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

#include <Geom2d_Parabola.hxx>

Inheritance diagram for Geom2d_Parabola:

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Public Member Functions
	Geom2d_Parabola (const gp_Parab2d &Prb)
	Creates a parabola from a non persistent one.

	Geom2d_Parabola (const gp_Ax2d &MirrorAxis, const Standard_Real Focal, const Standard_Boolean Sense=Standard_True)
	Creates a parabola with its "MirrorAxis" and it's focal length "Focal". MirrorAxis is the axis of symmetry of the curve, it is the "XAxis". The "YAxis" is parallel to the directrix of the parabola and is in the direct sense if Sense is True. The "Location" point of "MirrorAxis" is the vertex of the parabola Raised if Focal < 0.0.

	Geom2d_Parabola (const gp_Ax22d &Axis, const Standard_Real Focal)
	Creates a parabola with its Axis and it's focal length "Focal". The XDirection of Axis is the axis of symmetry of the curve, it is the "XAxis". The "YAxis" is parallel to the directrix of the parabola. The "Location" point of "Axis" is the vertex of the parabola. Raised if Focal < 0.0.

	Geom2d_Parabola (const gp_Ax2d &D, const gp_Pnt2d &F)
	D is the directrix of the parabola and F the focus point. The symmetry axis "XAxis" of the parabola is normal to the directrix and pass through the focus point F, but its "Location" point is the vertex of the parabola. The "YAxis" of the parabola is parallel to D and its "Location" point is the vertex of the parabola.

void	SetFocal (const Standard_Real Focal)
	Assigns the value Focal to the focal length of this parabola. Exceptions Standard_ConstructionError if Focal is negative.

void	SetParab2d (const gp_Parab2d &Prb)
	Converts the gp_Parab2d parabola Prb into this parabola.

gp_Parab2d	Parab2d () const
	Returns the non persistent parabola from gp with the same geometric properties as <me>.

Standard_Real	ReversedParameter (const Standard_Real U) const override
	Computes the parameter on the reversed parabola for the point of parameter U on this parabola. For a parabola, the returned value is -U.

Standard_Real	FirstParameter () const override
	Returns RealFirst from Standard.

Standard_Real	LastParameter () const override
	Returns RealLast from Standard.

Standard_Boolean	IsClosed () const override
	Returns False.

Standard_Boolean	IsPeriodic () const override
	Returns False.

gp_Ax2d	Directrix () const
	The directrix is parallel to the "YAxis" of the parabola. The "Location" point of the directrix is the intersection point between the directrix and the symmetry axis ("XAxis") of the parabola.

Standard_Real	Eccentricity () const override
	Returns the eccentricity e = 1.0.

gp_Pnt2d	Focus () const
	Computes the focus of this parabola The focus is on the positive side of the "X Axis" of the local coordinate system of the parabola.

Standard_Real	Focal () const
	Computes the focal length of this parabola. The focal length is the distance between the apex and the focus of the parabola.

Standard_Real	Parameter () const
	Computes the parameter of this parabola, which is the distance between its focus and its directrix. This distance is twice the focal length. If P is the parameter of the parabola, the equation of the parabola in its local coordinate system is: Y*2 = 2.P*X.

void	D0 (const Standard_Real U, gp_Pnt2d &P) const override
	Returns in P the point of parameter U. If U = 0 the returned point is the origin of the XAxis and the YAxis of the parabola and it is the vertex of the parabola. P = S + F * (U * U * XDir + * U * YDir) where S is the vertex of the parabola, XDir the XDirection and YDir the YDirection of the parabola's local coordinate system.

void	D1 (const Standard_Real U, gp_Pnt2d &P, gp_Vec2d &V1) const override
	Returns the point P of parameter U and the first derivative V1.

void	D2 (const Standard_Real U, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2) const override
	Returns the point P of parameter U, the first and second derivatives V1 and V2.

void	D3 (const Standard_Real U, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2, gp_Vec2d &V3) const override
	Returns the point P of parameter U, the first second and third derivatives V1 V2 and V3.

gp_Vec2d	DN (const Standard_Real U, const Standard_Integer N) const override
	For the point of parameter U of this parabola, computes the vector corresponding to the Nth derivative. Exceptions Standard_RangeError if N is less than 1.

void	Transform (const gp_Trsf2d &T) override
	Applies the transformation T to this parabola.

Standard_Real	TransformedParameter (const Standard_Real U, const gp_Trsf2d &T) const override
	Computes the parameter on the transformed parabola, for the point of parameter U on this parabola. For a parabola, the returned value is equal to U multiplied by the scale factor of transformation T.

Standard_Real	ParametricTransformation (const gp_Trsf2d &T) const override
	Returns a coefficient to compute the parameter on the transformed curve for the transform of the point on <me>.

Handle< Geom2d_Geometry >	Copy () const override
	Creates a new object, which is a copy of this parabola.

virtual void	DumpJson (Standard_OStream &theOStream, Standard_Integer theDepth=-1) const override
	Dumps the content of me into the stream.

Public Member Functions inherited from Geom2d_Conic
void	SetAxis (const gp_Ax22d &theA)
	Modifies this conic, redefining its local coordinate system partially, by assigning theA as its axis.

void	SetXAxis (const gp_Ax2d &theAX)
	Assigns the origin and unit vector of axis theA to the origin of the local coordinate system of this conic and X Direction. The other unit vector of the local coordinate system of this conic is recomputed normal to theA, without changing the orientation of the local coordinate system (right-handed or left-handed).

void	SetYAxis (const gp_Ax2d &theAY)
	Assigns the origin and unit vector of axis theA to the origin of the local coordinate system of this conic and Y Direction. The other unit vector of the local coordinate system of this conic is recomputed normal to theA, without changing the orientation of the local coordinate system (right-handed or left-handed).

void	SetLocation (const gp_Pnt2d &theP)
	Modifies this conic, redefining its local coordinate system partially, by assigning theP as its origin.

gp_Ax2d	XAxis () const
	Returns the "XAxis" of the conic. This axis defines the origin of parametrization of the conic. This axis and the "Yaxis" define the local coordinate system of the conic. -C++: return const&.

gp_Ax2d	YAxis () const
	Returns the "YAxis" of the conic. The "YAxis" is perpendicular to the "Xaxis".

const gp_Pnt2d &	Location () const
	Returns the location point of the conic. For the circle, the ellipse and the hyperbola it is the center of the conic. For the parabola it is the vertex of the parabola.

const gp_Ax22d &	Position () const
	Returns the local coordinates system of the conic.

void	Reverse () override
	Reverses the direction of parameterization of <me>. The local coordinate system of the conic is modified.

GeomAbs_Shape	Continuity () const override
	Returns GeomAbs_CN which is the global continuity of any conic.

Standard_Boolean	IsCN (const Standard_Integer N) const override
	Returns True, the order of continuity of a conic is infinite.

Public Member Functions inherited from Geom2d_Curve
Handle< Geom2d_Curve >	Reversed () const
	Creates a reversed duplicate Changes the orientation of this curve. The first and last parameters are not changed, but the parametric direction of the curve is reversed. If the curve is bounded:

virtual Standard_Real	Period () const
	Returns the period of this curve. raises if the curve is not periodic.

gp_Pnt2d	Value (const Standard_Real U) const
	Computes the point of parameter U on <me>. If the curve is periodic then the returned point is P(U) with U = Ustart + (U - Uend) where Ustart and Uend are the parametric bounds of the curve.

Public Member Functions inherited from Geom2d_Geometry
void	Mirror (const gp_Pnt2d &P)
	Performs the symmetrical transformation of a Geometry with respect to the point P which is the center of the symmetry and assigns the result to this geometric object.

void	Mirror (const gp_Ax2d &A)
	Performs the symmetrical transformation of a Geometry with respect to an axis placement which is the axis of the symmetry.

void	Rotate (const gp_Pnt2d &P, const Standard_Real Ang)
	Rotates a Geometry. P is the center of the rotation. Ang is the angular value of the rotation in radians.

void	Scale (const gp_Pnt2d &P, const Standard_Real S)
	Scales a Geometry. S is the scaling value.

void	Translate (const gp_Vec2d &V)
	Translates a Geometry. V is the vector of the translation.

void	Translate (const gp_Pnt2d &P1, const gp_Pnt2d &P2)
	Translates a Geometry from the point P1 to the point P2.

Handle< Geom2d_Geometry >	Mirrored (const gp_Pnt2d &P) const

Handle< Geom2d_Geometry >	Mirrored (const gp_Ax2d &A) const

Handle< Geom2d_Geometry >	Rotated (const gp_Pnt2d &P, const Standard_Real Ang) const

Handle< Geom2d_Geometry >	Scaled (const gp_Pnt2d &P, const Standard_Real S) const

Handle< Geom2d_Geometry >	Transformed (const gp_Trsf2d &T) const

Handle< Geom2d_Geometry >	Translated (const gp_Vec2d &V) const

Handle< Geom2d_Geometry >	Translated (const gp_Pnt2d &P1, const gp_Pnt2d &P2) const

Public Member Functions inherited from Standard_Transient
	Standard_Transient ()
	Empty constructor.

	Standard_Transient (const Standard_Transient &)
	Copy constructor – does nothing.

Standard_Transient &	operator= (const Standard_Transient &)
	Assignment operator, needed to avoid copying reference counter.

virtual	~Standard_Transient ()
	Destructor must be virtual.

virtual const opencascade::handle< Standard_Type > &	DynamicType () const
	Returns a type descriptor about this object.

Standard_Boolean	IsInstance (const opencascade::handle< Standard_Type > &theType) const
	Returns a true value if this is an instance of Type.

Standard_Boolean	IsInstance (const Standard_CString theTypeName) const
	Returns a true value if this is an instance of TypeName.

Standard_Boolean	IsKind (const opencascade::handle< Standard_Type > &theType) const
	Returns true if this is an instance of Type or an instance of any class that inherits from Type. Note that multiple inheritance is not supported by OCCT RTTI mechanism.

Standard_Boolean	IsKind (const Standard_CString theTypeName) const
	Returns true if this is an instance of TypeName or an instance of any class that inherits from TypeName. Note that multiple inheritance is not supported by OCCT RTTI mechanism.

Standard_Transient *	This () const
	Returns non-const pointer to this object (like const_cast). For protection against creating handle to objects allocated in stack or call from constructor, it will raise exception Standard_ProgramError if reference counter is zero.

Standard_Integer	GetRefCount () const noexcept
	Get the reference counter of this object.

void	IncrementRefCounter () noexcept
	Increments the reference counter of this object.

Standard_Integer	DecrementRefCounter () noexcept
	Decrements the reference counter of this object; returns the decremented value.

virtual void	Delete () const
	Memory deallocator for transient classes.

Additional Inherited Members
Public Types inherited from Standard_Transient
typedef void	base_type
	Returns a type descriptor about this object.

Static Public Member Functions inherited from Standard_Transient
static constexpr const char *	get_type_name ()
	Returns a type descriptor about this object.

static const opencascade::handle< Standard_Type > &	get_type_descriptor ()
	Returns type descriptor of Standard_Transient class.

Protected Attributes inherited from Geom2d_Conic
gp_Ax22d	pos

Detailed Description

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

the origin is the apex of the parabola, and
the "X Axis" defines 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. The orientation (direct or indirect) of the local coordinate system gives an explicit orientation to the parabola, determining the direction in which the parameter increases along the parabola. The Geom_Parabola parabola is parameterized as follows: P(U) = O + U*U/(4.*F)*XDir + U*YDir, where:
P is the point of parameter U,
O, XDir and YDir are respectively the origin, "X Direction" and "Y Direction" of its local coordinate system,
F is the focal length of the parabola. The parameter of the parabola is therefore its Y coordinate in the local coordinate system, with the "X Axis" of the local coordinate system defining the origin of the parameter. The parameter range is ] -infinite,+infinite [.

Constructor & Destructor Documentation

◆ Geom2d_Parabola() [1/4]

Geom2d_Parabola::Geom2d_Parabola ( const gp_Parab2d & Prb )

Creates a parabola from a non persistent one.

