An axis-aligned N-dimensional bounding box class template of fixed dimension with supporting functions. More...

Classes
struct	mi::math::Bbox_struct<T, DIM>
	Storage class for an axis-aligned N-dimensional bounding box class template of fixed dimension. More...

class	mi::math::Bbox<T, DIM>
	Axis-aligned N-dimensional bounding box class template of fixed dimension. More...

Typedefs
typedef math::Vector<T, DIM>	mi::math::Bbox<T, DIM>::Vector
	Corresponding vector type. More...

typedef Bbox_struct<T, DIM>	mi::math::Bbox<T, DIM>::Pod_type
	POD class corresponding to this bounding box. More...

typedef Vector	mi::math::Bbox<T, DIM>::value_type
	Coordinate type. More...

typedef Size	mi::math::Bbox<T, DIM>::size_type
	Size type, unsigned. More...

typedef Difference	mi::math::Bbox<T, DIM>::difference_type
	Difference type, signed. More...

typedef Vector *	mi::math::Bbox<T, DIM>::pointer
	Mutable pointer to vector. More...

typedef const Vector *	mi::math::Bbox<T, DIM>::const_pointer
	Const pointer to vector. More...

typedef Vector &	mi::math::Bbox<T, DIM>::reference
	Mutable reference to vector. More...

typedef const Vector &	mi::math::Bbox<T, DIM>::const_reference
	Const reference to vector. More...

Enumerations
enum	mi::math::Bbox<T, DIM>::Uninitialized_tag { mi::math::Bbox<T, DIM>::UNINITIALIZED_TAG }
	Enum type used to tag a special constructor that does not initialize the elements of the constructed bounding box. More...

Functions
static Size	mi::math::Bbox<T, DIM>::size ()
	Constant size of the bounding box. More...

static Size	mi::math::Bbox<T, DIM>::max_size ()
	Constant maximum size of the bounding box. More...

void	mi::math::Bbox<T, DIM>::clear ()
	Reinitializes this bounding box to the empty space. More...

	mi::math::Bbox<T, DIM>::Bbox ()
	Bounding box initialized to the empty space, see also the clear function. More...

	mi::math::Bbox<T, DIM>::Bbox (Uninitialized_tag)
	Bounding box with its elements not initialized. More...

	mi::math::Bbox<T, DIM>::Bbox (const Bbox<T, DIM> &other)=default
	Default copy constructor. More...

	mi::math::Bbox<T, DIM>::Bbox (const Bbox_struct<T, DIM> &bbox_struct)
	Bounding box initialized from corresponding POD type. More...

	mi::math::Bbox<T, DIM>::Bbox (const Vector &point)
	Bounding box initialized to a single `point`. More...

	mi::math::Bbox<T, DIM>::Bbox (const Vector &nmin, const Vector &nmax)
	Bounding box initialized to the new extreme corner vectors, `nmin` and `nmax`. More...

	mi::math::Bbox<T, DIM>::Bbox (T min_x, T max_x)
	1D bounding box (interval) initialized to the new extreme corner vectors, (min_x) and (max_x). More...

	mi::math::Bbox<T, DIM>::Bbox (T min_x, T min_y, T max_x, T max_y)
	2D bounding box (interval) initialized to the new extreme corner vectors, (min_x,min_y) and (max_x,max_y). More...

	mi::math::Bbox<T, DIM>::Bbox (T min_x, T min_y, T min_z, T max_x, T max_y, T max_z)
	3D bounding box (interval) initialized to the new extreme corner vectors, (min_x,min_y,min_z) and (max_x,max_y,max_z). More...

template<typename InputIterator>
	mi::math::Bbox<T, DIM>::Bbox (InputIterator first, InputIterator last)
	Constructs a bounding box from a range [`first`, `last`) of items. More...

template<typename T2>
	mi::math::Bbox<T, DIM>::Bbox (const Bbox<T2, DIM> &other)
	Template constructor that allows explicit conversions from other bounding boxes with assignment compatible element value type. More...

template<typename T2>
	mi::math::Bbox<T, DIM>::Bbox (const Bbox_struct<T2, DIM> &other)
	Template constructor that allows explicit conversions from other POD type with assignment compatible element value type. More...

Bbox &	mi::math::Bbox<T, DIM>::operator= (const Bbox &other)
	Assignment. More...

Bbox &	mi::math::Bbox<T, DIM>::operator= (const Bbox_struct<T, DIM> &other)
	Assignment from corresponding POD type. More...

	mi::math::Bbox<T, DIM>::operator Bbox_struct<T, DIM> () const
	Conversion to corresponding POD type. More...

Vector *	mi::math::Bbox<T, DIM>::begin ()
	Returns the pointer to the first vector, `min`. More...

const Vector *	mi::math::Bbox<T, DIM>::begin () const
	Returns the pointer to the first vector, `min`. More...

Vector *	mi::math::Bbox<T, DIM>::end ()
	Returns the past-the-end pointer. More...

const Vector *	mi::math::Bbox<T, DIM>::end () const
	Returns the past-the-end pointer. More...

Vector &	mi::math::Bbox<T, DIM>::operator[] (Size i)
	Returns the vector `min` for `i==0`, and the vector `max` for `i==1`. More...

const Vector &	mi::math::Bbox<T, DIM>::operator[] (Size i) const
	Returns the vector `min` for `i==0`, and the vector `max` for `i==1`. More...

bool	mi::math::Bbox<T, DIM>::empty () const
	Returns `true` if the box is empty. More...

Size	mi::math::Bbox<T, DIM>::rank () const
	Returns the rank of the bounding box. More...

bool	mi::math::Bbox<T, DIM>::is_point () const
	Returns `true` the bounding box is a single point. More...

bool	mi::math::Bbox<T, DIM>::is_line () const
	Returns `true` the bounding box is an axis-aligned line. More...

bool	mi::math::Bbox<T, DIM>::is_plane () const
	Returns `true` the bounding box is an axis-aligned plane. More...

bool	mi::math::Bbox<T, DIM>::is_volume () const
	Returns `true` the bounding box has a volume. More...

bool	mi::math::Bbox<T, DIM>::contains (const Vector &vec) const
	Returns `true` if the point is inside or on the boundary of the bounding box. More...

bool	mi::math::Bbox<T, DIM>::intersects (const Bbox &other) const
	Returns `true` if this bounding box and the `other` bounding box intersect in their interiors or on their boundaries. More...

void	mi::math::Bbox<T, DIM>::insert (const Bbox &other)
	Assigns the union of this bounding box and the `other` bounding box to this bounding box. More...

void	mi::math::Bbox<T, DIM>::insert (const Vector &point)
	Assigns the union of this bounding box and the `point` to this bounding box. More...

template<typename InputIterator>
void	mi::math::Bbox<T, DIM>::insert (InputIterator first, InputIterator last)
	Inserts a range [`first`,`last`) of items into this bounding box. More...

Bbox	mi::math::Bbox<T, DIM>::add_motionbox (const Bbox &vbox, T t) const
	Returns the translation of this bounding box by vectors that are inside the scaled bounding box of vectors, i.e., `t*vbox`. More...

void	mi::math::Bbox<T, DIM>::push_back (const Bbox &other)
	Assigns the union of this bounding box and the `other` bounding box to this bounding box. More...

void	mi::math::Bbox<T, DIM>::robust_grow (T eps=T(1.0e-5f))
	Robustly grows the bounding box by a value computed automatically from the bounding box dimensions and location in space. More...

T	mi::math::Bbox<T, DIM>::volume () const
	Returns the volume of the bounding box. More...

T	mi::math::Bbox<T, DIM>::diagonal_length () const
	Returns the length of the diagonal. More...

Size	mi::math::Bbox<T, DIM>::largest_extent_index () const
	Returns the index of the dimension in which the bounding box has its largest extent, i.e., 0=x, 1=y, 2=z. More...

Vector	mi::math::Bbox<T, DIM>::center () const
	Returns the center point of the bounding box. More...

Vector	mi::math::Bbox<T, DIM>::extent () const
	Returns the size of the bounding box. More...

template<typename T , Size DIM>
Bbox<T, DIM>	mi::math::operator+ (const Bbox<T, DIM> &bbox, T value)
	Returns a bounding box that is the `bbox` increased by a constant `value` at each face, i.e., `value` is added to `bbox.max` and subtracted from `bbox.min`. More...

template<typename T , Size DIM>
Bbox<T, DIM>	mi::math::operator- (const Bbox<T, DIM> &bbox, T value)
	Returns a bounding box that is the `bbox` shrunk by a constant `value` at each face, i.e., `value` is subtracted from `bbox.max` and added to `bbox.min`. More...

template<typename T , Size DIM>
Bbox<T, DIM>	mi::math::operator* (const Bbox<T, DIM> &bbox, T factor)
	Returns a bounding box that is a version of `bbox` scaled by `factor`, i.e., `bbox.max` and `bbox.min` are multiplied by `factor`. More...

template<typename T , Size DIM>
Bbox<T, DIM>	mi::math::operator/ (const Bbox<T, DIM> &bbox, T divisor)
	Returns a bounding box that is a version of `bbox` divided by `divisor`, i.e., `bbox.max` and `bbox.min` are divided by `divisor`. More...

template<typename T , Size DIM>
Bbox<T, DIM> &	mi::math::operator+= (Bbox<T, DIM> &bbox, T value)
	Increases `bbox` by a constant `value` at each face, i.e., `value` is added to `bbox.max` and subtracted from `bbox.min`. More...

template<typename T , Size DIM>
Bbox<T, DIM> &	mi::math::operator-= (Bbox<T, DIM> &bbox, T value)
	Shrinks `bbox` by a constant `value` at each face, i.e., `value` is subtracted from `bbox.max` and added to `bbox.min`. More...

template<typename T , Size DIM>
Bbox<T, DIM> &	mi::math::operator*= (Bbox<T, DIM> &bbox, T factor)
	Scales `bbox` by `factor`, i.e., `bbox.max` and `bbox.min` are multiplied by `factor`. More...

template<typename T , Size DIM>
Bbox<T, DIM> &	mi::math::operator/= (Bbox<T, DIM> &bbox, T divisor)
	Divide `bbox` by `divisor`, i.e., `bbox.max` and `bbox.min` are divided by `divisor`. More...

template<typename T , Size DIM>
bool	mi::math::operator== (const Bbox<T, DIM> &lhs, const Bbox<T, DIM> &rhs)
	Returns `true` if `lhs` is elementwise equal to `rhs`. More...

template<typename T , Size DIM>
bool	mi::math::operator!= (const Bbox<T, DIM> &lhs, const Bbox<T, DIM> &rhs)
	Returns `true` if `lhs` is elementwise not equal to `rhs`. More...

template<typename T , Size DIM>
bool	mi::math::operator< (const Bbox<T, DIM> &lhs, const Bbox<T, DIM> &rhs)
	Returns `true` if `lhs` is lexicographically less than `rhs`. More...

template<typename T , Size DIM>
bool	mi::math::operator<= (const Bbox<T, DIM> &lhs, const Bbox<T, DIM> &rhs)
	Returns `true` if `lhs` is lexicographically less than or equal to `rhs`. More...

template<typename T , Size DIM>
bool	mi::math::operator> (const Bbox<T, DIM> &lhs, const Bbox<T, DIM> &rhs)
	Returns `true` if `lhs` is lexicographically greater than `rhs`. More...

template<typename T , Size DIM>
bool	mi::math::operator>= (const Bbox<T, DIM> &lhs, const Bbox<T, DIM> &rhs)
	Returns `true` if `lhs` is lexicographically greater than or equal to `rhs`. More...

template<typename T , Size DIM>
Bbox<T, DIM>	mi::math::lerp (const Bbox<T, DIM> &bbox1, const Bbox<T, DIM> &bbox2, T t)
	Returns the linear interpolation between `bbox1` and `bbox2`, i.e., it returns `(1-t) * bbox1 + t * bbox2`. More...

template<typename T , Size DIM>
Bbox<T, DIM>	mi::math::clip (const Bbox<T, DIM> &bbox1, const Bbox<T, DIM> &bbox2)
	Clip `bbox1` at `bbox2` and return the result. More...

template<typename TT , typename T>
Bbox<T, 3>	mi::math::transform_point (const Matrix<TT, 4, 4> &mat, const Bbox<T, 3> &bbox)
	Returns the 3D bounding box transformed by a matrix. More...

template<typename TT , typename T>
Bbox<T, 3>	mi::math::transform_vector (const Matrix<TT, 4, 4> &mat, const Bbox<T, 3> &bbox)
	Returns the 3D bounding box transformed by a matrix. More...

Variables
Vector_struct<T, DIM>	mi::math::Bbox_struct<T, DIM>::min
	Elementwise minimal bounding box corner. More...

Vector_struct<T, DIM>	mi::math::Bbox_struct<T, DIM>::max
	Elementwise maximal bounding box corner. More...

static const Size	mi::math::Bbox<T, DIM>::DIMENSION = DIM
	Constant dimension of the vectors. More...

static const Size	mi::math::Bbox<T, DIM>::SIZE = 2
	Constant size of the bounding box. More...

Vector	mi::math::Bbox<T, DIM>::min
	Elementwise minimal bounding box corner. More...

Vector	mi::math::Bbox<T, DIM>::max
	Elementwise maximal bounding box corner. More...

Detailed Description

An axis-aligned N-dimensional bounding box class template of fixed dimension with supporting functions.

Include File:: #include <mi/math/bbox.h>

Typedef Documentation

^◆ const_pointer

template<typename T , Size DIM>

typedef const Vector* mi::math::Bbox<T, DIM>::const_pointer

Const pointer to vector.

^◆ const_reference

template<typename T , Size DIM>

typedef const Vector& mi::math::Bbox<T, DIM>::const_reference

Const reference to vector.

^◆ difference_type

template<typename T , Size DIM>

typedef Difference mi::math::Bbox<T, DIM>::difference_type

Difference type, signed.

^◆ Pod_type

template<typename T , Size DIM>

typedef Bbox_struct<T,DIM> mi::math::Bbox<T, DIM>::Pod_type

POD class corresponding to this bounding box.

^◆ pointer

template<typename T , Size DIM>

typedef Vector* mi::math::Bbox<T, DIM>::pointer

Mutable pointer to vector.

^◆ reference

template<typename T , Size DIM>

typedef Vector& mi::math::Bbox<T, DIM>::reference

Mutable reference to vector.

^◆ size_type

template<typename T , Size DIM>

typedef Size mi::math::Bbox<T, DIM>::size_type

Size type, unsigned.

^◆ value_type

template<typename T , Size DIM>

typedef Vector mi::math::Bbox<T, DIM>::value_type

Coordinate type.

^◆ Vector

template<typename T , Size DIM>

typedef math::Vector<T,DIM> mi::math::Bbox<T, DIM>::Vector

Corresponding vector type.

Enumeration Type Documentation

^◆ Uninitialized_tag

template<typename T , Size DIM>

enum mi::math::Bbox::Uninitialized_tag

Enum type used to tag a special constructor that does not initialize the elements of the constructed bounding box.

Enumerator
UNINITIALIZED_TAG	Enum value used to call a special constructor that does not initialize the elements of the constructed bounding box.

Function Documentation

^◆ add_motionbox()

template<typename T , Size DIM>

Bbox mi::math::Bbox<T, DIM>::add_motionbox	(	const Bbox<T, DIM> &	vbox,
		T	t
	)		const

inline

Returns the translation of this bounding box by vectors that are inside the scaled bounding box of vectors, i.e., t*vbox.

Precondition: this bounding box and vbox are not empty

Parameters

vbox	vector bounding box to add
t	scale parameter. A negative scale inverts `vbox`.

^◆ Bbox() [1/12]

template<typename T , Size DIM>

mi::math::Bbox<T, DIM>::Bbox ( )

inline

Bounding box initialized to the empty space, see also the clear function.

The vector min is set elementwise to mi::base::numeric_traits<T>::max() and the vector max is set elementwise to mi::base::numeric_traits<T>::negative_max(). This initialization allows to insert points and other bounding boxes; a cleared bounding box will take the value of the first inserted point or bound box.

^◆ Bbox() [2/12]

template<typename T , Size DIM>

mi::math::Bbox<T, DIM>::Bbox ( const Bbox<T, DIM> & other )

default

Default copy constructor.

^◆ Bbox() [3/12]

template<typename T , Size DIM>

template<typename T2>

mi::math::Bbox<T, DIM>::Bbox ( const Bbox<T2, DIM> & other )

inlineexplicit

Template constructor that allows explicit conversions from other bounding boxes with assignment compatible element value type.

^◆ Bbox() [4/12]

template<typename T , Size DIM>

mi::math::Bbox<T, DIM>::Bbox ( const Bbox_struct<T, DIM> & bbox_struct )

inline

Bounding box initialized from corresponding POD type.

^◆ Bbox() [5/12]

template<typename T , Size DIM>

template<typename T2>

mi::math::Bbox<T, DIM>::Bbox ( const Bbox_struct<T2, DIM> & other )

inlineexplicit

Template constructor that allows explicit conversions from other POD type with assignment compatible element value type.

^◆ Bbox() [6/12]

template<typename T , Size DIM>

mi::math::Bbox<T, DIM>::Bbox	(	const Vector &	nmin,
		const Vector &	nmax
	)

inline

Bounding box initialized to the new extreme corner vectors, nmin and nmax.

Parameters

nmin	`min` corner vector
nmax	`max` corner vector

^◆ Bbox() [7/12]

template<typename T , Size DIM>

mi::math::Bbox<T, DIM>::Bbox ( const Vector & point )

inlineexplicit

Bounding box initialized to a single point.

^◆ Bbox() [8/12]

template<typename T , Size DIM>

template<typename InputIterator>

mi::math::Bbox<T, DIM>::Bbox	(	InputIterator	first,
		InputIterator	last
	)

Constructs a bounding box from a range [first, last) of items.

The value type of InputIterator can be either Vector to insert points, or it can be Bbox to insert bounding boxes.

Parameters

first	first element of the sequence to insert
last	past-the-end position of sequence to insert

^◆ Bbox() [9/12]

template<typename T , Size DIM>

mi::math::Bbox<T, DIM>::Bbox	(	T	min_x,
		T	max_x
	)

inline

1D bounding box (interval) initialized to the new extreme corner vectors, (min_x) and (max_x).

Precondition: DIM == 1

Parameters

min_x	x-coordinate of `min` corner vector
max_x	x coordinate of `max` corner vector

^◆ Bbox() [10/12]

template<typename T , Size DIM>

mi::math::Bbox<T, DIM>::Bbox	(	T	min_x,
		T	min_y,
		T	max_x,
		T	max_y
	)

inline

2D bounding box (interval) initialized to the new extreme corner vectors, (min_x,min_y) and (max_x,max_y).

Precondition: DIM == 2

Parameters

min_x	x-coordinate of `min` corner vector
min_y	y-coordinate of `min` corner vector
max_x	x coordinate of `max` corner vector
max_y	y coordinate of `max` corner vector

^◆ Bbox() [11/12]

template<typename T , Size DIM>

mi::math::Bbox<T, DIM>::Bbox	(	T	min_x,
		T	min_y,
		T	min_z,
		T	max_x,
		T	max_y,
		T	max_z
	)

inline

3D bounding box (interval) initialized to the new extreme corner vectors, (min_x,min_y,min_z) and (max_x,max_y,max_z).

