Axis aligned box sphere. More...

#include <boxsphere.h>

Inheritance diagram for BoxSphere:

Public Member Functions
	BoxSphere ()
	Empty.

	BoxSphere (const Box &, const double &=0.0)
	Create a box-sphere. More...

	BoxSphere (const Vector &, const Vector &, const double &=0.0)
	Create a box-sphere given two opposite corners and a radius. More...

	BoxSphere (const Vector &, const double &, const double &=0.0)
	Create a box sphere given a center point and the half side length. More...

	BoxSphere (const BoxSphere &, const BoxSphere &)
	Create a box-sphere embedding two box spheres. More...

	BoxSphere (const BoxSphere &, const Frame &)
	Creates a box-sphere. More...

	BoxSphere (const BoxSphere &, const Matrix &)
	Create a box-sphere. More...

	~BoxSphere ()
	Empty.

Vector &	operator[] (int)
	Returns either end vertex of the box-sphere.

Vector	operator[] (int) const
	Overloaded.

double	Radius () const
	Returns the radius of the box-sphere. More...

double	R (const Vector &) const
	Computes the squared distance between the box-sphere and a point. More...

double	Signed (const Vector &) const
	Computes the signed distance between the box-sphere and a point. More...

int	Intersect (const Ray &, double &, double &) const
	Computes the intersection between a box and a ray. More...

int	Intersect (const Ray &, double &, double &, Vector &, Vector &) const
	Compute the intersection between the object and a ray. More...

bool	Inside (const Vector &) const
	Check if a point is inside the box-sphere. More...

double	Volume () const
	Compute the volume of a box-sphere.

double	Area () const
	Compute the area of a box-sphere.

Static Public Attributes
static constexpr const double	epsilon = 1.0e-5
	Epsilon value.

Protected Attributes
double	r
	Radius.

Protected Attributes inherited from Box
Vector	a
	Lower vertex.

Vector	b
	Upper vertex.

Friends
BoxSphere	operator+ (const BoxSphere &, const BoxSphere &)
	Compute the Minkowski sum of two box-spheres. More...

BoxSphere	operator* (const double &, const BoxSphere &)
	Scale a box-sphere by a scalar factor. More...

BoxSphere	operator* (const BoxSphere &, const double &)
	Overloaded. More...

std::ostream &	operator<< (std::ostream &, const BoxSphere &)
	Overloaded. More...

Additional Inherited Members
Protected Member Functions inherited from Box
	Box ()
	Empty.

	Box (const double &)
	Create a cube centered at the origin and of given half side length. More...

	Box (const Vector &)
	Create an empty box given one vertex. More...

	Box (const Vector &, const Vector &)
	Create a box given two opposite corners. More...

	Box (const Vector &, const double &)
	Create a box given a center point and the half side length. More...

	Box (const Vector &, const double &, const double &, const double &)
	Create a box given a center point and its width, length, and height. More...

	Box (const double &, const double &, const double &)
	Create a box given its sizes. More...

	Box (const Vector *, int)
	Creates the bounding box of a set of points. More...

	Box (const QVector< Vector > &)
	Creates the bounding box of a set of points. More...

	Box (const Box &, const Box &)
	Create a box embedding two boxes. More...

	Box (const Box &, const Frame &)
	Creates an axis aligned bounding box from a box and a frame. More...

	Box (const Box &, const FrameScaled &)
	Creates an axis aligned bounding box from a box and a frame. More...

	Box (const Box &, const Matrix &)
	Creates an axis aligned bounding box from a box and a transformation matrix. More...

	~Box ()
	Empty.

Vector &	operator[] (int)
	Returns either end vertex of the box.

Vector	operator[] (int) const
	Overloaded.

Vector	Center () const
	Returns the center of the box.

Vector	Vertex (int) const
	Returns the k-th vertex of the box. More...

Vector	Vertex (int, int, int, int, int, int) const
	Compute the coordinates of a grid aligned point. More...

Segment	Edge (int) const
	Compute the k-th edge segment of the box. More...

Plane	Face (int) const
	Compute the k-th plane of the box. More...

Vector	Size () const
	Compute the size (width, length and height) of a box. More...

Vector	Diagonal () const
	Returns the diagonal of the box.

double	Radius () const
	Returns the radius of the box, i.e. the length of the half diagonal of the box.

double	R (const Vector &) const
	Computes the squared Euclidean distance between the box and a point. More...

double	Signed (const Vector &) const
	Computes the signed distance between the box and a point. More...

