Defines a non persistent transformation in 2D space. This transformation is a general transformation. It can be a gp_Trsf2d, an affinity, or you can define your own transformation giving the corresponding matrix of transformation. More...

#include <gp_GTrsf2d.hxx>

Public Member Functions
	gp_GTrsf2d ()
	returns identity transformation.

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

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

void	SetAffinity (const gp_Ax2d &theA, const Standard_Real theRatio)
	Changes this transformation into an affinity of ratio theRatio with respect to the axis theA. 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 theA, the vectors HP and HP' satisfy: HP' = theRatio * HP.

void	SetValue (const Standard_Integer theRow, const Standard_Integer theCol, const Standard_Real theValue)
	Replaces the coefficient (theRow, theCol) of the matrix representing this transformation by theValue, Raises OutOfRange if theRow < 1 or theRow > 2 or theCol < 1 or theCol > 3.

void	SetTranslationPart (const gp_XY &theCoord)
	Replaces the translation part of this transformation by the coordinates of the number pair theCoord.

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

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

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

Standard_Boolean	IsSingular () const
	Returns true if this transformation is singular (and 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_TrsfForm	Form () const
	Returns the nature of the transformation. It can be 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.

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

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

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

Standard_Real	operator() (const Standard_Integer theRow, const Standard_Integer theCol) const

void	Invert ()

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

gp_GTrsf2d	Multiplied (const gp_GTrsf2d &theT) const
	Computes the transformation composed with theT and <me>. In a C++ implementation you can also write Tcomposed = <me> * theT. Example :

gp_GTrsf2d	operator* (const gp_GTrsf2d &theT) const

void	Multiply (const gp_GTrsf2d &theT)

void	operator*= (const gp_GTrsf2d &theT)

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

void	Power (const Standard_Integer theN)

gp_GTrsf2d	Powered (const Standard_Integer theN) const
	Computes the following composition of transformations <me> * <me> * .......* <me>, theN time. if theN = 0 <me> = Identity if theN < 0 <me> = <me>.Inverse() ........... <me>.Inverse().

void	Transforms (gp_XY &theCoord) const

gp_XY	Transformed (const gp_XY &theCoord) const

void	Transforms (Standard_Real &theX, Standard_Real &theY) const
	Applies this transformation to the coordinates:

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.

Detailed Description

Defines a non persistent transformation in 2D space. This transformation is a general transformation. It can be a gp_Trsf2d, an affinity, or you can define your own transformation giving the corresponding matrix of transformation.

With a gp_GTrsf2d you can transform only a doublet of coordinates gp_XY. It is not possible to transform other geometric objects because these transformations can change the nature of non-elementary geometric objects. A gp_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 gp_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() [1/3]

gp_GTrsf2d::gp_GTrsf2d ( )

inline

returns identity transformation.

◆ gp_GTrsf2d() [2/3]

gp_GTrsf2d::gp_GTrsf2d ( const gp_Trsf2d & theT )

inline

Converts the gp_Trsf2d transformation theT into a general transformation.

◆ gp_GTrsf2d() [3/3]

gp_GTrsf2d::gp_GTrsf2d	(	const gp_Mat2d &	theM,
		const gp_XY &	theV )

inline

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

Member Function Documentation

◆ Form()

gp_TrsfForm gp_GTrsf2d::Form ( ) const

inline

Returns the nature of the transformation. It can be 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.

◆ Invert()

void gp_GTrsf2d::Invert ( )

◆ Inverted()

gp_GTrsf2d gp_GTrsf2d::Inverted ( ) const

inline

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

◆ IsNegative()

Standard_Boolean gp_GTrsf2d::IsNegative ( ) const

inline

Returns true if the determinant of the vectorial part of this transformation is negative.

◆ IsSingular()

Standard_Boolean gp_GTrsf2d::IsSingular ( ) const

inline

Returns true if this transformation is singular (and 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.

◆ Multiplied()

gp_GTrsf2d gp_GTrsf2d::Multiplied ( const gp_GTrsf2d & theT ) const

inline

Computes the transformation composed with theT and <me>. In a C++ implementation you can also write Tcomposed = <me> * theT. Example :

gp_GTrsf2d T1, T2, Tcomp; ...............
//composition :
Tcomp = T2.Multiplied(T1);         // or   (Tcomp = T2 * T1)
// transformation of a point
gp_XY P(10.,3.);
gp_XY P1(P);
Tcomp.Transforms(P1);               //using Tcomp
gp_XY P2(P);
T1.Transforms(P2);                  //using T1 then T2
T2.Transforms(P2);                  // P1 = P2 !!!

