gp_Trsf2d Class Reference

Defines a non-persistent transformation in 2D space. The following transformations are implemented : More...

#include <gp_Trsf2d.hxx>

Public Member Functions
constexpr	gp_Trsf2d () noexcept
	Returns identity transformation.
	gp_Trsf2d (const gp_Trsf &theT)
	Creates a 2d transformation in the XY plane from a 3d transformation .
void	SetMirror (const gp_Pnt2d &theP) noexcept
	Changes the transformation into a symmetrical transformation. theP is the center of the symmetry.
void	SetMirror (const gp_Ax2d &theA) noexcept
	Changes the transformation into a symmetrical transformation. theA is the center of the axial symmetry.
void	SetRotation (const gp_Pnt2d &theP, const double theAng)
	Changes the transformation into a rotation. theP is the rotation's center and theAng is the angular value of the rotation in radian.
void	SetScale (const gp_Pnt2d &theP, const double theS)
	Changes the transformation into a scale. theP is the center of the scale and theS is the scaling value.
void	SetTransformation (const gp_Ax2d &theFromSystem1, const gp_Ax2d &theToSystem2)
	Changes a transformation allowing passage from the coordinate system "theFromSystem1" to the coordinate system "theToSystem2".
void	SetTransformation (const gp_Ax2d &theToSystem)
	Changes the transformation allowing passage from the basic coordinate system {P(0.,0.,0.), VX (1.,0.,0.), VY (0.,1.,0.)} to the local coordinate system defined with the Ax2d theToSystem.
void	SetTranslation (const gp_Vec2d &theV)
	Changes the transformation into a translation. theV is the vector of the translation.
void	SetTranslation (const gp_Pnt2d &theP1, const gp_Pnt2d &theP2)
	Makes the transformation into a translation from the point theP1 to the point theP2.
void	SetTranslationPart (const gp_Vec2d &theV)
	Replaces the translation vector with theV.
void	SetScaleFactor (const double theS)
	Modifies the scale factor.
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 (relative to a point or an axis), a scaling transformation, or a compound transformation.
constexpr double	ScaleFactor () const noexcept
	Returns the scale factor.
constexpr const gp_XY &	TranslationPart () const noexcept
	Returns the translation part of the transformation's matrix.
gp_Mat2d	VectorialPart () const
	Returns the vectorial part of the transformation. It is a 2*2 matrix which includes the scale factor.
constexpr const gp_Mat2d &	HVectorialPart () const noexcept
	Returns the homogeneous vectorial part of the transformation. It is a 2*2 matrix which doesn't include the scale factor. The coefficients of this matrix must be multiplied by the scale factor to obtain the coefficients of the transformation.
double	RotationPart () const
	Returns the angle corresponding to the rotational component of the transformation matrix (operation opposite to SetRotation()).
constexpr double	Value (const int theRow, const int theCol) const
	Returns the coefficients of the transformation's matrix. It is a 2 rows * 3 columns matrix. Raises OutOfRange if theRow < 1 or theRow > 2 or theCol < 1 or theCol > 3.
void	Invert ()
gp_Trsf2d	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.
gp_Trsf2d	Multiplied (const gp_Trsf2d &theT) const
gp_Trsf2d	operator* (const gp_Trsf2d &theT) const
void	Multiply (const gp_Trsf2d &theT)
	Computes the transformation composed from <me> and theT. <me> = <me> * theT.
void	operator*= (const gp_Trsf2d &theT)
void	PreMultiply (const gp_Trsf2d &theT)
	Computes the transformation composed from <me> and theT. <me> = theT * <me>.
void	Power (const int theN)
gp_Trsf2d	Powered (const int theN)
	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) const noexcept
constexpr void	Transforms (gp_XY &theCoord) const noexcept
	Transforms a doublet XY with a Trsf2d.
void	SetValues (const double a11, const double a12, const double a13, const double a21, const double a22, const double a23)
	Sets the coefficients of the transformation. The transformation of the point x,y is the point x',y' with :

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

Detailed Description

Defines a non-persistent transformation in 2D space. The following transformations are implemented :

• Translation, Rotation, Scale
• Symmetry with respect to a point and a line. Complex transformations can be obtained by combining the previous elementary transformations using the method Multiply. The transformations can be represented as follow :

     V1   V2   T       XY        XY
  | a11  a12  a13 |   | x |     | x'|
  | a21  a22  a23 |   | y |     | y'|
  |  0    0    1  |   | 1 |     | 1 |

  where {V1, V2} 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_Trsf2d() [1/2]

gp_Trsf2d::gp_Trsf2d ( )

inlineconstexprnoexcept

Returns identity transformation.

gp_Trsf2d() [2/2]

gp_Trsf2d::gp_Trsf2d ( const gp_Trsf & theT )

inline

Creates a 2d transformation in the XY plane from a 3d transformation .

Member Function Documentation

Form()

gp_TrsfForm gp_Trsf2d::Form ( ) const

inlineconstexprnoexcept

Returns the nature of the transformation. It can be an identity transformation, a rotation, a translation, a mirror (relative to a point or an axis), a scaling transformation, or a compound transformation.

HVectorialPart()

const gp_Mat2d & gp_Trsf2d::HVectorialPart ( ) const

inlineconstexprnoexcept

Returns the homogeneous vectorial part of the transformation. It is a 2*2 matrix which doesn't include the scale factor. The coefficients of this matrix must be multiplied by the scale factor to obtain the coefficients of the transformation.

Invert()

void gp_Trsf2d::Invert

(

)

Inverted()

gp_Trsf2d gp_Trsf2d::Inverted ( ) const

inlinenodiscard

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.

IsNegative()

bool gp_Trsf2d::IsNegative ( ) const

inlineconstexprnoexcept

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

Multiplied()

gp_Trsf2d gp_Trsf2d::Multiplied ( const gp_Trsf2d & theT ) const

inlinenodiscard

Multiply()

void gp_Trsf2d::Multiply

(

const gp_Trsf2d &

theT

)

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

operator*()

gp_Trsf2d gp_Trsf2d::operator* ( const gp_Trsf2d & theT ) const

inlinenodiscard

operator*=()

void gp_Trsf2d::operator*= ( const gp_Trsf2d & theT )

inline

Orthogonalize()

void gp_Trsf2d::Orthogonalize ( )

protected

Makes orthogonalization of "matrix".

Power()

void gp_Trsf2d::Power

(

const int

theN

)

Powered()

gp_Trsf2d gp_Trsf2d::Powered ( const int theN )

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_Trsf2d::PreMultiply

(

const gp_Trsf2d &

theT

)

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

RotationPart()

double gp_Trsf2d::RotationPart

(

)

const

Returns the angle corresponding to the rotational component of the transformation matrix (operation opposite to SetRotation()).

ScaleFactor()

double gp_Trsf2d::ScaleFactor ( ) const

inlineconstexprnoexcept

Returns the scale factor.

SetMirror() [1/2]

void gp_Trsf2d::SetMirror ( const gp_Ax2d & theA )

noexcept

Changes the transformation into a symmetrical transformation. theA is the center of the axial symmetry.

SetMirror() [2/2]

void gp_Trsf2d::SetMirror ( const gp_Pnt2d & theP )

inlinenoexcept

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

SetRotation()

void gp_Trsf2d::SetRotation ( const gp_Pnt2d & theP, const double theAng )

inline

Changes the transformation into a rotation. theP is the rotation's center and theAng is the angular value of the rotation in radian.

SetScale()

void gp_Trsf2d::SetScale ( const gp_Pnt2d & theP, const double theS )

inline

Changes the transformation into a scale. theP is the center of the scale and theS is the scaling value.

SetScaleFactor()

void gp_Trsf2d::SetScaleFactor

(

const double

theS

)

Modifies the scale factor.

SetTransformation() [1/2]

void gp_Trsf2d::SetTransformation	(	const gp_Ax2d &	theFromSystem1,
		const gp_Ax2d &	theToSystem2 )

Changes a transformation allowing passage from the coordinate system "theFromSystem1" to the coordinate system "theToSystem2".

SetTransformation() [2/2]

void gp_Trsf2d::SetTransformation

(

const gp_Ax2d &

theToSystem

)

Changes the transformation allowing passage from the basic coordinate system {P(0.,0.,0.), VX (1.,0.,0.), VY (0.,1.,0.)} to the local coordinate system defined with the Ax2d theToSystem.

SetTranslation() [1/2]

void gp_Trsf2d::SetTranslation ( const gp_Pnt2d & theP1, const gp_Pnt2d & theP2 )

inline

Makes the transformation into a translation from the point theP1 to the point theP2.

SetTranslation() [2/2]

void gp_Trsf2d::SetTranslation ( const gp_Vec2d & theV )

inline

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

SetTranslationPart()

void gp_Trsf2d::SetTranslationPart

(

const gp_Vec2d &

theV

)

Replaces the translation vector with theV.

SetValues()

void gp_Trsf2d::SetValues	(	const double	a11,
		const double	a12,
		const double	a13,
		const double	a21,
		const double	a22,
		const double	a23 )

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

x' = a11 x + a12 y + a13
y' = a21 x + a22 y + a23

The method Value(i,j) will return aij. Raises ConstructionError if the determinant of the aij is null. If the matrix as not a uniform scale it will be orthogonalized before future using.

Transforms() [1/2]

void gp_Trsf2d::Transforms ( double & theX, double & theY ) const

inlineconstexprnoexcept

Transforms() [2/2]

void gp_Trsf2d::Transforms ( gp_XY & theCoord ) const

inlineconstexprnoexcept

Transforms a doublet XY with a Trsf2d.

TranslationPart()

const gp_XY & gp_Trsf2d::TranslationPart ( ) const

inlineconstexprnoexcept

Returns the translation part of the transformation's matrix.

Value()

double gp_Trsf2d::Value ( const int theRow, const int theCol ) const

inlineconstexpr

Returns the coefficients of the transformation's matrix. It is a 2 rows * 3 columns matrix. Raises OutOfRange if theRow < 1 or theRow > 2 or theCol < 1 or theCol > 3.

VectorialPart()

gp_Mat2d gp_Trsf2d::VectorialPart

(

)

const

Returns the vectorial part of the transformation. It is a 2*2 matrix which includes the scale factor.

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

• gp_Trsf2d.hxx