◆ Geom2d_Parabola() [2/4]

Geom2d_Parabola::Geom2d_Parabola	(	const gp_Ax2d &	MirrorAxis,
		const Standard_Real	Focal,
		const Standard_Boolean	Sense = `Standard_True`
	)

Creates a parabola with its "MirrorAxis" and it's focal length "Focal". MirrorAxis is the axis of symmetry of the curve, it is the "XAxis". The "YAxis" is parallel to the directrix of the parabola and is in the direct sense if Sense is True. The "Location" point of "MirrorAxis" is the vertex of the parabola Raised if Focal < 0.0.

◆ Geom2d_Parabola() [3/4]

Geom2d_Parabola::Geom2d_Parabola	(	const gp_Ax22d &	Axis,
		const Standard_Real	Focal
	)

Creates a parabola with its Axis and it's focal length "Focal". The XDirection of Axis is the axis of symmetry of the curve, it is the "XAxis". The "YAxis" is parallel to the directrix of the parabola. The "Location" point of "Axis" is the vertex of the parabola. Raised if Focal < 0.0.

◆ Geom2d_Parabola() [4/4]

Geom2d_Parabola::Geom2d_Parabola	(	const gp_Ax2d &	D,
		const gp_Pnt2d &	F
	)

D is the directrix of the parabola and F the focus point. The symmetry axis "XAxis" of the parabola is normal to the directrix and pass through the focus point F, but its "Location" point is the vertex of the parabola. The "YAxis" of the parabola is parallel to D and its "Location" point is the vertex of the parabola.

Member Function Documentation

◆ Copy()

Handle< Geom2d_Geometry > Geom2d_Parabola::Copy ( ) const

overridevirtual

Creates a new object, which is a copy of this parabola.

Implements Geom2d_Geometry.

◆ D0()

void Geom2d_Parabola::D0	(	const Standard_Real	U,
		gp_Pnt2d &	P
	)		const

overridevirtual

Returns in P the point of parameter U. If U = 0 the returned point is the origin of the XAxis and the YAxis of the parabola and it is the vertex of the parabola. P = S + F * (U * U * XDir + * U * YDir) where S is the vertex of the parabola, XDir the XDirection and YDir the YDirection of the parabola's local coordinate system.

Implements Geom2d_Curve.

◆ D1()

void Geom2d_Parabola::D1	(	const Standard_Real	U,
		gp_Pnt2d &	P,
		gp_Vec2d &	V1
	)		const

overridevirtual

Returns the point P of parameter U and the first derivative V1.

Implements Geom2d_Curve.

◆ D2()

void Geom2d_Parabola::D2	(	const Standard_Real	U,
		gp_Pnt2d &	P,
		gp_Vec2d &	V1,
		gp_Vec2d &	V2
	)		const

overridevirtual

Returns the point P of parameter U, the first and second derivatives V1 and V2.

Implements Geom2d_Curve.

◆ D3()

void Geom2d_Parabola::D3	(	const Standard_Real	U,
		gp_Pnt2d &	P,
		gp_Vec2d &	V1,
		gp_Vec2d &	V2,
		gp_Vec2d &	V3
	)		const

overridevirtual

Returns the point P of parameter U, the first second and third derivatives V1 V2 and V3.

Implements Geom2d_Curve.

◆ Directrix()

gp_Ax2d Geom2d_Parabola::Directrix ( ) const

The directrix is parallel to the "YAxis" of the parabola. The "Location" point of the directrix is the intersection point between the directrix and the symmetry axis ("XAxis") of the parabola.

◆ DN()

gp_Vec2d Geom2d_Parabola::DN	(	const Standard_Real	U,
		const Standard_Integer	N
	)		const

overridevirtual

For the point of parameter U of this parabola, computes the vector corresponding to the Nth derivative. Exceptions Standard_RangeError if N is less than 1.

Implements Geom2d_Curve.

◆ DumpJson()

virtual void Geom2d_Parabola::DumpJson	(	Standard_OStream &	theOStream,
		Standard_Integer	theDepth = `-1`
	)		const

overridevirtual

Dumps the content of me into the stream.

Reimplemented from Geom2d_Conic.

◆ Eccentricity()

Standard_Real Geom2d_Parabola::Eccentricity ( ) const

overridevirtual

Returns the eccentricity e = 1.0.

Implements Geom2d_Conic.

◆ FirstParameter()

Standard_Real Geom2d_Parabola::FirstParameter ( ) const

overridevirtual

Returns RealFirst from Standard.

Implements Geom2d_Curve.

◆ Focal()

Standard_Real Geom2d_Parabola::Focal ( ) const

Computes the focal length of this parabola. The focal length is the distance between the apex and the focus of the parabola.

◆ Focus()

gp_Pnt2d Geom2d_Parabola::Focus ( ) const

Computes the focus of this parabola The focus is on the positive side of the "X Axis" of the local coordinate system of the parabola.

◆ IsClosed()

Standard_Boolean Geom2d_Parabola::IsClosed ( ) const

overridevirtual

Returns False.

Implements Geom2d_Curve.

◆ IsPeriodic()

Standard_Boolean Geom2d_Parabola::IsPeriodic ( ) const

overridevirtual

Returns False.

Implements Geom2d_Curve.

◆ LastParameter()

Standard_Real Geom2d_Parabola::LastParameter ( ) const

overridevirtual

Returns RealLast from Standard.

Implements Geom2d_Curve.

◆ Parab2d()

gp_Parab2d Geom2d_Parabola::Parab2d ( ) const

Returns the non persistent parabola from gp with the same geometric properties as <me>.

◆ Parameter()

Standard_Real Geom2d_Parabola::Parameter ( ) const

Computes the parameter of this parabola, which is the distance between its focus and its directrix. This distance is twice the focal length. If P is the parameter of the parabola, the equation of the parabola in its local coordinate system is: Y**2 = 2.*P*X.

◆ ParametricTransformation()

Standard_Real Geom2d_Parabola::ParametricTransformation ( const gp_Trsf2d & T ) const

overridevirtual

Returns a coefficient to compute the parameter on the transformed curve for the transform of the point on <me>.

Transformed(T)->Value(U * ParametricTransformation(T))

is the same point as

Value(U).Transformed(T)

This methods returns T.ScaleFactor()

Reimplemented from Geom2d_Curve.

◆ ReversedParameter()

Standard_Real Geom2d_Parabola::ReversedParameter ( const Standard_Real U ) const

overridevirtual

Computes the parameter on the reversed parabola for the point of parameter U on this parabola. For a parabola, the returned value is -U.

Implements Geom2d_Conic.

◆ SetFocal()

void Geom2d_Parabola::SetFocal ( const Standard_Real Focal )

Assigns the value Focal to the focal length of this parabola. Exceptions Standard_ConstructionError if Focal is negative.

◆ SetParab2d()

void Geom2d_Parabola::SetParab2d ( const gp_Parab2d & Prb )

Converts the gp_Parab2d parabola Prb into this parabola.

◆ Transform()

void Geom2d_Parabola::Transform ( const gp_Trsf2d & T )

overridevirtual

Applies the transformation T to this parabola.

Implements Geom2d_Geometry.

◆ TransformedParameter()

Standard_Real Geom2d_Parabola::TransformedParameter	(	const Standard_Real	U,
		const gp_Trsf2d &	T
	)		const

overridevirtual

Computes the parameter on the transformed parabola, for the point of parameter U on this parabola. For a parabola, the returned value is equal to U multiplied by the scale factor of transformation T.

Reimplemented from Geom2d_Curve.

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

Geom2d_Parabola.hxx

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ Geom2d_Parabola() [1/4]

◆ Geom2d_Parabola() [2/4]

◆ Geom2d_Parabola() [3/4]

◆ Geom2d_Parabola() [4/4]

Member Function Documentation

◆ Copy()

◆ D0()

◆ D1()

◆ D2()

◆ D3()

◆ Directrix()

◆ DN()

◆ DumpJson()

◆ Eccentricity()

◆ FirstParameter()

◆ Focal()

◆ Focus()

◆ IsClosed()

◆ IsPeriodic()

◆ LastParameter()

◆ Parab2d()

◆ Parameter()

◆ ParametricTransformation()

◆ ReversedParameter()

◆ SetFocal()

◆ SetParab2d()

◆ Transform()

◆ TransformedParameter()