The three-dimensional point. More...

#include <mb_cart_point3d.h>

Collaboration diagram for MbCartPoint3D:

Public Member Functions
	MbCartPoint3D ()
	Constructor without parameters. A point is located at the origin of global coordinates.

	MbCartPoint3D (const MbCartPoint3D &p)
	Copy-constructor.

	MbCartPoint3D (const MbFloatPoint3D &)
	Copy-constructor.

	MbCartPoint3D (double xx, double yy, double zz)
	Constructor by coordinates.

	MbCartPoint3D (const MbCartPoint3D &p, const MbMatrix3D &matr)
	Constructor by a point in a local coordinate system. More...

	MbCartPoint3D (const MbCartPoint &p, const MbPlacement3D &place)
	Constructor by a two-dimensional point. More...

void	Init (const MbCartPoint &p, const MbPlacement3D &place)
	The initialization by two-dimensional point. More...

void	Init (const MbCartPoint &p)
	The initialization by two-dimensional point.

template<class Point >
MbCartPoint3D &	Init (const Point &p)
	Initialize by another point.

MbCartPoint3D &	Init (double xx, double yy, double zz)
	Initialize by coordinates.

MbCartPoint3D &	Transform (const MbMatrix3D &)
	Transform according to the matrix.

MbCartPoint3D &	Move (double dx, double dy, double dz)
	Translate along a vector.

MbCartPoint3D &	Move (const MbVector3D &to)
	Translate along a vector.

MbCartPoint3D &	Rotate (const MbAxis3D &, double angle)
	Rotate around an axis.

double	DistanceToPoint (const MbCartPoint3D &) const
	The distance to a point.

void	SetZero ()
	Set coordinates to zero.

double	DistanceToPoint2 (const MbCartPoint3D &to) const
	The squared distance between two points. More...

void	MoveAlongLine (const MbCartPoint3D &to, double delta)
	Translate in the direction of the "to" point on the "delta" distance.

void	GoNearToPoint (const MbCartPoint3D &to, double ratio)
	Translate along the direction. More...

void	Maximum (const MbCartPoint3D &p)
	The initialization by the maximum coordinates. More...

void	Minimum (const MbCartPoint3D &p)
	The initialization by the minimal coordinates. More...

void	Perspective (double znear)
	Increase coordinates x and y in ( znear / z ) times. More...

void	Mirror (const MbCartPoint3D &p0, const MbVector3D &dir)
	The specular reflection of a point relative to a plane. More...

void	Scale (double sx, double sy, double sz)
	Scale the coordinates. More...

void	Scale (double s)
	Scale the coordinates. More...

double	MaxFactor () const
	Get the maximum absolute coordinate

bool	SetRoundedValue (bool total, double eps)
	Rounded with eps tolerance. More...

void	GetProperties (MbProperties &)
	Get properties of the object.

void	SetProperties (const MbProperties &)
	Set properties of the object.

bool	IsSame (const MbCartPoint3D &other, double accuracy) const
	Are the objects equal? More...

bool	IsUndefined () const
	Is the point undefined?

Logical and arithmetical operations.
void	operator+= (const MbVector3D &)
	Add a vector.

void	operator-= (const MbVector3D &)
	Subtract a vector.

void	operator+= (const MbCartPoint3D &)
	Add point coordinates.

void	operator-= (const MbCartPoint3D &)
	Subtract point coordinates.

void	operator*= (double factor)
	Multiply coordinates by a factor.

void	operator/= (double factor)
	Divide coordinates by a factor.

bool	operator== (const MbCartPoint3D &) const
	Check for equality.

bool	operator!= (const MbCartPoint3D &) const
	Check for inequality.

bool	operator< (const MbCartPoint3D &) const
	Check for "less".

bool	operator> (const MbCartPoint3D &) const
	Check for "greater".

MbCartPoint3D &	operator= (const MbCartPoint3D &)
	Assign coordinates of another point to the point.

MbCartPoint3D &	operator= (const MbFloatPoint3D &)
	Assign coordinates of another point to the point.

MbCartPoint3D &	operator= (const MbVector3D &)
	Assign vector components to the point.

MbCartPoint3D &	operator= (const MbHomogeneous3D &)
	Assign values of uniform coordinates to the point.

MbCartPoint3D	operator+ (const MbVector3D &) const
	Add a point and vector.

MbCartPoint3D	operator- (const MbVector3D &) const
	Subtract a vector from the point.

MbVector3D	operator+ (const MbCartPoint3D &) const
	Add two points.

MbVector3D	operator- (const MbCartPoint3D &) const
	Subtract a point from the point.

