Open CASCADE Technology  7.3.1.dev
Public Member Functions
gp_GTrsf2d Class Reference

Defines a non persistent transformation in 2D space. 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. 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 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 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 this transformation is negative. More...
 
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. More...
 
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. More...
 
const gp_XYTranslationPart () const
 Returns the translation part of the GTrsf2d. More...
 
const gp_Mat2dVectorialPart () 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. 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...
 
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 Multiply (const gp_GTrsf2d &T)
 
void operator*= (const gp_GTrsf2d &T)
 
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 <me> * <me> * .......* <me>, N time. if N = 0 <me> = Identity if N < 0 <me> = <me>.Inverse() *...........* <me>.Inverse(). 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...
 

Detailed Description

Defines a non persistent transformation in 2D space. 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() [1/3]

gp_GTrsf2d::gp_GTrsf2d ( )

returns identity transformation.

◆ gp_GTrsf2d() [2/3]

gp_GTrsf2d::gp_GTrsf2d ( const gp_Trsf2d T)

Converts the gp_Trsf2d transformation T into a general transformation.

◆ gp_GTrsf2d() [3/3]

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

◆ Form()

gp_TrsfForm gp_GTrsf2d::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.

◆ Invert()

void gp_GTrsf2d::Invert ( )

◆ Inverted()

gp_GTrsf2d gp_GTrsf2d::Inverted ( ) const

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

◆ IsNegative()

Standard_Boolean gp_GTrsf2d::IsNegative ( ) const

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

◆ IsSingular()

Standard_Boolean gp_GTrsf2d::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.

◆ Multiplied()

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 !!!

◆ Multiply()

void gp_GTrsf2d::Multiply ( const gp_GTrsf2d T)

◆ operator()()

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

◆ operator*()

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

◆ operator*=()

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

◆ Power()

void gp_GTrsf2d::Power ( const Standard_Integer  N)

◆ Powered()

gp_GTrsf2d gp_GTrsf2d::Powered ( const Standard_Integer  N) const

Computes the following composition of transformations <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.

◆ PreMultiply()

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.

◆ SetAffinity()

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.

◆ SetTranslationPart()

void gp_GTrsf2d::SetTranslationPart ( const gp_XY Coord)

Replacesthe translation part of this transformation by the coordinates of the number pair Coord.

◆ SetTrsf2d()

void gp_GTrsf2d::SetTrsf2d ( const gp_Trsf2d T)

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

◆ SetValue()

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

◆ SetVectorialPart()

void gp_GTrsf2d::SetVectorialPart ( const gp_Mat2d Matrix)

Replaces the vectorial part of this transformation by Matrix.

◆ Transformed()

gp_XY gp_GTrsf2d::Transformed ( const gp_XY Coord) const

◆ Transforms() [1/2]

void gp_GTrsf2d::Transforms ( gp_XY Coord) const

◆ Transforms() [2/2]

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.

◆ TranslationPart()

const gp_XY& gp_GTrsf2d::TranslationPart ( ) const

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  Row,
const Standard_Integer  Col 
) const

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

◆ VectorialPart()

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: