients.

Note: This constructor is only available for 3D rays.

◆ Ray() [7/7]

template<typename Real, Integer N>

template<typename OtherReal>

AABBtree::Ray< Real, N >::Ray ( Ray< OtherReal, N > const & r )

inlineexplicit

Copy constructor for a ray given another ray with a different scalar type.

Parameters

[in] r Ray to copy.

Template Parameters

OtherReal Type of the scalar coefficients of the ray to copy.

Member Function Documentation

◆ cast()

template<typename Real, Integer N>

template<typename NewReal>

Ray< NewReal, N > AABBtree::Ray< Real, N >::cast ( ) const

inline

Cast the current object to a new scalar type.

Template Parameters

NewReal the new scalar type

Note: If the new real type is equal to the current scalar type currently used, then this function returns a const reference to the current object.

◆ contains()

template<typename Real, Integer N>

bool AABBtree::Ray< Real, N >::contains	(	Point const &	p,
		Real	tol = DUMMY_TOL ) const

inline

Check if the point is inside the ray.

Parameters

[in]	p	Point to check.
[in]	tol	Tolerance to use for the containment.

Returns: True if the point is inside the ray, false otherwise.

◆ direction() [1/2]

template<typename Real, Integer N>

Vector & AABBtree::Ray< Real, N >::direction ( )

inline

Get the reference to the ray direction.

Returns: The reference to the ray direction.

◆ direction() [2/2]

template<typename Real, Integer N>

Vector const & AABBtree::Ray< Real, N >::direction ( ) const

inline

Get the const reference to the ray direction.

Returns: The const reference to the ray direction.

◆ distance() [1/2]

template<typename Real, Integer N>

Real AABBtree::Ray< Real, N >::distance	(	Point const &	p,
		Point &	c,
		Real	tol = DUMMY_TOL ) const

inline

Compute the distance between the current ray a given point, returning a point at the given distance.

Parameters

[in]	p	Point to compute the distance to.
[out]	c	Closest point on the ray.
[in]	tol	Tolerance to use for the intersection.

Returns: The distance between the ray and the point.

◆ distance() [2/2]

template<typename Real, Integer N>

Real AABBtree::Ray< Real, N >::distance	(	Point const &	p,
		Real	tol = DUMMY_TOL ) const

inline

Compute the distance between the current ray a given point.

Parameters

[in]	p	Point to compute the distance to.
[in]	tol	Tolerance to use for the intersection.

Returns: The distance between the ray and the point.

◆ exterior_distance() [1/2]

template<typename Real, Integer N>

Real AABBtree::Ray< Real, N >::exterior_distance	(	Box< Real, N > const &	b,
		Point &	p1,
		Point &	p2,
		Real	tol = DUMMY_TOL ) const

inline

Compute the exterior (or maximum) distance between the current ray a given box, and return two points at the maximum distance.

Parameters

[in]	b	Box to compute the distance to.
[out]	p1	First point at the maximum distance (on the current ray).
[out]	p2	Second point at the maximum distance (on the box).
[in]	tol	Tolerance to use for the distance computation.

Returns: The distance between the ray and the box.

Note: The distance is positive if the ray and the box do not intersect, zero otherwise.

◆ exterior_distance() [2/2]

template<typename Real, Integer N>

Real AABBtree::Ray< Real, N >::exterior_distance	(	Box< Real, N > const &	b,
		Real	tol = DUMMY_TOL ) const

inline

Compute the exterior (or maximum) distance between the current ray a given box.

Parameters

[in]	b	Box to compute the distance to.
[in]	tol	Tolerance to use for the distance computation.

Returns: The distance between the ray and the box.

Note: The distance is positive if the ray and the box do not intersect, zero otherwise.

◆ interior_distance() [1/2]

template<typename Real, Integer N>

Real AABBtree::Ray< Real, N >::interior_distance	(	Box< Real, N > const &	b,
		Point &	p1,
		Point &	p2,
		Real	tol = DUMMY_TOL ) const

inline

Compute the interior (or minimum) distance between the current ray a given box, returning two points at the minimum distance.

Parameters

[in]	b	Box to compute the distance to.
[out]	p1	First point at the minimum distance (on the current ray).
[out]	p2	Second point at the minimum distance (on the box).
[in]	tol	Tolerance to use for the distance computation.

Returns: The distance between the ray and the box.

Note: The distance is positive if the ray and the box do not intersect, zero otherwise.

◆ interior_distance() [2/2]

template<typename Real, Integer N>

Real AABBtree::Ray< Real, N >::interior_distance	(	Box< Real, N > const &	b,
		Real	tol = DUMMY_TOL ) const

inline

Compute the interior (or minimum) distance between the current ray a given box.

Parameters

[in]	b	Box to compute the distance to.
[in]	tol	Tolerance to use for the distance computation.