Precondition: DIM == 3

Parameters

min_x	x-coordinate of `min` corner vector
min_y	y-coordinate of `min` corner vector
min_z	z-coordinate of `min` corner vector
max_x	x coordinate of `max` corner vector
max_y	y coordinate of `max` corner vector
max_z	z coordinate of `max` corner vector

^◆ Bbox() [12/12]

template<typename T , Size DIM>

mi::math::Bbox<T, DIM>::Bbox ( Uninitialized_tag )

inlineexplicit

Bounding box with its elements not initialized.

^◆ begin() [1/2]

template<typename T , Size DIM>

Vector * mi::math::Bbox<T, DIM>::begin ( )

inline

Returns the pointer to the first vector, min.

^◆ begin() [2/2]

template<typename T , Size DIM>

const Vector * mi::math::Bbox<T, DIM>::begin ( ) const

inline

Returns the pointer to the first vector, min.

^◆ center()

template<typename T , Size DIM>

Vector mi::math::Bbox<T, DIM>::center ( ) const

inline

Returns the center point of the bounding box.

^◆ clear()

template<typename T , Size DIM>

void mi::math::Bbox<T, DIM>::clear ( )

inline

Reinitializes this bounding box to the empty space.

The vector min is set elementwise to mi::base::numeric_traits<T>::max() and the vector max is set elementwise to mi::base::numeric_traits<T>::negative_max(). This initialization allows to insert points and other bounding boxes; a cleared bounding box will take the value of the first inserted point or bound box.

^◆ clip()

template<typename T , Size DIM>

Bbox<T, DIM> mi::math::clip	(	const Bbox<T, DIM> &	bbox1,
		const Bbox<T, DIM> &	bbox2
	)

inline

Clip bbox1 at bbox2 and return the result.

I.e., the resulting bbox is the intersection of bbox1 with bbox2.

Parameters

bbox1	first bounding box
bbox2	second bounding box

^◆ contains()

template<typename T , Size DIM>

bool mi::math::Bbox<T, DIM>::contains ( const Vector & vec ) const

inline

Returns true if the point is inside or on the boundary of the bounding box.

^◆ diagonal_length()

template<typename T , Size DIM>

T mi::math::Bbox<T, DIM>::diagonal_length ( ) const

inline

Returns the length of the diagonal.

Precondition: the bounding box is not empty

^◆ empty()

template<typename T , Size DIM>

bool mi::math::Bbox<T, DIM>::empty ( ) const

inline

Returns true if the box is empty.

For example, the box is empty after the default constructor or the clear() method call.

^◆ end() [1/2]

template<typename T , Size DIM>

Vector * mi::math::Bbox<T, DIM>::end ( )

inline

Returns the past-the-end pointer.

The range [begin(),end()) forms the range [min,max].

^◆ end() [2/2]

template<typename T , Size DIM>

const Vector * mi::math::Bbox<T, DIM>::end ( ) const

inline

Returns the past-the-end pointer.

The range [begin(),end()) forms the range [min,max].

^◆ extent()

template<typename T , Size DIM>

Vector mi::math::Bbox<T, DIM>::extent ( ) const

inline

Returns the size of the bounding box.

^◆ insert() [1/3]

template<typename T , Size DIM>

void mi::math::Bbox<T, DIM>::insert ( const Bbox<T, DIM> & other )

inline

Assigns the union of this bounding box and the other bounding box to this bounding box.

^◆ insert() [2/3]

template<typename T , Size DIM>

void mi::math::Bbox<T, DIM>::insert ( const Vector & point )

inline

Assigns the union of this bounding box and the point to this bounding box.

^◆ insert() [3/3]

template<typename T , Size DIM>

template<typename InputIterator>

void mi::math::Bbox<T, DIM>::insert	(	InputIterator	first,
		InputIterator	last
	)

Inserts a range [first,last) of items into this bounding box.

The value type of InputIterator can be either Vector to insert points, or it can be Bbox to insert bounding boxes.

Parameters

first	first element of the sequence to insert
last	past-the-end position of sequence to insert

^◆ intersects()

template<typename T , Size DIM>

bool mi::math::Bbox<T, DIM>::intersects ( const Bbox<T, DIM> & other ) const

inline

Returns true if this bounding box and the other bounding box intersect in their interiors or on their boundaries.

^◆ is_line()

template<typename T , Size DIM>

bool mi::math::Bbox<T, DIM>::is_line ( ) const

inline

Returns true the bounding box is an axis-aligned line.

Returns: true if rank() returns 1

^◆ is_plane()

template<typename T , Size DIM>

bool mi::math::Bbox<T, DIM>::is_plane ( ) const

inline

Returns true the bounding box is an axis-aligned plane.

Returns: true if rank() returns 2

^◆ is_point()

template<typename T , Size DIM>

bool mi::math::Bbox<T, DIM>::is_point ( ) const

inline

Returns true the bounding box is a single point.

^◆ is_volume()

template<typename T , Size DIM>

bool mi::math::Bbox<T, DIM>::is_volume ( ) const

inline

Returns true the bounding box has a volume.

Returns: true if rank() returns 3

^◆ largest_extent_index()

template<typename T , Size DIM>

Size mi::math::Bbox<T, DIM>::largest_extent_index ( ) const

inline

Returns the index of the dimension in which the bounding box has its largest extent, i.e., 0=x, 1=y, 2=z.

^◆ lerp()

template<typename T , Size DIM>

Bbox<T, DIM> mi::math::lerp	(	const Bbox<T, DIM> &	bbox1,
		const Bbox<T, DIM> &	bbox2,
		T	t
	)

inline

Returns the linear interpolation between bbox1 and bbox2, i.e., it returns (1-t) * bbox1 + t * bbox2.

Precondition: bbox1 and bbox2 are not empty.

Parameters

bbox1	one bounding box
bbox2	second bounding box
t	interpolation parameter in [0,1]

^◆ max_size()

template<typename T , Size DIM>

static Size mi::math::Bbox<T, DIM>::max_size ( )

inlinestatic

Constant maximum size of the bounding box.

^◆ operator Bbox_struct<T, DIM>()

template<typename T , Size DIM>

mi::math::Bbox<T, DIM>::operator Bbox_struct<T, DIM> ( ) const

inline

Conversion to corresponding POD type.

^◆ operator!=()

template<typename T , Size DIM>

bool mi::math::operator!=	(	const Bbox<T, DIM> &	lhs,
		const Bbox<T, DIM> &	rhs
	)

inline

Returns true if lhs is elementwise not equal to rhs.

^◆ operator*()

template<typename T , Size DIM>

Bbox<T, DIM> mi::math::operator*	(	const Bbox<T, DIM> &	bbox,
		T	factor
	)

inline

Returns a bounding box that is a version of bbox scaled by factor, i.e., bbox.max and bbox.min are multiplied by factor.

Precondition: bbox is not empty

^◆ operator*=()

template<typename T , Size DIM>

Bbox<T, DIM> & mi::math::operator*=	(	Bbox<T, DIM> &	bbox,
		T	factor
	)

inline

Scales bbox by factor, i.e., bbox.max and bbox.min are multiplied by factor.

Precondition: bbox is not empty

^◆ operator+()

template<typename T , Size DIM>

Bbox<T, DIM> mi::math::operator+	(	const Bbox<T, DIM> &	bbox,
		T	value
	)

inline

Returns a bounding box that is the bbox increased by a constant value at each face, i.e., value is added to bbox.max and subtracted from bbox.min.

Precondition: bbox is not empty

^◆ operator+=()

template<typename T , Size DIM>

Bbox<T, DIM> & mi::math::operator+=	(	Bbox<T, DIM> &	bbox,
		T	value
	)

inline

Increases bbox by a constant value at each face, i.e., value is added to bbox.max and subtracted from bbox.min.

Precondition: bbox is not empty

^◆ operator-()

template<typename T , Size DIM>

Bbox<T, DIM> mi::math::operator-	(	const Bbox<T, DIM> &	bbox,
		T	value
	)

inline

Returns a bounding box that is the bbox shrunk by a constant value at each face, i.e., value is subtracted from bbox.max and added to bbox.min.

Precondition: bbox is not empty

^◆ operator-=()

template<typename T , Size DIM>

Bbox<T, DIM> & mi::math::operator-=	(	Bbox<T, DIM> &	bbox,
		T	value
	)

inline

Shrinks bbox by a constant value at each face, i.e., value is subtracted from bbox.max and added to bbox.min.

Precondition: bbox is not empty

^◆ operator/()

template<typename T , Size DIM>

Bbox<T, DIM> mi::math::operator/	(	const Bbox<T, DIM> &	bbox,
		T	divisor
	)

inline

Returns a bounding box that is a version of bbox divided by divisor, i.e., bbox.max and bbox.min are divided by divisor.

Precondition: bbox is not empty and divisor is not zero

^◆ operator/=()

template<typename T , Size DIM>

Bbox<T, DIM> & mi::math::operator/=	(	Bbox<T, DIM> &	bbox,
		T	divisor
	)

inline

Divide bbox by divisor, i.e., bbox.max and bbox.min are divided by divisor.

Precondition: bbox is not empty and divisor is not zero

^◆ operator<()

template<typename T , Size DIM>

bool mi::math::operator<	(	const Bbox<T, DIM> &	lhs,
		const Bbox<T, DIM> &	rhs
	)

inline

Returns true if lhs is lexicographically less than rhs.

See also: Definition: Lexicographic order and comparison

^◆ operator<=()

template<typename T , Size DIM>

bool mi::math::operator<=	(	const Bbox<T, DIM> &	lhs,
		const Bbox<T, DIM> &	rhs
	)

inline

Returns true if lhs is lexicographically less than or equal to rhs.

See also: Definition: Lexicographic order and comparison

^◆ operator=() [1/2]

template<typename T , Size DIM>

Bbox & mi::math::Bbox<T, DIM>::operator= ( const Bbox<T, DIM> & other )

inline

Assignment.

^◆ operator=() [2/2]

template<typename T , Size DIM>

Bbox & mi::math::Bbox<T, DIM>::operator= ( const Bbox_struct<T, DIM> & other )

inline

Assignment from corresponding POD type.

^◆ operator==()

template<typename T , Size DIM>

bool mi::math::operator==	(	const Bbox<T, DIM> &	lhs,
		const Bbox<T, DIM> &	rhs
	)

inline

Returns true if lhs is elementwise equal to rhs.

^◆ operator>()

template<typename T , Size DIM>

bool mi::math::operator>	(	const Bbox<T, DIM> &	lhs,
		const Bbox<T, DIM> &	rhs
	)

inline

Returns true if lhs is lexicographically greater than rhs.

See also: Definition: Lexicographic order and comparison

^◆ operator>=()

template<typename T , Size DIM>

bool mi::math::operator>=	(	const Bbox<T, DIM> &	lhs,
		const Bbox<T, DIM> &	rhs
	)

inline

Returns true if lhs is lexicographically greater than or equal to rhs.

See also: Definition: Lexicographic order and comparison

^◆ operator[]() [1/2]

template<typename T , Size DIM>

Vector & mi::math::Bbox<T, DIM>::operator[] ( Size i )

inline

Returns the vector min for i==0, and the vector max for i==1.

^◆ operator[]() [2/2]

template<typename T , Size DIM>

const Vector & mi::math::Bbox<T, DIM>::operator[] ( Size i ) const

inline

Returns the vector min for i==0, and the vector max for i==1.

^◆ push_back()

template<typename T , Size DIM>

void mi::math::Bbox<T, DIM>::push_back ( const Bbox<T, DIM> & other )

inline

Assigns the union of this bounding box and the other bounding box to this bounding box.

Makes the bounding box compatible with the std::back_inserter function, which allows you to use STL functions, such as std::copy to compute the union of a sequence of bounding boxes.

^◆ rank()

template<typename T , Size DIM>

Size mi::math::Bbox<T, DIM>::rank ( ) const

inline

Returns the rank of the bounding box.

Returns: 0 if the bounding box is a point or empty, 1 if it is an axis-aligned line, 2 if it is an axis-aligned plane, and 3 if it has a volume.

^◆ robust_grow()

template<typename T , Size DIM>

void mi::math::Bbox<T, DIM>::robust_grow ( T eps = T(1.0e-5f) )

Robustly grows the bounding box by a value computed automatically from the bounding box dimensions and location in space.

If a bounding box is far away from the origin, just enlarging the bounding box by eps * (largest box extent) may result in cancellation. To avoid cancellation problems, this method computes the value for enlarging the box by computing coordinatewise the sum of the absolute values of the min and max coordinates and the bounding box extent. It takes then the maximum of all these sums, multiplies it by eps, adds it to bbox.max and subtracts it from bbox.min, enlarging the bounding box by an equal amount on all sides. grow factor

^◆ size()

template<typename T , Size DIM>

static Size mi::math::Bbox<T, DIM>::size ( )

inlinestatic

Constant size of the bounding box.

^◆ transform_point()

template<typename TT , typename T>

Bbox<T, 3> mi::math::transform_point	(	const Matrix<TT, 4, 4> &	mat,
		const Bbox<T, 3> &	bbox
	)

Returns the 3D bounding box transformed by a matrix.

The transformation (including the translation) is applied to the eight bounding box corners (interpreted as points) and a new axis aligned bounding box is computed for these transformed corners.

Note: The transformed bounding box is likely to be a more pessimistic approximation of a geometry that was approximated by the original bounding box. Transforming the approximated geometry and computing a new bounding box gives usually a tighter bounding box.

Parameters

mat	4x4 transformation matrix
bbox	the bounding box to transform

^◆ transform_vector()

template<typename TT , typename T>

Bbox<T, 3> mi::math::transform_vector	(	const Matrix<TT, 4, 4> &	mat,
		const Bbox<T, 3> &	bbox
	)

Returns the 3D bounding box transformed by a matrix.

The transformation (excluding the translation) is applied to the eight bounding box corners (interpreted as vectors) and a new axis aligned bounding box is computed for these transformed corners.

Parameters

mat	4x4 transformation matrix
bbox	the bounding box to transform

^◆ volume()

template<typename T , Size DIM>

T mi::math::Bbox<T, DIM>::volume ( ) const

inline

Returns the volume of the bounding box.

Variable Documentation

^◆ DIMENSION

template<typename T , Size DIM>

const Size mi::math::Bbox<T, DIM>::DIMENSION = DIM

static

Constant dimension of the vectors.

^◆ max [1/2]

template<typename T , Size DIM>

Vector_struct<T,DIM> mi::math::Bbox_struct<T, DIM>::max

Elementwise maximal bounding box corner.

^◆ max [2/2]

template<typename T , Size DIM>

Vector mi::math::Bbox<T, DIM>::max

Elementwise maximal bounding box corner.

^◆ min [1/2]

template<typename T , Size DIM>

Vector_struct<T,DIM> mi::math::Bbox_struct<T, DIM>::min

Elementwise minimal bounding box corner.

^◆ min [2/2]

template<typename T , Size DIM>

Vector mi::math::Bbox<T, DIM>::min

Elementwise minimal bounding box corner.

^◆ SIZE

template<typename T , Size DIM>

const Size mi::math::Bbox<T, DIM>::SIZE = 2

static

Constant size of the bounding box.

Classes

Typedefs

Enumerations

Functions

Variables

Detailed Description

Typedef Documentation

◆ const_pointer

◆ const_reference

◆ difference_type

◆ Pod_type

◆ pointer

◆ reference

◆ size_type

◆ value_type

◆ Vector

Enumeration Type Documentation

◆ Uninitialized_tag

Function Documentation

◆ add_motionbox()

◆ Bbox() [1/12]

◆ Bbox() [2/12]

◆ Bbox() [3/12]

◆ Bbox() [4/12]

◆ Bbox() [5/12]

◆ Bbox() [6/12]

◆ Bbox() [7/12]

◆ Bbox() [8/12]

◆ Bbox() [9/12]

◆ Bbox() [10/12]

◆ Bbox() [11/12]

◆ Bbox() [12/12]

◆ begin() [1/2]

◆ begin() [2/2]

◆ center()

◆ clear()

◆ clip()

◆ contains()

◆ diagonal_length()

◆ empty()

◆ end() [1/2]

◆ end() [2/2]

◆ extent()

◆ insert() [1/3]

◆ insert() [2/3]

◆ insert() [3/3]

◆ intersects()

◆ is_line()

◆ is_plane()

◆ is_point()

◆ is_volume()

◆ largest_extent_index()

◆ lerp()

◆ max_size()

◆ operator Bbox_struct<T, DIM>()

◆ operator!=()

◆ operator*()

◆ operator*=()

◆ operator+()

◆ operator+=()

◆ operator-()

◆ operator-=()

◆ operator/()

◆ operator/=()

◆ operator<()

◆ operator<=()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator==()

◆ operator>()

◆ operator>=()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ push_back()

◆ rank()

◆ robust_grow()

◆ size()

◆ transform_point()

◆ transform_vector()

◆ volume()

^◆ const_pointer

^◆ const_reference

^◆ difference_type

^◆ Pod_type

^◆ pointer

^◆ reference

^◆ size_type

^◆ value_type

^◆ Vector

^◆ Uninitialized_tag

^◆ add_motionbox()

^◆ Bbox() [1/12]

^◆ Bbox() [2/12]

^◆ Bbox() [3/12]

^◆ Bbox() [4/12]

^◆ Bbox() [5/12]

^◆ Bbox() [6/12]

^◆ Bbox() [7/12]

^◆ Bbox() [8/12]

^◆ Bbox() [9/12]

^◆ Bbox() [10/12]

^◆ Bbox() [11/12]

^◆ Bbox() [12/12]

^◆ begin() [1/2]

^◆ begin() [2/2]

^◆ center()

^◆ clear()

^◆ clip()

^◆ contains()

^◆ diagonal_length()

^◆ empty()

^◆ end() [1/2]

^◆ end() [2/2]

^◆ extent()

^◆ insert() [1/3]

^◆ insert() [2/3]

^◆ insert() [3/3]

^◆ intersects()

^◆ is_line()

^◆ is_plane()

^◆ is_point()

^◆ is_volume()

^◆ largest_extent_index()

^◆ lerp()

^◆ max_size()

^◆ operator Bbox_struct<T, DIM>()

^◆ operator!=()

^◆ operator*()

^◆ operator*=()

^◆ operator+()

^◆ operator+=()

^◆ operator-()

^◆ operator-=()

^◆ operator/()

^◆ operator/=()

^◆ operator<()

^◆ operator<=()

^◆ operator=() [1/2]

^◆ operator=() [2/2]

^◆ operator==()

^◆ operator>()

^◆ operator>=()

^◆ operator[]() [1/2]

^◆ operator[]() [2/2]

^◆ push_back()

^◆ rank()

^◆ robust_grow()

^◆ size()

^◆ transform_point()

^◆ transform_vector()

^◆ volume()

^◆ DIMENSION

^◆ max [1/2]

^◆ max [2/2]

^◆ min [1/2]

^◆ min [2/2]

^◆ SIZE