The extended matrix of transformation in a three-dimensional space. More...

#include <mb_matrix3d.h>

Collaboration diagram for MbMatrix3D:

Public Member Functions
	MbMatrix3D ()
	Default constructor. Defines the identity matrix.

	MbMatrix3D (const MbMatrix3D &init)
	The copy constructor.

	MbMatrix3D (const MbPlacement3D &place)
	The constructor by placement.

	MbMatrix3D (const MbMatrix &m)
	The constructor by a two-dimensional matrix.

	MbMatrix3D (const MbMatrix3D &A, const MbMatrix3D &B)
	The constructor by two matrices. More...

	~MbMatrix3D ()
	Destructor.

void	MouldCavityScale (MbCartPoint3D &fixedPoint, double deltaX, double deltaY, double deltaZ)
	Get the matrix for scale of a mold cavern. More...

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

void	Normalize ()
	Normalize.

bool	CalculateFixedPoint (MbCartPoint3D &fixedPoint) const
	Calculate a fixed point of transformation.

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

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

Initialization functions.
MbMatrix3D &	Init ()
	Initialize a matrix as unit one.

MbMatrix3D &	Init (const MbMatrix3D &)
	Initialize by elements of another matrix.

MbMatrix3D &	Init (const MbMatrix &)
	Initialize by a two-dimensional matrix.

MbMatrix3D &	Init (const MbPlacement3D &)
	Initialize by a placement.

MbMatrix3D &	Init (const MbMatrix3D &a, const MbMatrix3D &b)
	Initialize by the product of given matrices. More...

Functions for check of matrices properties.
bool	IsInvert () const
	Get an attribute of negativity of the determinant of a rotation matrix.

bool	IsSingle () const
	Get an attribute of unit matrix.

bool	IsSingleEps (double eps=PARAM_EPSILON) const
	Get an attribute of the identity matrix with a given tolerance.

bool	IsTranslation () const
	Get an attribute of inequality to zero of translation vector.

bool	IsRotation () const
	Get an attribute of non-identity of a rotation matrix.

bool	IsReflection () const
	Get an attribute of negativity of the determinant of a rotation matrix.

bool	IsLeft () const
	Get an attribute of the left-definite matrix.

bool	IsOrt () const
	Get an attribute of orthogonality for the case if the matrix is affine.

bool	IsOrthogonal () const
	Get an attribute of orthogonality for the case if the matrix is a rotation matrix.

bool	IsAffine () const
	Get an attribute that the rotational matrix is arbitrary and affine.

bool	IsScaling () const
	Get an attribute of inequality to 1.0 of a scale component. More...

bool	IsPerspective () const

bool	IsUnSet () const
	Check whether bit flags are not set.

bool	IsSame (const MbMatrix3D &, double accuracy) const
	Determine whether an object is equal?

bool	IsAbsIdentical (const MbMatrix3D &m) const
	Get an attribute of unit matrices.

bool	IsTranslationOnly () const
	Get an attribute that there is only translation.

bool	IsSubstitutionOnly (double epsilon=METRIC_EPSILON) const
	Are the axis described by the matrix local system coincide with global axes up to a 90-degree rotation?

bool	IsIsotropic (double &l) const
	Get an attribute of isotropism. More...

Functions of access to matrix elements.
double	El (size_t i, size_t j) const
	Get an element of the matrix.

const double *	GetEl () const
	Get a pointer to the first matrix element.

const MbVector3D &	GetAxisX () const
	Get the first row (the X-axis).

const MbVector3D &	GetAxisY () const
	Get the second row (the Y-axis).

const MbVector3D &	GetAxisZ () const
	Get the third row (the Z-axis).

const MbCartPoint3D &	GetOrigin () const
	Get the fourth row (the origin of coordinates)

MbVector3D	GetColumn (size_t i) const
	Get the i-th column vector of the matrix.

MbVector3D	GetRow (size_t i) const
	Get the i-th row-vector of the matrix.

MbHomogeneous3D	GetFullColumn (size_t i) const
	Get the i-th column vector of the matrix.

MbHomogeneous3D	GetFullRow (size_t i) const
	Get the i-th row-vector of the matrix.

void	GetOffset (MbCartPoint3D &p) const
	Get components of matrix translation.

Functions for matrix elements modification.
void	SetEl (const double *_el)
	Assign a value to matrix elements. More...

GLdouble *	SetEl ()
	Get an array of matrix elements. More...

void	El (size_t i, size_t j, double e)
	Assign a value to the matrix element. More...

void	AddEl (size_t i, size_t j, double e)
	Add a number to the matrix element. More...

void	MulEl (size_t i, size_t j, double e)
	Multiply the matrix element by a number. More...

MbVector3D &	SetAxisX ()
	Get the first row (the X-axis).

MbVector3D &	SetAxisY ()
	Get the second row (the Y-axis).

MbVector3D &	SetAxisZ ()
	Get the third row (the Z-axis).

MbCartPoint3D &	SetOrigin ()
	Give the fourth row (the origin of coordinates)

void	SetOriginZ (double or_z)
	Set Z component of the origin.

void	SetColumn (size_t i, const MbCartPoint3D &)
	Set values in the i-th column of the matrix.

void	SetColumn (size_t i, const MbVector3D &)
	Set values in the i-th column of the matrix.

void	SetColumn (size_t i, const MbHomogeneous3D &)
	Set values in the i-th column of the matrix.

void	SetRow (size_t i, const MbCartPoint3D &)
	Set values in the i-th row of the matrix.

void	SetRow (size_t i, const MbVector3D &)
	Set values in the i-th row of the matrix.

void	SetRow (size_t i, const MbHomogeneous3D &)
	Set values in the i-th row of the matrix.

void	SetOffset (const MbCartPoint3D &p)
	Set components of matrix translation.

void	SetFlag (bool bReflection, bool bAffine=false, bool bOrt=true) const
	Set the flag of state. More...

Matrices multiplication.
void	Multiply (const MbMatrix3D &b)
	Multiply by a matrix: this = this * b;.

void	Multiply (const MbMatrix3D &a, const MbMatrix3D &b)
	Multiply matrices this = a * b.

Scaling functions.
void	Scale (double sx, double sy, double sz)
	Scale by X, Y and Z. More...

void	Scale (double s)
	Scale by X, Y and Z.

void	ScaleX (double s)
	Scale by X.

void	ScaleY (double s)
	Scale by Y.

void	ScaleZ (double s)
	Scale by Z.

void	ScaleAxes (double s)
	Scale by X, Y and Z without translation.

double	GetScaleX () const
	Get scaling coefficient by X.

double	GetScaleY () const
	Get scaling coefficient by Y.

double	GetScaleZ () const
	Get scaling coefficient by Z.

Functions of matrix transformations: translation, rotation, etc.
void	Move (const MbVector3D &to)
	Translate by a given vector.

void	Move (double dx, double dy, double dz)
	Translate by given increments.

void	MoveZero ()
	Translate to null.

MbMatrix3D &	RotateAbout (const MbVector3D &axisDir, double angle)
	Rotate around an axis. More...

MbMatrix3D &	Rotate (const MbAxis3D &axis, double angle)
	Rotate around axis by angle.

MbMatrix3D &	Rotate (int axis, double angle)
	Rotate around an axis. More...

void	TransformLength (double &len, int axis=1) const
	Transform the length. More...

void	TransformCoord2D (double &x, double &y) const
	Transform coordinates. More...

MbMatrix3D &	Transform (const MbMatrix3D &matr)
	Transform according to the given matrix.

void	Invert (size_t n)
	Invert the axis.

MbMatrix3D &	Symmetry (const MbCartPoint3D &origin, const MbVector3D &normal)
	Set the matrix to symmetry transformation (reflection). More...

MbMatrix3D &	Symmetry (const MbCartPoint3D &origin, const MbVector3D &vx, const MbVector3D &vy)
	Set the matrix to symmetry transformation (reflection). More...

Calculation of the algebraic properties of a matrix.
void	Adj ()
	Transpose a matrix.

double	Delta (size_t line, size_t column, size_t dim) const
	Calculate the algebraic adjunct.

double	Det (size_t dim) const
	Calculate the determinant of a matrix.

MbMatrix3D &	Div (MbMatrix3D &) const
	Calculate inverse matrix. More...

Overload of arithmetical and logical operations.
MbMatrix3D	operator* (const MbMatrix3D &m) const
	Multiply by a matrix: M = this * m.

MbMatrix3D &	operator*= (const MbMatrix3D &m)
	Multiply by a matrix: this = this * m.

MbMatrix3D &	operator= (const MbMatrix3D &m)
	Assign a value.

void	operator+= (const MbMatrix3D &)
	Add matrices.

void	operator-= (const MbMatrix3D &)
	Subtract a matrix from the matrix.

void	operator*= (double factor)
	Multiply the matrix by a number.

void	operator/= (double factor)
	Divide the matrix by a number.

bool	operator== (const MbMatrix3D &) const
	Compare with a matrix (tolerance - LENGTH_EPSILON).

double &	operator() (size_t i, size_t j)
	Access to a matrix element by a reference.

const double &	operator() (size_t i, size_t j) const
	The value of a matrix element.

Static Public Attributes
static const MbMatrix3D	identity
	Identity matrix, I = diag(1,1,1,1);.

Detailed Description

The extended matrix of transformation in a three-dimensional space.

The extended matrix of transformation in a three-dimensional space.
The extended matrix has dimension (4, 4) and is a regular matrix bordered below by a translation vector and by the null column to the right. The transformation of point "p" by the matrix "M" has the form: r = p * M (the row of coordinates is multiplied by the matrix to the left).
The transformation matrix from a local coordinate system can be obtained as follows:
the first row must be filled with the corresponding components of the first vector of a locale system, the second row must be filled with the corresponding components of the second vector of a local system, the third row must be filled with the corresponding components of the third vector of a locale system, the last row of the matrix must be filled with the corresponding coordinates of a local system origin. The matrix of transformation consists of four blocks:

| R, P |
| V, S |
where R - is a rotation matrix, the tensor with dimension (3, 3), V - translation vector, tensor (0, 3), P - perspective vector, tensor (3, 0) (always is null) S - scalar of scale transformation (the unit). \ n To speed up the calculation the matrix has additional data - flag of state.
Use "Get..." methods to get data of matrix from the outside.
To modify data of a matrix from the outside use "Set..." methods which automatically reset the system flag to unspecified state.

Constructor & Destructor Documentation

◆ MbMatrix3D()

MbMatrix3D::MbMatrix3D	(	const MbMatrix3D &	A,
		const MbMatrix3D &	B
	)

inlineexplicit

The constructor by two matrices.

Matrix is defined as the product of two initial matrices: C = (B * A).

Parameters

[in] A,B - Initial matrices.

Member Function Documentation

◆ Init()

MbMatrix3D& MbMatrix3D::Init	(	const MbMatrix3D &	a,
		const MbMatrix3D &	b
	)

Initialize by the product of given matrices.

Initialize by the product of given matrices. this = b * a (!= a * b)!!!.

Parameters

[in] a,b - Initial matrices.

◆ IsScaling()

bool MbMatrix3D::IsScaling ( ) const

inline

Get an attribute of inequality to 1.0 of a scale component.

Get an attribute of inequality to zero of perspective vector.

◆ IsIsotropic()

bool MbMatrix3D::IsIsotropic ( double & l ) const

Get an attribute of isotropism.

Checks whether the matrix is ??orthogonal with equal lengths of
X, Y and Z axes (circle remains a circle)

Parameters

[out] l - The length of the X, Y and Z axes orts.

Returns: Returns true if the matrix is isotropic.

◆ SetEl() [1/2]

void MbMatrix3D::SetEl ( const double * _el )

inline

Assign a value to matrix elements.

Matrix elements are initialized by elements of initial array.

Parameters

[in] _el - Initial array.

◆ SetEl() [2/2]

GLdouble* MbMatrix3D::SetEl ( )

inline

Get an array of matrix elements.

ONLY FOR OGL !!!

Returns: The pointer to the array of the matrix elements.

◆ El()

void MbMatrix3D::El	(	size_t	i,
		size_t	j,
		double	e
	)

inline

Assign a value to the matrix element.

Parameters

[in]	i	- A row index.
[in]	j	- A column index.
[in]	e	- Initial value which to be assigned to an element of the matrix.

◆ AddEl()

void MbMatrix3D::AddEl	(	size_t	i,
		size_t	j,
		double	e
	)

inline

Add a number to the matrix element.

Parameters

[in]	i	- A row index.
[in]	j	- A column index.
[in]	e	- Initial number which to be added to the matrix element.

◆ MulEl()

void MbMatrix3D::MulEl	(	size_t	i,
		size_t	j,
		double	e
	)

inline

Multiply the matrix element by a number.

Parameters

[in]	i	- A row index.
[in]	j	- A column index.
[in]	e	- Initial number by which to multiply the matrix element.

◆ SetFlag()

void MbMatrix3D::SetFlag	(	bool	bReflection,
		bool	bAffine = `false`,
		bool	bOrt = `true`
	)		const

Set the flag of state.

Parameters

[in]	bReflection	- Negativity flag of the rotation matrix determinant.
[in]	bAffine	- Affinity flag.
[in]	bOrt	- Orthogonality flag.

◆ Scale()

void MbMatrix3D::Scale	(	double	sx,
		double	sy,
		double	sz
	)

Scale by X, Y and Z.

Parameters

[in] sx,sy,sz - Scaling coefficients for each axis.

◆ RotateAbout()

MbMatrix3D& MbMatrix3D::RotateAbout	(	const MbVector3D &	axisDir,
		double	angle
	)

Rotate around an axis.

Rotate around an axis which passes through the origin in the axisDir direction.

Parameters

[in]	axisDir	- A vector which defines the direction of rotation.
[in]	angle	- A rotation angle.

Returns: Returns the reference to this matrix.

◆ Rotate()

MbMatrix3D& MbMatrix3D::Rotate	(	int	axis,
		double	angle
	)

Rotate around an axis.

Rotate around the X, Y, or Z axis.

Parameters

[in]	axis	- The number of axis, i.e. AXIS_0X, AXIS_0Y or AXIS_0Z.
[in]	angle	- A rotation angle.

Returns: Returns the reference to this matrix.

◆ TransformLength()

void MbMatrix3D::TransformLength	(	double &	len,
		int	axis = `1`
	)		const

Transform the length.

The length is transformed according to a matrix (*this).

Parameters

[in,out]	len	- A length.
[in]	axis	- An axis on which the length is measured.

◆ TransformCoord2D()

void MbMatrix3D::TransformCoord2D	(	double &	x,
		double &	y
	)		const

inline

Transform coordinates.

Coordinates are transformed according to a matrix. Two coordinates are transformed (z=0).

Parameters

[in,out] x,y - Coordinates by x and y.

◆ Symmetry() [1/2]

MbMatrix3D& MbMatrix3D::Symmetry	(	const MbCartPoint3D &	origin,
		const MbVector3D &	normal
	)

Set the matrix to symmetry transformation (reflection).

The matrix of symmetry transformation is found relative to the plane which is defined by a point and normal.

Parameters

[in]	origin	- A point of plane.
[in]	normal	- The normal of a plane.

Returns: Returns the reference to this matrix.

◆ Symmetry() [2/2]

MbMatrix3D& MbMatrix3D::Symmetry	(	const MbCartPoint3D &	origin,
		const MbVector3D &	vx,
		const MbVector3D &	vy
	)

Set the matrix to symmetry transformation (reflection).

The matrix of symmetry transformation is found relative to the plane which is defined by a point and two vectors.

Parameters

[in]	origin	- A point of plane (an origin).
[in]	vx,vy	- Vectors which parallel for a plane.

Returns: Returns the reference to this matrix.

◆ Div()

MbMatrix3D& MbMatrix3D::Div ( MbMatrix3D & ) const

Calculate inverse matrix.

Returns: The function returns the argument passed by reference with the result of calculating the inverse matrix.

◆ MouldCavityScale()

void MbMatrix3D::MouldCavityScale	(	MbCartPoint3D &	fixedPoint,
		double	deltaX,
		double	deltaY,
		double	deltaZ
	)

Get the matrix for scale of a mold cavern.

Parameters

[in]	fixedPoint	- Fixed point.
[in]	deltaX,deltaY,deltaZ	- Relative increment of size in the direction of corresponding coordinate.

◆ SetRoundedValue()

bool MbMatrix3D::SetRoundedValue	(	bool	total,
		double	eps
	)

Round with eps tolerance.

Parameters

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

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

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

mb_matrix3d.h

Public Member Functions

Static Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ MbMatrix3D()

Member Function Documentation

◆ Init()

◆ IsScaling()

◆ IsIsotropic()

◆ SetEl() [1/2]

◆ SetEl() [2/2]

◆ El()

◆ AddEl()

◆ MulEl()

◆ SetFlag()

◆ Scale()

◆ RotateAbout()

◆ Rotate()

◆ TransformLength()

◆ TransformCoord2D()

◆ Symmetry() [1/2]

◆ Symmetry() [2/2]

◆ Div()

◆ MouldCavityScale()

◆ SetRoundedValue()