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.
More...

#include <gp_Trsf.hxx>

Public Member Functions
	gp_Trsf ()
	Returns the identity transformation. More...

	gp_Trsf (const gp_Trsf2d &T)
	Creates a 3D transformation from the 2D transformation T. <br> The resulting transformation has a homogeneous vectorial part, V3, and a translation part, T3, built from T: a11 a12 0 a13 V3 = a21 a22 0 T3 = a23 0 0 1. 0 It also has the same scale factor as T. This guarantees (by projection) that the transformation which would be performed by T 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 &P)
	Makes the transformation into a symmetrical transformation. P is the center of the symmetry. More...

void	SetMirror (const gp_Ax1 &A1)
	Makes the transformation into a symmetrical transformation. A1 is the center of the axial symmetry. More...

void	SetMirror (const gp_Ax2 &A2)
	Makes the transformation into a symmetrical transformation. A2 is the center of the planar symmetry and defines the plane of symmetry by its origin, "X <br> Direction" and "Y Direction". More...

void	SetRotation (const gp_Ax1 &A1, const Standard_Real Ang)
	Changes the transformation into a rotation. A1 is the rotation axis and Ang is the angular value of the rotation in radians. More...

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

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

void	SetDisplacement (const gp_Ax3 &FromSystem1, const gp_Ax3 &ToSystem2)
	Modifies this transformation so that it transforms the coordinate system defined by FromSystem1 into the one defined by ToSystem2. After this modification, this transformation transforms: More...

void	SetTransformation (const gp_Ax3 &FromSystem1, const gp_Ax3 &ToSystem2)
	Modifies this transformation so that it transforms the <br> 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 "FromSystem1" to the coordinate system "ToSystem2". Example : In a C++ implementation : Real x1, y1, z1; // are the coordinates of a point in the // local system FromSystem1 Real x2, y2, z2; // are the coordinates of a point in the // local system ToSystem2 gp_Pnt P1 (x1, y1, z1) Trsf T; T.SetTransformation (FromSystem1, ToSystem2); gp_Pnt P2 = P1.Transformed (T); P2.Coord (x2, y2, z2); More...

void	SetTransformation (const gp_Ax3 &ToSystem)
	Modifies this transformation so that it transforms the <br> 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 ToSystem. Use in the same way as the previous method. FromSystem1 is defaulted to the absolute coordinate system. More...

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

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

void	SetTranslation (const gp_Pnt &P1, const gp_Pnt &P2)
	Makes the transformation into a translation where the translation vector is the vector (P1, P2) defined from point P1 to point P2. More...

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

void	SetScaleFactor (const Standard_Real S)
	Modifies the scale factor. <br> Raises ConstructionError If S is null. More...

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, const Standard_Real Tolang, const Standard_Real TolDist)
	Sets the coefficients of the transformation. The <br> transformation of the point x,y,z is the point <br> x',y',z' with : <br> x' = a11 x + a12 y + a13 z + a14 y' = a21 x + a22 y + a23 z + a24 z' = a31 x + a32 y + a43 z + a34 Tolang and TolDist are used to test for null angles and null distances to determine the form of the transformation (identity, translation, etc..). The method Value(i,j) will return aij. Raises ConstructionError if the determinant of the aij is null. Or if the matrix as not a uniform scale. More...

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

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

const gp_XYZ &	TranslationPart () 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_Mat &	HVectorialPart () 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 Row, const Standard_Integer Col) 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 Row < 1 or Row > 3 or Col < 1 or Col > 4 More...

void	Invert ()

gp_Trsf	Inverted () const
	Computes the reverse transformation <br> 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 : Trsf T1, T2, Tcomp; ............... Tcomp = T2.Multiplied(T1); // or (Tcomp = T2 * T1) Pnt P1(10.,3.,4.); Pnt P2 = P1.Transformed(Tcomp); //using Tcomp Pnt P3 = P1.Transformed(T1); //using T1 then T2 P3.Transform(T2); // P3 = P2 !!! More...

gp_Trsf	Multiplied (const gp_Trsf &T) const

gp_Trsf	operator* (const gp_Trsf &T) const

void	Multiply (const gp_Trsf &T)
	Computes the transformation composed with T and <me>. In a C++ implementation you can also write Tcomposed = <me> * T. Example : Trsf T1, T2, Tcomp; ............... //composition : Tcomp = T2.Multiplied(T1); // or (Tcomp = T2 * T1) // transformation of a point Pnt P1(10.,3.,4.); Pnt P2 = P1.Transformed(Tcomp); //using Tcomp Pnt P3 = P1.Transformed(T1); //using T1 then T2 P3.Transform(T2); // P3 = P2 !!! Computes the transformation composed with <me> and T. <me> = T * <me> More...

