Defines a non persistent transformation in 2D space. <br>

This transformation is a general transformation.
It can be a Trsf2d from package gp, an affinity, or you can
define your own transformation giving the corresponding
matrix of transformation.

With a GTrsf2d you can transform only a doublet of coordinates
XY. It is not possible to transform other geometric objects
because these transformations can change the nature of non-
elementary geometric objects.
A GTrsf2d is represented with a 2 rows * 3 columns matrix :

V1 V2 T XY XY
| a11 a12 a14 | | x | | x'|
| a21 a22 a24 | | y | | y'|
| 0 0 1 | | 1 | | 1 |

where {V1, V2} defines the vectorial part of the
transformation and T defines the translation part of
the transformation.
Warning
A GTrsf2d transformation is only applicable on
coordinates. Be careful if you apply such a
transformation to all the points of a geometric object,
as this can change the nature of the object and thus
render it incoherent!
Typically, a circle is transformed into an ellipse by an
affinity transformation. To avoid modifying the nature of
an object, use a gp_Trsf2d transformation instead, as
objects of this class respect the nature of geometric objects.
More...

#include <gp_GTrsf2d.hxx>

Public Member Functions
	gp_GTrsf2d ()
	returns identity transformation. More...

	gp_GTrsf2d (const gp_Trsf2d &T)
	Converts the gp_Trsf2d transformation T into a general transformation. More...

	gp_GTrsf2d (const gp_Mat2d &M, const gp_XY &V)
	Creates a transformation based on the matrix M and the vector V where M defines the vectorial part of the transformation, and V the translation part. More...

void	SetAffinity (const gp_Ax2d &A, const Standard_Real Ratio)
	Changes this transformation into an affinity of ratio Ratio with respect to the axis A. Note: An affinity is a point-by-point transformation that transforms any point P into a point P' such that if H is the orthogonal projection of P on the axis A, the vectors HP and HP' satisfy: HP' = Ratio * HP. More...

void	SetValue (const Standard_Integer Row, const Standard_Integer Col, const Standard_Real Value)
	Replaces the coefficient (Row, Col) of the matrix representing <br> this transformation by Value, Raises OutOfRange if Row < 1 or Row > 2 or Col < 1 or Col > 3 More...

void	SetTranslationPart (const gp_XY &Coord)
	Replacesthe translation part of this <br> transformation by the coordinates of the number pair Coord. More...

void	SetTrsf2d (const gp_Trsf2d &T)
	Assigns the vectorial and translation parts of T to this transformation. More...

void	SetVectorialPart (const gp_Mat2d &Matrix)
	Replaces the vectorial part of this transformation by Matrix. More...

Standard_Boolean	IsNegative () const
	Returns true if the determinant of the vectorial part of <br> this transformation is negative. More...

Standard_Boolean	IsSingular () const
	Returns true if this transformation is singular (and <br> therefore, cannot be inverted). Note: The Gauss LU decomposition is used to invert the transformation matrix. Consequently, the transformation is considered as singular if the largest pivot found is less than or equal to gp::Resolution(). Warning If this transformation is singular, it cannot be inverted. More...

gp_TrsfForm	Form () const
	Returns the nature of the transformation. It can be <br> an identity transformation, a rotation, a translation, a mirror transformation (relative to a point or axis), a scaling transformation, a compound transformation or some other type of transformation. More...

const gp_XY &	TranslationPart () const
	Returns the translation part of the GTrsf2d. More...

const gp_Mat2d &	VectorialPart () const
	Computes the vectorial part of the GTrsf2d. The returned Matrix is a 2*2 matrix. More...

Standard_Real	Value (const Standard_Integer Row, const Standard_Integer Col) const
	Returns the coefficients of the global matrix of transformation. <br> Raised OutOfRange if Row < 1 or Row > 2 or Col < 1 or Col > 3 More...

Standard_Real	operator() (const Standard_Integer Row, const Standard_Integer Col) const

void	Invert ()

gp_GTrsf2d	Inverted () const
	Computes the reverse transformation. Raised an exception if the matrix of the transformation is not inversible. More...

void	Multiply (const gp_GTrsf2d &T)

void	operator*= (const gp_GTrsf2d &T)

gp_GTrsf2d	Multiplied (const gp_GTrsf2d &T) const
	Computes the transformation composed with T and <me>. In a C++ implementation you can also write Tcomposed = <me> * T. Example : GTrsf2d T1, T2, Tcomp; ............... //composition : Tcomp = T2.Multiplied(T1); // or (Tcomp = T2 * T1) // transformation of a point XY P(10.,3.); XY P1(P); Tcomp.Transforms(P1); //using Tcomp XY P2(P); T1.Transforms(P2); //using T1 then T2 T2.Transforms(P2); // P1 = P2 !!! More...

