The abstract class Conic describes the common behavior of conic curves in 2D space and, in particular, their general characteristics. The Geom2d package provides four specific classes of conics: Geom2d_Circle, Geom2d_Ellipse, Geom2d_Hyperbola and Geom2d_Parabola. A conic is positioned in the plane with a coordinate system (gp_Ax22d object), where the origin is the center of the conic (or the apex in case of a parabola). This coordinate system is the local coordinate system of the conic. It gives the conic an explicit orientation, determining the direction in which the parameter increases along the conic. The "X Axis" of the local coordinate system also defines the origin of the parameter of the conic. More...

#include <Geom2d_Conic.hxx>

Inheritance diagram for Geom2d_Conic:

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Public Member Functions
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".

virtual double	Eccentricity () const =0
	returns the eccentricity value of the conic e. e = 0 for a circle 0 < e < 1 for an ellipse (e = 0 if MajorRadius = MinorRadius) e > 1 for a hyperbola e = 1 for a parabola

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.

double	ReversedParameter (const double U) const override=0
	Returns the parameter on the reversed curve for the point of parameter U on <me>.

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.

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

Public Member Functions inherited from Geom2d_Curve
virtual double	TransformedParameter (const double U, const gp_Trsf2d &T) const
	Computes the parameter on the curve transformed by T for the point of parameter U on this curve. Note: this function generally returns U but it can be redefined (for example, on a line).

virtual double	ParametricTransformation (const gp_Trsf2d &T) const
	Returns the coefficient required to compute the parametric transformation of this curve when transformation T is applied. This coefficient is the ratio between the parameter of a point on this curve and the parameter of the transformed point on the new curve transformed by T. Note: this function generally returns 1. but it can be redefined (for example, on a line).

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	FirstParameter () const =0
	Returns the value of the first parameter. Warnings : It can be RealFirst or RealLast from package Standard if the curve is infinite.

virtual double	LastParameter () const =0
	Value of the last parameter. Warnings : It can be RealFirst or RealLast from package Standard if the curve is infinite.

virtual bool	IsClosed () const =0
	Returns true if the curve is closed. Examples : Some curves such as circle are always closed, others such as line are never closed (by definition). Some Curves such as OffsetCurve can be closed or not. These curves are considered as closed if the distance between the first point and the last point of the curve is lower or equal to the Resolution from package gp which is a fixed criterion independent of the application.

virtual bool	IsPeriodic () const =0
	Returns true if the parameter of the curve is periodic. It is possible only if the curve is closed and if the following relation is satisfied : for each parametric value U the distance between the point P(u) and the point P (u + T) is lower or equal to Resolution from package gp, T is the period and must be a constant. There are three possibilities : . the curve is never periodic by definition (SegmentLine) . the curve is always periodic by definition (Circle) . the curve can be defined as periodic (BSpline). In this case a function SetPeriodic allows you to give the shape of the curve. The general rule for this case is : if a curve can be periodic or not the default periodicity set is non periodic and you have to turn (explicitly) the curve into a periodic curve if you want the curve to be periodic.

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

virtual gp_Pnt2d	EvalD0 (const double U) const =0
	Computes the point of parameter U. Raises an exception on failure.

virtual ResD1	EvalD1 (const double U) const =0
	Computes the point and first derivative at parameter U. Raises an exception if the curve continuity is not C1.

virtual ResD2	EvalD2 (const double U) const =0
	Computes the point and first two derivatives at parameter U. Raises an exception if the curve continuity is not C2.

virtual ResD3	EvalD3 (const double U) const =0
	Computes the point and first three derivatives at parameter U. Raises an exception if the curve continuity is not C3.

virtual gp_Vec2d	EvalDN (const double U, const int N) const =0
	Computes the Nth derivative at parameter U. Raises an exception if the curve continuity is not CN, or N < 1.

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.

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

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.

virtual void	Transform (const gp_Trsf2d &T)=0
	Transformation of a geometric object. This transformation can be a translation, a rotation, a symmetry, a scaling or a complex transformation obtained by combination of the previous elementaries transformations. (see class Transformation of the package Geom2d). The following transformations have the same properties as the previous ones but they don't modified the object itself. A copy of the object is returned.

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

virtual occ::handle< Geom2d_Geometry >	Copy () const =0

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.

Protected Attributes
gp_Ax22d	pos

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.

Detailed Description

The abstract class Conic describes the common behavior of conic curves in 2D space and, in particular, their general characteristics. The Geom2d package provides four specific classes of conics: Geom2d_Circle, Geom2d_Ellipse, Geom2d_Hyperbola and Geom2d_Parabola. A conic is positioned in the plane with a coordinate system (gp_Ax22d object), where the origin is the center of the conic (or the apex in case of a parabola). This coordinate system is the local coordinate system of the conic. It gives the conic an explicit orientation, determining the direction in which the parameter increases along the conic. The "X Axis" of the local coordinate system also defines the origin of the parameter of the conic.

Member Function Documentation

◆ Continuity()

GeomAbs_Shape Geom2d_Conic::Continuity ( ) const

overridevirtual

Returns GeomAbs_CN which is the global continuity of any conic.

Implements Geom2d_Curve.

◆ DumpJson()

void Geom2d_Conic::DumpJson	(	Standard_OStream &	theOStream,
		int	theDepth = -1 ) const

overridevirtual

Dumps the content of me into the stream.

Reimplemented from Geom2d_Geometry.

Reimplemented in Geom2d_Ellipse, Geom2d_Hyperbola, and Geom2d_Parabola.

◆ Eccentricity()

virtual double Geom2d_Conic::Eccentricity ( ) const

pure virtual

returns the eccentricity value of the conic e. e = 0 for a circle 0 < e < 1 for an ellipse (e = 0 if MajorRadius = MinorRadius) e > 1 for a hyperbola e = 1 for a parabola

Implemented in Geom2d_Circle, Geom2d_Ellipse, Geom2d_Hyperbola, and Geom2d_Parabola.

◆ IsCN()

bool Geom2d_Conic::IsCN ( const int N ) const

overridevirtual

Returns True, the order of continuity of a conic is infinite.

Implements Geom2d_Curve.

◆ Location()

const gp_Pnt2d & Geom2d_Conic::Location ( ) const

inline

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.

◆ Position()

const gp_Ax22d & Geom2d_Conic::Position ( ) const

inline

Returns the local coordinates system of the conic.

◆ Reverse()

void Geom2d_Conic::Reverse ( )

overridevirtual

Reverses the direction of parameterization of <me>. The local coordinate system of the conic is modified.

Implements Geom2d_Curve.

◆ ReversedParameter()

double Geom2d_Conic::ReversedParameter ( const double U ) const

overridepure virtual

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

Implements Geom2d_Curve.

Implemented in Geom2d_Circle, Geom2d_Ellipse, Geom2d_Hyperbola, and Geom2d_Parabola.

◆ SetAxis()

void Geom2d_Conic::SetAxis ( const gp_Ax22d & theA )

inline

Modifies this conic, redefining its local coordinate system partially, by assigning theA as its axis.

◆ SetLocation()

void Geom2d_Conic::SetLocation ( const gp_Pnt2d & theP )

inline

Modifies this conic, redefining its local coordinate system partially, by assigning theP as its origin.

◆ SetXAxis()

void Geom2d_Conic::SetXAxis ( const gp_Ax2d & theAX )

inline

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).

◆ SetYAxis()

void Geom2d_Conic::SetYAxis ( const gp_Ax2d & theAY )

inline

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).

◆ XAxis()

gp_Ax2d Geom2d_Conic::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&.

◆ YAxis()

gp_Ax2d Geom2d_Conic::YAxis ( ) const

Returns the "YAxis" of the conic. The "YAxis" is perpendicular to the "Xaxis".

Field Documentation

◆ pos

gp_Ax22d Geom2d_Conic::pos

protected

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

Geom2d_Conic.hxx

Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ Continuity()

◆ DumpJson()

◆ Eccentricity()

◆ IsCN()

◆ Location()

◆ Position()

◆ Reverse()

◆ ReversedParameter()

◆ SetAxis()

◆ SetLocation()

◆ SetXAxis()

◆ SetYAxis()

◆ XAxis()

◆ YAxis()

Field Documentation

◆ pos