◆ Multiply()

void gp_GTrsf2d::Multiply ( const gp_GTrsf2d & theT )

◆ operator()()

Standard_Real gp_GTrsf2d::operator()	(	const Standard_Integer	theRow,
		const Standard_Integer	theCol ) const

inline

◆ operator*()

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

inline

◆ operator*=()

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

inline

◆ Power()

void gp_GTrsf2d::Power ( const Standard_Integer theN )

◆ Powered()

gp_GTrsf2d gp_GTrsf2d::Powered ( const Standard_Integer theN ) const

inline

Computes the following composition of transformations <me> * <me> * .......* <me>, theN time. if theN = 0 <me> = Identity if theN < 0 <me> = <me>.Inverse() ........... <me>.Inverse().

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

◆ PreMultiply()

void gp_GTrsf2d::PreMultiply ( const gp_GTrsf2d & theT )

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

◆ SetAffinity()

void gp_GTrsf2d::SetAffinity	(	const gp_Ax2d &	theA,
		const Standard_Real	theRatio )

Changes this transformation into an affinity of ratio theRatio with respect to the axis theA. 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 theA, the vectors HP and HP' satisfy: HP' = theRatio * HP.

◆ SetTranslationPart()

void gp_GTrsf2d::SetTranslationPart ( const gp_XY & theCoord )

Replaces the translation part of this transformation by the coordinates of the number pair theCoord.

◆ SetTrsf2d()

void gp_GTrsf2d::SetTrsf2d ( const gp_Trsf2d & theT )

inline

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

◆ SetValue()

void gp_GTrsf2d::SetValue	(	const Standard_Integer	theRow,
		const Standard_Integer	theCol,
		const Standard_Real	theValue )

inline

Replaces the coefficient (theRow, theCol) of the matrix representing this transformation by theValue, Raises OutOfRange if theRow < 1 or theRow > 2 or theCol < 1 or theCol > 3.

◆ SetVectorialPart()

void gp_GTrsf2d::SetVectorialPart ( const gp_Mat2d & theMatrix )

inline

Replaces the vectorial part of this transformation by theMatrix.

◆ Transformed()

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

inline

◆ Transforms() [1/2]

void gp_GTrsf2d::Transforms ( gp_XY & theCoord ) const

inline

◆ Transforms() [2/2]

void gp_GTrsf2d::Transforms	(	Standard_Real &	theX,
		Standard_Real &	theY ) const

inline

Applies this transformation to the coordinates:

of the number pair Coord, or
X and Y.

Note:

Transforms modifies theX, theY, or the coordinate pair Coord, while
Transformed creates a new coordinate pair.

◆ TranslationPart()

const gp_XY & gp_GTrsf2d::TranslationPart ( ) const

inline

Returns the translation part of the GTrsf2d.

◆ Trsf2d()

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.

◆ Value()

Standard_Real gp_GTrsf2d::Value	(	const Standard_Integer	theRow,
		const Standard_Integer	theCol ) const

inline

Returns the coefficients of the global matrix of transformation. Raised OutOfRange if theRow < 1 or theRow > 2 or theCol < 1 or theCol > 3.

◆ VectorialPart()

const gp_Mat2d & gp_GTrsf2d::VectorialPart ( ) const

inline

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

◆ gp_GTrsf2d() [1/3]

◆ gp_GTrsf2d() [2/3]

◆ gp_GTrsf2d() [3/3]

Member Function Documentation

◆ Form()

◆ Invert()

◆ Inverted()

◆ IsNegative()

◆ IsSingular()

◆ Multiplied()

◆ Multiply()

◆ operator()()

◆ operator*()

◆ operator*=()

◆ Power()

◆ Powered()

◆ PreMultiply()

◆ SetAffinity()

◆ SetTranslationPart()

◆ SetTrsf2d()

◆ SetValue()

◆ SetVectorialPart()

◆ Transformed()

◆ Transforms() [1/2]

◆ Transforms() [2/2]

◆ TranslationPart()

◆ Trsf2d()

◆ Value()

◆ VectorialPart()