Returns: The distance between the ray and the box.

Note: The distance is positive if the ray and the box do not intersect, zero otherwise.

◆ intersect()

template<typename Real, Integer N>

bool AABBtree::Ray< Real, N >::intersect	(	Box< Real, N > const &	b,
		Point &	c,
		Point &	f,
		Real	tol = DUMMY_TOL ) const

inline

Check if the current ray intersects a given axis-aligned box.

Parameters

[in]	b	Box to check.
[out]	c	Closest intersection point.
[out]	f	Farthest intersection point.
[in]	tol	Tolerance to use for the intersection.

Returns: True if the current ray intersects the given box, false otherwise.

◆ intersects()

template<typename Real, Integer N>

bool AABBtree::Ray< Real, N >::intersects	(	Box< Real, N > const &	b,
		Real	tol = DUMMY_TOL ) const

inline

Check if the current ray intersects a given axis-aligned box.

Parameters

[in]	b	Box to check.
[in]	tol	Tolerance to use for the intersection.

Returns: True if the current ray intersects the given box, false otherwise.

◆ is_approx()

template<typename Real, Integer N>

bool AABBtree::Ray< Real, N >::is_approx	(	Ray< Real, N > const &	r,
		Real const	tol = DUMMY_TOL ) const

inline

Check if the current ray is approximately equal to another ray.

Parameters

[in]	r	Ray to compare with.
[in]	tol	Tolerance to use for the comparison.

◆ normalize()

template<typename Real, Integer N>

Ray & AABBtree::Ray< Real, N >::normalize ( )

inline

Normalize the direction of the ray.

Returns: A reference to the current ray.

◆ normalized()

template<typename Real, Integer N>

Ray AABBtree::Ray< Real, N >::normalized ( ) const

inline

Normalize the direction of the ray.

Returns: A copy of the current normalized ray.

◆ origin() [1/2]

template<typename Real, Integer N>

Point & AABBtree::Ray< Real, N >::origin ( )

inline

Get the reference to the ray origin.

Returns: The reference to the ray origin.

◆ origin() [2/2]

template<typename Real, Integer N>

Point const & AABBtree::Ray< Real, N >::origin ( ) const

inline

Get the const reference to the ray origin.

Returns: The const reference to the ray origin.

◆ print()

template<typename Real, Integer N>

void AABBtree::Ray< Real, N >::print ( std::ostream & os ) const

inline

Print the ray info to an output stream.

Parameters

[in] os Output stream to print the ray info to.

◆ squared_distance() [1/2]

template<typename Real, Integer N>

Real AABBtree::Ray< Real, N >::squared_distance	(	Point const &	p,
		Point &	c,
		Real	tol = DUMMY_TOL ) const

inline

Compute the squared distance between the current ray a given point, returning a point at the given distance.

Parameters

[in]	p	Point to compute the distance to.
[out]	c	Closest point on the ray.
[in]	tol	Tolerance to use for the intersection.

Returns: The squared distance between the ray and the point.

◆ squared_distance() [2/2]

template<typename Real, Integer N>

Real AABBtree::Ray< Real, N >::squared_distance	(	Point const &	p,
		Real	tol = DUMMY_TOL ) const

inline

Compute the squared distance between the current ray a given point.

Parameters

[in]	p	Point to compute the squared distance to.
[in]	tol	Tolerance to use for the intersection.

Returns: The squared distance between the ray and the point.

◆ squared_exterior_distance() [1/2]

template<typename Real, Integer N>

Real AABBtree::Ray< Real, N >::squared_exterior_distance	(	Box< Real, N > const &	b,
		Point &	p1,
		Point &	p2,
		Real	tol = DUMMY_TOL ) const

inline

Compute the squared exterior (or maximum) distance between the current ray a given box, returning two points at the maximum distance.

Parameters

[in]	b	Box to compute the squared distance to.
[out]	p1	First point at the maximum distance (on the current ray).
[out]	p2	Second point at the maximum distance (on the box).
[in]	tol	Tolerance to use for the distance computation.

Returns: The squared distance between the ray and the box.

◆ squared_exterior_distance() [2/2]

template<typename Real, Integer N>

Real AABBtree::Ray< Real, N >::squared_exterior_distance	(	Box< Real, N > const &	b,
		Real	tol = DUMMY_TOL ) const

inline

Compute the squared exterior (or maximum) distance between the current ray a given box.

Parameters

[in]	b	Box to compute the squared distance to.
[in]	tol	Tolerance to use for the distance computation.

Returns: The squared distance between the ray and the box.

Note: The squared distance is positive if one box is not contained in the other, zero otherwise.

◆ squared_interior_distance() [1/2]

template<typename Real, Integer N>

Real AABBtree::Ray< Real, N >::squared_interior_distance	(	Box< Real, N > const &	b,
		Point &	p1,
		Point &	p2,
		Real	tol = DUMMY_TOL ) const

inline

Compute the squared interior (or minimum) distance between the current ray a given box, returning two points at the minimum distance.

Parameters

[in]	b	Box to compute the squared distance to.
[out]	p1	First point at the minimum distance (on the current ray).
[out]	p2	Second point at the minimum distance (on the box).
[in]	tol	Tolerance to use for the distance computation.

Returns: The squared distance between the ray and the box.

Note: The squared distance is positive if the ray and the box do not intersect, zero otherwise.

◆ squared_interior_distance() [2/2]

template<typename Real, Integer N>

Real AABBtree::Ray< Real, N >::squared_interior_distance	(	Box< Real, N > const &	b,
		Real	tol = DUMMY_TOL ) const

inline

Compute the squared interior (or minimum) distance between the current ray a given box.

Parameters

[in]	b	Box to compute the squared distance to.
[in]	tol	Tolerance to use for the distance computation.

Returns: The squared distance between the ray and the box.

Note: The squared distance is positive if the ray and the box do not intersect, zero otherwise.

◆ transform()

template<typename Real, Integer N>

template<typename Transform>

Ray & AABBtree::Ray< Real, N >::transform ( Transform const & t )

inline

Transform the current ray by a given vector.

Parameters

[in] t Transformation to apply to the ray.

Returns: A reference to the current ray.

Template Parameters

Transform Type of the transformation.

◆ transformed()

template<typename Real, Integer N>

template<typename Transform>

Ray AABBtree::Ray< Real, N >::transformed ( Transform const & t ) const

inline

Transform the current ray by a given vector.

Parameters

[in] t Transformation to apply to the ray.

Returns: A copy of the current transformed ray.

Template Parameters

Transform Type of the transformation.

◆ translate()

template<typename Real, Integer N>

Ray & AABBtree::Ray< Real, N >::translate ( Vector const & t )

inline

Translate the current ray by a given vector.

Parameters

[in] t Vector to translate the ray by.

Returns: A reference to the current ray.

◆ translated()

template<typename Real, Integer N>

Ray AABBtree::Ray< Real, N >::translated ( Vector const & t ) const

inline

Translate the current ray by a given vector.

Parameters

[in] t Vector to translate the ray by.

Returns: A copy of the current translated ray.

Member Data Documentation

◆ DUMMY_TOL

template<typename Real, Integer N>

Real AABBtree::Ray< Real, N >::DUMMY_TOL {EPS*static_cast<Real>(100.0)}

staticconstexprprivate

Default tolerance for the scalar type

◆ EPS

template<typename Real, Integer N>

Real AABBtree::Ray< Real, N >::EPS {std::numeric_limits<Real>::epsilon()}

staticconstexprprivate

Machine epsilon for the scalar type.

◆ INF

template<typename Real, Integer N>

Real AABBtree::Ray< Real, N >::INF {std::numeric_limits<Real>::infinity()}

staticconstexprprivate

Infinity value for the scalar type.

◆ m_direction

template<typename Real, Integer N>

Vector AABBtree::Ray< Real, N >::m_direction

private

Direction vector of the ray (not necessarily normalized).

◆ m_origin

template<typename Real, Integer N>

Point AABBtree::Ray< Real, N >::m_origin

private

Origin point of the ray.

The documentation for this class was generated from the following files:

include/AABBtree/Box.hxx
include/AABBtree/Ray.hxx

Public Member Functions

Private Types

Private Attributes

Static Private Attributes

Detailed Description

Member Typedef Documentation

◆ Point

◆ Vector

Constructor & Destructor Documentation

◆ ~Ray()

◆ Ray() [1/7]

◆ Ray() [2/7]

◆ Ray() [3/7]

◆ Ray() [4/7]

◆ Ray() [5/7]

◆ Ray() [6/7]

◆ Ray() [7/7]

Member Function Documentation

◆ cast()

◆ contains()

◆ direction() [1/2]

◆ direction() [2/2]

◆ distance() [1/2]

◆ distance() [2/2]

◆ exterior_distance() [1/2]

◆ exterior_distance() [2/2]

◆ interior_distance() [1/2]

◆ interior_distance() [2/2]

◆ intersect()

◆ intersects()

◆ is_approx()

◆ normalize()

◆ normalized()

◆ origin() [1/2]

◆ origin() [2/2]

◆ print()

◆ squared_distance() [1/2]

◆ squared_distance() [2/2]

◆ squared_exterior_distance() [1/2]

◆ squared_exterior_distance() [2/2]

◆ squared_interior_distance() [1/2]

◆ squared_interior_distance() [2/2]

◆ transform()

◆ transformed()

◆ translate()

◆ translated()

Member Data Documentation

◆ DUMMY_TOL

◆ EPS

◆ INF

◆ m_direction

◆ m_origin