AABBtree::Box< Real, N > Class Template Reference

A class representing an axis-aligned bounding box (AABB) in N-dimensional space. More...

#include <Box.hxx>

Public Types
enum class	Side : Integer { LEFT = -1 , INSIDE = 0 , RIGHT = +1 }

Public Member Functions
	~Box ()=default
	Box ()
	Box (Box const &b)
	Box (Point const &t_min, Point const &t_max)
	Box (Point const &p)
template<typename = std::enable_if<N == 1>>
	Box (Real const x_min, Real const x_max)
template<typename = std::enable_if<N == 2>>
	Box (Real const x_min, Real const y_min, Real const x_max, Real const y_max)
template<typename = std::enable_if<N == 3>>
	Box (Real const x_min, Real const y_min, Real const z_min, Real const x_max, Real const y_max, Real const z_max)
template<typename OtherReal>
	Box (Box< OtherReal, N > const &b)
Box &	operator= (Box const &b)=default
template<typename NewReal>
Box< NewReal, N >	cast () const
Point const &	min () const
Point &	min ()
Point const &	max () const
Point &	max ()
void	reorder ()
bool	is_empty () const
bool	is_approx (Box const &b, Real const tol) const
bool	is_degenerate (Real const tol) const
Integer	longest_axis () const
Integer	longest_axis (Real &max_length, Real &mid_point) const
void	sort_axes_length (Vector &sizes, Eigen::Vector< Integer, N > &ipos) const
Point	baricenter () const
Real	baricenter (Integer i) const
Real	volume () const
Real	surface () const
Vector	diagonal () const
void	set_degenerate (Point const &p)
void	set_empty ()
bool	intersects (Box const &b) const
bool	intersect (Box const &b_in, Box &b_out) const
Box	merged (Box const &b) const
Box &	translate (Vector const &t)
Box	translated (Vector const &t) const
template<typename Transform>
Box	transformed (Transform const &t) const
template<typename Transform>
Box &	transform (Transform const &t)
Side	which_side (Real const x, Real const tol, Integer const dim) const
bool	contains (Point const &p) const
bool	intersects (Point const &p) const
bool	contains (Box const &b) const
template<typename Derived>
Box &	extend (Point const &p)
Box &	extend (Box const &b)
Real	squared_interior_distance (Point const &p) const
Real	squared_interior_distance (Point const &p, Point &c) const
Real	interior_distance (Point const &p) const
Real	interior_distance (Point const &p, Point &c) const
Real	squared_exterior_distance (Point const &p) const
Real	squared_exterior_distance (Point const &p, Point &f) const
Real	exterior_distance (Point const &p) const
Real	exterior_distance (Point const &p, Point &f) const
Real	squared_interior_distance (Box const &b) const
Real	squared_interior_distance (Box const &b, Point &p1, Point &p2) const
Real	interior_distance (Box const &b) const
Real	interior_distance (Box const &b, Point &p1, Point &p2) const
Real	squared_exterior_distance (Box const &b) const
Real	squared_exterior_distance (Box const &b, Point &p1, Point &p2) const
Real	exterior_distance (Box const &b) const
Real	exterior_distance (Box const &b, Point &p1, Point &p2) const
bool	intersects (Ray< Real, N > const &r, Real tol=DUMMY_TOL) const
bool	intersect (Ray< Real, N > const &r, Point &c, Point &f, Real tol=DUMMY_TOL) const
Real	squared_interior_distance (Ray< Real, N > const &r, Real tol=DUMMY_TOL) const
Real	squared_interior_distance (Ray< Real, N > const &r, Point &p1, Point &p2, Real tol=DUMMY_TOL) const
Real	interior_distance (Ray< Real, N > const &r, Real tol=DUMMY_TOL) const
Real	interior_distance (Ray< Real, N > const &r, Point &p1, Point &p2, Real tol=DUMMY_TOL) const
Real	squared_exterior_distance (Ray< Real, N > const &r, Real tol=DUMMY_TOL) const
Real	squared_exterior_distance (Ray< Real, N > const &r, Point &p1, Point &p2, Real tol=DUMMY_TOL) const
Real	exterior_distance (Ray< Real, N > const &r, Real tol=DUMMY_TOL) const
Real	exterior_distance (Ray< Real, N > const &r, 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>
using	BoxUniquePtr = AABBtree::BoxUniquePtr<Real, N>
using	BoxUniquePtrList = AABBtree::BoxUniquePtrList<Real, N>

Private Attributes
Point	m_min
Point	m_max

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::Box< Real, N >

This class represents an axis-aligned bounding box (AABB) defined by two opposite corners:

• Minimum corner (lower bounds in all dimensions);
• Maximum corner (upper bounds in all dimensions).

The Box class provides various geometric operations including:

• Intersection and containment tests;
• Distance calculations;
• Transformation operations;
• Volume and surface area computations.

Template Parameters

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

Note

The box is considered empty if any component of the minimum corner is greater than the corresponding component of the maximum corner.

All methods are thread-safe unless explicitly noted otherwise.

Member Typedef Documentation

BoxUniquePtr

template<typename Real, Integer N>

using AABBtree::Box< Real, N >::BoxUniquePtr = AABBtree::BoxUniquePtr<Real, N>

private

BoxUniquePtrList

template<typename Real, Integer N>

using AABBtree::Box< Real, N >::BoxUniquePtrList = AABBtree::BoxUniquePtrList<Real, N>

private

Point

template<typename Real, Integer N>

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

private

Vector

template<typename Real, Integer N>

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

private

Member Enumeration Documentation

Side

template<typename Real, Integer N>

enum class AABBtree::Box::Side : Integer

strong

Enumeration for relative position with respect to the box.

Enumerator
LEFT	-1
INSIDE	0
RIGHT	+1

Constructor & Destructor Documentation

~Box()

template<typename Real, Integer N>

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

default

Class destructor for the axis-aligned box.

Box() [1/8]

template<typename Real, Integer N>

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

inline

Default constructor creating an empty box whether the minimal and maximal corners are set to the maximum and minimum representable values, respectively.

Box() [2/8]

template<typename Real, Integer N>

AABBtree::Box< Real, N >::Box ( Box< Real, N > const & b )

inline

Copy constructor for a axis-aligned box given another box.

Parameters

[in]

b

Box to copy.

Box() [3/8]

template<typename Real, Integer N>

AABBtree::Box< Real, N >::Box ( Point const & t_min, Point const & t_max )

inline

Class constructor for a axis-aligned box given the minimal and maximal corners.

Parameters

[in]	t_min	Minimal corner of the box.
[in]	t_max	Maximal corner of the box.

Warning

If the reordering is not performed, and the minimal corner is greater than the maximal corner in any dimension, undefined behavior may occur.

Box() [4/8]

template<typename Real, Integer N>

AABBtree::Box< Real, N >::Box ( Point const & p )

inline

Class constructor for a axis-aligned box containing a single point.

Parameters

[in]

p

Point to be contained in the box.

Box() [5/8]

template<typename Real, Integer N>

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

AABBtree::Box< Real, N >::Box ( Real const x_min, Real const x_max )

inline

Class constructor for the 1D axis-aligned bounding box.

Parameters

[in]	x_min	Minimal \( x \)-axis corner of the box.
[in]	x_max	Maximal \( x \)-axis corner of the box.

Template Parameters

T	Type of the scalar coefficients.

Note

This constructor is only available for 1D boxes.

Box() [6/8]

template<typename Real, Integer N>

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

AABBtree::Box< Real, N >::Box ( Real const x_min, Real const y_min, Real const x_max, Real const y_max )

inline

Class constructor for the 2D axis-aligned bounding box.

Parameters

[in]	x_min	Minimal \( x \)-axis corner of the box.
[in]	y_min	Minimal \( y \)-axis corner of the box.
[in]	x_max	Maximal \( x \)-axis corner of the box.
[in]	y_max	Maximal \( y \)-axis corner of the box.

Template Parameters

T	Type of the scalar coefficients.

Note

This constructor is only available for 2D boxes.

Box() [7/8]

template<typename Real, Integer N>

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

AABBtree::Box< Real, N >::Box ( Real const x_min, Real const y_min, Real const z_min, Real const x_max, Real const y_max, Real const z_max )

inline

Class constructor for the 3D axis-aligned bounding box.

Parameters

[in]	x_min	Minimal \( x \)-axis corner of the box.
[in]	y_min	Minimal \( y \)-axis corner of the box.
[in]	z_min	Minimal \( z \)-axis corner of the box.
[in]	x_max	Maximal \( x \)-axis corner of the box.
[in]	y_max	Maximal \( y \)-axis corner of the box.
[in]	z_max	Maximal \( z \)-axis corner of the box.

Template Parameters

T	Type of the scalar coefficients.

Note

This constructor is only available for 3D boxes.

Box() [8/8]

template<typename Real, Integer N>

template<typename OtherReal>

AABBtree::Box< Real, N >::Box ( Box< OtherReal, N > const & b )

inlineexplicit

Copy constructor for a axis-aligned box given another box with a different scalar type.

Parameters

[in]

b

Box to copy.

Template Parameters

OtherReal

Type of the scalar coefficients of the box to copy.

Member Function Documentation

baricenter() [1/2]

template<typename Real, Integer N>

Point AABBtree::Box< Real, N >::baricenter ( ) const

inline

Compute the barycenter of the box.

Returns

Point at the center of the box.

baricenter() [2/2]

template<typename Real, Integer N>

Real AABBtree::Box< Real, N >::baricenter ( Integer i ) const

inline

Compute the barycenter coordinate along a specific dimension.

Parameters

[in]

i

Dimension index.

Returns

Barycenter coordinate along the i-thdimension.

cast()

template<typename Real, Integer N>

template<typename NewReal>

Box< NewReal, N > AABBtree::Box< 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() [1/2]

template<typename Real, Integer N>

bool AABBtree::Box< Real, N >::contains ( Box< Real, N > const & b ) const

inline

Check if this box completely contains another box.

Parameters

[in]

b

Box to check.

Returns

True if the box is entirely within this box, false otherwise.

contains() [2/2]

template<typename Real, Integer N>

bool AABBtree::Box< Real, N >::contains ( Point const & p ) const

inline

Check if a point is inside the box.

Parameters

[in]

p

Point to check.

Returns

True if point is inside or on boundary, false otherwise.

diagonal()

template<typename Real, Integer N>

Vector AABBtree::Box< Real, N >::diagonal ( ) const

inline

Compute the diagonal vector of the box.

Returns

Vector from minimum to maximal corner.

Note

For the length of the diagonal, use diagonal().norm() .

extend() [1/2]

template<typename Real, Integer N>

Box & AABBtree::Box< Real, N >::extend ( Box< Real, N > const & b )

inline

Extend this box to contain another box.

Parameters

[in]

b

Box to include.

Returns

Reference to this box after extension.

Note

Merging with an empty box may result in a box bigger than *this .

extend() [2/2]

template<typename Real, Integer N>

template<typename Derived>

Box & AABBtree::Box< Real, N >::extend ( Point const & p )

inline

Extend this box to contain a point.

Parameters

[in]

p

Point to include.

Returns

Reference to this box after extension.

exterior_distance() [1/6]

template<typename Real, Integer N>

Real AABBtree::Box< Real, N >::exterior_distance ( Box< Real, N > const & b ) const

inline

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

Parameters

[in]

b

Box to compute the distance to.

Returns

The distance between the boxes.

Note

The distance is positive if the boxes do not intersect, zero otherwise.

exterior_distance() [2/6]

template<typename Real, Integer N>

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

inline

Compute the exterior (or maximum) distance between the current box 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.
[out]	p2	Second point at the maximum distance.

Returns

The distance between the boxes.

Note

The distance is positive if the boxes do not intersect, zero otherwise.

exterior_distance() [3/6]

template<typename Real, Integer N>

Real AABBtree::Box< Real, N >::exterior_distance ( Point const & p ) const

inline

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

Parameters

[in]

p

Point to compute the distance to.

Returns

The distance between the box and the point.

Note

The distance is positive if the point is outside the box, zero otherwise.

exterior_distance() [4/6]

template<typename Real, Integer N>

Real AABBtree::Box< Real, N >::exterior_distance ( Point const & p, Point & f ) const

inline

Compute the exterior (or maximum) distance between the current box a given point, returning a point at the given distance.

Parameters

[in]	p	Point to compute the distance to.
[out]	f	Farthest point to the box.

Returns

The distance between the box and the point.

Note

The returned value is positive if the point is outside the box, zero otherwise.

exterior_distance() [5/6]

template<typename Real, Integer N>

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

inline

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

Parameters

[in]	r	Ray to compute the distance to.
[out]	p1	First point at the maximum distance (on the current box).
[out]	p2	Second point at the maximum distance (on the ray).
[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() [6/6]

template<typename Real, Integer N>

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

inline

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

Parameters

[in]	r	Ray 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() [1/6]

template<typename Real, Integer N>

Real AABBtree::Box< Real, N >::interior_distance ( Box< Real, N > const & b ) const

inline

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

Parameters

[in]

b

Box to compute the distance to.

Returns

The distance between the boxes.

Note

The distance is positive if the boxes do not intersect, zero otherwise.

interior_distance() [2/6]

template<typename Real, Integer N>

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

inline

Compute the interior (or minimum) distance between the current box 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.
[out]	p2	Second point at the minimum distance.

Returns

The distance between the boxes.

Note

The distance is positive if the boxes do not intersect, zero otherwise.

interior_distance() [3/6]

template<typename Real, Integer N>

Real AABBtree::Box< Real, N >::interior_distance ( Point const & p ) const

inline

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

Parameters

[in]

p

Point to compute the distance to.

Returns

The distance between the box and the point.

Note

The distance is positive if the point is outside the box, zero otherwise.

interior_distance() [4/6]

template<typename Real, Integer N>

Real AABBtree::Box< Real, N >::interior_distance ( Point const & p, Point & c ) const

inline

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

Parameters

[in]	p	Point to compute the distance to.
[out]	c	Closest point to the box.

Returns

The distance between the box and the point.

Note

The returned value is positive if the point is outside the box, zero otherwise.

interior_distance() [5/6]

template<typename Real, Integer N>

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

inline

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

Parameters

[in]	r	Ray to compute the distance to.
[out]	p1	First point at the minimum distance (on the current box).
[out]	p2	Second point at the minimum distance (on the ray).
[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() [6/6]

template<typename Real, Integer N>

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

inline

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

Parameters

[in]	r	Ray 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() [1/2]

template<typename Real, Integer N>

bool AABBtree::Box< Real, N >::intersect ( Box< Real, N > const & b_in, Box< Real, N > & b_out ) const

inline

Compute the intersection of this box with another box.

Parameters

[in]	b_in	Box to intersect with.
[out]	b_out	Resulting intersection box.

Returns

True if intersection exists, false otherwise.

intersect() [2/2]

template<typename Real, Integer N>

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

inline

Check if the current box intersects a given ray.

Parameters

[in]	r	Ray 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 box intersects the given ray, false otherwise.

intersects() [1/3]

template<typename Real, Integer N>

bool AABBtree::Box< Real, N >::intersects ( Box< Real, N > const & b ) const

inline

Check if this box intersects with another box.

Parameters

[in]

b

Box to check for intersection.

Returns

True if boxes intersect, false otherwise.

intersects() [2/3]

template<typename Real, Integer N>

bool AABBtree::Box< Real, N >::intersects ( Point const & p ) const

inline

Check if a point intersects the box.

Parameters

[in]

p

Point to check.

Returns

True if point is inside or on boundary, false otherwise.

Note

Equivalent to contains() for points.

intersects() [3/3]

template<typename Real, Integer N>

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

inline

Check if the current box intersects a given ray.

Parameters

[in]	r	Ray to check.
[in]	tol	Tolerance to use for the intersection.

Returns

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

is_approx()

template<typename Real, Integer N>

bool AABBtree::Box< Real, N >::is_approx ( Box< Real, N > const & b, Real const tol ) const

inline

Check if this box is approximately equal to another box.

Parameters

[in]	b	Box to compare with.
[in]	tol	Tolerance for the comparison.

Returns

True if boxes are approximately equal within tolerance.

is_degenerate()

template<typename Real, Integer N>

bool AABBtree::Box< Real, N >::is_degenerate ( Real const tol ) const

inline

Check if the current box is degenrate, i.e., it has zero volume.

Parameters

[in]

tol

Tolerance to use for the comparison.

Returns

True if the box is degenerate, false otherwise.

is_empty()

template<typename Real, Integer N>

bool AABBtree::Box< Real, N >::is_empty ( ) const

inline

Check if the box is empty, i.e., the minimal corner is greater than the maximal corner in any dimension.

Returns

True if the box is empty, false otherwise.

longest_axis() [1/2]

template<typename Real, Integer N>

Integer AABBtree::Box< Real, N >::longest_axis ( ) const

inline

Find the longest axis of the box.

