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
constexpr	gp_GTrsf () noexcept
	Returns the Identity transformation.
	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.
constexpr	gp_GTrsf (const gp_Mat &theM, const gp_XYZ &theV) noexcept
	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.
void	SetAffinity (const gp_Ax1 &theA1, const double 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.
void	SetAffinity (const gp_Ax2 &theA2, const double 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.
void	SetValue (const int theRow, const int theCol, const double 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.
constexpr void	SetVectorialPart (const gp_Mat &theMatrix) noexcept
	Replaces the vectorial part of this transformation by theMatrix.
void	SetTranslationPart (const gp_XYZ &theCoord)
	Replaces the translation part of this transformation by the coordinates of the number triple theCoord.
void	SetTrsf (const gp_Trsf &theT)
	Assigns the vectorial and translation parts of theT to this transformation.
constexpr bool	IsNegative () const noexcept
	Returns true if the determinant of the vectorial part of this transformation is negative.
constexpr bool	IsSingular () const noexcept
	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.
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, a compound transformation or some other type of transformation.
void	SetForm ()
	verify and set the shape of the GTrsf Other or CompoundTrsf Ex :
constexpr const gp_XYZ &	TranslationPart () const noexcept
	Returns the translation part of the GTrsf.
constexpr const gp_Mat &	VectorialPart () const noexcept
	Computes the vectorial part of the GTrsf. The returned Matrix is a 3*3 matrix.
constexpr double	Value (const int theRow, const int 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.
double	operator() (const int theRow, const int theCol) const
void	Invert ()
gp_GTrsf	Inverted () const
	Computes the reverse transformation. Raises an exception if the matrix of the transformation is not inversible.
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 :
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.
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.
void	Power (const int theN)
gp_GTrsf	Powered (const int theN) const
	Computes:
constexpr void	Transforms (gp_XYZ &theCoord) const noexcept
constexpr void	Transforms (double &theX, double &theY, double &theZ) const noexcept
	Transforms a triplet XYZ with a GTrsf.
gp_Trsf	Trsf () const
template<class T >
void	GetMat4 (NCollection_Mat4< T > &theMat) const
	Convert transformation to 4x4 matrix.
template<class T >
void	SetMat4 (const NCollection_Mat4< T > &theMat)
	Convert transformation from 4x4 matrix.
void	DumpJson (Standard_OStream &theOStream, int theDepth=-1) const
	Dumps the content of me into the stream.

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 |

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.

Constructor & Destructor Documentation

gp_GTrsf() [1/3]

constexpr gp_GTrsf::gp_GTrsf ( )

inlineconstexprnoexcept

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]

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

inlineconstexprnoexcept

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.

Member Function Documentation

DumpJson()

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

Dumps the content of me into the stream.

Form()

constexpr gp_TrsfForm gp_GTrsf::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, 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()

constexpr bool gp_GTrsf::IsNegative ( ) const

inlineconstexprnoexcept

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

IsSingular()

constexpr bool gp_GTrsf::IsSingular ( ) const

inlineconstexprnoexcept

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 !!!

Multiply()

void gp_GTrsf::Multiply

(

const gp_GTrsf &

theT

)

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

operator()()

double gp_GTrsf::operator() ( const int theRow, const int 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 int

theN

)

Powered()

gp_GTrsf gp_GTrsf::Powered ( const int 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 double 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 double 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();

SetMat4()

template<class T >

void gp_GTrsf::SetMat4 ( const NCollection_Mat4< T > & theMat )

inline

Convert transformation from 4x4 matrix.

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 int theRow, const int theCol, const double 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()

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

inlineconstexprnoexcept

Replaces the vectorial part of this transformation by theMatrix.

Transforms() [1/2]

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

inlineconstexprnoexcept

Transforms a triplet XYZ with a GTrsf.

Transforms() [2/2]

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

inlineconstexprnoexcept

TranslationPart()

constexpr const gp_XYZ & gp_GTrsf::TranslationPart ( ) const

inlineconstexprnoexcept

Returns the translation part of the GTrsf.

Trsf()

gp_Trsf gp_GTrsf::Trsf ( ) const

inline

Value()

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

inlineconstexpr

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

VectorialPart()

constexpr const gp_Mat & gp_GTrsf::VectorialPart ( ) const

inlineconstexprnoexcept

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

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

• gp_GTrsf.hxx