Open CASCADE Technology  7.6.0.dev

# gp_GTrsf Class Reference

Defines a non-persistent transformation in 3D space. This transformation is a general transformation. It can be a gp_Trsf, an affinity, or you can define your own transformation giving the matrix of transformation. More...

`#include <gp_GTrsf.hxx>`

## Public Member Functions

gp_GTrsf ()
Returns the Identity transformation. More...

gp_GTrsf (const gp_Trsf &theT)
Converts the gp_Trsf transformation theT into a general transformation, i.e. Returns a GTrsf with the same matrix of coefficients as the Trsf theT. More...

gp_GTrsf (const gp_Mat &theM, const gp_XYZ &theV)
Creates a transformation based on the matrix theM and the vector theV where theM defines the vectorial part of the transformation, and V the translation part, or. More...

void SetAffinity (const gp_Ax1 &theA1, const Standard_Real theRatio)
Changes this transformation into an affinity of ratio theRatio with respect to the axis theA1. 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 theA1 or the plane A2, the vectors HP and HP' satisfy: HP' = theRatio * HP. More...

void SetAffinity (const gp_Ax2 &theA2, const Standard_Real theRatio)
Changes this transformation into an affinity of ratio theRatio with respect to the plane defined by the origin, the "X Direction" and the "Y Direction" of coordinate system theA2. 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 A1 or the plane theA2, the vectors HP and HP' satisfy: HP' = theRatio * HP. More...

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 > 3 or theCol < 1 or theCol > 4. More...

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

void SetTranslationPart (const gp_XYZ &theCoord)
Replaces the translation part of this transformation by the coordinates of the number triple theCoord. More...

void SetTrsf (const gp_Trsf &theT)
Assigns the vectorial and translation parts of theT to this transformation. 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, an axis or a plane), a scaling transformation, a compound transformation or some other type of transformation. More...

void SetForm ()
verify and set the shape of the GTrsf Other or CompoundTrsf Ex : More...

const gp_XYZTranslationPart () const
Returns the translation part of the GTrsf. More...

const gp_MatVectorialPart () const
Computes the vectorial part of the GTrsf. The returned Matrix is a 3*3 matrix. More...

Standard_Real Value (const Standard_Integer theRow, const Standard_Integer theCol) const
Returns the coefficients of the global matrix of transformation. Raises OutOfRange if theRow < 1 or theRow > 3 or theCol < 1 or theCol > 4. More...

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

void Invert ()

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

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

gp_GTrsf operator* (const gp_GTrsf &theT) const

void Multiply (const gp_GTrsf &theT)
Computes the transformation composed with <me> and theT. <me> = <me> * theT. More...

void operator*= (const gp_GTrsf &theT)

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

void Power (const Standard_Integer theN)

gp_GTrsf Powered (const Standard_Integer theN) const
Computes: More...

void Transforms (gp_XYZ &theCoord) const

void Transforms (Standard_Real &theX, Standard_Real &theY, Standard_Real &theZ) const
Transforms a triplet XYZ with a GTrsf. More...

gp_Trsf Trsf () const

template<class T >
void GetMat4 (NCollection_Mat4< T > &theMat) const
Convert transformation to 4x4 matrix. More...

void DumpJson (Standard_OStream &theOStream, Standard_Integer theDepth=-1) const
Dumps the content of me into the stream. More...

## Detailed Description

Defines a non-persistent transformation in 3D space. This transformation is a general transformation. It can be a gp_Trsf, an affinity, or you can define your own transformation giving the matrix of transformation.

With a gp_GTrsf you can transform only a triplet of coordinates gp_XYZ. It is not possible to transform other geometric objects because these transformations can change the nature of non-elementary geometric objects. The transformation gp_GTrsf can be represented as follow:

V1 V2 V3 T XYZ XYZ
| a11 a12 a13 a14 | | x | | x'|
| a21 a22 a23 a24 | | y | | y'|
| a31 a32 a33 a34 | | z | = | z'|
| 0 0 0 1 | | 1 | | 1 |
GLint GLint GLint z
Definition: OpenGl_GLESExtensions.hxx:166
GLint GLint GLint GLint GLint x
Definition: OpenGl_GLESExtensions.hxx:128

where {V1, V2, V3} define the vectorial part of the transformation and T defines the translation part of the transformation. Warning A gp_GTrsf transformation is only applicable to coordinates. Be careful if you apply such a transformation to all 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_Trsf transformation instead, as objects of this class respect the nature of geometric objects.

## ◆ gp_GTrsf() [1/3]

 gp_GTrsf::gp_GTrsf ( )
inline

Returns the Identity transformation.

## ◆ gp_GTrsf() [2/3]

 gp_GTrsf::gp_GTrsf ( const gp_Trsf & theT )
inline

Converts the gp_Trsf transformation theT into a general transformation, i.e. Returns a GTrsf with the same matrix of coefficients as the Trsf theT.

## ◆ gp_GTrsf() [3/3]

 gp_GTrsf::gp_GTrsf ( const gp_Mat & theM, const gp_XYZ & theV )
inline

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

## ◆ DumpJson()

 void gp_GTrsf::DumpJson ( Standard_OStream & theOStream, Standard_Integer theDepth = `-1` ) const

Dumps the content of me into the stream.

## ◆ Form()

 gp_TrsfForm gp_GTrsf::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, an axis or a plane), a scaling transformation, a compound transformation or some other type of transformation.

## ◆ GetMat4()

template<class T >
 void gp_GTrsf::GetMat4 ( NCollection_Mat4< T > & theMat ) const
inline

Convert transformation to 4x4 matrix.

## ◆ Invert()

 void gp_GTrsf::Invert ( )

## ◆ Inverted()

 gp_GTrsf gp_GTrsf::Inverted ( ) const
inline

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

## ◆ IsNegative()

 Standard_Boolean gp_GTrsf::IsNegative ( ) const
inline

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

## ◆ IsSingular()

 Standard_Boolean gp_GTrsf::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_GTrsf gp_GTrsf::Multiplied ( const gp_GTrsf & theT ) const
inline

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

gp_GTrsf T1, T2, Tcomp; ...............
//composition :
Tcomp = T2.Multiplied(T1); // or (Tcomp = T2 * T1)
// transformation of a point
gp_XYZ P(10.,3.,4.);
gp_XYZ P1(P);
Tcomp.Transforms(P1); //using Tcomp
gp_XYZ P2(P);
T1.Transforms(P2); //using T1 then T2
T2.Transforms(P2); // P1 = P2 !!!
Defines a non-persistent transformation in 3D space. This transformation is a general transformation....
Definition: gp_GTrsf.hxx:61
void Transforms(gp_XYZ &theCoord) const
Definition: gp_GTrsf.hxx:396
gp_GTrsf Multiplied(const gp_GTrsf &theT) const
Computes the transformation composed from theT and <me>. In a C++ implementation you can also write T...
Definition: gp_GTrsf.hxx:213
This class describes a cartesian coordinate entity in 3D space {X,Y,Z}. This entity is used for algeb...
Definition: gp_XYZ.hxx:32

## ◆ Multiply()

 void gp_GTrsf::Multiply ( const gp_GTrsf & theT )

Computes the transformation composed with <me> and theT. <me> = <me> * theT.

## ◆ operator()()

 Standard_Real gp_GTrsf::operator() ( const Standard_Integer theRow, const Standard_Integer theCol ) const
inline

## ◆ operator*()

 gp_GTrsf gp_GTrsf::operator* ( const gp_GTrsf & theT ) const
inline

## ◆ operator*=()

 void gp_GTrsf::operator*= ( const gp_GTrsf & theT )
inline

## ◆ Power()

 void gp_GTrsf::Power ( const Standard_Integer theN )

## ◆ Powered()

 gp_GTrsf gp_GTrsf::Powered ( const Standard_Integer theN ) const
inline

Computes:

• the product of this transformation multiplied by itself theN times, if theN is positive, or
• the product of the inverse of this transformation multiplied by itself |theN| times, if theN is negative. If theN equals zero, the result is equal to the Identity transformation. I.e.: <me> * <me> * .......* <me>, theN time. if theN =0 <me> = Identity if theN < 0 <me> = <me>.Inverse() *...........* <me>.Inverse().

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

## ◆ PreMultiply()

 void gp_GTrsf::PreMultiply ( const gp_GTrsf & theT )

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

## ◆ SetAffinity() [1/2]

 void gp_GTrsf::SetAffinity ( const gp_Ax1 & theA1, const Standard_Real theRatio )
inline

Changes this transformation into an affinity of ratio theRatio with respect to the axis theA1. 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 theA1 or the plane A2, the vectors HP and HP' satisfy: HP' = theRatio * HP.

## ◆ SetAffinity() [2/2]

 void gp_GTrsf::SetAffinity ( const gp_Ax2 & theA2, const Standard_Real theRatio )
inline

Changes this transformation into an affinity of ratio theRatio with respect to the plane defined by the origin, the "X Direction" and the "Y Direction" of coordinate system theA2. 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 A1 or the plane theA2, the vectors HP and HP' satisfy: HP' = theRatio * HP.

## ◆ SetForm()

 void gp_GTrsf::SetForm ( )

verify and set the shape of the GTrsf Other or CompoundTrsf Ex :

myGTrsf.SetValue(row1,col1,val1);
myGTrsf.SetValue(row2,col2,val2);
...
myGTrsf.SetForm();

## ◆ SetTranslationPart()

 void gp_GTrsf::SetTranslationPart ( const gp_XYZ & theCoord )

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

## ◆ SetTrsf()

 void gp_GTrsf::SetTrsf ( const gp_Trsf & theT )
inline

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

## ◆ SetValue()

 void gp_GTrsf::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 > 3 or theCol < 1 or theCol > 4.

## ◆ SetVectorialPart()

 void gp_GTrsf::SetVectorialPart ( const gp_Mat & theMatrix )
inline

Replaces the vectorial part of this transformation by theMatrix.

## ◆ Transforms() [1/2]

 void gp_GTrsf::Transforms ( gp_XYZ & theCoord ) const
inline

## ◆ Transforms() [2/2]

 void gp_GTrsf::Transforms ( Standard_Real & theX, Standard_Real & theY, Standard_Real & theZ ) const
inline

Transforms a triplet XYZ with a GTrsf.

## ◆ TranslationPart()

 const gp_XYZ& gp_GTrsf::TranslationPart ( ) const
inline

Returns the translation part of the GTrsf.

## ◆ Trsf()

 gp_Trsf gp_GTrsf::Trsf ( ) const
inline

## ◆ Value()

 Standard_Real gp_GTrsf::Value ( const Standard_Integer theRow, const Standard_Integer theCol ) const
inline

Returns the coefficients of the global matrix of transformation. Raises OutOfRange if theRow < 1 or theRow > 3 or theCol < 1 or theCol > 4.

## ◆ VectorialPart()

 const gp_Mat& gp_GTrsf::VectorialPart ( ) const
inline

Computes the vectorial part of the GTrsf. The returned Matrix is a 3*3 matrix.

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