gp_GTrsf2d Class Reference

Defines a non persistent transformation in 2D space. This transformation is a general transformation. It can be a gp_Trsf2d, an affinity, or you can define your own transformation giving the corresponding matrix of transformation. More...

#include <gp_GTrsf2d.hxx>

Public Member Functions
constexpr	gp_GTrsf2d () noexcept
	returns identity transformation.
	gp_GTrsf2d (const gp_Trsf2d &theT)
	Converts the gp_Trsf2d transformation theT into a general transformation.
constexpr	gp_GTrsf2d (const gp_Mat2d &theM, const gp_XY &theV) noexcept
	Creates a transformation based on the matrix theM and the vector theV where theM defines the vectorial part of the transformation, and theV the translation part.
void	SetAffinity (const gp_Ax2d &theA, const double theRatio)
	Changes this transformation into an affinity of ratio theRatio with respect to the axis theA. 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 theA, 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 > 2 or theCol < 1 or theCol > 3.
void	SetTranslationPart (const gp_XY &theCoord)
	Replaces the translation part of this transformation by the coordinates of the number pair theCoord.
void	SetTrsf2d (const gp_Trsf2d &theT)
	Assigns the vectorial and translation parts of theT to this transformation.
constexpr void	SetVectorialPart (const gp_Mat2d &theMatrix) noexcept
	Replaces the vectorial part of this transformation by theMatrix.
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 or axis), a scaling transformation, a compound transformation or some other type of transformation.
constexpr const gp_XY &	TranslationPart () const noexcept
	Returns the translation part of the GTrsf2d.
constexpr const gp_Mat2d &	VectorialPart () const noexcept
	Computes the vectorial part of the GTrsf2d. The returned Matrix is a 2*2 matrix.
constexpr double	Value (const int theRow, const int theCol) const
	Returns the coefficients of the global matrix of transformation. Raised OutOfRange if theRow < 1 or theRow > 2 or theCol < 1 or theCol > 3.
double	operator() (const int theRow, const int theCol) const
void	Invert ()
gp_GTrsf2d	Inverted () const
	Computes the reverse transformation. Raised an exception if the matrix of the transformation is not inversible.
gp_GTrsf2d	Multiplied (const gp_GTrsf2d &theT) const
	Computes the transformation composed with theT and <me>. In a C++ implementation you can also write Tcomposed = <me> * theT. Example :
gp_GTrsf2d	operator* (const gp_GTrsf2d &theT) const
void	Multiply (const gp_GTrsf2d &theT)
void	operator*= (const gp_GTrsf2d &theT)
void	PreMultiply (const gp_GTrsf2d &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_GTrsf2d	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 (gp_XY &theCoord) const noexcept
constexpr gp_XY	Transformed (const gp_XY &theCoord) const noexcept
constexpr void	Transforms (double &theX, double &theY) const noexcept
	Applies this transformation to the coordinates:
gp_Trsf2d	Trsf2d () const
	Converts this transformation into a gp_Trsf2d transformation. Exceptions Standard_ConstructionError if this transformation cannot be converted, i.e. if its form is gp_Other.

Detailed Description

Defines a non persistent transformation in 2D space. This transformation is a general transformation. It can be a gp_Trsf2d, an affinity, or you can define your own transformation giving the corresponding matrix of transformation.

With a gp_GTrsf2d you can transform only a doublet of coordinates gp_XY. It is not possible to transform other geometric objects because these transformations can change the nature of non-elementary geometric objects. A gp_GTrsf2d is represented with a 2 rows * 3 columns matrix:

   V1   V2   T        XY         XY
| a11  a12  a14 |   | x |      | x'|
| a21  a22  a24 |   | 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. Warning A gp_GTrsf2d transformation is only applicable on coordinates. Be careful if you apply such a transformation to all the 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_Trsf2d transformation instead, as objects of this class respect the nature of geometric objects.

Constructor & Destructor Documentation

gp_GTrsf2d() [1/3]

constexpr gp_GTrsf2d::gp_GTrsf2d ( )

inlineconstexprnoexcept

returns identity transformation.

gp_GTrsf2d() [2/3]

gp_GTrsf2d::gp_GTrsf2d ( const gp_Trsf2d & theT )

inline

Converts the gp_Trsf2d transformation theT into a general transformation.

gp_GTrsf2d() [3/3]

constexpr gp_GTrsf2d::gp_GTrsf2d ( const gp_Mat2d & theM, const gp_XY & theV )

inlineconstexprnoexcept

Creates a transformation based on the matrix theM and the vector theV where theM defines the vectorial part of the transformation, and theV the translation part.

Member Function Documentation

Form()

constexpr gp_TrsfForm gp_GTrsf2d::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 or axis), a scaling transformation, a compound transformation or some other type of transformation.

Invert()

void gp_GTrsf2d::Invert

(

)

Inverted()

gp_GTrsf2d gp_GTrsf2d::Inverted ( ) const

inline

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

IsNegative()

constexpr bool gp_GTrsf2d::IsNegative ( ) const

inlineconstexprnoexcept

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

IsSingular()

constexpr bool gp_GTrsf2d::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_GTrsf2d gp_GTrsf2d::Multiplied ( const gp_GTrsf2d & theT ) const

inline

Computes the transformation composed with theT and <me>. In a C++ implementation you can also write Tcomposed = <me> * theT. Example :

gp_GTrsf2d T1, T2, Tcomp; ...............
//composition :
Tcomp = T2.Multiplied(T1);         // or   (Tcomp = T2 * T1)
// transformation of a point
gp_XY P(10.,3.);
gp_XY P1(P);
Tcomp.Transforms(P1);               //using Tcomp
gp_XY P2(P);
T1.Transforms(P2);                  //using T1 then T2
T2.Transforms(P2);                  // P1 = P2 !!!

Multiply()

void gp_GTrsf2d::Multiply

(

const gp_GTrsf2d &

theT

)

operator()()

double gp_GTrsf2d::operator() ( const int theRow, const int theCol ) const

inline

operator*()

gp_GTrsf2d gp_GTrsf2d::operator* ( const gp_GTrsf2d & theT ) const

inline

operator*=()

void gp_GTrsf2d::operator*= ( const gp_GTrsf2d & theT )

inline

Power()

void gp_GTrsf2d::Power

(

const int

theN

)

Powered()

gp_GTrsf2d gp_GTrsf2d::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 an exception if theN < 0 and if the matrix of the transformation is not inversible.

PreMultiply()

void gp_GTrsf2d::PreMultiply

(

const gp_GTrsf2d &

theT

)

Computes the product of the transformation theT and this transformation, and assigns the result to this transformation: this = theT * this.

SetAffinity()

void gp_GTrsf2d::SetAffinity	(	const gp_Ax2d &	theA,
		const double	theRatio )

Changes this transformation into an affinity of ratio theRatio with respect to the axis theA. 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 theA, the vectors HP and HP' satisfy: HP' = theRatio * HP.

SetTranslationPart()

void gp_GTrsf2d::SetTranslationPart

(

const gp_XY &

theCoord

)

Replaces the translation part of this transformation by the coordinates of the number pair theCoord.

SetTrsf2d()

void gp_GTrsf2d::SetTrsf2d ( const gp_Trsf2d & theT )

inline

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

SetValue()

void gp_GTrsf2d::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 > 2 or theCol < 1 or theCol > 3.

SetVectorialPart()

constexpr void gp_GTrsf2d::SetVectorialPart ( const gp_Mat2d & theMatrix )

inlineconstexprnoexcept

Replaces the vectorial part of this transformation by theMatrix.

Transformed()

constexpr gp_XY gp_GTrsf2d::Transformed ( const gp_XY & theCoord ) const

inlineconstexprnoexcept

Transforms() [1/2]

constexpr void gp_GTrsf2d::Transforms ( double & theX, double & theY ) const

inlineconstexprnoexcept

Applies this transformation to the coordinates:

• of the number pair Coord, or
• X and Y.

Note:

• Transforms modifies theX, theY, or the coordinate pair Coord, while
• Transformed creates a new coordinate pair.

Transforms() [2/2]

constexpr void gp_GTrsf2d::Transforms ( gp_XY & theCoord ) const

inlineconstexprnoexcept

TranslationPart()

constexpr const gp_XY & gp_GTrsf2d::TranslationPart ( ) const

inlineconstexprnoexcept

Returns the translation part of the GTrsf2d.

Trsf2d()

gp_Trsf2d gp_GTrsf2d::Trsf2d

(

)

const

Converts this transformation into a gp_Trsf2d transformation. Exceptions Standard_ConstructionError if this transformation cannot be converted, i.e. if its form is gp_Other.

Value()

constexpr double gp_GTrsf2d::Value ( const int theRow, const int theCol ) const

inlineconstexpr

Returns the coefficients of the global matrix of transformation. Raised OutOfRange if theRow < 1 or theRow > 2 or theCol < 1 or theCol > 3.

VectorialPart()

constexpr const gp_Mat2d & gp_GTrsf2d::VectorialPart ( ) const

inlineconstexprnoexcept

Computes the vectorial part of the GTrsf2d. The returned Matrix is a 2*2 matrix.

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

• gp_GTrsf2d.hxx