The abstract class Conic describes the common behavior of conic curves in 3D space and, in particular, their general characteristics. The Geom package provides four concrete classes of conics: Geom_Circle, Geom_Ellipse, Geom_Hyperbola and Geom_Parabola. A conic is positioned in space with a right-handed coordinate system (gp_Ax2 object), where: More...

#include <Geom_Conic.hxx>

Inheritance diagram for Geom_Conic:

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Public Member Functions
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.

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 Exceptions Standard_DomainError in the case of a hyperbola if its major radius is null.

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.

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
	The continuity of the conic is Cn.

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

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

Public Member Functions inherited from Geom_Curve
virtual double	TransformedParameter (const double U, const gp_Trsf &T) const
	Returns the parameter on the transformed curve for the transform of the point of parameter U on <me>.

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

occ::handle< Geom_Curve >	Reversed () const
	Returns a copy of <me> reversed.

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

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

virtual bool	IsClosed () const =0
	Returns true if the curve is closed. 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
	Is the parametrization of the curve 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. Exceptions Standard_NoSuchObject if this curve is not periodic.

virtual gp_Pnt	EvalD0 (const double U) const =0
	Computes the point of parameter U. Raises an exception on failure (e.g. OffsetCurve at singular point).

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_Vec	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_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>.

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

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.

virtual void	Transform (const gp_Trsf &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 Geom).

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

virtual occ::handle< Geom_Geometry >	Copy () const =0
	Creates a new object which is a copy of this geometric object.

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_Ax2	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 3D space and, in particular, their general characteristics. The Geom package provides four concrete classes of conics: Geom_Circle, Geom_Ellipse, Geom_Hyperbola and Geom_Parabola. A conic is positioned in space with a right-handed coordinate system (gp_Ax2 object), where:

the origin is the center of the conic (or the apex in the case of a parabola),
the origin, "X Direction" and "Y Direction" define the plane of the conic. This coordinate system is the local coordinate system of the conic. The "main Direction" of this coordinate system is the vector normal to the plane of the conic. 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 conic. The "main Direction" of the local coordinate system gives an explicit orientation to the conic, 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

◆ Axis()

const gp_Ax1 & Geom_Conic::Axis ( ) const

inline

Returns the "main Axis" of this conic. This axis is normal to the plane of the conic.

◆ Continuity()

GeomAbs_Shape Geom_Conic::Continuity ( ) const

overridevirtual

The continuity of the conic is Cn.

Implements Geom_Curve.

◆ DumpJson()

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

overridevirtual

Dumps the content of me into the stream.

Reimplemented from Geom_Geometry.

Reimplemented in Geom_Ellipse, Geom_Hyperbola, and Geom_Parabola.

◆ Eccentricity()

virtual double Geom_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 Exceptions Standard_DomainError in the case of a hyperbola if its major radius is null.

Implemented in Geom_Circle, Geom_Ellipse, Geom_Hyperbola, and Geom_Parabola.

◆ IsCN()

bool Geom_Conic::IsCN ( const int N ) const

overridevirtual

Returns True. Raised if N < 0.

Implements Geom_Curve.

◆ Location()

const gp_Pnt & Geom_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 Apex of the parabola.

◆ Position()

const gp_Ax2 & Geom_Conic::Position ( ) const

inline

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.

◆ Reverse()

void Geom_Conic::Reverse ( )

overridevirtual

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

Implements Geom_Curve.

◆ ReversedParameter()

double Geom_Conic::ReversedParameter ( const double U ) const

overridepure virtual

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

Implements Geom_Curve.

Implemented in Geom_Circle, Geom_Ellipse, Geom_Hyperbola, and Geom_Parabola.

◆ SetAxis()

void Geom_Conic::SetAxis ( const gp_Ax1 & theA1 )

inline

Changes the orientation of the conic's plane. The normal axis to the plane is A1. The XAxis and the YAxis are recomputed.

raised if the A1 is parallel to the XAxis of the conic.

◆ SetLocation()

void Geom_Conic::SetLocation ( const gp_Pnt & theP )

inline

changes the location point of the conic.

◆ SetPosition()

void Geom_Conic::SetPosition ( const gp_Ax2 & theA2 )

inline

changes the local coordinate system of the conic.

◆ XAxis()

gp_Ax1 Geom_Conic::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.

◆ YAxis()

gp_Ax1 Geom_Conic::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.

Field Documentation

◆ pos

gp_Ax2 Geom_Conic::pos

protected

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

Geom_Conic.hxx

Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ Axis()

◆ Continuity()

◆ DumpJson()

◆ Eccentricity()

◆ IsCN()

◆ Location()

◆ Position()

◆ Reverse()

◆ ReversedParameter()

◆ SetAxis()

◆ SetLocation()

◆ SetPosition()

◆ XAxis()

◆ YAxis()

Field Documentation

◆ pos