gp_GTrsf2d	operator* (const gp_GTrsf2d &T) const

void	PreMultiply (const gp_GTrsf2d &T)
	Computes the product of the transformation T and this transformation, and assigns the result to this transformation: this = T * this More...

void	Power (const Standard_Integer N)

gp_GTrsf2d	Powered (const Standard_Integer N) const
	Computes the following composition of transformations <br> <me> * <me> * .......* <me>, N time. if N = 0 <me> = Identity if N < 0 <me> = <me>.Inverse() ........... <me>.Inverse(). Raises an exception if N < 0 and if the matrix of the transformation is not inversible. More...

void	Transforms (gp_XY &Coord) const

gp_XY	Transformed (const gp_XY &Coord) const

void	Transforms (Standard_Real &X, Standard_Real &Y) const
	Applies this transformation to the coordinates: More...

gp_Trsf2d	Trsf2d () const
	Converts this transformation into a gp_Trsf2d transformation. Exceptions Standard_ConstructionError if this transformation cannot be converted, i.e. if its form is gp_Other. More...

const gp_Mat2d &	_CSFDB_Getgp_GTrsf2dmatrix () const

const gp_XY &	_CSFDB_Getgp_GTrsf2dloc () const

gp_TrsfForm	_CSFDB_Getgp_GTrsf2dshape () const

void	_CSFDB_Setgp_GTrsf2dshape (const gp_TrsfForm p)

Standard_Real	_CSFDB_Getgp_GTrsf2dscale () const

void	_CSFDB_Setgp_GTrsf2dscale (const Standard_Real p)

Detailed Description

Defines a non persistent transformation in 2D space. <br>

This transformation is a general transformation.
It can be a Trsf2d from package gp, an affinity, or you can
define your own transformation giving the corresponding
matrix of transformation.

With a GTrsf2d you can transform only a doublet of coordinates
XY. It is not possible to transform other geometric objects
because these transformations can change the nature of non-
elementary geometric objects.
A GTrsf2d is represented with a 2 rows * 3 columns matrix :

V1 V2 T XY XY
| a11 a12 a14 | | x | | x'|
| a21 a22 a24 | | y | | y'|
| 0 0 1 | | 1 | | 1 |

where {V1, V2} defines the vectorial part of the
transformation and T defines the translation part of
the transformation.
Warning
A GTrsf2d transformation is only applicable on
coordinates. Be careful if you apply such a
transformation to all the points of a geometric object,
as this can change the nature of the object and thus
render it incoherent!
Typically, a circle is transformed into an ellipse by an
affinity transformation. To avoid modifying the nature of
an object, use a gp_Trsf2d transformation instead, as
objects of this class respect the nature of geometric objects.

Constructor & Destructor Documentation

gp_GTrsf2d::gp_GTrsf2d ( )

returns identity transformation.

gp_GTrsf2d::gp_GTrsf2d ( const gp_Trsf2d & T )

Converts the gp_Trsf2d transformation T into a
general transformation.

gp_GTrsf2d::gp_GTrsf2d	(	const gp_Mat2d &	M,
		const gp_XY &	V
	)

Creates a transformation based on the matrix M and the
vector V where M defines the vectorial part of the
transformation, and V the translation part.

Member Function Documentation

const gp_XY& gp_GTrsf2d::_CSFDB_Getgp_GTrsf2dloc ( ) const

inline

const gp_Mat2d& gp_GTrsf2d::_CSFDB_Getgp_GTrsf2dmatrix ( ) const

inline

Standard_Real gp_GTrsf2d::_CSFDB_Getgp_GTrsf2dscale ( ) const

inline

gp_TrsfForm gp_GTrsf2d::_CSFDB_Getgp_GTrsf2dshape ( ) const

inline

void gp_GTrsf2d::_CSFDB_Setgp_GTrsf2dscale ( const Standard_Real p )

inline

void gp_GTrsf2d::_CSFDB_Setgp_GTrsf2dshape ( const gp_TrsfForm p )

inline

gp_TrsfForm gp_GTrsf2d::Form ( ) const

Returns the nature of the transformation.  It can be <br>

an identity transformation, a rotation, a translation, a mirror
transformation (relative to a point or axis), a scaling
transformation, a compound transformation or some
other type of transformation.

void gp_GTrsf2d::Invert ( )

gp_GTrsf2d gp_GTrsf2d::Inverted ( ) const

Computes the reverse transformation.
Raised an exception if the matrix of the transformation
is not inversible.

Standard_Boolean gp_GTrsf2d::IsNegative ( ) const

Returns true if the determinant of the vectorial part of <br>

this transformation is negative.

Standard_Boolean gp_GTrsf2d::IsSingular ( ) const

 Returns true if this transformation is singular (and <br>

therefore, cannot be inverted).
Note: The Gauss LU decomposition is used to invert the
transformation matrix. Consequently, the transformation
is considered as singular if the largest pivot found is less
than or equal to gp::Resolution().
Warning
If this transformation is singular, it cannot be inverted.

gp_GTrsf2d gp_GTrsf2d::Multiplied ( const gp_GTrsf2d & T ) const

Computes the transformation composed with T and <me>.
In a C++ implementation you can also write Tcomposed = <me> * T.
Example :
GTrsf2d T1, T2, Tcomp; ...............
//composition :
Tcomp = T2.Multiplied(T1); // or (Tcomp = T2 * T1)
// transformation of a point
XY P(10.,3.);
XY P1(P);
Tcomp.Transforms(P1); //using Tcomp
XY P2(P);
T1.Transforms(P2); //using T1 then T2
T2.Transforms(P2); // P1 = P2 !!!

void gp_GTrsf2d::Multiply ( const gp_GTrsf2d & T )

Standard_Real gp_GTrsf2d::operator()	(	const Standard_Integer	Row,
		const Standard_Integer	Col
	)		const

inline

gp_GTrsf2d gp_GTrsf2d::operator* ( const gp_GTrsf2d & T ) const

inline

void gp_GTrsf2d::operator*= ( const gp_GTrsf2d & T )

inline

void gp_GTrsf2d::Power ( const Standard_Integer N )

gp_GTrsf2d gp_GTrsf2d::Powered ( const Standard_Integer N ) const

Computes the following composition of transformations <br>

<me> * <me> * .......* <me>, N time.
if N = 0 <me> = Identity
if N < 0 <me> = <me>.Inverse() *...........* <me>.Inverse().

Raises an exception if N < 0 and if the matrix of the
transformation is not inversible.

void gp_GTrsf2d::PreMultiply ( const gp_GTrsf2d & T )

Computes the product of the transformation T and this
transformation, and assigns the result to this transformation:
this = T * this

void gp_GTrsf2d::SetAffinity	(	const gp_Ax2d &	A,
		const Standard_Real	Ratio
	)

Changes this transformation into an affinity of ratio Ratio
with respect to the axis A.
Note: An affinity is a point-by-point transformation that
transforms any point P into a point P' such that if H is
the orthogonal projection of P on the axis A, the vectors
HP and HP' satisfy: HP' = Ratio * HP.

void gp_GTrsf2d::SetTranslationPart ( const gp_XY & Coord )

 Replacesthe translation part of this <br>

transformation by the coordinates of the number pair Coord.

void gp_GTrsf2d::SetTrsf2d ( const gp_Trsf2d & T )

Assigns the vectorial and translation parts of T to this transformation.

void gp_GTrsf2d::SetValue	(	const Standard_Integer	Row,
		const Standard_Integer	Col,
		const Standard_Real	Value
	)

Replaces   the coefficient (Row, Col) of the matrix representing <br>

this transformation by Value,
Raises OutOfRange if Row < 1 or Row > 2 or Col < 1 or Col > 3

void gp_GTrsf2d::SetVectorialPart ( const gp_Mat2d & Matrix )

Replaces the vectorial part of this transformation by Matrix.

gp_XY gp_GTrsf2d::Transformed ( const gp_XY & Coord ) const

void gp_GTrsf2d::Transforms ( gp_XY & Coord ) const

void gp_GTrsf2d::Transforms	(	Standard_Real &	X,
		Standard_Real &	Y
	)		const

Applies this transformation to the coordinates:

of the number pair Coord, or
X and Y.

Note:
Transforms modifies X, Y, or the coordinate pair Coord, while
Transformed creates a new coordinate pair.

const gp_XY& gp_GTrsf2d::TranslationPart ( ) const

Returns the translation part of the GTrsf2d.

gp_Trsf2d gp_GTrsf2d::Trsf2d ( ) const

Converts this transformation into a gp_Trsf2d transformation.
Exceptions
Standard_ConstructionError if this transformation
cannot be converted, i.e. if its form is gp_Other.

Standard_Real gp_GTrsf2d::Value	(	const Standard_Integer	Row,
		const Standard_Integer	Col
	)		const

Returns the coefficients of the global matrix of transformation. <br>

Raised OutOfRange if Row < 1 or Row > 2 or Col < 1 or Col > 3

const gp_Mat2d& gp_GTrsf2d::VectorialPart ( ) const

Computes the vectorial part of the GTrsf2d. The returned
Matrix is a 2*2 matrix.

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

gp_GTrsf2d.hxx

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation