Box Class Reference

#include <Box.hpp>

Inheritance diagram for Box:

Public Member Functions
	Box ()
	Box (double xmin, double ymin, double zmin, double xmax, double ymax, double zmax)
	Box (Vec rmin, Vec rmax)
void	cellIndices (int &i, int &j, int &k, Vec r, int nx, int ny, int nz) const
Vec	center () const
bool	contains (const Box &box) const
bool	contains (double x, double y, double z) const
bool	contains (Vec r) const
double	diagonal () const
void	extend (const Box &box)
const Box &	extent () const
void	extent (double &xmin, double &ymin, double &zmin, double &xmax, double &ymax, double &zmax) const
Vec	fracPos (double xfrac, double yfrac, double zfrac) const
Vec	fracPos (int xd, int yd, int zd, int xn, int yn, int zn) const
bool	intersects (const Box &box) const
bool	intersects (Vec r, const Vec k, double &smin, double &smax) const
bool	intersects (Vec rc, double r) const
Vec	rmax () const
Vec	rmin () const
double	volume () const
Vec	widths () const
double	xmax () const
double	xmin () const
double	xwidth () const
double	ymax () const
double	ymin () const
double	ywidth () const
double	zmax () const
double	zmin () const
double	zwidth () const

Protected Member Functions
void	setExtent (const Box &extent)
void	setExtent (double xmin, double ymin, double zmin, double xmax, double ymax, double zmax)

Private Attributes
double	_xmax
double	_xmin
double	_ymax
double	_ymin
double	_zmax
double	_zmin

Detailed Description

Box is a low-level class for working with three-dimensional "boxes": each instance represents a cuboid that is lined up with the cartesian coordinate axes. A box is represented by means of its six cartesian coordinates \((x_\text{min},y_\text{min},z_\text{min}, \,x_\text{max},y_\text{max},z_\text{max})\) which are stored in data members with similar names. The class offers functions to retrieve various (mostly trivial) properties of the box, including its coordinates and widths in each direction and its volume. A Box instance is essentially immutable: once created it can no longer be changed. There is one exception to this rule: a derived class can replace the complete Box contents through the setExtent() function.

The Box class is largely implemented inline (in this header file). Most compilers optimize away all overhead so that using this class is just as efficient as directly writing the code in terms of the box components.

Constructor & Destructor Documentation

Box() [1/3]

Box::Box ( )

inline

The default constructor creates an empty box at the origin, i.e. it initializes all box coordinates to zero.

Box() [2/3]

Box::Box ( double xmin, double ymin, double zmin, double xmax, double ymax, double zmax )

inline

This constructor initializes the box coordinates to the values provided as arguments.

Box() [3/3]

Box::Box ( Vec rmin, Vec rmax )

inline

This constructor initializes the box coordinates to the components of the provided Vec objects, respectively specifying the minimum and maximum position.

Member Function Documentation

cellIndices()

void Box::cellIndices ( int & i, int & j, int & k, Vec r, int nx, int ny, int nz ) const

inline

This function calculates the cell indices for a given position, assuming that the box would be partitioned in a given number of cells in each spatial direction.

center()

Vec Box::center ( ) const

inline

This function returns the position corresponding to the center of the box

\[ x=\tfrac12 (x_\text{min}+x_\text{max}) \]

\[ y=\tfrac12 (y_\text{min}+y_\text{max}) \]

\[ z=\tfrac12 (x_\text{min}+z_\text{max}) \]

contains() [1/3]

bool Box::contains ( const Box & box ) const

inline

This function returns true if the given box is inside this box, false otherwise.

contains() [2/3]

bool Box::contains ( double x, double y, double z ) const

inline

This function returns true if the position \((x,y,z)\) is inside the box, false otherwise.

contains() [3/3]

bool Box::contains ( Vec r ) const

inline

This function returns true if the position \({\bf{r}}\) is inside the box, false otherwise.

diagonal()

double Box::diagonal ( ) const

inline

This function returns the length of the diagonal of the box, i.e. \(\sqrt{ (x_\text{max}-x_\text{min})^2 + (y_\text{max}-y_\text{min})^2 + (z_\text{max}-z_\text{min})^2 }\).

extend()

void Box::extend ( const Box & box )

inline

This function extends the receiving box so that it contains both the specified and the original box.

extent() [1/2]

const Box & Box::extent ( ) const

inline

This function returns a reference to the receiving box object. It is useful for explicitly retrieving the box object from instances of classes based on Box.

extent() [2/2]

void Box::extent ( double & xmin, double & ymin, double & zmin, double & xmax, double & ymax, double & zmax ) const

inline

This function stores the \((x_\text{min},y_\text{min},z_\text{min}, \,x_\text{max},y_\text{max},z_\text{max})\) coordinates of the box in the provided arguments.

fracPos() [1/2]

Vec Box::fracPos ( double xfrac, double yfrac, double zfrac ) const

inline

This function returns a position in the box determined by a given fraction in each spatial direction

\[ x=x_\text{min}+x_\text{frac}\times(x_\text{max}-x_\text{min}) \]

\[ y=y_\text{min}+y_\text{frac}\times(y_\text{max}-y_\text{min}) \]

\[ z=z_\text{min}+z_\text{frac}\times(z_\text{max}-z_\text{min}) \]

The specified fractions must be between zero and one; this is not checked by the function.

fracPos() [2/2]

Vec Box::fracPos ( int xd, int yd, int zd, int xn, int yn, int zn ) const

inline

This function returns a position in the box determined by a given fraction in each spatial direction.

\[ x=x_\text{min}+\frac{x_\text{d}}{x_\text{n}}\times(x_\text{max}-x_\text{min}) \]

\[ y=y_\text{min}+\frac{y_\text{d}}{y_\text{n}}\times(y_\text{max}-y_\text{min}) \]

\[ z=z_\text{min}+\frac{z_\text{d}}{z_\text{n}}\times(z_\text{max}-z_\text{min}) \]

Each of the fractions is specified as the quotient of two integers; the integers are converted to floating point before the division is made. The quotients must be between zero and one; this is not checked by the function.

intersects() [1/3]

bool Box::intersects ( const Box & box ) const

inline

This function returns true if the given box and this box have a non-zero intersection, false otherwise.

intersects() [2/3]

bool Box::intersects	(	Vec	r,
		const Vec	k,
		double &	smin,
		double &	smax ) const

This function intersects the receiving axis-aligned bounding box with a ray (half-line) defined by the specified starting position \(\bf{r}\) and direction \(\bf{k}\). If the ray intersects the box, the function returns true after storing the near and far intersection distances relative to the starting position in \(s_\mathrm{min}\) and \(s_\mathrm{max}\), respectively. If the starting position is inside the box, the nearest intersection distance is set to zero. In other words, the following relation always holds: \(0\le s_\mathrm{min} < s_\mathrm{max}\).

If the ray does not intersect the box, the function returns false and the values of \(s_\mathrm{min}\) and \(s_\mathrm{max}\) are undefined. A ray that "touches" the box border in a single point is not considered to intersect the box. A ray along an edge or face on the lower side of the box is considered to intersect the box, while ray along an edge or face on the upper side of the box is considered not to intersect the box. This approach avoids duplicate intersection of adjacent boxes.

The function employs the slab method originated by Kay and Kajiya (1986) and adapted by Haines (1989) as described in "Geometric Tools for Computer Graphics" by Scheider and Eberly (2003, Elsevier).

intersects() [3/3]

bool Box::intersects	(	Vec	rc,
		double	r ) const

This function intersects the receiving axis-aligned bounding box with a sphere defined by the specified center position \({\bf{r}}_\mathrm{c}\) and radius \(r\). It returns true if the box and the sphere intersect, and false otherwise.

The function employs the algorithm due to Jim Arvo described in "Graphics Gems" (1990).

rmax()

Vec Box::rmax ( ) const

inline

This function returns the maximum position \({\bf{r}}_\text{max}\) of the box.

rmin()

Vec Box::rmin ( ) const

inline

This function returns the minimum position \({\bf{r}}_\text{min}\) of the box.

setExtent() [1/2]

void Box::setExtent ( const Box & extent )

inlineprotected

This function replaces the extent of the box with the newly specified values. This function is intended for use in derived classes only.

setExtent() [2/2]

void Box::setExtent ( double xmin, double ymin, double zmin, double xmax, double ymax, double zmax )

inlineprotected

This function replaces the extent of the box with the newly specified values. This function is intended for use in derived classes only.

volume()

double Box::volume ( ) const

inline

This function returns the volume \((x_\text{max}-x_\text{min}) \times (y_\text{max}-y_\text{min}) \times (z_\text{max}-z_\text{min})\) of the box.

widths()

Vec Box::widths ( ) const

inline

This function returns the widths \((x_\text{max}-x_\text{min}, y_\text{max}-y_\text{min}, z_\text{max}-z_\text{min})\) of the box as a Vec object.

xmax()

double Box::xmax ( ) const

inline

This function returns the \(x_\text{max}\) coordinate of the box.

xmin()

double Box::xmin ( ) const

inline

This function returns the \(x_\text{min}\) coordinate of the box.

xwidth()

double Box::xwidth ( ) const

inline

This function returns the width \(x_\text{max}-x_\text{min}\) of the box.

ymax()

double Box::ymax ( ) const

inline

This function returns the \(y_\text{max}\) coordinate of the box.

ymin()

double Box::ymin ( ) const

inline

This function returns the \(y_\text{min}\) coordinate of the box.

ywidth()

double Box::ywidth ( ) const

inline

This function returns the width \(y_\text{max}-y_\text{min}\) of the box.

zmax()

double Box::zmax ( ) const

inline

This function returns the \(z_\text{max}\) coordinate of the box.

zmin()

double Box::zmin ( ) const

inline

This function returns the \(z_\text{min}\) coordinate of the box.

zwidth()

double Box::zwidth ( ) const

inline

This function returns the width \(z_\text{max}-z_\text{min}\) of the box.

Member Data Documentation

_xmin

double Box::_xmin

private

These data members represent the cartesian vector components

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

• Box.hpp