The bounding box. More...

#include <mb_cube.h>

Collaboration diagram for MbCube:

Public Member Functions
	MbCube ()
	The empty constructor.

	MbCube (const MbCube &init)
	Copy constructor.

	MbCube (double xmin, double ymin, double zmin, double xmax, double ymax, double zmax, bool normalize=false)
	The constructor by coordinates. More...

	MbCube (const MbCartPoint3D &p0, const MbCartPoint3D &p1, bool normalize=false)
	The constructor by two points. More...

bool	IsEmpty () const
	The check for emptiness. More...

void	SetEmpty ()
	Set empty ("reverted").

void	Set (double xmin, double ymin, double zmin, double xmax, double ymax, double zmax, bool normalize=false)
	Initialize by coordinates. More...

void	Set (const MbCartPoint3D &p0, const MbCartPoint3D &p1, bool normalize=false)
	Initialize by two points. More...

void	Init (const MbCube &init)
	Initialize by another bounding box.

void	Init (const MbCartPoint3D &p0, const MbCartPoint3D &p1)
	Initialize by two points. More...

void	AddRect (const MbRect &r, const MbPlacement3D &place)
	Add bounding box. More...

void	ProjectionRect (const MbPlacement3D &place, MbRect &rect) const
	A projection onto the placement. More...

void	ProjectionRect (const MbPlacement3D &place, const MbVector3D &dir, MbRect &rect) const
	A projection onto the placement along a vector in either of two directions. More...

void	ProjectionRect (const MbCurve3D &curve, bool ext, MbRect1D &rect) const
	Calculate a parametric interval of the curve covering the projection of the box on the curve.

void	Normalize ()
	Normalize itself.

MbeItemLocation	GetLocation (const MbPlacement3D &pl, double eps) const
	Define the box position relative to the plane. More...

bool	InsideLocation (const MbPlacement3D &place, MbRect &rect, double eps) const
	Define the box position relative to the tube. More...

void	Include (double x, double y, double z)
	Enclose a point specified as XYZ. More...

template<class Point >
void	Include (const Point &)
	Enclose a point.

double	GetVolume (double eps=Math::metricRegion) const
	Give the volume of a box.

double	GetSquare (double eps=Math::metricRegion) const
	Give half of the area of the box faces.

double	GetLengthX () const
	Give the size of the X side of a box.

double	GetLengthY () const
	Give the size of the Y side of a box.

double	GetLengthZ () const
	Give the size of the Z side of a box.

double	GetDiagonal () const
	Give the size of box diagonal.

double	DistanceToPoint (const MbCartPoint3D &point) const
	Calculate the distance to the nearest boundary of the bounding box. More...

double	DistanceToPoint2 (const MbCartPoint3D &point) const
	Calculate the square of distance to a point.

double	DistanceToCube (const MbCube &cube, double eps=Math::metricRegion) const
	Calculate the distance to the box. More...

void	Enlarge (double delta)
	Expand the box in all directions on a "delta" amount.

void	Enlarge (double dx, double dy, double dz)
	Expand the box in all directions on a corresponding amount.

void	Move (const MbVector3D &to)
	Translate along a vector.

void	Transform (const MbMatrix3D &matrix)
	Transform according to the matrix.

void	Scale (double sx, double sy, double sz)
	Scale.

bool	IsSame (const MbCube &other, double accuracy) const
	Determine whether an object is equal?

double	GetMin (size_t k) const
	Access to a coordinate by an index.

double	GetMax (size_t k) const
	Access to a coordinate by an index.

double	GetSideLength (size_t k) const
	Get side length.

const MbCube &	GetCube () const
	Give itself.

size_t	GetVerticesCount () const
	Number of vertices.

size_t	GetVertices (std::vector< MbCartPoint3D > &points) const
	Give all vertices of the box. More...

void	GetVertex (ptrdiff_t index, MbCartPoint3D &p) const
	Get a box vertex by an index. More...

void	GetEdgeCentre (ptrdiff_t index, MbCartPoint3D &p) const
	Give the center of an edge by an index. More...

void	GetFaceCentre (ptrdiff_t index, MbCartPoint3D &p) const
	Give the center of a face by an index. More...

void	GetCentre (MbCartPoint3D &p) const
	Give the box center.

void	GetCenter (MbCartPoint3D &p) const
	Give the box center.

MbCartPoint3D	Centre () const
	The center of bounding box.

bool	GetControlPoint (size_t pIndex, MbCartPoint3D &p) const
	Give a box control point by its number. More...

size_t	GetControlPoints (SArray< MbCartPoint3D > &points) const
	Give all control points of the box. More...

size_t	GetNearestControlIndex (const MbCartPoint3D &p) const
	Give the number of the nearest control point of the box. More...

size_t	GetFixedControlIndex (size_t index) const
	Give the number of the opposite point. More...

bool	CalculateMatrix (size_t pIndex, const MbCartPoint3D &point, const MbCartPoint3D &fixedPoint, bool useFixed, bool isotropy, MbMatrix3D &matrix) const
	Calculate a deformation matrix. More...

Functions for access to fields.
void	SetXMin (double s)
	Set the minimal coordinate by X.

void	SetYMin (double s)
	Set the minimal coordinate by Y.

void	SetZMin (double s)
	Set the minimal coordinate by Z.

void	SetXMax (double s)
	Set the maximal coordinate by X.

void	SetYMax (double s)
	Set the maximal coordinate by Y.

void	SetZMax (double s)
	Set the maximal coordinate by Z.

double	GetXMin () const
	Give the minimal coordinate by X.

double	GetYMin () const
	Give the minimal coordinate by Y.

double	GetZMin () const
	Give the minimal coordinate by Z.

double	GetXMax () const
	Give the maximal coordinate by X.

double	GetYMax () const
	Give the maximal coordinate by Y.

double	GetZMax () const
	Give the maximal coordinate by Z.

Overload of logical operations.
void	operator= (const MbCube &)
	Assign a value.

template<class Point >
MbCube &	operator\|= (const Point &)
	Enclose a point.

MbCube &	operator\|= (const MbCube &)
	Enclose a bounding box.

bool	operator== (const MbCube &) const
	The equality operator.

bool	operator!= (const MbCube &) const
	The inequality operator.

The boolean operations of a box with a point, line, plane and another box.
template<class Point >
bool	Contains (const Point &) const
	Check whether a point is inside the box or not. More...

template<class Point >
bool	Contains (const Point &, double eps) const
	Check whether a point is inside the box or not. More...

bool	Contains (const MbCube &) const
	Check whether a box is inside another box or not. More...

bool	Contains (const MbCube &, double eps) const
	Check whether a box is inside another box or not. More...

bool	Intersect (const MbCube &other, double eps=(c3d::MIN_RADIUS+c3d::MIN_RADIUS)) const
	Whether the box intersects another box or not. More...

bool	Intersect (const MbPlacement3D &pl, double eps=c3d::MIN_RADIUS) const
	Whether the box intersects the XY plane of a local coordinate system or not. More...

bool	Intersect (const MbCartPoint3D &, const MbVector3D &, double eps=Math::metricRegion) const
	Whether the box intersects the line or not. More...

bool	Intersect (const MbCartPoint3D &p, const MbVector3D &axis, SArray< double > &param, double delta=Math::metricRegion) const
	Find an intersection of a line with the box "surface". More...

bool	Intersect (const MbPlacement3D &placement, double radius, SArray< double > &param, double delta=Math::metricRegion) const
	The intersection of the box with a circle. More...

bool	Intersection (const MbCube &cube1, const MbCube &cube2, double eps=c3d::MIN_RADIUS)
	A box of intersection of two boxes. More...

bool	Union (const MbCube &cube1, const MbCube &cube2)
	A box of union of two boxes. More...

Static Public Member Functions
static size_t	GetDimension ()
	The number of point coordinates.

Public Attributes
MbCartPoint3D	pmin
	A point of a box diagonal with minimal coordinates.

MbCartPoint3D	pmax
	A point of a box diagonal with maximal coordinates.

Detailed Description

The bounding box.

The bounding box is a domain (block) of 3D-space bounded by parallelepiped with edges parallel to the axes of coordinate system.
It is used for quick estimation of the proximity or non-intersection of three-dimensional objects, which are contained in the "box". Faces of "box" are parallel to planes of coordinate system. The bounding box is described by a pair of points which are located on the main diagonal of a box.

Constructor & Destructor Documentation

◆ MbCube() [1/2]

MbCube::MbCube	(	double	xmin,
		double	ymin,
		double	zmin,
		double	xmax,
		double	ymax,
		double	zmax,
		bool	normalize = `false`
	)

inline

The constructor by coordinates.

Parameters

[in]	xmin,ymin,zmin	- Coordinates of a box corner point with minimal coordinates.
[in]	xmax,ymax,zmax	- Coordinates of a box corner point with maximal coordinates.
[in]	normalize	- Normalize itself.

◆ MbCube() [2/2]

MbCube::MbCube	(	const MbCartPoint3D &	p0,
		const MbCartPoint3D &	p1,
		bool	normalize = `false`
	)

inline

The constructor by two points.

Parameters

[in]	p0	- A point of a box corner with minimal coordinates.
[in]	p1	- A point of a box corner with maximal coordinates.
[in]	normalize	- Normalize itself.

Member Function Documentation

◆ IsEmpty()

bool MbCube::IsEmpty ( ) const

inline

The check for emptiness.

A bounding box is empty if it doesn't contain any points of 3D-space

◆ Set() [1/2]

void MbCube::Set	(	double	xmin,
		double	ymin,
		double	zmin,
		double	xmax,
		double	ymax,
		double	zmax,
		bool	normalize = `false`
	)

inline

Initialize by coordinates.

Parameters

[in]	xmin,ymin,zmin	- Coordinates of a box corner point with minimal coordinates.
[in]	xmax,ymax,zmax	- Coordinates of a box corner point with maximal coordinates.
[in]	normalize	- Normalize itself.

◆ Set() [2/2]

void MbCube::Set	(	const MbCartPoint3D &	p0,
		const MbCartPoint3D &	p1,
		bool	normalize = `false`
	)

inline

Initialize by two points.

Parameters

[in]	p0	- A point of a box corner with minimal coordinates.
[in]	p1	- A point of a box corner with maximal coordinates.
[in]	normalize	- Normalize itself.

◆ Init()

void MbCube::Init	(	const MbCartPoint3D &	p0,
		const MbCartPoint3D &	p1
	)

inline

Initialize by two points.

Initialized box is normalized.

Parameters

[in]	p0	- A point of a box corner with minimal coordinates.
[in]	p1	- A point of a box corner with maximal coordinates.

◆ AddRect()

void MbCube::AddRect	(	const MbRect &	r,
		const MbPlacement3D &	place
	)

Add bounding box.

A bounding box is added in the local coordinate system of the initial box.

Parameters

[in]	r	- A bounding box.
[in]	place	- A local coordinate system.

◆ ProjectionRect() [1/2]

void MbCube::ProjectionRect	(	const MbPlacement3D &	place,
		MbRect &	rect
	)		const

A projection onto the placement.

Calculates a rectangle covering a projection of the box onto the placement.

Parameters

[in]	place	- A local coordinate system.
[out]	rect	- A rectangle covering a required projection.

◆ ProjectionRect() [2/2]

void MbCube::ProjectionRect	(	const MbPlacement3D &	place,
		const MbVector3D &	dir,
		MbRect &	rect
	)		const

A projection onto the placement along a vector in either of two directions.

Calculates a rectangle covering a projection of the box onto the placement along a vector in either of two directions.

Parameters

[in]	place	- A local coordinate system.
[in]	dir	- A direction vector.
[out]	rect	- A rectangle covering a required projection.

◆ GetLocation()

MbeItemLocation MbCube::GetLocation	(	const MbPlacement3D &	pl,
		double	eps
	)		const

Define the box position relative to the plane.

Define the box position relative to the plane XY of a local coordinate system, the Z axis of the local coordinate system is not taken into account here.

Parameters

[in]	pl	- A local coordinate system which defines a plane.
[in]	eps	- A metric tolerance.

Returns: Iloc_OnItem - box intersects the XY plane of a local coordinate system,
iloc_InItem - box is located over the XY plane of a local coordinate system,
iloc_OutOfItem - box is located under the XY plane of a local coordinate system.

◆ InsideLocation()

bool MbCube::InsideLocation	(	const MbPlacement3D &	place,
		MbRect &	rect,
		double	eps
	)		const

Define the box position relative to the tube.

Determine whether the box is inside the tube of rectangular section, given by a rectangle in the XY plane of a local coordinate system.

Parameters

[in]	place	- A local coordinate system in the XY plane of which a tube section is located.
[in]	rect	- A rectangle which defines a tube section.
[in]	eps	- A metric tolerance.

Returns: Returns true if the box is inside the tube.

◆ Include()

void MbCube::Include	(	double	x,
		double	y,
		double	z
	)

inline

Enclose a point specified as XYZ.

Parameters

[in] x,y,z - Coordinates of a point which has to be included in the box.

◆ Contains() [1/4]

template<class Point >

bool MbCube::Contains ( const Point & p ) const

inline

Check whether a point is inside the box or not.

Returns: Returns true if it is inside.

◆ Contains() [2/4]

template<class Point >

bool MbCube::Contains	(	const Point &	p,
		double	eps
	)		const

inline

Check whether a point is inside the box or not.

Parameters

[in] eps - A metric tolerance.

Returns: Returns true if it is inside.

◆ Contains() [3/4]

bool MbCube::Contains ( const MbCube & box ) const

inline

Check whether a box is inside another box or not.

Returns: Returns true if a box contains another.

◆ Contains() [4/4]

bool MbCube::Contains	(	const MbCube &	box,
		double	eps
	)		const

inline

Check whether a box is inside another box or not.

Returns: Returns true if a box contains another.

◆ Intersect() [1/5]

bool MbCube::Intersect	(	const MbCube &	other,
		double	eps = `(c3d::MIN_RADIUS+c3d::MIN_RADIUS)`
	)		const

Whether the box intersects another box or not.

Parameters

[in]	other	- Another box.
[in]	eps	- A metric tolerance.

Returns: Returns true if it intersects.

◆ Intersect() [2/5]

bool MbCube::Intersect	(	const MbPlacement3D &	pl,
		double	eps = `c3d::MIN_RADIUS`
	)		const

Whether the box intersects the XY plane of a local coordinate system or not.

Parameters

[in]	pl	- A placement which defines a plane.
[in]	eps	- A metric tolerance.

Returns: Returns true if it intersects.

◆ Intersect() [3/5]

bool MbCube::Intersect	(	const MbCartPoint3D &	,
		const MbVector3D &	,
		double	eps = `Math::metricRegion`
	)		const

Whether the box intersects the line or not.

A line is given by a point and vector.

Parameters

[in] eps - A metric tolerance.

Returns: Returns true if it intersects.

◆ Intersect() [4/5]

bool MbCube::Intersect	(	const MbCartPoint3D &	p,
		const MbVector3D &	axis,
		SArray< double > &	param,
		double	delta = `Math::metricRegion`
	)		const

Find an intersection of a line with the box "surface".

Parameters

[in]	p	- The point on the line.
[in]	axis	- A vector which defines the direction of the line.
[out]	param	- Intersection points.
[in]	delta	- A metric tolerance.

Returns: Returns true if intersection exists,
false otherwise.

◆ Intersect() [5/5]

bool MbCube::Intersect	(	const MbPlacement3D &	placement,
		double	radius,
		SArray< double > &	param,
		double	delta = `Math::metricRegion`
	)		const

The intersection of the box with a circle.

Parameters

[in]	placement	- A circle placement.
[in]	radius	- The circle radius.
[out]	param	- Intersection points.
[in]	delta	- A metric tolerance.

Returns: Returns true if intersection exists,
false otherwise.

◆ Intersection()

bool MbCube::Intersection	(	const MbCube &	cube1,
		const MbCube &	cube2,
		double	eps = `c3d::MIN_RADIUS`
	)

A box of intersection of two boxes.

Parameters

[in]	cube1,cube2	- Input boxes.
[in]	eps	- A metric tolerance.

Returns: Returns true if intersection exists,
false otherwise.

◆ Union()

bool MbCube::Union	(	const MbCube &	cube1,
		const MbCube &	cube2
	)

A box of union of two boxes.

Parameters

[in] cube1,cube2 - Input boxes.

Returns: Returns false if the result box is empty,
true otherwise.

◆ DistanceToPoint()

double MbCube::DistanceToPoint ( const MbCartPoint3D & point ) const

inline

Calculate the distance to the nearest boundary of the bounding box.

The calculated distance is negative if the point is inside, and is positive if it is outside.

Parameters

[in] point - The investigated point.

Returns: Returns the distance to the boundary.

◆ DistanceToCube()

double MbCube::DistanceToCube	(	const MbCube &	cube,
		double	eps = `Math::metricRegion`
	)		const

Calculate the distance to the box.

It returns zero if the boxes intersect or one is contained in the other.

Parameters

[in]	cube	- Other cube.
[in]	eps	- A metric tolerance.

Returns: Returns the distance to the boundary.

◆ GetVertices()

size_t MbCube::GetVertices ( std::vector< MbCartPoint3D > & points ) const

Give all vertices of the box.

Parameters

[out] points - Vertices.

Returns: The number of vertices. Null if the box is empty.

◆ GetVertex()

void MbCube::GetVertex	(	ptrdiff_t	index,
		MbCartPoint3D &	p
	)		const

Get a box vertex by an index.

Parameters

[in]	index	- An initial index. 0 <= index <= 7.
[out]	p	- Required vertex.

◆ GetEdgeCentre()

void MbCube::GetEdgeCentre	(	ptrdiff_t	index,
		MbCartPoint3D &	p
	)		const

Give the center of an edge by an index.

Parameters

[in]	index	- An initial index. 0 <= index <= 12 ("general number" minus CUBE_VERTEX_COUNT).
[out]	p	- Coordinates of an edge center.

◆ GetFaceCentre()

void MbCube::GetFaceCentre	(	ptrdiff_t	index,
		MbCartPoint3D &	p
	)		const

Give the center of a face by an index.

Parameters

[in]	index	- An initial index. 0 <= index <= 5 ("general number" minus CUBE_VERTEX_COUNT minus CUBE_EDGES_COUNT).
[out]	p	- Coordinates of an edge center.

◆ GetControlPoint()

bool MbCube::GetControlPoint	(	size_t	pIndex,
		MbCartPoint3D &	p
	)		const

Give a box control point by its number.

General numeration of box control points: 0-7 vertices, 8-19 middles of edges, 20-25 centers of faces.

Parameters

[in]	pIndex	- A number of control points.
[out]	p	- Coordinates of control point.

Returns: Returns false if the box is empty or the index has an invalid value,
true otherwise.

◆ GetControlPoints()

size_t MbCube::GetControlPoints ( SArray< MbCartPoint3D > & points ) const

Give all control points of the box.

All control points of the box: 8 vertices, 12 middles of edges, 6 centers of faces.

Parameters

[out] points - Control points.

Returns: The number of control points. Null if the box is empty.

◆ GetNearestControlIndex()

size_t MbCube::GetNearestControlIndex ( const MbCartPoint3D & p ) const

Give the number of the nearest control point of the box.

Parameters

[in] p - An initial point for which the nearest control point of the box is searched.

Returns: A number of a point.

◆ GetFixedControlIndex()

size_t MbCube::GetFixedControlIndex ( size_t index ) const

Give the number of the opposite point.

For a box point with the "index" number give the number of the opposite point, which can be used as fixed.

Parameters

[in] index - The number of the initial point.

Returns: A number of the opposite point.

◆ CalculateMatrix()

bool MbCube::CalculateMatrix	(	size_t	pIndex,
		const MbCartPoint3D &	point,
		const MbCartPoint3D &	fixedPoint,
		bool	useFixed,
		bool	isotropy,
		MbMatrix3D &	matrix
	)		const

Calculate a deformation matrix.

A deformation matrix is calculated according to the new position of box control point "point" with the index "pIndex".

Parameters

[in]	pIndex	- A number of a moved point (0-7 vertices, 8-19 middles of edges, 20-25 centers of faces).
[in]	point	- A point with which the box point with the "pIndex" number has to be joined.
[in]	fixedPoint	- A fixed point. It is used if useFixed = true.
[in]	useFixed	- Use a fixed point (true); if useFixed = false, then the opposite point of the box will be fixed.
[in]	isotropy	- The same scales of the axes (true); the scales are proportional to the shift projections of the considered point on the sides of the box (false)
[out]	matrix	- Calculated transformation matrix.

Returns: Returns true if the matrix was found.

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

mb_cube.h

Public Member Functions

Static Public Member Functions

Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ MbCube() [1/2]

◆ MbCube() [2/2]

Member Function Documentation

◆ IsEmpty()

◆ Set() [1/2]

◆ Set() [2/2]

◆ Init()

◆ AddRect()

◆ ProjectionRect() [1/2]

◆ ProjectionRect() [2/2]

◆ GetLocation()

◆ InsideLocation()

◆ Include()

◆ Contains() [1/4]

◆ Contains() [2/4]

◆ Contains() [3/4]

◆ Contains() [4/4]

◆ Intersect() [1/5]

◆ Intersect() [2/5]

◆ Intersect() [3/5]

◆ Intersect() [4/5]

◆ Intersect() [5/5]

◆ Intersection()

◆ Union()

◆ DistanceToPoint()

◆ DistanceToCube()

◆ GetVertices()

◆ GetVertex()

◆ GetEdgeCentre()

◆ GetFaceCentre()

◆ GetControlPoint()

◆ GetControlPoints()

◆ GetNearestControlIndex()

◆ GetFixedControlIndex()

◆ CalculateMatrix()