void	operator*= (const gp_Trsf &T)

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

void	Power (const Standard_Integer N)

gp_Trsf	Powered (const Standard_Integer N)
	Computes the following composition of transformations <br> <me> * <me> * .......* <me>, N time. if N = 0 <me> = Identity if N < 0 <me> = <me>.Inverse() ........... <me>.Inverse(). Raises if N < 0 and if the matrix of the transformation not inversible. More...

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

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

Standard_Real	_CSFDB_Getgp_Trsfscale () const

void	_CSFDB_Setgp_Trsfscale (const Standard_Real p)

gp_TrsfForm	_CSFDB_Getgp_Trsfshape () const

void	_CSFDB_Setgp_Trsfshape (const gp_TrsfForm p)

const gp_Mat &	_CSFDB_Getgp_Trsfmatrix () const

const gp_XYZ &	_CSFDB_Getgp_Trsfloc () const

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.

Constructor & Destructor Documentation

gp_Trsf::gp_Trsf ( )

Returns the identity transformation.

gp_Trsf::gp_Trsf ( const gp_Trsf2d & T )

 Creates  a 3D transformation from the 2D transformation T. <br>

The resulting transformation has a homogeneous
vectorial part, V3, and a translation part, T3, built from T:
a11 a12
0 a13
V3 = a21 a22 0 T3
= a23
0 0 1.
0
It also has the same scale factor as T. This
guarantees (by projection) that the transformation
which would be performed by T 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

const gp_XYZ& gp_Trsf::_CSFDB_Getgp_Trsfloc ( ) const

inline

const gp_Mat& gp_Trsf::_CSFDB_Getgp_Trsfmatrix ( ) const

inline

Standard_Real gp_Trsf::_CSFDB_Getgp_Trsfscale ( ) const

inline

gp_TrsfForm gp_Trsf::_CSFDB_Getgp_Trsfshape ( ) const

inline

void gp_Trsf::_CSFDB_Setgp_Trsfscale ( const Standard_Real p )

inline

void gp_Trsf::_CSFDB_Setgp_Trsfshape ( const gp_TrsfForm p )

inline

gp_TrsfForm gp_Trsf::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, or a compound transformation.

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.

gp_Quaternion gp_Trsf::GetRotation ( ) const

Returns quaternion representing rotational part of the transformation.

const gp_Mat& gp_Trsf::HVectorialPart ( ) 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.

void gp_Trsf::Invert ( )

gp_Trsf gp_Trsf::Inverted ( ) const

Computes the reverse transformation <br>

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 :
Trsf T1, T2, Tcomp; ...............
Tcomp = T2.Multiplied(T1); // or (Tcomp = T2 * T1)
Pnt P1(10.,3.,4.);
Pnt P2 = P1.Transformed(Tcomp); //using Tcomp
Pnt P3 = P1.Transformed(T1); //using T1 then T2
P3.Transform(T2); // P3 = P2 !!!

Standard_Boolean gp_Trsf::IsNegative ( ) const

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

this transformation is negative.

gp_Trsf gp_Trsf::Multiplied ( const gp_Trsf & T ) const

void gp_Trsf::Multiply ( const gp_Trsf & T )

Computes the transformation composed with T and <me>.
In a C++ implementation you can also write Tcomposed = <me> * T.
Example :
Trsf T1, T2, Tcomp; ...............
//composition :
Tcomp = T2.Multiplied(T1); // or (Tcomp = T2 * T1)
// transformation of a point
Pnt P1(10.,3.,4.);
Pnt P2 = P1.Transformed(Tcomp); //using Tcomp
Pnt P3 = P1.Transformed(T1); //using T1 then T2
P3.Transform(T2); // P3 = P2 !!!
Computes the transformation composed with <me> and T.
<me> = T * <me>

gp_Trsf gp_Trsf::operator* ( const gp_Trsf & T ) const

inline

void gp_Trsf::operator*= ( const gp_Trsf & T )

inline

void gp_Trsf::Power ( const Standard_Integer N )

gp_Trsf gp_Trsf::Powered ( const Standard_Integer N )

Computes the following composition of transformations <br>

<me> * <me> * .......* <me>, N time.
if N = 0 <me> = Identity
if N < 0 <me> = <me>.Inverse() *...........* <me>.Inverse().

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

void gp_Trsf::PreMultiply ( const gp_Trsf & T )

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

Standard_Real gp_Trsf::ScaleFactor ( ) const

Returns the scale factor.

void gp_Trsf::SetDisplacement	(	const gp_Ax3 &	FromSystem1,
		const gp_Ax3 &	ToSystem2
	)

Modifies this transformation so that it transforms the
coordinate system defined by FromSystem1 into the
one defined by ToSystem2. After this modification, this
transformation transforms:

the origin of FromSystem1 into the origin of ToSystem2,
the "X Direction" of FromSystem1 into the "X <br> Direction" of ToSystem2,
the "Y Direction" of FromSystem1 into the "Y <br> Direction" of ToSystem2, and
the "main Direction" of FromSystem1 into the "main <br> Direction" of ToSystem2.
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.

void gp_Trsf::SetMirror ( const gp_Pnt & P )

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

void gp_Trsf::SetMirror ( const gp_Ax1 & A1 )

Makes the transformation into a symmetrical transformation.
A1 is the center of the axial symmetry.

void gp_Trsf::SetMirror ( const gp_Ax2 & A2 )

Makes the transformation into a symmetrical transformation.
A2 is the center of the planar symmetry
and defines the plane of symmetry by its origin, "X <br> Direction" and "Y Direction".

void gp_Trsf::SetRotation	(	const gp_Ax1 &	A1,
		const Standard_Real	Ang
	)

Changes the transformation into a rotation.
A1 is the rotation axis and Ang is the angular value of the
rotation in radians.

void gp_Trsf::SetRotation ( const gp_Quaternion & R )

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

void gp_Trsf::SetScale	(	const gp_Pnt &	P,
		const Standard_Real	S
	)

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

void gp_Trsf::SetScaleFactor ( const Standard_Real S )

  Modifies the scale factor. <br>

Raises ConstructionError If S is null.

void gp_Trsf::SetTransformation	(	const gp_Ax3 &	FromSystem1,
		const gp_Ax3 &	ToSystem2
	)

 Modifies this transformation so that it transforms the <br>

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 "FromSystem1" to the coordinate system "ToSystem2".
Example :
In a C++ implementation :
Real x1, y1, z1; // are the coordinates of a point in the
// local system FromSystem1
Real x2, y2, z2; // are the coordinates of a point in the
// local system ToSystem2
gp_Pnt P1 (x1, y1, z1)
Trsf T;
T.SetTransformation (FromSystem1, ToSystem2);
gp_Pnt P2 = P1.Transformed (T);
P2.Coord (x2, y2, z2);

void gp_Trsf::SetTransformation ( const gp_Ax3 & ToSystem )

Modifies this transformation so that it transforms the <br>

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 ToSystem.
Use in the same way as the previous method. FromSystem1 is
defaulted to the absolute coordinate system.

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

Sets transformation by directly specified rotation and translation.

void gp_Trsf::SetTranslation ( const gp_Vec & V )

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

void gp_Trsf::SetTranslation	(	const gp_Pnt &	P1,
		const gp_Pnt &	P2
	)

Makes the transformation into a translation where the translation vector
is the vector (P1, P2) defined from point P1 to point P2.

void gp_Trsf::SetTranslationPart ( const gp_Vec & V )

Replaces the translation vector with the vector V.

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,
		const Standard_Real	Tolang,
		const Standard_Real	TolDist
	)

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

x' = a11 x + a12 y + a13 z + a14
y' = a21 x + a22 y + a23 z + a24
z' = a31 x + a32 y + a43 z + a34

Tolang and TolDist are used to test for null
angles and null distances to determine the form of
the transformation (identity, translation, etc..).

The method Value(i,j) will return aij.
Raises ConstructionError if the determinant of the aij is null. Or if
the matrix as not a uniform scale.

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

void gp_Trsf::Transforms ( gp_XYZ & Coord ) const

Transformation of a triplet XYZ with a Trsf

const gp_XYZ& gp_Trsf::TranslationPart ( ) const

Returns the translation part of the transformation's matrix

Standard_Real gp_Trsf::Value	(	const Standard_Integer	Row,
		const Standard_Integer	Col
	)		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 Row < 1 or Row > 3 or Col < 1 or Col > 4

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:

gp_Trsf.hxx

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation