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

#include <mb_matrix.h>

Collaboration diagram for MbMatrix:

Public Member Functions
	MbMatrix ()
	Default constructor.

	MbMatrix (const MbMatrix &init)
	Copy constructor.

	MbMatrix (const MbPlacement &place)
	The constructor by placement.

	MbMatrix (const MbCartPoint &pnt, const MbDirection &dir)
	The constructor by a point and a normalized vector. More...

	MbMatrix (const MbCartPoint &pc, double sx, double sy)
	The constructor of scaling matrix by x and y. More...

	MbMatrix (const MbCartPoint &pc, double angle)
	The constructor of rotation matrix. More...

	~MbMatrix ()
	Destructor.

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

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

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

MbMatrix &	Init (const MbCartPoint &pnt, const MbDirection &dir)
	Initialize a matrix by a point and normalized vector. More...

MbMatrix &	Init (const MbCartPoint &pc, double sx, double sy)
	Initialize scaling matrix by x and y. More...

MbMatrix &	Init (const MbCartPoint &pc, double angle)
	Initialize a rotation matrix. More...

MbMatrix &	Set (const MbPlacement &place)
	Initialize a matrix according to a placement. More...

MbMatrix &	SetZero ()
	Set a zero matrix.

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

bool	IsInvertEps (double eps=EXTENT_EPSILON) 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=LENGTH_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	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 MbMatrix &, double accuracy) const
	Determine whether an object is equal?

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...

bool	CanTransformGabarit () const
	Is it possible to transform a bounding box without distortion?

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

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

const MbCartPoint &	GetOrigin () const
	Get the third row (the origin of coordinates)

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

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

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

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

Functions for matrix elements modification.
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...

void	SetColumn (size_t icol, const MbCartPoint &column)
	Assign point coordinates values to column elements. More...

void	SetColumn (size_t icol, const MbVector &column)
	Assign vector components values to column elements. More...

void	SetColumn (size_t icol, const MbHomogeneous &column)
	Assign coordinates of the uniform point to column elements. More...

void	SetRow (size_t irow, const MbVector &row)
	Assign vector components values to row elements. More...

void	SetRow (size_t irow, const MbCartPoint &row)
	Assign point coordinates values to row elements. More...

void	SetRow (size_t irow, const MbHomogeneous &row)
	Assign coordinates of the uniform point to row elements. More...

void	SetOrigin (const MbCartPoint &p)
	Set components of matrix translation.

Matrices multiplication.
MbMatrix &	PreMultiply (const MbMatrix &)
	Multiply a matrix on the left.

MbMatrix &	PostMultiply (const MbMatrix &)
	Multiply a matrix on the right.

Scaling functions.
MbMatrix &	Scale (double s)
	Scale by X and Y.

void	ScaleX (double s)
	Scale by X.

void	ScaleY (double s)
	Scale by Y.

double	GetScaleX () const
	Get scaling coefficient by X.

double	GetScaleY () const
	Get scaling coefficient by Y.

bool	IsDifferentScale () const
	Check differences of scaling coefficients (X and Y).

Functions of matrix transformations: translation, rotation, etc.
void	Shift (double shift)
	Shift by X and Y.

void	ShiftX (double shift)
	Shift by X.

void	ShiftY (double shift)
	Shift by Y.

MbMatrix &	Move (const MbVector &v)
	Translate by the vector (multiply by translation matrix on the right).

MbMatrix &	Move (double dx, double dy)
	Translate by given increments.

MbMatrix &	Rotate (double angle)
	Rotate by an angle. More...

MbMatrix &	Rotate (const MbDirection &)
	Rotate according to the direction vector. More...

MbMatrix &	Rotate (const MbCartPoint &, const MbDirection &angle)
	Rotate at angle around a point. More...

void	TransformCoord (double x, double y, double &xn, double &yn) const
	Transform coordinates. More...

void	TransformScalarX (double &len) const
	Transform the length in the direction of 0X. More...

MbMatrix &	Symmetry (const MbCartPoint &origin, const MbVector &normal)
	Set the matrix to symmetry transformation (reflection). More...

MbMatrix &	Symmetry (const MbCartPoint &origin, const MbDirection &direction)
	Find a matrix for transformation of symmetry relative to a line given by a point and direction.

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.

void	Div (MbMatrix &, double eps=DOUBLE_EPSILON) const
	Calculate inverse matrix.

double	NormMax () const
	Maximal element of the matrix in absolute value.

Overload of arithmetical and logical operations.
MbMatrix	operator* (const MbMatrix &) const
	Multiply by the matrix on the right.

MbMatrix &	operator*= (const MbMatrix &m)
	Multiply by the matrix on the right.

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

bool	operator== (const MbMatrix &) 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 MbMatrix	identity
	Identity matrix, I = diag(1,1,1);.

Protected Attributes
double	el [MATRIX_DIM_2D][MATRIX_DIM_2D]
	Elements of matrix.

Friends
void	MulMatrix (const MbMatrix &, const MbMatrix &, MbMatrix &)
	Multiply matrices. More...

Detailed Description

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

The extended matrix of transformation in a two-dimensional space.
The extended matrix has dimension (3, 3) 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 local system, the second row must be filled with the corresponding components of the second vector of a local 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 (2, 2), V - translation vector, tensor (0, 2), P - perspective vector, the tensor (2, 0) (always null), S - scalar of scale transformation (the unit). \ n

Constructor & Destructor Documentation

◆ MbMatrix() [1/3]

MbMatrix::MbMatrix	(	const MbCartPoint &	pnt,
		const MbDirection &	dir
	)

inline

The constructor by a point and a normalized vector.

The constructor by a point and a normalized vector

Parameters

[in]	pnt	- A point. Sets translation relative to zero.
[in]	dir	- Unit vector. Sets a rotation.

◆ MbMatrix() [2/3]

MbMatrix::MbMatrix	(	const MbCartPoint &	pc,
		double	sx,
		double	sy
	)

inline

The constructor of scaling matrix by x and y.

Parameters

[in]	pnt	- A point. Sets translation relative to zero.
[in]	sx,sy	- Scaling coefficients by x and y, respectively.

◆ MbMatrix() [3/3]

MbMatrix::MbMatrix	(	const MbCartPoint &	pc,
		double	angle
	)

inline

The constructor of rotation matrix.

The constructor of rotation matrix around the point "pc" on the angle "angle".

Parameters

[in]	pc	- A point.
[in]	angle	- A rotation angle.

Member Function Documentation

◆ Init() [1/3]

MbMatrix & MbMatrix::Init	(	const MbCartPoint &	pnt,
		const MbDirection &	dir
	)

inline

Initialize a matrix by a point and normalized vector.

Parameters

[in]	pnt	- A point. Sets translation relative to zero.
[in]	dir	- Unit vector. Sets a rotation.

◆ Init() [2/3]

MbMatrix& MbMatrix::Init	(	const MbCartPoint &	pc,
		double	sx,
		double	sy
	)

Initialize scaling matrix by x and y.

Parameters

[in]	pnt	- A point. Sets translation relative to zero.
[in]	sx,sy	- Scaling coefficients by the x and y, respectively.

◆ Init() [3/3]

MbMatrix& MbMatrix::Init	(	const MbCartPoint &	pc,
		double	angle
	)

Initialize a rotation matrix.

Initialize a rotation matrix around the point "pc" on the angle "angle".

Parameters

[in]	pc	- A point.
[in]	angle	- A rotation angle.

◆ Set()

MbMatrix& MbMatrix::Set ( const MbPlacement & place )

Initialize a matrix according to a placement.

Parameters

[in] place - The initial placement.

◆ IsScaling()

bool MbMatrix::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 MbMatrix::IsIsotropic ( double & l ) const

Get an attribute of isotropism.

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

Parameters

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

Returns: Returns true if the matrix is isotropic.

◆ El()

void MbMatrix::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 MbMatrix::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 MbMatrix::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.

◆ SetColumn() [1/3]

void MbMatrix::SetColumn	(	size_t	icol,
		const MbCartPoint &	column
	)

Assign point coordinates values to column elements.

Parameters

[in]	icol	- A column index.
[in]	column	- The initial point.

◆ SetColumn() [2/3]

void MbMatrix::SetColumn	(	size_t	icol,
		const MbVector &	column
	)

Assign vector components values to column elements.

Parameters

[in]	icol	- A column index.
[in]	column	- The initial vector.

◆ SetColumn() [3/3]

void MbMatrix::SetColumn	(	size_t	icol,
		const MbHomogeneous &	column
	)

Assign coordinates of the uniform point to column elements.

Parameters

[in]	icol	- A column index.
[in]	column	- The initial point.

◆ SetRow() [1/3]

void MbMatrix::SetRow	(	size_t	irow,
		const MbVector &	row
	)

Assign vector components values to row elements.

Parameters

[in]	irow	- A column index.
[in]	row	- The initial vector.

◆ SetRow() [2/3]

void MbMatrix::SetRow	(	size_t	irow,
		const MbCartPoint &	row
	)

Assign point coordinates values to row elements.

Parameters

[in]	irow	- A column index.
[in]	row	- The initial point.

◆ SetRow() [3/3]

void MbMatrix::SetRow	(	size_t	irow,
		const MbHomogeneous &	row
	)

Assign coordinates of the uniform point to row elements.

Parameters

[in]	irow	- A column index.
[in]	row	- The initial point.

◆ Rotate() [1/3]

MbMatrix& MbMatrix::Rotate ( double angle )

Rotate by an angle.

Rotation is around the axis Z.

Parameters

[in] angle - A rotation angle.

◆ Rotate() [2/3]

MbMatrix& MbMatrix::Rotate ( const MbDirection & )

Rotate according to the direction vector.

Rotation is around the Z axis, because matrix is two-dimensional. A direction vector defines a rotation angle.

Parameters

[in] - A direction vector.

◆ Rotate() [3/3]

MbMatrix& MbMatrix::Rotate	(	const MbCartPoint &	,
		const MbDirection &	angle
	)

Rotate at angle around a point.

Parameters

[in]	-	A point.
[in]	angle	- A direction vector which defines a rotation angle

◆ TransformCoord()

void MbMatrix::TransformCoord	(	double	x,
		double	y,
		double &	xn,
		double &	yn
	)		const

inline

Transform coordinates.

Coordinates are transformed according to a matrix.

Parameters

[in]	x,y	- Old coordinates by x and y.
[in]	xn,yn	- Transformed coordinates.

◆ TransformScalarX()

void MbMatrix::TransformScalarX ( double & len ) const

inline

Transform the length in the direction of 0X.

The length is transformed according to a matrix. If the matrix has a different scales for the X and Y, then the scale by Y is ignored.

Parameters

[in,out] len - The length in the direction of 0X.

◆ Symmetry()

MbMatrix& MbMatrix::Symmetry	(	const MbCartPoint &	origin,
		const MbVector &	normal
	)

Set the matrix to symmetry transformation (reflection).

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

Parameters

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

Friends And Related Function Documentation

◆ MulMatrix

void MulMatrix	(	const MbMatrix &	,
		const MbMatrix &	,
		MbMatrix &
	)

friend

Multiply matrices.

Multiply m1 matrix by m2 matrix (instead of res = m1 * m2).

Parameters

[in]	m1,m2	- Initial matrices.
[out]	res	- The required matrix.

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

mb_matrix.h

Public Member Functions

Static Public Attributes

Protected Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ MbMatrix() [1/3]

◆ MbMatrix() [2/3]

◆ MbMatrix() [3/3]

Member Function Documentation

◆ Init() [1/3]

◆ Init() [2/3]

◆ Init() [3/3]

◆ Set()

◆ IsScaling()

◆ IsIsotropic()

◆ El()

◆ AddEl()

◆ MulEl()

◆ SetColumn() [1/3]

◆ SetColumn() [2/3]

◆ SetColumn() [3/3]

◆ SetRow() [1/3]

◆ SetRow() [2/3]

◆ SetRow() [3/3]

◆ Rotate() [1/3]

◆ Rotate() [2/3]

◆ Rotate() [3/3]

◆ TransformCoord()

◆ TransformScalarX()

◆ Symmetry()

Friends And Related Function Documentation

◆ MulMatrix