Defines a non-persistent transformation in 3D space. <br>

This transformation is a general transformation.
It can be a Trsf from gp, an affinity, or you can define
your own transformation giving the matrix of transformation.

With a Gtrsf you can transform only a triplet of coordinates
XYZ. It is not possible to transform other geometric objects
because these transformations can change the nature of non-
elementary geometric objects.
The transformation 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 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.
More...

#include <gp_GTrsf.hxx>

Public Member Functions
	gp_GTrsf ()
	Returns the Identity transformation. More...

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

	gp_GTrsf (const gp_Mat &M, const gp_XYZ &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, or More...

void	SetAffinity (const gp_Ax1 &A1, const Standard_Real Ratio)
	Changes this transformation into an affinity of ratio Ratio <br> with respect to the axis A1. 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 A2, the vectors HP and HP' satisfy: HP' = Ratio * HP. More...

void	SetAffinity (const gp_Ax2 &A2, const Standard_Real Ratio)
	Changes this transformation into an affinity of ratio Ratio <br> with respect to the plane defined by the origin, the "X Direction" and the "Y Direction" of coordinate system A2. 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 A2, 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 <br> this transformation by Value. Raises OutOfRange if Row < 1 or Row > 3 or Col < 1 or Col > 4 More...

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

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

void	SetTrsf (const gp_Trsf &T)
	Assigns the vectorial and translation parts of T to this transformation. More...

Standard_Boolean	IsNegative () const
	Returns true if the determinant of the vectorial part of <br> this transformation is negative. More...

Standard_Boolean	IsSingular () const
	Returns true if this transformation is singular (and <br> 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 <br> 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 : myGTrsf.SetValue(row1,col1,val1); myGTrsf.SetValue(row2,col2,val2); ... myGTrsf.SetForm(); More...

const gp_XYZ &	TranslationPart () const
	Returns the translation part of the GTrsf. More...

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

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

Standard_Real	operator() (const Standard_Integer Row, const Standard_Integer Col) const

void	Invert ()

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

void	Multiply (const gp_GTrsf &T)
	Computes the transformation composed from T and <me>. <br> In a C++ implementation you can also write Tcomposed = <me> * T. Example : GTrsf T1, T2, Tcomp; ............... //composition : Tcomp = T2.Multiplied(T1); // or (Tcomp = T2 * T1) // transformation of a point XYZ P(10.,3.,4.); XYZ P1(P); Tcomp.Transforms(P1); //using Tcomp XYZ P2(P); T1.Transforms(P2); //using T1 then T2 T2.Transforms(P2); // P1 = P2 !!! C++: alias operator *= More...

gp_GTrsf	Multiplied (const gp_GTrsf &T) const
	Computes the transformation composed with <me> and T. <me> = T * <me> More...

void	PreMultiply (const gp_GTrsf &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_GTrsf	Powered (const Standard_Integer N) const
	Computes: More...

void	Transforms (gp_XYZ &Coord) const

void	Transforms (Standard_Real &X, Standard_Real &Y, Standard_Real &Z) const
	Transforms a triplet XYZ with a GTrsf. More...

gp_Trsf	Trsf () const

const gp_Mat &	_CSFDB_Getgp_GTrsfmatrix () const

const gp_XYZ &	_CSFDB_Getgp_GTrsfloc () const

gp_TrsfForm	_CSFDB_Getgp_GTrsfshape () const

void	_CSFDB_Setgp_GTrsfshape (const gp_TrsfForm p)

Standard_Real	_CSFDB_Getgp_GTrsfscale () const

void	_CSFDB_Setgp_GTrsfscale (const Standard_Real p)

Detailed Description

Defines a non-persistent transformation in 3D space. <br>

This transformation is a general transformation.
It can be a Trsf from gp, an affinity, or you can define
your own transformation giving the matrix of transformation.

With a Gtrsf you can transform only a triplet of coordinates
XYZ. It is not possible to transform other geometric objects
because these transformations can change the nature of non-
elementary geometric objects.
The transformation 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 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::gp_GTrsf ( )

Returns the Identity transformation.

gp_GTrsf::gp_GTrsf ( const gp_Trsf & T )

Converts the gp_Trsf transformation T into a <br>

general transformation, i.e. Returns a GTrsf with
the same matrix of coefficients as the Trsf T.

gp_GTrsf::gp_GTrsf	(	const gp_Mat &	M,
		const gp_XYZ &	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, or

Member Function Documentation

const gp_XYZ& gp_GTrsf::_CSFDB_Getgp_GTrsfloc ( ) const

inline

const gp_Mat& gp_GTrsf::_CSFDB_Getgp_GTrsfmatrix ( ) const

inline

Standard_Real gp_GTrsf::_CSFDB_Getgp_GTrsfscale ( ) const

inline

gp_TrsfForm gp_GTrsf::_CSFDB_Getgp_GTrsfshape ( ) const

inline

void gp_GTrsf::_CSFDB_Setgp_GTrsfscale ( const Standard_Real p )

inline

void gp_GTrsf::_CSFDB_Setgp_GTrsfshape ( const gp_TrsfForm p )

inline

gp_TrsfForm gp_GTrsf::Form ( ) const

Returns the nature of the transformation.  It can be an <br>

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 gp_GTrsf::Invert ( )

gp_GTrsf gp_GTrsf::Inverted ( ) const

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

Standard_Boolean gp_GTrsf::IsNegative ( ) const

 Returns true if the determinant of the vectorial part of <br>

this transformation is negative.

Standard_Boolean gp_GTrsf::IsSingular ( ) const

Returns true if this transformation is singular (and <br>

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.

gp_GTrsf gp_GTrsf::Multiplied ( const gp_GTrsf & T ) const

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

void gp_GTrsf::Multiply ( const gp_GTrsf & T )

Computes the transformation composed from T and <me>. <br>

In a C++ implementation you can also write Tcomposed = <me> * T.
Example :
GTrsf T1, T2, Tcomp; ...............
//composition :
Tcomp = T2.Multiplied(T1); // or (Tcomp = T2 * T1)
// transformation of a point
XYZ P(10.,3.,4.);
XYZ P1(P);
Tcomp.Transforms(P1); //using Tcomp
XYZ P2(P);
T1.Transforms(P2); //using T1 then T2
T2.Transforms(P2); // P1 = P2 !!!
C++: alias operator *=

Standard_Real gp_GTrsf::operator()	(	const Standard_Integer	Row,
		const Standard_Integer	Col
	)		const

inline

void gp_GTrsf::Power ( const Standard_Integer N )

gp_GTrsf gp_GTrsf::Powered ( const Standard_Integer N ) const

Computes:

the product of this transformation multiplied by itself
N times, if N is positive, or

the product of the inverse of this transformation
multiplied by itself |N| times, if N is negative.
If N equals zero, the result is equal to the Identity
transformation.
I.e.: <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 not inversible.

void gp_GTrsf::PreMultiply ( const gp_GTrsf & T )

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

void gp_GTrsf::SetAffinity	(	const gp_Ax1 &	A1,
		const Standard_Real	Ratio
	)

 Changes this transformation into an affinity of ratio Ratio <br>

with respect to the axis A1.
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 A2, the vectors HP and HP' satisfy:
HP' = Ratio * HP.

void gp_GTrsf::SetAffinity	(	const gp_Ax2 &	A2,
		const Standard_Real	Ratio
	)

 Changes this transformation into an affinity of ratio Ratio <br>

with respect to the plane defined by the origin, the "X Direction" and
the "Y Direction" of coordinate system A2.
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 A2, the vectors HP and HP' satisfy:
HP' = Ratio * HP.

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();

void gp_GTrsf::SetTranslationPart ( const gp_XYZ & Coord )

 Replaces the translation part of <br>

this transformation by the coordinates of the number triple Coord.

void gp_GTrsf::SetTrsf ( const gp_Trsf & T )

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

void gp_GTrsf::SetValue	(	const Standard_Integer	Row,
		const Standard_Integer	Col,
		const Standard_Real	Value
	)

Replaces  the coefficient (Row, Col) of the matrix representing <br>

this transformation by Value. Raises OutOfRange
if Row < 1 or Row > 3 or Col < 1 or Col > 4

void gp_GTrsf::SetVectorialPart ( const gp_Mat & Matrix )

Replaces the vectorial part of this transformation by Matrix.

void gp_GTrsf::Transforms ( gp_XYZ & Coord ) const

void gp_GTrsf::Transforms	(	Standard_Real &	X,
		Standard_Real &	Y,
		Standard_Real &	Z
	)		const

Transforms a triplet XYZ with a GTrsf.

const gp_XYZ& gp_GTrsf::TranslationPart ( ) const

Returns the translation part of the GTrsf.

gp_Trsf gp_GTrsf::Trsf ( ) const

Standard_Real gp_GTrsf::Value	(	const Standard_Integer	Row,
		const Standard_Integer	Col
	)		const

Returns the coefficients of the global matrix of transformation. <br>

Raises OutOfRange if Row < 1 or Row > 3 or Col < 1 or Col > 4

const gp_Mat& gp_GTrsf::VectorialPart ( ) const

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:

gp_GTrsf.hxx

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation