Open CASCADE Technology  7.3.1.dev
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.

## ◆ 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.

## ◆ 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: