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
constexpr	gp_Trsf () noexcept
	Returns the identity transformation.
	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.
constexpr void	SetMirror (const gp_Pnt &theP) noexcept
	Makes the transformation into a symmetrical transformation. theP is the center of the symmetry.
void	SetMirror (const gp_Ax1 &theA1) noexcept
	Makes the transformation into a symmetrical transformation. theA1 is the center of the axial symmetry.
void	SetMirror (const gp_Ax2 &theA2) noexcept
	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".
void	SetRotation (const gp_Ax1 &theA1, const double theAng)
	Changes the transformation into a rotation. theA1 is the rotation axis and theAng is the angular value of the rotation in radians.
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.
void	SetRotationPart (const gp_Quaternion &theR)
	Replaces the rotation part with specified quaternion.
void	SetScale (const gp_Pnt &theP, const double 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.
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:
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 :
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.
void	SetTransformation (const gp_Quaternion &R, const gp_Vec &theT)
	Sets transformation by directly specified rotation and translation.
constexpr void	SetTranslation (const gp_Vec &theV) noexcept
	Changes the transformation into a translation. theV is the vector of the translation.
constexpr void	SetTranslation (const gp_Pnt &theP1, const gp_Pnt &theP2) noexcept
	Makes the transformation into a translation where the translation vector is the vector (theP1, theP2) defined from point theP1 to point theP2.
void	SetTranslationPart (const gp_Vec &theV) noexcept
	Replaces the translation vector with the vector theV.
void	SetScaleFactor (const double theS)
	Modifies the scale factor. Raises ConstructionError If theS is null.
constexpr void	SetForm (const gp_TrsfForm theP) noexcept
void	SetValues (const double a11, const double a12, const double a13, const double a14, const double a21, const double a22, const double a23, const double a24, const double a31, const double a32, const double a33, const double a34)
	Sets the coefficients of the transformation. The transformation of the point x,y,z is the point x',y',z' with :
constexpr bool	IsNegative () const noexcept
	Returns true if the determinant of the vectorial part of this transformation is negative.
constexpr gp_TrsfForm	Form () const noexcept
	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.
constexpr double	ScaleFactor () const noexcept
	Returns the scale factor.
constexpr const gp_XYZ &	TranslationPart () const noexcept
	Returns the translation part of the transformation's matrix.
bool	GetRotation (gp_XYZ &theAxis, double &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.
gp_Quaternion	GetRotation () const
	Returns quaternion representing rotational part of the transformation.
constexpr gp_Mat	VectorialPart () const noexcept
	Returns the vectorial part of the transformation. It is a 3*3 matrix which includes the scale factor.
constexpr const gp_Mat &	HVectorialPart () const noexcept
	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.
constexpr double	Value (const int theRow, const int 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.
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 :
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.
void	operator*= (const gp_Trsf &theT)
void	PreMultiply (const gp_Trsf &theT)
	Computes the transformation composed with <me> and T. <me> = theT * <me>
void	Power (const int theN)
gp_Trsf	Powered (const int 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().
constexpr void	Transforms (double &theX, double &theY, double &theZ) const noexcept
constexpr void	Transforms (gp_XYZ &theCoord) const noexcept
	Transformation of a triplet XYZ with a Trsf.
template<class T >
void	GetMat4 (NCollection_Mat4< T > &theMat) const
	Convert transformation to 4x4 matrix.
void	DumpJson (Standard_OStream &theOStream, int theDepth=-1) const
	Dumps the content of me into the stream.
bool	InitFromJson (const Standard_SStream &theSStream, int &theStreamPos)
	Inits the content of me from the stream.

Protected Member Functions
void	Orthogonalize ()
	Makes orthogonalization of "matrix".

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 |

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.

Constructor & Destructor Documentation

gp_Trsf() [1/2]

constexpr gp_Trsf::gp_Trsf ( )

inlineconstexprnoexcept

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.

Member Function Documentation

DumpJson()

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

Dumps the content of me into the stream.

Form()

constexpr gp_TrsfForm gp_Trsf::Form ( ) const

inlineconstexprnoexcept

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]

bool gp_Trsf::GetRotation	(	gp_XYZ &	theAxis,
		double &	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()

constexpr const gp_Mat & gp_Trsf::HVectorialPart ( ) const

inlineconstexprnoexcept

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()

bool gp_Trsf::InitFromJson	(	const Standard_SStream &	theSStream,
		int &	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 !!!

IsNegative()

constexpr bool gp_Trsf::IsNegative ( ) const

inlineconstexprnoexcept

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 int

theN

)

Powered()

gp_Trsf gp_Trsf::Powered ( const int 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()

constexpr double gp_Trsf::ScaleFactor ( ) const

inlineconstexprnoexcept

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()

constexpr void gp_Trsf::SetForm ( const gp_TrsfForm theP )

inlineconstexprnoexcept

SetMirror() [1/3]

void gp_Trsf::SetMirror ( const gp_Ax1 & theA1 )

noexcept

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 )

noexcept

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]

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

inlineconstexprnoexcept

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 double	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 double	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 double

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)
gp_Trsf T;
T.SetTransformation (theFromSystem1, theToSystem2);
gp_Pnt P2 = P1.Transformed (T);
P2.Coord (x2, y2, z2);

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]

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

inlineconstexprnoexcept

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]

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

inlineconstexprnoexcept

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

SetTranslationPart()

void gp_Trsf::SetTranslationPart ( const gp_Vec & theV )

noexcept

Replaces the translation vector with the vector theV.

SetValues()

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

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]

constexpr void gp_Trsf::Transforms ( double & theX, double & theY, double & theZ ) const

inlineconstexprnoexcept

Transforms() [2/2]

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

inlineconstexprnoexcept

Transformation of a triplet XYZ with a Trsf.

TranslationPart()

constexpr const gp_XYZ & gp_Trsf::TranslationPart ( ) const

inlineconstexprnoexcept

Returns the translation part of the transformation's matrix.

Value()

constexpr double gp_Trsf::Value ( const int theRow, const int theCol ) const

inlineconstexpr

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()

constexpr gp_Mat gp_Trsf::VectorialPart ( ) const

inlineconstexprnoexcept

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

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

• gp_Trsf.hxx