# gp_Trsf Class Reference

Defines a non-persistent transformation in 3D space. The following transformations are implemented : . Translation, Rotation, Scale . Symmetry with respect to a point, a line, a plane. Complex transformations can be obtained by combining the previous elementary transformations using the method Multiply. The transformations can be represented as follow : More...

`#include <gp_Trsf.hxx>`

## Public Member Functions

gp_Trsf ()
Returns the identity transformation. More...

gp_Trsf (const gp_Trsf2d &theT)
Creates a 3D transformation from the 2D transformation theT. The resulting transformation has a homogeneous vectorial part, V3, and a translation part, T3, built from theT: a11 a12 0 a13 V3 = a21 a22 0 T3 = a23 0 0 1. 0 It also has the same scale factor as theT. This guarantees (by projection) that the transformation which would be performed by theT in a plane (2D space) is performed by the resulting transformation in the xOy plane of the 3D space, (i.e. in the plane defined by the origin (0., 0., 0.) and the vectors DX (1., 0., 0.), and DY (0., 1., 0.)). The scale factor is applied to the entire space. More...

void SetMirror (const gp_Pnt &theP)
Makes the transformation into a symmetrical transformation. theP is the center of the symmetry. More...

void SetMirror (const gp_Ax1 &theA1)
Makes the transformation into a symmetrical transformation. theA1 is the center of the axial symmetry. More...

void SetMirror (const gp_Ax2 &theA2)
Makes the transformation into a symmetrical transformation. theA2 is the center of the planar symmetry and defines the plane of symmetry by its origin, "X Direction" and "Y Direction". More...

void SetRotation (const gp_Ax1 &theA1, const Standard_Real theAng)
Changes the transformation into a rotation. theA1 is the rotation axis and theAng is the angular value of the rotation in radians. More...

void SetRotation (const gp_Quaternion &theR)
Changes the transformation into a rotation defined by quaternion. Note that rotation is performed around origin, i.e. no translation is involved. More...

void SetRotationPart (const gp_Quaternion &theR)
Replaces the rotation part with specified quaternion. More...

void SetScale (const gp_Pnt &theP, const Standard_Real theS)
Changes the transformation into a scale. theP is the center of the scale and theS is the scaling value. Raises ConstructionError If <theS> is null. More...

void SetDisplacement (const gp_Ax3 &theFromSystem1, const gp_Ax3 &theToSystem2)
Modifies this transformation so that it transforms the coordinate system defined by theFromSystem1 into the one defined by theToSystem2. After this modification, this transformation transforms: More...

void SetTransformation (const gp_Ax3 &theFromSystem1, const gp_Ax3 &theToSystem2)
Modifies this transformation so that it transforms the coordinates of any point, (x, y, z), relative to a source coordinate system into the coordinates (x', y', z') which are relative to a target coordinate system, but which represent the same point The transformation is from the coordinate system "theFromSystem1" to the coordinate system "theToSystem2". Example : More...

void SetTransformation (const gp_Ax3 &theToSystem)
Modifies this transformation so that it transforms the coordinates of any point, (x, y, z), relative to a source coordinate system into the coordinates (x', y', z') which are relative to a target coordinate system, but which represent the same point The transformation is from the default coordinate system. More...

void SetTransformation (const gp_Quaternion &R, const gp_Vec &theT)
Sets transformation by directly specified rotation and translation. More...

void SetTranslation (const gp_Vec &theV)
Changes the transformation into a translation. theV is the vector of the translation. More...

void SetTranslation (const gp_Pnt &theP1, const gp_Pnt &theP2)
Makes the transformation into a translation where the translation vector is the vector (theP1, theP2) defined from point theP1 to point theP2. More...

void SetTranslationPart (const gp_Vec &theV)
Replaces the translation vector with the vector theV. More...

void SetScaleFactor (const Standard_Real theS)
Modifies the scale factor. Raises ConstructionError If theS is null. More...

void SetForm (const gp_TrsfForm theP)

void SetValues (const Standard_Real a11, const Standard_Real a12, const Standard_Real a13, const Standard_Real a14, const Standard_Real a21, const Standard_Real a22, const Standard_Real a23, const Standard_Real a24, const Standard_Real a31, const Standard_Real a32, const Standard_Real a33, const Standard_Real a34)
Sets the coefficients of the transformation. The transformation of the point x,y,z is the point x',y',z' with : More...

Standard_Boolean IsNegative () const
Returns true if the determinant of the vectorial part of this transformation is negative. 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, or a compound transformation. More...

Standard_Real ScaleFactor () const
Returns the scale factor. More...

const gp_XYZTranslationPart () const
Returns the translation part of the transformation's matrix. More...

Standard_Boolean GetRotation (gp_XYZ &theAxis, Standard_Real &theAngle) const
Returns the boolean True if there is non-zero rotation. In the presence of rotation, the output parameters store the axis and the angle of rotation. The method always returns positive value "theAngle", i.e., 0. < theAngle <= PI. Note that this rotation is defined only by the vectorial part of the transformation; generally you would need to check also the translational part to obtain the axis (gp_Ax1) of rotation. More...

gp_Quaternion GetRotation () const
Returns quaternion representing rotational part of the transformation. More...

gp_Mat VectorialPart () const
Returns the vectorial part of the transformation. It is a 3*3 matrix which includes the scale factor. More...

const gp_MatHVectorialPart () const
Computes the homogeneous vectorial part of the transformation. It is a 3*3 matrix which doesn't include the scale factor. In other words, the vectorial part of this transformation is equal to its homogeneous vectorial part, multiplied by the scale factor. The coefficients of this matrix must be multiplied by the scale factor to obtain the coefficients of the transformation. More...

Standard_Real Value (const Standard_Integer theRow, const Standard_Integer theCol) const
Returns the coefficients of the transformation's matrix. It is a 3 rows * 4 columns matrix. This coefficient includes the scale factor. Raises OutOfRanged if theRow < 1 or theRow > 3 or theCol < 1 or theCol > 4. More...

void Invert ()

gp_Trsf Inverted () const
Computes the reverse transformation Raises an exception if the matrix of the transformation is not inversible, it means that the scale factor is lower or equal to Resolution from package gp. Computes the transformation composed with T and <me>. In a C++ implementation you can also write Tcomposed = <me> * T. Example : More...

gp_Trsf Multiplied (const gp_Trsf &theT) const

gp_Trsf operator* (const gp_Trsf &theT) const

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

void operator*= (const gp_Trsf &theT)

void PreMultiply (const gp_Trsf &theT)
Computes the transformation composed with <me> and T. <me> = theT * <me> More...

void Power (const Standard_Integer theN)

gp_Trsf 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(). More...

void Transforms (Standard_Real &theX, Standard_Real &theY, Standard_Real &theZ) const

void Transforms (gp_XYZ &theCoord) const
Transformation of a triplet XYZ with a Trsf. More...

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...

Standard_Boolean InitFromJson (const Standard_SStream &theSStream, Standard_Integer &theStreamPos)
Inits the content of me from the stream. More...

## Protected Member Functions

void Orthogonalize ()
Makes orthogonalization of "matrix". More...

## Detailed Description

Defines a non-persistent transformation in 3D space. The following transformations are implemented : . Translation, Rotation, Scale . Symmetry with respect to a point, a line, a plane. Complex transformations can be obtained by combining the previous elementary transformations using the method Multiply. The transformations 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:170
GLint GLint GLint GLint GLint x
Definition: OpenGl_GLESExtensions.hxx:132

where {V1, V2, V3} defines the vectorial part of the transformation and T defines the translation part of the transformation. This transformation never change the nature of the objects.

## ◆ gp_Trsf() [1/2]

 gp_Trsf::gp_Trsf ( )
inline

Returns the identity transformation.

## ◆ gp_Trsf() [2/2]

 gp_Trsf::gp_Trsf ( const gp_Trsf2d & theT )

Creates a 3D transformation from the 2D transformation theT. The resulting transformation has a homogeneous vectorial part, V3, and a translation part, T3, built from theT: a11 a12 0 a13 V3 = a21 a22 0 T3 = a23 0 0 1. 0 It also has the same scale factor as theT. This guarantees (by projection) that the transformation which would be performed by theT in a plane (2D space) is performed by the resulting transformation in the xOy plane of the 3D space, (i.e. in the plane defined by the origin (0., 0., 0.) and the vectors DX (1., 0., 0.), and DY (0., 1., 0.)). The scale factor is applied to the entire space.

## ◆ DumpJson()

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

Dumps the content of me into the stream.

## ◆ Form()

 gp_TrsfForm gp_Trsf::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, or a compound transformation.

## ◆ GetMat4()

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

Convert transformation to 4x4 matrix.

## ◆ GetRotation() [1/2]

 gp_Quaternion gp_Trsf::GetRotation ( ) const

Returns quaternion representing rotational part of the transformation.

## ◆ GetRotation() [2/2]

 Standard_Boolean gp_Trsf::GetRotation ( gp_XYZ & theAxis, Standard_Real & theAngle ) const

Returns the boolean True if there is non-zero rotation. In the presence of rotation, the output parameters store the axis and the angle of rotation. The method always returns positive value "theAngle", i.e., 0. < theAngle <= PI. Note that this rotation is defined only by the vectorial part of the transformation; generally you would need to check also the translational part to obtain the axis (gp_Ax1) of rotation.

## ◆ HVectorialPart()

 const gp_Mat& gp_Trsf::HVectorialPart ( ) const
inline

Computes the homogeneous vectorial part of the transformation. It is a 3*3 matrix which doesn't include the scale factor. In other words, the vectorial part of this transformation is equal to its homogeneous vectorial part, multiplied by the scale factor. The coefficients of this matrix must be multiplied by the scale factor to obtain the coefficients of the transformation.

## ◆ InitFromJson()

 Standard_Boolean gp_Trsf::InitFromJson ( const Standard_SStream & theSStream, Standard_Integer & theStreamPos )

Inits the content of me from the stream.

## ◆ Invert()

 void gp_Trsf::Invert ( )

## ◆ Inverted()

 gp_Trsf gp_Trsf::Inverted ( ) const
inline

Computes the reverse transformation Raises an exception if the matrix of the transformation is not inversible, it means that the scale factor is lower or equal to Resolution from package gp. Computes the transformation composed with T and <me>. In a C++ implementation you can also write Tcomposed = <me> * T. Example :

gp_Trsf T1, T2, Tcomp; ...............
Tcomp = T2.Multiplied(T1); // or (Tcomp = T2 * T1)
gp_Pnt P1(10.,3.,4.);
gp_Pnt P2 = P1.Transformed(Tcomp); // using Tcomp
gp_Pnt P3 = P1.Transformed(T1); // using T1 then T2
P3.Transform(T2); // P3 = P2 !!!
Defines a 3D cartesian point.
Definition: gp_Pnt.hxx:32
gp_Pnt Transformed(const gp_Trsf &theT) const
Definition: gp_Pnt.hxx:178
void Transform(const gp_Trsf &theT)
Transforms a point with the transformation T.
Defines a non-persistent transformation in 3D space. The following transformations are implemented : ...
Definition: gp_Trsf.hxx:59
gp_Trsf Multiplied(const gp_Trsf &theT) const
Definition: gp_Trsf.hxx:276

## ◆ IsNegative()

 Standard_Boolean gp_Trsf::IsNegative ( ) const
inline

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

## ◆ Multiplied()

 gp_Trsf gp_Trsf::Multiplied ( const gp_Trsf & theT ) const
inline

## ◆ Multiply()

 void gp_Trsf::Multiply ( const gp_Trsf & theT )

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

## ◆ operator*()

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

## ◆ operator*=()

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

## ◆ Orthogonalize()

 void gp_Trsf::Orthogonalize ( )
protected

Makes orthogonalization of "matrix".

## ◆ Power()

 void gp_Trsf::Power ( const Standard_Integer theN )

## ◆ Powered()

 gp_Trsf gp_Trsf::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 if theN < 0 and if the matrix of the transformation not inversible.

## ◆ PreMultiply()

 void gp_Trsf::PreMultiply ( const gp_Trsf & theT )

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

## ◆ ScaleFactor()

 Standard_Real gp_Trsf::ScaleFactor ( ) const
inline

Returns the scale factor.

## ◆ SetDisplacement()

 void gp_Trsf::SetDisplacement ( const gp_Ax3 & theFromSystem1, const gp_Ax3 & theToSystem2 )

Modifies this transformation so that it transforms the coordinate system defined by theFromSystem1 into the one defined by theToSystem2. After this modification, this transformation transforms:

• the origin of theFromSystem1 into the origin of theToSystem2,
• the "X Direction" of theFromSystem1 into the "X Direction" of theToSystem2,
• the "Y Direction" of theFromSystem1 into the "Y Direction" of theToSystem2, and
• the "main Direction" of theFromSystem1 into the "main Direction" of theToSystem2. Warning When you know the coordinates of a point in one coordinate system and you want to express these coordinates in another one, do not use the transformation resulting from this function. Use the transformation that results from SetTransformation instead. SetDisplacement and SetTransformation create related transformations: the vectorial part of one is the inverse of the vectorial part of the other.

## ◆ SetForm()

 void gp_Trsf::SetForm ( const gp_TrsfForm theP )
inline

## ◆ SetMirror() [1/3]

 void gp_Trsf::SetMirror ( const gp_Ax1 & theA1 )

Makes the transformation into a symmetrical transformation. theA1 is the center of the axial symmetry.

## ◆ SetMirror() [2/3]

 void gp_Trsf::SetMirror ( const gp_Ax2 & theA2 )

Makes the transformation into a symmetrical transformation. theA2 is the center of the planar symmetry and defines the plane of symmetry by its origin, "X Direction" and "Y Direction".

## ◆ SetMirror() [3/3]

 void gp_Trsf::SetMirror ( const gp_Pnt & theP )
inline

Makes the transformation into a symmetrical transformation. theP is the center of the symmetry.

## ◆ SetRotation() [1/2]

 void gp_Trsf::SetRotation ( const gp_Ax1 & theA1, const Standard_Real theAng )

Changes the transformation into a rotation. theA1 is the rotation axis and theAng is the angular value of the rotation in radians.

## ◆ SetRotation() [2/2]

 void gp_Trsf::SetRotation ( const gp_Quaternion & theR )

Changes the transformation into a rotation defined by quaternion. Note that rotation is performed around origin, i.e. no translation is involved.

## ◆ SetRotationPart()

 void gp_Trsf::SetRotationPart ( const gp_Quaternion & theR )

Replaces the rotation part with specified quaternion.

## ◆ SetScale()

 void gp_Trsf::SetScale ( const gp_Pnt & theP, const Standard_Real theS )

Changes the transformation into a scale. theP is the center of the scale and theS is the scaling value. Raises ConstructionError If <theS> is null.

## ◆ SetScaleFactor()

 void gp_Trsf::SetScaleFactor ( const Standard_Real theS )

Modifies the scale factor. Raises ConstructionError If theS is null.

## ◆ SetTransformation() [1/3]

 void gp_Trsf::SetTransformation ( const gp_Ax3 & theFromSystem1, const gp_Ax3 & theToSystem2 )

Modifies this transformation so that it transforms the coordinates of any point, (x, y, z), relative to a source coordinate system into the coordinates (x', y', z') which are relative to a target coordinate system, but which represent the same point The transformation is from the coordinate system "theFromSystem1" to the coordinate system "theToSystem2". Example :

gp_Ax3 theFromSystem1, theToSystem2;
double x1, y1, z1; // are the coordinates of a point in the local system theFromSystem1
double x2, y2, z2; // are the coordinates of a point in the local system theToSystem2
gp_Pnt P1 (x1, y1, z1)
T.SetTransformation (theFromSystem1, theToSystem2);
gp_Pnt P2 = P1.Transformed (T);
P2.Coord (x2, y2, z2);
Describes a coordinate system in 3D space. Unlike a gp_Ax2 coordinate system, a gp_Ax3 can be right-h...
Definition: gp_Ax3.hxx:63
Standard_Real Coord(const Standard_Integer theIndex) const
Returns the coordinate of corresponding to the value of theIndex : theIndex = 1 => X is returned theI...
Definition: gp_Pnt.hxx:84
void SetTransformation(const gp_Ax3 &theFromSystem1, const gp_Ax3 &theToSystem2)
Modifies this transformation so that it transforms the coordinates of any point, (x,...

## ◆ SetTransformation() [2/3]

 void gp_Trsf::SetTransformation ( const gp_Ax3 & theToSystem )

Modifies this transformation so that it transforms the coordinates of any point, (x, y, z), relative to a source coordinate system into the coordinates (x', y', z') which are relative to a target coordinate system, but which represent the same point The transformation is from the default coordinate system.

{P(0.,0.,0.), VX (1.,0.,0.), VY (0.,1.,0.), VZ (0., 0. ,1.) }

to the local coordinate system defined with the Ax3 theToSystem. Use in the same way as the previous method. FromSystem1 is defaulted to the absolute coordinate system.

## ◆ SetTransformation() [3/3]

 void gp_Trsf::SetTransformation ( const gp_Quaternion & R, const gp_Vec & theT )

Sets transformation by directly specified rotation and translation.

## ◆ SetTranslation() [1/2]

 void gp_Trsf::SetTranslation ( const gp_Pnt & theP1, const gp_Pnt & theP2 )
inline

Makes the transformation into a translation where the translation vector is the vector (theP1, theP2) defined from point theP1 to point theP2.

## ◆ SetTranslation() [2/2]

 void gp_Trsf::SetTranslation ( const gp_Vec & theV )
inline

Changes the transformation into a translation. theV is the vector of the translation.

## ◆ SetTranslationPart()

 void gp_Trsf::SetTranslationPart ( const gp_Vec & theV )

Replaces the translation vector with the vector theV.

## ◆ SetValues()

 void gp_Trsf::SetValues ( const Standard_Real a11, const Standard_Real a12, const Standard_Real a13, const Standard_Real a14, const Standard_Real a21, const Standard_Real a22, const Standard_Real a23, const Standard_Real a24, const Standard_Real a31, const Standard_Real a32, const Standard_Real a33, const Standard_Real a34 )

Sets the coefficients of the transformation. The transformation of the point x,y,z is the point x',y',z' with :

x' = a11 x + a12 y + a13 z + a14
y' = a21 x + a22 y + a23 z + a24
z' = a31 x + a32 y + a33 z + a34
GLint GLint GLint GLint GLint GLint y
Definition: OpenGl_GLESExtensions.hxx:132

The method Value(i,j) will return aij. Raises ConstructionError if the determinant of the aij is null. The matrix is orthogonalized before future using.

## ◆ Transforms() [1/2]

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

Transformation of a triplet XYZ with a Trsf.

## ◆ Transforms() [2/2]

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

## ◆ TranslationPart()

 const gp_XYZ& gp_Trsf::TranslationPart ( ) const
inline

Returns the translation part of the transformation's matrix.

## ◆ Value()

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

Returns the coefficients of the transformation's matrix. It is a 3 rows * 4 columns matrix. This coefficient includes the scale factor. Raises OutOfRanged if theRow < 1 or theRow > 3 or theCol < 1 or theCol > 4.

## ◆ VectorialPart()

 gp_Mat gp_Trsf::VectorialPart ( ) const

Returns the vectorial part of the transformation. It is a 3*3 matrix which includes the scale factor.

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