MbCartPoint3D	operator- () const
	The unary minus.

MbCartPoint3D	operator* (const MbMatrix3D &) const
	Calculate the point as this copy transformed by the matrix.

double &	operator[] (size_t i)
	Access to a coordinate by an index.

double	operator[] (size_t i) const
	The value of a coordinate by an index.

The functions of addition and multiplication of points with points and vectors.
MbCartPoint3D &	SetAdd (const MbCartPoint3D &v1, const MbVector3D &v2)
	Equate coordinates to sum of point coordinates and vector coordinates. More...

MbCartPoint3D &	SetDec (const MbCartPoint3D &v1, const MbVector3D &v2)
	Equate difference between the coordinates of point and vector to coordinates. More...

MbCartPoint3D &	Set (const MbCartPoint3D &v1, const MbVector3D &v2, double t2)
	Equate coordinates to sum of point coordinates and vector coordinates. More...

MbCartPoint3D &	Set (const MbCartPoint3D &v1, const MbVector3D &v2, double t2, const MbVector3D &v3, double t3)
	Equate coordinates to sum of point coordinates and two vectors coordinates. More...

MbCartPoint3D &	Set (const MbVector3D &v1, double t1, const MbVector3D &v2, double t2)
	Equate sum of the components of two vectors to coordinates. More...

MbCartPoint3D &	Set (const MbVector3D &v1, double t1, const MbVector3D &v2, double t2, const MbVector3D &v3, double t3, const MbVector3D &v4, double t4)
	Equate coordinates to sum of the components of four vectors. More...

MbCartPoint3D &	Set (const MbCartPoint3D &v1, double t1, const MbCartPoint3D &v2, double t2)
	Equate coordinates to sum of two points coordinates. More...

MbCartPoint3D &	Set (const MbCartPoint3D &v1, double t1, const MbCartPoint3D &v2, double t2, const MbCartPoint3D &v3, double t3)
	Equate coordinates to sum of three points coordinates. More...

MbCartPoint3D &	Set (const MbCartPoint3D &v1, double t1, const MbCartPoint3D &v2, double t2, const MbCartPoint3D &v3, double t3, const MbCartPoint3D &v4, double t4)
	Equate coordinates to sum of four points coordinates. More...

void	Add (const MbVector3D &v1, double t1)
	Increase coordinates by values of vector components. More...

void	Add (const MbVector3D &v1, double t1, const MbVector3D &v2, double t2)
	Increase coordinates by values of two vectors components. More...

void	Add (const MbVector3D &v1, double t1, const MbVector3D &v2, double t2, const MbVector3D &v3, double t3)
	Increase coordinates by values of three vectors components. More...

void	Add (const MbVector3D &v1, double t1, const MbVector3D &v2, double t2, const MbVector3D &v3, double t3, const MbVector3D &v4, double t4)
	Increase coordinates by components values of four vectors. More...

void	Add (const MbCartPoint3D &v1, double t1)
	Increase coordinates by values of point coordinates. More...

void	Add (const MbCartPoint3D &v1, double t1, const MbCartPoint3D &v2, double t2, const MbCartPoint3D &v3, double t3)
	Increase coordinates by values of three points coordinates. More...

void	Add (const MbCartPoint3D &v1, double t1, const MbCartPoint3D &v2, double t2, const MbCartPoint3D &v3, double t3, const MbCartPoint3D &v4, double t4)
	Increase coordinates by values of four points coordinates. More...

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

Public Attributes
double	x
	A first coordinate of point.

double	y
	A second coordinate of point.

double	z
	A third coordinate of point.

Static Public Attributes
static const MbCartPoint3D	origin
	The origin or { 0, 0, 0 }.

Detailed Description

The three-dimensional point.

The three-dimensional point (cartesian point) is defined by three coordinates in a cartesian coordinate system. The point is named cartesian in honor of French scientist Rene Descartes (lat. Renatus Cartesius).
A point can be defined by radius-vector. A radius-vector describes transform which translates a start point of a cartesian coordinate system to a space point with the given coordinates in this system.

Constructor & Destructor Documentation

◆ MbCartPoint3D() [1/2]

MbCartPoint3D::MbCartPoint3D	(	const MbCartPoint3D &	p,
		const MbMatrix3D &	matr
	)

Constructor by a point in a local coordinate system.

A transition matrix is given for transforming of a point to the global coordinate system from a local coordinate system.

Parameters

[in]	p	- A point in the local coordinate system.
[in]	matr	- A transition matrix from the local coordinate system to the global coordinate system.

◆ MbCartPoint3D() [2/2]

MbCartPoint3D::MbCartPoint3D	(	const MbCartPoint &	p,
		const MbPlacement3D &	place
	)

Constructor by a two-dimensional point.

A two-dimensional point is located in the XOY plane defined by a local coordinate system.

Parameters

[in]	p	- A two-dimensional point.
[in]	place	- The initial local coordinate system.

Member Function Documentation

◆ Init()

void MbCartPoint3D::Init	(	const MbCartPoint &	p,
		const MbPlacement3D &	place
	)

The initialization by two-dimensional point.

A two-dimensional point is located in the XOY plane defined by a local coordinate system.

Parameters

[in]	p	- A two-dimensional point.
[in]	place	- The initial local coordinate system.

◆ DistanceToPoint2()

double MbCartPoint3D::DistanceToPoint2 ( const MbCartPoint3D & to ) const

inline

The squared distance between two points.

Calculate the squared distance from point to point.

Parameters

[in] to - A point.

Returns: The squared distance between two points.

◆ GoNearToPoint()

void MbCartPoint3D::GoNearToPoint	(	const MbCartPoint3D &	to,
		double	ratio
	)

inline

Translate along the direction.

The translation in the direction of point "to" to the distance which is defined by the ratio of "ratio" and the distance between points.

Parameters

[in]	to	- A point.
[in]	ratio	- A distance part.

◆ Maximum()

void MbCartPoint3D::Maximum ( const MbCartPoint3D & p )

inline

The initialization by the maximum coordinates.

A coordinate x (or y, z) of a point is initialized by maximum value which is got from comparison of corresponding coordinate of initial point and point given in function argument.

Parameters

[in] p - A given point.

◆ Minimum()

void MbCartPoint3D::Minimum ( const MbCartPoint3D & p )

inline

The initialization by the minimal coordinates.

A coordinate x (or y, z) of a point is initialized by minimal value which is got from comparison of corresponding coordinate of initial point and point given in function argument.

Parameters

[in] p - A given point.

◆ Perspective()

void MbCartPoint3D::Perspective ( double znear )

Increase coordinates x and y in ( znear / z ) times.

The increase of coordinates is produced for a perspective transformation. A point must be located in a local or view coordinate system. Z-coordinate of a point can't be equal to zero.

Parameters

[in] znear - The value znear/z defines the scale factor.

◆ Mirror()

void MbCartPoint3D::Mirror	(	const MbCartPoint3D &	p0,
		const MbVector3D &	dir
	)

inline

The specular reflection of a point relative to a plane.

The specular reflection of a point relative to a plane with origin "p0" and normal "dir".

Parameters

[in]	p0	- A point of plane of symmetry.
[in]	dir	- A direction of normal of plane of symmetry.

◆ SetAdd()

MbCartPoint3D & MbCartPoint3D::SetAdd	(	const MbCartPoint3D &	v1,
		const MbVector3D &	v2
	)

inline

Equate coordinates to sum of point coordinates and vector coordinates.

Parameters

[in]	v1	- The initial point.
[in]	v2	- The initial vector.

◆ SetDec()

MbCartPoint3D & MbCartPoint3D::SetDec	(	const MbCartPoint3D &	v1,
		const MbVector3D &	v2
	)

inline

Equate difference between the coordinates of point and vector to coordinates.

Parameters

[in]	v1	- The initial point.
[in]	v2	- The initial vector.

◆ Set() [1/7]

MbCartPoint3D & MbCartPoint3D::Set	(	const MbCartPoint3D &	v1,
		const MbVector3D &	v2,
		double	t2
	)

inline

Equate coordinates to sum of point coordinates and vector coordinates.

Equate coordinates to sum of v1 point coordinates and v2 vector coordinates multiplied by t2.

Parameters

[in]	v1	- The initial point.
[in]	v2	- The initial vector.
[in]	t2	- Factor the coordinates of the initial vector v2 are multiplied by.

◆ Set() [2/7]

MbCartPoint3D & MbCartPoint3D::Set	(	const MbCartPoint3D &	v1,
		const MbVector3D &	v2,
		double	t2,
		const MbVector3D &	v3,
		double	t3
	)

inline

Equate coordinates to sum of point coordinates and two vectors coordinates.

Equate coordinates to sum of v1 point coordinates and v2 and v3 vectors coordinates multiplied by the numbers t2 and t3 respectively.

Parameters

[in]	v1	- The initial point.
[in]	v2,v3	- The initial vectors.
[in]	t2,t3	- Coordinates of v2 and v3 vectors are multiplied by these numbers respectively.

◆ Set() [3/7]

MbCartPoint3D & MbCartPoint3D::Set	(	const MbVector3D &	v1,
		double	t1,
		const MbVector3D &	v2,
		double	t2
	)

inline

Equate sum of the components of two vectors to coordinates.

Equate coordinates to sum of v1 and v2 vectors components multiplied by the numbers t1 and t2 respectively.

Parameters

[in]	v1,v2	- The initial vectors.
[in]	t1,t2	- Coordinates of v1 and v2 vectors are multiplied by these numbers respectively.

◆ Set() [4/7]

MbCartPoint3D & MbCartPoint3D::Set	(	const MbVector3D &	v1,
		double	t1,
		const MbVector3D &	v2,
		double	t2,
		const MbVector3D &	v3,
		double	t3,
		const MbVector3D &	v4,
		double	t4
	)

inline

Equate coordinates to sum of the components of four vectors.

Equate coordinates to sum of v1, v2, v3 and v4 vectors components multiplied by the numbers t1, t2, t3 and t4 respectively.

Parameters

[in]	v1,v2,v3,v4	- The initial vectors.
[in]	t1,t2,t3,t4	- Coordinates of v1, v2, v3 and v4 vectors are multiplied by these numbers respectively.

◆ Set() [5/7]

MbCartPoint3D & MbCartPoint3D::Set	(	const MbCartPoint3D &	v1,
		double	t1,
		const MbCartPoint3D &	v2,
		double	t2
	)

inline

Equate coordinates to sum of two points coordinates.

Equate coordinates to sum of v1 and v2 points coordinates multiplied by the numbers t1 and t2 respectively.

Parameters

[in]	v1,v2	- Initial points.
[in]	t1,t2	- Coordinates of v1 and v2 points are multiplied by these numbers respectively.

◆ Set() [6/7]

MbCartPoint3D & MbCartPoint3D::Set	(	const MbCartPoint3D &	v1,
		double	t1,
		const MbCartPoint3D &	v2,
		double	t2,
		const MbCartPoint3D &	v3,
		double	t3
	)

inline

Equate coordinates to sum of three points coordinates.

Equate coordinates to sum of v1, v2 and v3 points coordinates multiplied by the numbers t1, t2 and t3 respectively.

Parameters

[in]	v1,v2,v3	- Initial points.
[in]	t1,t2,t3	- Coordinates of v1, v2 and v3 points are multiplied by these numbers respectively.

◆ Set() [7/7]

MbCartPoint3D & MbCartPoint3D::Set	(	const MbCartPoint3D &	v1,
		double	t1,
		const MbCartPoint3D &	v2,
		double	t2,
		const MbCartPoint3D &	v3,
		double	t3,
		const MbCartPoint3D &	v4,
		double	t4
	)

inline

Equate coordinates to sum of four points coordinates.

Equate coordinates to sum of v1, v2, v3 and v4 points coordinates multiplied by the numbers t1, t2, t3 and t4 respectively.

Parameters

[in]	v1,v2,v3,v4	- Initial points.
[in]	t1,t2,t3,t4	- Coordinates of v1, v2, v3 and v4 points are multiplied by these numbers respectively.

◆ Add() [1/7]

void MbCartPoint3D::Add	(	const MbVector3D &	v1,
		double	t1
	)

inline

Increase coordinates by values of vector components.

Increase coordinates by values of v1 vector components multiplied by t1.

Parameters

[in]	v1	- The initial vector.
[in]	t1	- Coordinates of the initial vector v1 are multiplied by this number.

◆ Add() [2/7]

void MbCartPoint3D::Add	(	const MbVector3D &	v1,
		double	t1,
		const MbVector3D &	v2,
		double	t2
	)

inline

Increase coordinates by values of two vectors components.

Increase coordinates by values of v1 and v2 vectors components multiplied by the numbers t1 and t2 respectively.

Parameters

[in]	v1,v2	- The initial vectors.
[in]	t1,t2	- Coordinates of v1 and v2 vectors are multiplied by these numbers respectively.

◆ Add() [3/7]

void MbCartPoint3D::Add	(	const MbVector3D &	v1,
		double	t1,
		const MbVector3D &	v2,
		double	t2,
		const MbVector3D &	v3,
		double	t3
	)

inline

Increase coordinates by values of three vectors components.

Increase coordinates by values of v1, v2 and v3 vectors components multiplied by the numbers t1, t2 and t3 respectively.

Parameters

[in]	v1,v2,v3	- The initial vectors.
[in]	t1,t2,t3	- Coordinates of v1, v2 and v3 vectors are multiplied by these numbers respectively.

◆ Add() [4/7]

void MbCartPoint3D::Add	(	const MbVector3D &	v1,
		double	t1,
		const MbVector3D &	v2,
		double	t2,
		const MbVector3D &	v3,
		double	t3,
		const MbVector3D &	v4,
		double	t4
	)

inline

Increase coordinates by components values of four vectors.

Increase coordinates by components values of vectors v1, v2, v3 and v4 multiplied by the numbers t1, t2, t3 and t4 respectively.

Parameters

[in]	v1,v2,v3,v4	- The initial vectors.
[in]	t1,t2,t3,t4	- Coordinates of v1, v2, v3 and v4 vectors are multiplied by these numbers respectively.

◆ Add() [5/7]

void MbCartPoint3D::Add	(	const MbCartPoint3D &	v1,
		double	t1
	)

inline

Increase coordinates by values of point coordinates.

Increase coordinates by values of v1 point coordinates multiplied by t1.

Parameters

[in]	v1	- The initial point.
[in]	t1	- Coordinates of the initial point v1 are multiplied by this number.

◆ Add() [6/7]

void MbCartPoint3D::Add	(	const MbCartPoint3D &	v1,
		double	t1,
		const MbCartPoint3D &	v2,
		double	t2,
		const MbCartPoint3D &	v3,
		double	t3
	)

inline

Increase coordinates by values of three points coordinates.

Increase coordinates by values of v1, v2 and v3 points coordinates multiplied by the numbers t1, t2 and t3 respectively.

Parameters

[in]	v1,v2,v3	- Initial points.
[in]	t1,t2,t3	- Coordinates of v1, v2 and v3 points are multiplied by these numbers respectively.

◆ Add() [7/7]

void MbCartPoint3D::Add	(	const MbCartPoint3D &	v1,
		double	t1,
		const MbCartPoint3D &	v2,
		double	t2,
		const MbCartPoint3D &	v3,
		double	t3,
		const MbCartPoint3D &	v4,
		double	t4
	)

inline

Increase coordinates by values of four points coordinates.

Increase coordinates by values of v1, v2, v3 and v4 points coordinates multiplied by the numbers t1, t2, t3 and t4 respectively.

Parameters

[in]	v1,v2,v3,v4	- Initial points.
[in]	t1,t2,t3,t4	- Coordinates of v1, v2, v3 and v4 points are multiplied by these numbers respectively.

◆ Scale() [1/2]

void MbCartPoint3D::Scale	(	double	sx,
		double	sy,
		double	sz
	)

inline

Scale the coordinates.

Parameters

[in] sx,sy,sz - Scale factors for x,y and z components respectively.

◆ Scale() [2/2]

void MbCartPoint3D::Scale ( double s )

inline

Scale the coordinates.

Parameters

[in] s - A scale factor.

◆ SetRoundedValue()

bool MbCartPoint3D::SetRoundedValue	(	bool	total,
		double	eps
	)

Rounded with eps tolerance.

Point coordinates are rounded with a given tolerance.

Parameters

[in]	total	- If true round anyway.
[in]	eps	- A round-off tolerance.

Returns: Returns true if round-off has been done.

◆ IsSame()

bool MbCartPoint3D::IsSame	(	const MbCartPoint3D &	other,
		double	accuracy
	)		const

inline

Are the objects equal?

The objects are equal if their data are equal with a given accuracy.

Parameters

[in]	other	- The object to compare.
[in]	accuracy	- The accuracy to compare.

Returns: Whether the objects are equal.

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

mb_cart_point3d.h

Public Member Functions

Static Public Member Functions

Public Attributes

Static Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ MbCartPoint3D() [1/2]

◆ MbCartPoint3D() [2/2]

Member Function Documentation

◆ Init()

◆ DistanceToPoint2()

◆ GoNearToPoint()

◆ Maximum()

◆ Minimum()

◆ Perspective()

◆ Mirror()

◆ SetAdd()

◆ SetDec()

◆ Set() [1/7]

◆ Set() [2/7]

◆ Set() [3/7]

◆ Set() [4/7]

◆ Set() [5/7]

◆ Set() [6/7]

◆ Set() [7/7]

◆ Add() [1/7]

◆ Add() [2/7]

◆ Add() [3/7]

◆ Add() [4/7]

◆ Add() [5/7]

◆ Add() [6/7]

◆ Add() [7/7]

◆ Scale() [1/2]

◆ Scale() [2/2]

◆ SetRoundedValue()

◆ IsSame()