Returns

Index of the dimension with the largest extent.

longest_axis() [2/2]

template<typename Real, Integer N>

Integer AABBtree::Box< Real, N >::longest_axis ( Real & max_length, Real & mid_point ) const

inline

Find the longest axis and compute its length and midpoint.

Parameters

[out]	max_length	Length of the longest axis.
[out]	mid_point	Midpoint of the longest axis.

Returns

Index of the dimension with the largest extent.

max() [1/2]

template<typename Real, Integer N>

Point & AABBtree::Box< Real, N >::max ( )

inline

Get a non const reference to the maximal corner.

Returns

The maximal corner of the box.

max() [2/2]

template<typename Real, Integer N>

Point const & AABBtree::Box< Real, N >::max ( ) const

inline

Get the maximal corner.

Returns

The maximal corner of the box.

merged()

template<typename Real, Integer N>

Box AABBtree::Box< Real, N >::merged ( Box< Real, N > const & b ) const

inline

Compute the union of this box with another box.

Parameters

[in]

b

Box to merge with.

Returns

The smallest box containing both boxes.

min() [1/2]

template<typename Real, Integer N>

Point & AABBtree::Box< Real, N >::min ( )

inline

Get a non const reference to the minimal corner.

Returns

The minimal corner of the box.

min() [2/2]

template<typename Real, Integer N>

Point const & AABBtree::Box< Real, N >::min ( ) const

inline

Get the minimal corner.

Returns

The minimal corner of the box.

operator=()

template<typename Real, Integer N>

Box & AABBtree::Box< Real, N >::operator= ( Box< Real, N > const & b )

default

Assignment perator for a axis-aligned box given another box.

Parameters

[in]

b

Box to copy.

Returns

A reference to the current box.

print()

template<typename Real, Integer N>

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

inline

Print the box info to an output stream.

Parameters

[in]

os

Output stream to print the box info to.

reorder()

template<typename Real, Integer N>

void AABBtree::Box< Real, N >::reorder ( )

inline

Reorder the corners of the box such that the minimal corner is less than the maximal corner.

set_degenerate()

template<typename Real, Integer N>

void AABBtree::Box< Real, N >::set_degenerate ( Point const & p )

inline

Set the box to be degenerate (containing a single point).

Parameters

[in]

p

Point to set the box to.

set_empty()

template<typename Real, Integer N>

void AABBtree::Box< Real, N >::set_empty ( )

inline

Set the box to be empty.

sort_axes_length()

template<typename Real, Integer N>

void AABBtree::Box< Real, N >::sort_axes_length ( Vector & sizes, Eigen::Vector< Integer, N > & ipos ) const

inline

Sort axes by their lengths in descending order.

Parameters

[out]	sizes	Vector to store the sizes of each dimension.
[out]	ipos	Vector to store the sorted dimension indices.

squared_exterior_distance() [1/6]

template<typename Real, Integer N>

Real AABBtree::Box< Real, N >::squared_exterior_distance ( Box< Real, N > const & b ) const

inline

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

Parameters

[in]

b

Box to compute the squared distance to.

Returns

The squared distance between the boxes.

Note

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

squared_exterior_distance() [2/6]

template<typename Real, Integer N>

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

inline

Compute the squared exterior (or maximum) distance between the current box 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.
[out]	p2	Second point at the maximum distance.

Returns

The squared distance between the boxes.

squared_exterior_distance() [3/6]

template<typename Real, Integer N>

Real AABBtree::Box< Real, N >::squared_exterior_distance ( Point const & p ) const

inline

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

Parameters

[in]

p

Point to compute the squared distance to.

Returns

The squared distance between the box and the point.

Note

The returned value is positive if the point is outside the box, zero otherwise.

squared_exterior_distance() [4/6]

template<typename Real, Integer N>

Real AABBtree::Box< Real, N >::squared_exterior_distance ( Point const & p, Point & f ) const

inline

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

Parameters

[in]	p	Point to compute the squared distance to.
[out]	f	Farthest point to the box.

Returns

The squared distance between the box and the point.

Note

The returned value is positive if the point is outside the box, zero otherwise.

squared_exterior_distance() [5/6]

template<typename Real, Integer N>

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

inline

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

Parameters

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

Returns

The squared distance between the ray and the box.

squared_exterior_distance() [6/6]

template<typename Real, Integer N>

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

inline

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

Parameters

[in]	r	Ray 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() [1/6]

template<typename Real, Integer N>

Real AABBtree::Box< Real, N >::squared_interior_distance ( Box< Real, N > const & b ) const

inline

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

Parameters

[in]

b

Box to compute the squared distance to.

Returns

The squared distance between the boxes.

Note

The squared distance is positive if the boxes do not intersect, zero otherwise.

squared_interior_distance() [2/6]

template<typename Real, Integer N>

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

inline

Compute the squared interior (or minimum) distance between the current box 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.
[out]	p2	Second point at the minimum distance.

Returns

The squared distance between the boxes.

Note

The squared distance is positive if the boxes do not intersect, zero otherwise.

squared_interior_distance() [3/6]

template<typename Real, Integer N>

Real AABBtree::Box< Real, N >::squared_interior_distance ( Point const & p ) const

inline

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

Parameters

[in]

p

Point to compute the squared distance to.

Returns

The squared distance between the box and the point.

Note

The returned value is positive if the point is outside the box, zero otherwise.

squared_interior_distance() [4/6]

template<typename Real, Integer N>

Real AABBtree::Box< Real, N >::squared_interior_distance ( Point const & p, Point & c ) const

inline

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

Parameters

[in]	p	Point to compute the squared distance to.
[out]	c	Closest point to the box.

Returns

The squared distance between the box and the point.

Note

The returned value is positive if the point is outside the box, zero otherwise.

squared_interior_distance() [5/6]

template<typename Real, Integer N>

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

inline

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

Parameters

[in]	r	Ray to compute the squared distance to.
[out]	p1	First point at the minimum distance (on the current box).
[out]	p2	Second point at the minimum distance (on the ray).
[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() [6/6]

template<typename Real, Integer N>

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

inline

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

Parameters

[in]	r	Ray 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.

surface()

template<typename Real, Integer N>

Real AABBtree::Box< Real, N >::surface ( ) const

inline

Compute the surface area of the box.

Returns

Sum of areas of all faces.

transform()

template<typename Real, Integer N>

template<typename Transform>

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

inline

Transform this box in-place.

Parameters

[in]

t

Transformation to apply.

Returns

Reference to this box after transformation.

Template Parameters

Transform

Type of the transformation.

Note

The resulting box may be larger than the original due to axis-alignment.

transformed()

template<typename Real, Integer N>

template<typename Transform>

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

inline

Create a transformed copy of this box.

Parameters

[in]

t

Transformation to apply.

Returns

New transformed box.

Template Parameters

Transform

Type of the transformation.

Note

The resulting box may be larger than the original due to axis-alignment.

translate()

template<typename Real, Integer N>

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

inline

Translate the box by a given vector.

Parameters

[in]

t

Translation vector.

Returns

Reference to this box after translation.

translated()

template<typename Real, Integer N>

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

inline

Create a translated copy of this box.

Parameters

[in]

t

Translation vector.

Returns

New translated box.

volume()

template<typename Real, Integer N>

Real AABBtree::Box< Real, N >::volume ( ) const

inline

Compute the volume of the box.

Returns

Product of sizes in all dimensions.

which_side()

template<typename Real, Integer N>

Side AABBtree::Box< Real, N >::which_side ( Real const x, Real const tol, Integer const dim ) const

inline

Classify a coordinate relative to the box in a specific dimension.

Parameters

[in]	x	Coordinate to classify.
[in]	tol	Tolerance for classification.
[in]	dim	Dimension to consider.

Returns

Side::LEFT if max[dim] < x+tol, Side::RIGHT if x-tol < min[dim], Side::INSIDE otherwise.

Member Data Documentation

DUMMY_TOL

template<typename Real, Integer N>

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

staticconstexprprivate

Machine epsilon for the scalar type.

INF

template<typename Real, Integer N>

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

staticconstexprprivate

Infinity value for the scalar type.

m_max

template<typename Real, Integer N>

Point AABBtree::Box< Real, N >::m_max

private

Maximal corner of the box (upper bounds in all dimensions).

m_min

template<typename Real, Integer N>

Point AABBtree::Box< Real, N >::m_min

private

Minimal corner of the box (lower bounds in all dimensions).

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

• include/AABBtree.hh
• include/AABBtree/Box.hxx