Vector	Normal (const Vector &) const
	Computes the normal vector between a point and a box. More...

double	R (const Box &) const
	Compute the squared Euclidean distance between two boxes. More...

double	RInfinity (const Box &) const
	Compute the maximum distance between two boxes. More...

int	Intersect (const Ray &) const
	Check the intersection between a box and a ray. More...

int	Intersect (const Ray &, double &, double &) const
	Computes the intersection between a box and a ray. More...

int	Intersect (const Ray &, double &) const
	Compute the first positive intersection between the box and a ray. More...

int	Intersect (const Ray &, double &, double &, Vector &, Vector &) const
	Compute the intersection between an axis aligned box and a ray. More...

int	Intersect (const Ray &, double &, Vector &) const
	Compute the first positive intersection between the box and a ray. More...

int	Intersect (const Vector &, const Vector &) const
	Check if a segment intersects an axis aligned box. More...

bool	Intersect (const Box &) const
	Check if the box intersects another box. More...

bool	Inside (const Box &) const
	Check if an argument box is inside the box. More...

bool	Inside (const Vector &) const
	Check if a point is inside the box. More...

Box	Intersection (const Box &) const
	Computes the intersection between two boxes. More...

int	Difference (const Box &, Box *) const
	Computes the difference between two boxes. More...

bool	Empty () const
	Check if a box is empty. More...

double	Volume () const
	Compute the volume of a box.

double	Area () const
	Compute the surface area of a box.

void	SetCubic ()
	Creates the tightest embedding cube from an arbitrarilly shaped box. More...

void	SetInscribedCubic ()
	Creates the biggest cube iscribed in the box. More...

Box	Cube () const
	Return the tightest embedding cube from an arbitrarilly shaped box. More...

void	Extend (const double &)
	Extend the limits of the box by a given distance. More...

Box	Extended (const double &) const
	Extend the limits of the box by a given distance. More...

void	Extend (const Vector &)
	Extend the limits of the box given a point. More...

void	SetParallelepipedic (const double &, int &, int &, int &)
	Creates a parallelepipedic box whose dimensions are integer multiples of a given input reference size. More...

void	SetParallelepipedic (int, int &, int &, int &)
	Inflates a box so that its dimensions should be a fraction of its maximum side length. More...

Box	Sub (int) const
	Computes the sub-box in the n-th octant. More...

int	Octant (const Vector &) const
	Compute the octant index of a vertex with respect to the box center. More...

void	Translate (const Vector &)
	Translates a box. More...

Box	Translated (const Vector &) const
	Translated box. More...

void	Scale (const double &)
	Scales a box. More...

void	Scale (const Vector &)
	Scales a box. More...

Box	Scaled (const Vector &) const
	Scales a box and return the scaled box. More...

Box	Offsetted (const Vector &) const
	Offets a box. More...

Box	Centered () const
	Compute the box translated to origin. More...

Box	Cut (const Vector &, const Vector &) const
	Compute the minimal box embedding the box cut by half space. More...

int	IntegerAxis () const
	Compute the axis which has the greater length.

Vector	RandomInside (Random &=Random::R239) const
	Generate a random vector inside the box. More...

Vector	RandomSurface (Random &=Random::R239) const
	Generate a random vector on the surface of the box. More...

QVector< Vector >	Poisson (const double &, int, Random &=Random::R239) const
	Compute a Poisson sphere distribution inside a box. More...

Static Protected Attributes inherited from Box
static constexpr const double	epsilon = 1.0e-5
	Epsilon value used to check intersections and some round off errors and for ray intersection tests.

static const Box	Infinity
	Largest box. More...

static const Box	Null
	Null box, equivalent to: More...

static const Box	Unit
	Unit box.

static const int	edge [24]
	Edge vertex indexes.

static const Vector	normal [6]
	Face normals.

Detailed Description

Axis aligned box sphere.

This object is defined as a rounded axis aligned box, i.e., the Minkowski sum between a box and a sphere.

The class stores the opposite corners as vectors, and a radius.

This class provides a set of functions, such as the intersection between a box and a ray, and implements the Minkowski sum by overloading some operators.

Constructor & Destructor Documentation

◆ BoxSphere() [1/6]

BoxSphere::BoxSphere	(	const Box &	box,
		const double &	r = `0.0`
	)

explicit

Create a box-sphere.

Parameters

box	The box.
r	Radius.

◆ BoxSphere() [2/6]

BoxSphere::BoxSphere	(	const Vector &	a,
		const Vector &	b,
		const double &	r = `0.0`
	)

explicit

Create a box-sphere given two opposite corners and a radius.

Note that this constructor does not check the coordinates of the two vectors.

Parameters

a,b	End vertices.
r	Radius.

◆ BoxSphere() [3/6]

BoxSphere::BoxSphere	(	const Vector &	c,
		const double &	a,
		const double &	r = `0.0`
	)

explicit

Create a box sphere given a center point and the half side length.

Parameters

c	Center.
a	Half side length.
r	Radius.

◆ BoxSphere() [4/6]

BoxSphere::BoxSphere	(	const BoxSphere &	x,
		const BoxSphere &	y
	)

explicit

Create a box-sphere embedding two box spheres.

Parameters

x,y	The two box-spheres.

◆ BoxSphere() [5/6]

BoxSphere::BoxSphere	(	const BoxSphere &	box,
		const Frame &	frame
	)

explicit

Creates a box-sphere.

Parameters

box	The box-sphere.
frame	The frame.

◆ BoxSphere() [6/6]

BoxSphere::BoxSphere	(	const BoxSphere &	box,
		const Matrix &	matrix
	)

explicit

Create a box-sphere.

Parameters

box	The box-sphere.
matrix	Transformation matrix.

Member Function Documentation

◆ Inside()

bool BoxSphere::Inside ( const Vector & p ) const

Check if a point is inside the box-sphere.

Parameters

p Point.

◆ Intersect() [1/2]

int BoxSphere::Intersect	(	const Ray &	ray,
		double &	ta,
		double &	tb
	)		const

Computes the intersection between a box and a ray.

Sorted intersection depths are returned if intersection occurs.

Parameters

ray	The ray.
ta,tb	Intersection depths.

◆ Intersect() [2/2]

int BoxSphere::Intersect	(	const Ray &	ray,
		double &	ta,
		double &	tb,
		Vector &	na,
		Vector &	nb
	)		const

Compute the intersection between the object and a ray.

Parameters

ray	The ray.
ta,tb	Intersection depths.
na,nb	Returned normals at intersection points.

Returns: The number of intersections.

◆ R()

double BoxSphere::R ( const Vector & p ) const

Computes the squared distance between the box-sphere and a point.

See also: Box::R(const Vector&) const

Parameters

p Point.

◆ Radius()

double BoxSphere::Radius ( ) const

inline

Returns the radius of the box-sphere.

Note that this function differs from Box::Radius() which returns the radius of a box.

◆ Signed()

double BoxSphere::Signed ( const Vector & p ) const

Computes the signed distance between the box-sphere and a point.

The computation is derived from the signed distance to the box:

double d=Box::Signed(p)-r;

Box::Signed

double Signed(const Vector &) const

Computes the signed distance between the box and a point.

Definition: box.cpp:389

BoxSphere::r

double r

Radius.

Definition: boxsphere.h:12

Parameters

p Point.

Friends And Related Function Documentation

◆ operator* [1/2]

BoxSphere operator*	(	const BoxSphere &	box,
		const double &	t
	)

friend

Overloaded.

Parameters

box	The box-sphere.
t	Scalar.

◆ operator* [2/2]

BoxSphere operator*	(	const double &	t,
		const BoxSphere &	box
	)

friend

Scale a box-sphere by a scalar factor.

Parameters

box	The box-sphere.
t	Scalar.

◆ operator+

BoxSphere operator+	(	const BoxSphere &	a,
		const BoxSphere &	b
	)

friend

Compute the Minkowski sum of two box-spheres.

Parameters

a,b	The box-spheres.

◆ operator<<

std::ostream & operator<<	(	std::ostream &	s,
		const BoxSphere &	box
	)

friend

Overloaded.

Parameters

s	Stream.
box	The sphere-box.

Public Member Functions

Static Public Attributes

Protected Attributes

Friends

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ BoxSphere() [1/6]

◆ BoxSphere() [2/6]

◆ BoxSphere() [3/6]

◆ BoxSphere() [4/6]

◆ BoxSphere() [5/6]

◆ BoxSphere() [6/6]

Member Function Documentation

◆ Inside()

◆ Intersect() [1/2]

◆ Intersect() [2/2]

◆ R()

◆ Radius()

◆ Signed()

Friends And Related Function Documentation

◆ operator* [1/2]

◆ operator* [2/2]

◆ operator+

◆ operator<<