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 double Focal, const bool Sense=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 double 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 double 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>.

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

double	FirstParameter () const final
	Returns RealFirst from Standard.

double	LastParameter () const final
	Returns RealLast from Standard.

bool	IsClosed () const final
	Returns False.

bool	IsPeriodic () const final
	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.

double	Eccentricity () const final
	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.

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

double	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.

gp_Pnt2d	EvalD0 (const double U) const final
	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.

Geom2d_Curve::ResD1	EvalD1 (const double U) const final
	Returns the point P of parameter U and the first derivative V1.

Geom2d_Curve::ResD2	EvalD2 (const double U) const final
	Returns the point P of parameter U, the first and second derivatives V1 and V2.

Geom2d_Curve::ResD3	EvalD3 (const double U) const final
	Returns the point P of parameter U, the first second and third derivatives V1 V2 and V3.

gp_Vec2d	EvalDN (const double U, const int N) const final
	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) final
	Applies the transformation T to this parabola.

double	TransformedParameter (const double U, const gp_Trsf2d &T) const final
	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.

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

occ::handle< Geom2d_Geometry >	Copy () const final
	Creates a new object, which is a copy of this parabola.

void	DumpJson (Standard_OStream &theOStream, int theDepth=-1) const final
	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.

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

Public Member Functions inherited from Geom2d_Curve
occ::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 double	Period () const
	Returns the period of this curve. raises if the curve is not periodic.

void	D0 (const double U, gp_Pnt2d &P) const
	Returns in P the point of parameter U.

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

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

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

gp_Vec2d	DN (const double U, const int N) const
	Computes the Nth derivative vector.

gp_Pnt2d	Value (const double U) const
	Computes the point of parameter U on <me>. Implemented with D0.

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 double 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 double 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.

occ::handle< Geom2d_Geometry >	Mirrored (const gp_Pnt2d &P) const

occ::handle< Geom2d_Geometry >	Mirrored (const gp_Ax2d &A) const

occ::handle< Geom2d_Geometry >	Rotated (const gp_Pnt2d &P, const double Ang) const

occ::handle< Geom2d_Geometry >	Scaled (const gp_Pnt2d &P, const double S) const

occ::handle< Geom2d_Geometry >	Transformed (const gp_Trsf2d &T) const

occ::handle< Geom2d_Geometry >	Translated (const gp_Vec2d &V) const

occ::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 ()=default
	Destructor must be virtual.

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

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

bool	IsInstance (const char *const theTypeName) const
	Returns a true value if this is an instance of TypeName.

bool	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.

bool	IsKind (const char *const 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.

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

void	IncrementRefCounter () noexcept
	Increments the reference counter of this object. Uses relaxed memory ordering since incrementing only requires atomicity, not synchronization with other memory operations.

int	DecrementRefCounter () noexcept
	Decrements the reference counter of this object; returns the decremented value. Uses release ordering for the decrement to ensure all writes to the object are visible before the count reaches zero. An acquire fence is added only when the count reaches zero, ensuring proper synchronization before deletion. This is more efficient than using acq_rel for every decrement.

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 double	Focal,
		const bool	Sense = 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 double	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()

occ::handle< Geom2d_Geometry > Geom2d_Parabola::Copy ( ) const

finalvirtual

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

Implements Geom2d_Geometry.

◆ 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.

◆ DumpJson()

void Geom2d_Parabola::DumpJson	(	Standard_OStream &	theOStream,
		int	theDepth = -1 ) const

finalvirtual

Dumps the content of me into the stream.

Reimplemented from Geom2d_Conic.

◆ Eccentricity()

double Geom2d_Parabola::Eccentricity ( ) const

finalvirtual

Returns the eccentricity e = 1.0.

Implements Geom2d_Conic.

◆ EvalD0()

gp_Pnt2d Geom2d_Parabola::EvalD0 ( const double U ) const

finalvirtual

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.

◆ EvalD1()

Geom2d_Curve::ResD1 Geom2d_Parabola::EvalD1 ( const double U ) const

finalvirtual

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

Implements Geom2d_Curve.

◆ EvalD2()

Geom2d_Curve::ResD2 Geom2d_Parabola::EvalD2 ( const double U ) const

finalvirtual

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

Implements Geom2d_Curve.

◆ EvalD3()

Geom2d_Curve::ResD3 Geom2d_Parabola::EvalD3 ( const double U ) const

finalvirtual

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

Implements Geom2d_Curve.

◆ EvalDN()

gp_Vec2d Geom2d_Parabola::EvalDN	(	const double	U,
		const int	N ) const

finalvirtual

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.

◆ FirstParameter()

double Geom2d_Parabola::FirstParameter ( ) const

finalvirtual

Returns RealFirst from Standard.

Implements Geom2d_Curve.

◆ Focal()

double 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()

bool Geom2d_Parabola::IsClosed ( ) const

finalvirtual

Returns False.

Implements Geom2d_Curve.

◆ IsPeriodic()

bool Geom2d_Parabola::IsPeriodic ( ) const

finalvirtual

Returns False.

Implements Geom2d_Curve.

◆ LastParameter()

double Geom2d_Parabola::LastParameter ( ) const

finalvirtual

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()

double 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()

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

finalvirtual

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()

double Geom2d_Parabola::ReversedParameter ( const double U ) const

finalvirtual

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 double 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 )

finalvirtual

Applies the transformation T to this parabola.

Implements Geom2d_Geometry.

◆ TransformedParameter()

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

finalvirtual

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()

◆ Directrix()

◆ DumpJson()

◆ Eccentricity()

◆ EvalD0()

◆ EvalD1()

◆ EvalD2()

◆ EvalD3()

◆ EvalDN()

◆ FirstParameter()

◆ Focal()

◆ Focus()

◆ IsClosed()

◆ IsPeriodic()

◆ LastParameter()

◆ Parab2d()

◆ Parameter()

◆ ParametricTransformation()

◆ ReversedParameter()

◆ SetFocal()

◆ SetParab2d()

◆ Transform()

◆ TransformedParameter()