Describes a parabola in 3D space. A parabola is defined by its focal length (i.e. the distance between its focus and its apex) and is positioned in space with a coordinate system (gp_Ax2 object) where: More...

#include <Geom_Parabola.hxx>

Inheritance diagram for Geom_Parabola:

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Public Member Functions
	Geom_Parabola (const gp_Parab &Prb)
	Creates a parabola from a non transient one.

	Geom_Parabola (const gp_Ax2 &A2, const double Focal)
	Creates a parabola with its local coordinate system "A2" and it's focal length "Focal". The XDirection of A2 defines the axis of symmetry of the parabola. The YDirection of A2 is parallel to the directrix of the parabola. The Location point of A2 is the vertex of the parabola Raised if Focal < 0.0.

	Geom_Parabola (const gp_Ax1 &D, const gp_Pnt &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. The normal to the plane of the parabola is the cross product between the XAxis and the YAxis.

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

void	SetParab (const gp_Parab &Prb)
	Converts the gp_Parab parabola Prb into this parabola.

gp_Parab	Parab () const
	Returns the non transient 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 the value of the first or last parameter of this parabola. This is, respectively:

double	LastParameter () const final
	Returns the value of the first or last parameter of this parabola. This is, respectively:

bool	IsClosed () const final
	Returns False.

bool	IsPeriodic () const final
	Returns False.

gp_Ax1	Directrix () const
	Computes the directrix of this parabola. This is a line normal to the axis of symmetry, in the plane of this parabola, located on the negative side of its axis of symmetry, at a distance from the apex equal to the focal length. The directrix is returned as an axis (gp_Ax1 object), where the origin is located on the "X Axis" of this parabola.

double	Eccentricity () const final
	Returns 1. (which is the eccentricity of any parabola).

gp_Pnt	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 distance of this parabola The focal distance 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_Pnt	EvalD0 (const double U) const final
	Returns 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.

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

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

Geom_Curve::ResD3	EvalD3 (const double U) const final
	Returns the point of parameter U, the first, second and third derivatives.

gp_Vec	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_Trsf &T) final
	Applies the transformation T to this parabola.

double	TransformedParameter (const double U, const gp_Trsf &T) const final
	Returns the parameter on the transformed curve for the transform of the point of parameter U on <me>.

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

occ::handle< Geom_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 Geom_Conic
void	SetAxis (const gp_Ax1 &theA1)
	Changes the orientation of the conic's plane. The normal axis to the plane is A1. The XAxis and the YAxis are recomputed.

void	SetLocation (const gp_Pnt &theP)
	changes the location point of the conic.

void	SetPosition (const gp_Ax2 &theA2)
	changes the local coordinate system of the conic.

const gp_Ax1 &	Axis () const
	Returns the "main Axis" of this conic. This axis is normal to the plane of the conic.

const gp_Pnt &	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 Apex of the parabola.

const gp_Ax2 &	Position () const
	Returns the local coordinates system of the conic. The main direction of the Axis2Placement is normal to the plane of the conic. The X direction of the Axis2placement is in the plane of the conic and corresponds to the origin for the conic's parametric value u.

gp_Ax1	XAxis () const
	Returns the XAxis of the conic. This axis defines the origin of parametrization of the conic. This axis is perpendicular to the Axis of the conic. This axis and the Yaxis define the plane of the conic.

gp_Ax1	YAxis () const
	Returns the YAxis of the conic. The YAxis is perpendicular to the Xaxis. This axis and the Xaxis define the plane 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
	The continuity of the conic is Cn.

bool	IsCN (const int N) const override
	Returns True. Raised if N < 0.

Public Member Functions inherited from Geom_Curve
occ::handle< Geom_Curve >	Reversed () const
	Returns a copy of <me> reversed.

virtual double	Period () const
	Returns the period of this curve. Exceptions Standard_NoSuchObject if this curve is not periodic.

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

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

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

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

gp_Vec	DN (const double U, const int N) const
	The returned vector gives the value of the derivative for the order of derivation N.

gp_Pnt	Value (const double U) const
	Computes the point of parameter U on <me>.

Public Member Functions inherited from Geom_Geometry
void	Mirror (const gp_Pnt &P)
	Performs the symmetrical transformation of a Geometry with respect to the point P which is the center of the symmetry.

void	Mirror (const gp_Ax1 &A1)
	Performs the symmetrical transformation of a Geometry with respect to an axis placement which is the axis of the symmetry.

void	Mirror (const gp_Ax2 &A2)
	Performs the symmetrical transformation of a Geometry with respect to a plane. The axis placement A2 locates the plane of the symmetry : (Location, XDirection, YDirection).

void	Rotate (const gp_Ax1 &A1, const double Ang)
	Rotates a Geometry. A1 is the axis of the rotation. Ang is the angular value of the rotation in radians.

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

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

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

occ::handle< Geom_Geometry >	Mirrored (const gp_Pnt &P) const

occ::handle< Geom_Geometry >	Mirrored (const gp_Ax1 &A1) const

occ::handle< Geom_Geometry >	Mirrored (const gp_Ax2 &A2) const

occ::handle< Geom_Geometry >	Rotated (const gp_Ax1 &A1, const double Ang) const

occ::handle< Geom_Geometry >	Scaled (const gp_Pnt &P, const double S) const

occ::handle< Geom_Geometry >	Transformed (const gp_Trsf &T) const

occ::handle< Geom_Geometry >	Translated (const gp_Vec &V) const

occ::handle< Geom_Geometry >	Translated (const gp_Pnt &P1, const gp_Pnt &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 Geom_Conic
gp_Ax2	pos

Detailed Description

Describes a parabola in 3D space. A parabola is defined by its focal length (i.e. the distance between its focus and its apex) and is positioned in space with a coordinate system (gp_Ax2 object) where:

the origin is the apex of the parabola,
the "X Axis" defines the axis of symmetry; the parabola is on the positive side of this axis,
the origin, "X Direction" and "Y Direction" define the plane of the parabola. This coordinate system is the local coordinate system of the parabola. The "main Direction" of this coordinate system is a vector normal to the plane of the parabola. The axis, of which the origin and unit vector are respectively the origin and "main Direction" of the local coordinate system, is termed the "Axis" or "main Axis" of the parabola. The "main Direction" 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

◆ Geom_Parabola() [1/3]

Geom_Parabola::Geom_Parabola ( const gp_Parab & Prb )

Creates a parabola from a non transient one.

◆ Geom_Parabola() [2/3]

Geom_Parabola::Geom_Parabola	(	const gp_Ax2 &	A2,
		const double	Focal )

Creates a parabola with its local coordinate system "A2" and it's focal length "Focal". The XDirection of A2 defines the axis of symmetry of the parabola. The YDirection of A2 is parallel to the directrix of the parabola. The Location point of A2 is the vertex of the parabola Raised if Focal < 0.0.

◆ Geom_Parabola() [3/3]

Geom_Parabola::Geom_Parabola	(	const gp_Ax1 &	D,
		const gp_Pnt &	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. The normal to the plane of the parabola is the cross product between the XAxis and the YAxis.

Member Function Documentation

◆ Copy()

occ::handle< Geom_Geometry > Geom_Parabola::Copy ( ) const

finalvirtual

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

Implements Geom_Geometry.

◆ Directrix()

gp_Ax1 Geom_Parabola::Directrix ( ) const

Computes the directrix of this parabola. This is a line normal to the axis of symmetry, in the plane of this parabola, located on the negative side of its axis of symmetry, at a distance from the apex equal to the focal length. The directrix is returned as an axis (gp_Ax1 object), where the origin is located on the "X Axis" of this parabola.

◆ DumpJson()

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

finalvirtual

Dumps the content of me into the stream.

Reimplemented from Geom_Conic.

◆ Eccentricity()

double Geom_Parabola::Eccentricity ( ) const

finalvirtual

Returns 1. (which is the eccentricity of any parabola).

Implements Geom_Conic.

◆ EvalD0()

gp_Pnt Geom_Parabola::EvalD0 ( const double U ) const

finalvirtual

Returns 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 Geom_Curve.

◆ EvalD1()

Geom_Curve::ResD1 Geom_Parabola::EvalD1 ( const double U ) const

finalvirtual

Returns the point of parameter U and the first derivative.

Implements Geom_Curve.

◆ EvalD2()

Geom_Curve::ResD2 Geom_Parabola::EvalD2 ( const double U ) const

finalvirtual

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

Implements Geom_Curve.

◆ EvalD3()

Geom_Curve::ResD3 Geom_Parabola::EvalD3 ( const double U ) const

finalvirtual

Returns the point of parameter U, the first, second and third derivatives.

Implements Geom_Curve.

◆ EvalDN()

gp_Vec Geom_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 Geom_Curve.

◆ FirstParameter()

double Geom_Parabola::FirstParameter ( ) const

finalvirtual

Returns the value of the first or last parameter of this parabola. This is, respectively:

double::RealFirst(), or
double::RealLast().

Implements Geom_Curve.

◆ Focal()

double Geom_Parabola::Focal ( ) const

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

◆ Focus()

gp_Pnt Geom_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 Geom_Parabola::IsClosed ( ) const

finalvirtual

Returns False.

Implements Geom_Curve.

◆ IsPeriodic()

bool Geom_Parabola::IsPeriodic ( ) const

finalvirtual

Returns False.

Implements Geom_Curve.

◆ LastParameter()

double Geom_Parabola::LastParameter ( ) const

finalvirtual

Returns the value of the first or last parameter of this parabola. This is, respectively:

double::RealFirst(), or
double::RealLast().

Implements Geom_Curve.

◆ Parab()

gp_Parab Geom_Parabola::Parab ( ) const

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

◆ Parameter()

double Geom_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 Geom_Parabola::ParametricTransformation ( const gp_Trsf & 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 Geom_Curve.

◆ ReversedParameter()

double Geom_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 Geom_Conic.

◆ SetFocal()

void Geom_Parabola::SetFocal ( const double Focal )

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

◆ SetParab()

void Geom_Parabola::SetParab ( const gp_Parab & Prb )

Converts the gp_Parab parabola Prb into this parabola.

◆ Transform()

void Geom_Parabola::Transform ( const gp_Trsf & T )

finalvirtual

Applies the transformation T to this parabola.

Implements Geom_Geometry.

◆ TransformedParameter()

double Geom_Parabola::TransformedParameter	(	const double	U,
		const gp_Trsf &	T ) const

finalvirtual

Returns the parameter on the transformed curve for the transform of the point of parameter U on <me>.

me->Transformed(T)->Value(me->TransformedParameter(U,T))

is the same point as

me->Value(U).Transformed(T)

This methods returns * T.ScaleFactor()

Reimplemented from Geom_Curve.

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

Geom_Parabola.hxx

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ Geom_Parabola() [1/3]

◆ Geom_Parabola() [2/3]

◆ Geom_Parabola() [3/3]

Member Function Documentation

◆ Copy()

◆ Directrix()

◆ DumpJson()

◆ Eccentricity()

◆ EvalD0()

◆ EvalD1()

◆ EvalD2()

◆ EvalD3()

◆ EvalDN()

◆ FirstParameter()

◆ Focal()

◆ Focus()

◆ IsClosed()

◆ IsPeriodic()

◆ LastParameter()

◆ Parab()

◆ Parameter()

◆ ParametricTransformation()

◆ ReversedParameter()

◆ SetFocal()

◆ SetParab()

◆ Transform()

◆ TransformedParameter()