gp_Parab2d Class Reference

Describes a parabola in the plane (2D space). A parabola is defined by its focal length (that is, the distance between its focus and apex) and positioned in the plane with a coordinate system (a gp_Ax22d object) where: More...

#include <gp_Parab2d.hxx>

Public Member Functions
constexpr	gp_Parab2d () noexcept
	Creates an indefinite parabola.
constexpr	gp_Parab2d (const gp_Ax2d &theMirrorAxis, const double theFocalLength, const bool theSense=true)
	Creates a parabola with its vertex point, its axis of symmetry ("XAxis") and its focal length. The sense of parametrization is given by theSense. If theSense == TRUE (by default) then right-handed coordinate system is used, otherwise - left-handed. Warnings : It is possible to have FocalLength = 0. In this case, the parabola looks like a line, which is parallel to the symmetry-axis. Raises ConstructionError if FocalLength < 0.0.
constexpr	gp_Parab2d (const gp_Ax22d &theAxes, const double theFocalLength)
	Creates a parabola with its vertex point, its axis of symmetry ("XAxis"), correspond Y-axis and its focal length. Warnings : It is possible to have FocalLength = 0. In this case, the parabola looks like a line, which is parallel to the symmetry-axis. Raises ConstructionError if Focal < 0.0.
	gp_Parab2d (const gp_Ax2d &theDirectrix, const gp_Pnt2d &theFocus, const bool theSense=true)
	Creates a parabola with the directrix and the focus point. Y-axis of the parabola (in User Coordinate System - UCS) is the direction of theDirectrix. X-axis always directs from theDirectrix to theFocus point and always comes through theFocus. Apex of the parabola is a middle point between the theFocus and the intersection point of theDirectrix and the X-axis. Warnings : It is possible to have FocalLength = 0 (when theFocus lies in theDirectrix). In this case, X-direction of the parabola is defined by theSense parameter. If theSense == TRUE (by default) then right-handed coordinate system is used, otherwise - left-handed. Result parabola will look like a line, which is perpendicular to the directrix.
void	SetFocal (const double theFocal)
	Changes the focal distance of the parabola Warnings : It is possible to have theFocal = 0. Raises ConstructionError if theFocal < 0.0.
constexpr void	SetLocation (const gp_Pnt2d &theP) noexcept
	Changes the "Location" point of the parabola. It is the vertex of the parabola.
constexpr void	SetMirrorAxis (const gp_Ax2d &theA)
	Modifies this parabola, by redefining its local coordinate system so that its origin and "X Direction" become those of the axis MA. The "Y Direction" of the local coordinate system is then recomputed. The orientation of the local coordinate system is not modified.
constexpr void	SetAxis (const gp_Ax22d &theA) noexcept
	Changes the local coordinate system of the parabola. The "Location" point of A becomes the vertex of the parabola.
void	Coefficients (double &theA, double &theB, double &theC, double &theD, double &theE, double &theF) const
	Computes the coefficients of the implicit equation of the parabola (in WCS - World Coordinate System).
gp_Ax2d	Directrix () const noexcept
	Computes the directrix of the parabola. The directrix is:
constexpr double	Focal () const noexcept
	Returns the distance between the vertex and the focus of the parabola.
gp_Pnt2d	Focus () const noexcept
	Returns the focus of the parabola.
constexpr const gp_Pnt2d &	Location () const noexcept
	Returns the vertex of the parabola.
gp_Ax2d	MirrorAxis () const noexcept
	Returns the symmetry axis of the parabola. The "Location" point of this axis is the vertex of the parabola.
constexpr const gp_Ax22d &	Axis () const noexcept
	Returns the local coordinate system of the parabola. The "Location" point of this axis is the vertex of the parabola.
constexpr double	Parameter () const noexcept
	Returns the distance between the focus and the directrix of the parabola.
void	Reverse () noexcept
gp_Parab2d	Reversed () const noexcept
	Reverses the orientation of the local coordinate system of this parabola (the "Y Direction" is reversed). Therefore, the implicit orientation of this parabola is reversed. Note:
constexpr bool	IsDirect () const noexcept
	Returns true if the local coordinate system is direct and false in the other case.
void	Mirror (const gp_Pnt2d &theP) noexcept
gp_Parab2d	Mirrored (const gp_Pnt2d &theP) const noexcept
	Performs the symmetrical transformation of a parabola with respect to the point theP which is the center of the symmetry.
void	Mirror (const gp_Ax2d &theA) noexcept
gp_Parab2d	Mirrored (const gp_Ax2d &theA) const noexcept
	Performs the symmetrical transformation of a parabola with respect to an axis placement which is the axis of the symmetry.
void	Rotate (const gp_Pnt2d &theP, const double theAng)
gp_Parab2d	Rotated (const gp_Pnt2d &theP, const double theAng) const
	Rotates a parabola. theP is the center of the rotation. theAng is the angular value of the rotation in radians.
void	Scale (const gp_Pnt2d &theP, const double theS)
gp_Parab2d	Scaled (const gp_Pnt2d &theP, const double theS) const
	Scales a parabola. theS is the scaling value. If theS is negative the direction of the symmetry axis "XAxis" is reversed and the direction of the "YAxis" too.
void	Transform (const gp_Trsf2d &theT)
gp_Parab2d	Transformed (const gp_Trsf2d &theT) const
	Transforms an parabola with the transformation theT from class Trsf2d.
constexpr void	Translate (const gp_Vec2d &theV) noexcept
constexpr gp_Parab2d	Translated (const gp_Vec2d &theV) const noexcept
	Translates a parabola in the direction of the vectorthe theV. The magnitude of the translation is the vector's magnitude.
constexpr void	Translate (const gp_Pnt2d &theP1, const gp_Pnt2d &theP2) noexcept
constexpr gp_Parab2d	Translated (const gp_Pnt2d &theP1, const gp_Pnt2d &theP2) const noexcept
	Translates a parabola from the point theP1 to the point theP2.

Detailed Description

Describes a parabola in the plane (2D space). A parabola is defined by its focal length (that is, the distance between its focus and apex) and positioned in the plane with a coordinate system (a gp_Ax22d object) where:

• the origin of the coordinate system is on the apex of the parabola, and
• the "X Axis" of the coordinate system is the axis of symmetry; the parabola is on the positive side of this axis. This coordinate system is the "local coordinate system" of the parabola. Its orientation (direct or indirect sense) gives an implicit orientation to the parabola. In this coordinate system, the equation for the parabola is:

  Y**2 = (2*P) * X.

  where P, referred to as the parameter of the parabola, is the distance between the focus and the directrix (P is twice the focal length). See Also GCE2d_MakeParab2d which provides functions for more complex parabola constructions Geom2d_Parabola which provides additional functions for constructing parabolas and works, in particular, with the parametric equations of parabolas

Constructor & Destructor Documentation

gp_Parab2d() [1/4]

constexpr gp_Parab2d::gp_Parab2d ( )

inlineconstexprnoexcept

Creates an indefinite parabola.

gp_Parab2d() [2/4]

constexpr gp_Parab2d::gp_Parab2d ( const gp_Ax2d & theMirrorAxis, const double theFocalLength, const bool theSense = true )

inlineconstexpr

Creates a parabola with its vertex point, its axis of symmetry ("XAxis") and its focal length. The sense of parametrization is given by theSense. If theSense == TRUE (by default) then right-handed coordinate system is used, otherwise - left-handed. Warnings : It is possible to have FocalLength = 0. In this case, the parabola looks like a line, which is parallel to the symmetry-axis. Raises ConstructionError if FocalLength < 0.0.

gp_Parab2d() [3/4]

constexpr gp_Parab2d::gp_Parab2d ( const gp_Ax22d & theAxes, const double theFocalLength )

inlineconstexpr

Creates a parabola with its vertex point, its axis of symmetry ("XAxis"), correspond Y-axis and its focal length. Warnings : It is possible to have FocalLength = 0. In this case, the parabola looks like a line, which is parallel to the symmetry-axis. Raises ConstructionError if Focal < 0.0.

gp_Parab2d() [4/4]

gp_Parab2d::gp_Parab2d	(	const gp_Ax2d &	theDirectrix,
		const gp_Pnt2d &	theFocus,
		const bool	theSense = true )

Creates a parabola with the directrix and the focus point. Y-axis of the parabola (in User Coordinate System - UCS) is the direction of theDirectrix. X-axis always directs from theDirectrix to theFocus point and always comes through theFocus. Apex of the parabola is a middle point between the theFocus and the intersection point of theDirectrix and the X-axis. Warnings : It is possible to have FocalLength = 0 (when theFocus lies in theDirectrix). In this case, X-direction of the parabola is defined by theSense parameter. If theSense == TRUE (by default) then right-handed coordinate system is used, otherwise - left-handed. Result parabola will look like a line, which is perpendicular to the directrix.

Member Function Documentation

Axis()

constexpr const gp_Ax22d & gp_Parab2d::Axis ( ) const

inlineconstexprnoexcept

Returns the local coordinate system of the parabola. The "Location" point of this axis is the vertex of the parabola.

Coefficients()

void gp_Parab2d::Coefficients	(	double &	theA,
		double &	theB,
		double &	theC,
		double &	theD,
		double &	theE,
		double &	theF ) const

Computes the coefficients of the implicit equation of the parabola (in WCS - World Coordinate System).

theA * (X**2) + theB * (Y**2) + 2*theC*(X*Y) + 2*theD*X + 2*theE*Y + theF = 0.

Directrix()

gp_Ax2d gp_Parab2d::Directrix ( ) const

inlinenoexcept

Computes the directrix of the parabola. The directrix is:

• a line parallel to the "Y Direction" of the local coordinate system of this parabola, and
• located on the negative side of the axis of symmetry, at a distance from the apex which is equal to the focal length of this parabola. The directrix is returned as an axis (a gp_Ax2d object), the origin of which is situated on the "X Axis" of this parabola.

Focal()

constexpr double gp_Parab2d::Focal ( ) const

inlineconstexprnoexcept

Returns the distance between the vertex and the focus of the parabola.

Focus()

gp_Pnt2d gp_Parab2d::Focus ( ) const

inlinenoexcept

Returns the focus of the parabola.

IsDirect()

constexpr bool gp_Parab2d::IsDirect ( ) const

inlineconstexprnoexcept

Returns true if the local coordinate system is direct and false in the other case.

Location()

constexpr const gp_Pnt2d & gp_Parab2d::Location ( ) const

inlineconstexprnoexcept

Returns the vertex of the parabola.

Mirror() [1/2]

void gp_Parab2d::Mirror ( const gp_Ax2d & theA )

noexcept

Mirror() [2/2]

void gp_Parab2d::Mirror ( const gp_Pnt2d & theP )

noexcept

MirrorAxis()

gp_Ax2d gp_Parab2d::MirrorAxis ( ) const

inlinenoexcept

Returns the symmetry axis of the parabola. The "Location" point of this axis is the vertex of the parabola.

Mirrored() [1/2]

gp_Parab2d gp_Parab2d::Mirrored ( const gp_Ax2d & theA ) const

noexcept

Performs the symmetrical transformation of a parabola with respect to an axis placement which is the axis of the symmetry.

Mirrored() [2/2]

gp_Parab2d gp_Parab2d::Mirrored ( const gp_Pnt2d & theP ) const

noexcept

Performs the symmetrical transformation of a parabola with respect to the point theP which is the center of the symmetry.

Parameter()

constexpr double gp_Parab2d::Parameter ( ) const

inlineconstexprnoexcept

Returns the distance between the focus and the directrix of the parabola.

Reverse()

void gp_Parab2d::Reverse ( )

inlinenoexcept

Reversed()

gp_Parab2d gp_Parab2d::Reversed ( ) const

inlinenoexcept

Reverses the orientation of the local coordinate system of this parabola (the "Y Direction" is reversed). Therefore, the implicit orientation of this parabola is reversed. Note:

• Reverse assigns the result to this parabola, while
• Reversed creates a new one.

Rotate()

void gp_Parab2d::Rotate ( const gp_Pnt2d & theP, const double theAng )

inline

Rotated()

gp_Parab2d gp_Parab2d::Rotated ( const gp_Pnt2d & theP, const double theAng ) const

inline

Rotates a parabola. theP is the center of the rotation. theAng is the angular value of the rotation in radians.

Scale()

void gp_Parab2d::Scale ( const gp_Pnt2d & theP, const double theS )

inline

Scaled()

gp_Parab2d gp_Parab2d::Scaled ( const gp_Pnt2d & theP, const double theS ) const

inline

Scales a parabola. theS is the scaling value. If theS is negative the direction of the symmetry axis "XAxis" is reversed and the direction of the "YAxis" too.

SetAxis()

constexpr void gp_Parab2d::SetAxis ( const gp_Ax22d & theA )

inlineconstexprnoexcept

Changes the local coordinate system of the parabola. The "Location" point of A becomes the vertex of the parabola.

SetFocal()

void gp_Parab2d::SetFocal ( const double theFocal )

inline

Changes the focal distance of the parabola Warnings : It is possible to have theFocal = 0. Raises ConstructionError if theFocal < 0.0.

SetLocation()

constexpr void gp_Parab2d::SetLocation ( const gp_Pnt2d & theP )

inlineconstexprnoexcept

Changes the "Location" point of the parabola. It is the vertex of the parabola.

SetMirrorAxis()

constexpr void gp_Parab2d::SetMirrorAxis ( const gp_Ax2d & theA )

inlineconstexpr

Modifies this parabola, by redefining its local coordinate system so that its origin and "X Direction" become those of the axis MA. The "Y Direction" of the local coordinate system is then recomputed. The orientation of the local coordinate system is not modified.

Transform()

void gp_Parab2d::Transform ( const gp_Trsf2d & theT )

inline

Transformed()

gp_Parab2d gp_Parab2d::Transformed ( const gp_Trsf2d & theT ) const

inline

Transforms an parabola with the transformation theT from class Trsf2d.

Translate() [1/2]

constexpr void gp_Parab2d::Translate ( const gp_Pnt2d & theP1, const gp_Pnt2d & theP2 )

inlineconstexprnoexcept

Translate() [2/2]

constexpr void gp_Parab2d::Translate ( const gp_Vec2d & theV )

inlineconstexprnoexcept

Translated() [1/2]

constexpr gp_Parab2d gp_Parab2d::Translated ( const gp_Pnt2d & theP1, const gp_Pnt2d & theP2 ) const

inlineconstexprnoexcept

Translates a parabola from the point theP1 to the point theP2.

Translated() [2/2]

constexpr gp_Parab2d gp_Parab2d::Translated ( const gp_Vec2d & theV ) const

inlineconstexprnoexcept

Translates a parabola in the direction of the vectorthe theV. The magnitude of the translation is the vector's magnitude.

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

• gp_Parab2d.hxx