The abstract class Curve describes the common behavior of curves in 3D space. The Geom package provides numerous concrete classes of derived curves, including lines, circles, conics, Bezier or BSpline curves, etc. The main characteristic of these curves is that they are parameterized. The Geom_Curve class shows: More...

#include <Geom_Curve.hxx>

Inheritance diagram for Geom_Curve:

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Data Structures
struct	ResD1
	Result of D1 evaluation: point and first derivative. More...

struct	ResD2
	Result of D2 evaluation: point and first two derivatives. More...

struct	ResD3
	Result of D3 evaluation: point and first three derivatives. More...

Public Member Functions
virtual void	Reverse ()=0
	Changes the direction of parametrization of <me>. The "FirstParameter" and the "LastParameter" are not changed but the orientation of the curve is modified. If the curve is bounded the StartPoint of the initial curve becomes the EndPoint of the reversed curve and the EndPoint of the initial curve becomes the StartPoint of the reversed curve.

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

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 GeomAbs_Shape	Continuity () const =0
	It is the global continuity of the curve C0 : only geometric continuity, C1 : continuity of the first derivative all along the Curve, C2 : continuity of the second derivative all along the Curve, C3 : continuity of the third derivative all along the Curve, G1 : tangency continuity all along the Curve, G2 : curvature continuity all along the Curve, CN : the order of continuity is infinite.

virtual bool	IsCN (const int N) const =0
	Returns true if the degree of continuity of this curve is at least N. Exceptions - Standard_RangeError if N is less than 0.

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.

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 Curve describes the common behavior of curves in 3D space. The Geom package provides numerous concrete classes of derived curves, including lines, circles, conics, Bezier or BSpline curves, etc. The main characteristic of these curves is that they are parameterized. The Geom_Curve class shows:

how to work with the parametric equation of a curve in order to calculate the point of parameter u, together with the vector tangent and the derivative vectors of order 2, 3,..., N at this point;
how to obtain general information about the curve (for example, level of continuity, closed characteristics, periodicity, bounds of the parameter field);
how the parameter changes when a geometric transformation is applied to the curve or when the orientation of the curve is inverted. All curves must have a geometric continuity: a curve is at least "C0". Generally, this property is checked at the time of construction or when the curve is edited. Where this is not the case, the documentation states so explicitly. Warning The Geom package does not prevent the construction of curves with null length or curves which self-intersect.

Member Function Documentation

◆ Continuity()

virtual GeomAbs_Shape Geom_Curve::Continuity ( ) const

pure virtual

It is the global continuity of the curve C0 : only geometric continuity, C1 : continuity of the first derivative all along the Curve, C2 : continuity of the second derivative all along the Curve, C3 : continuity of the third derivative all along the Curve, G1 : tangency continuity all along the Curve, G2 : curvature continuity all along the Curve, CN : the order of continuity is infinite.

Implemented in Geom_BezierCurve, Geom_BSplineCurve, Geom_Line, Geom_OffsetCurve, Geom_TrimmedCurve, GeomEval_AHTBezierCurve, GeomEval_CircularHelixCurve, GeomEval_SineWaveCurve, GeomEval_TBezierCurve, ShapeExtend_ComplexCurve, and Geom_Conic.

◆ D0()

void Geom_Curve::D0	(	const double	U,
		gp_Pnt &	P ) const

inline

Returns in P the point of parameter U.

◆ D1()

void Geom_Curve::D1	(	const double	U,
		gp_Pnt &	P,
		gp_Vec &	V1 ) const

inline

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

◆ D2()

void Geom_Curve::D2	(	const double	U,
		gp_Pnt &	P,
		gp_Vec &	V1,
		gp_Vec &	V2 ) const

inline

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

◆ D3()

void Geom_Curve::D3	(	const double	U,
		gp_Pnt &	P,
		gp_Vec &	V1,
		gp_Vec &	V2,
		gp_Vec &	V3 ) const

inline

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

◆ DN()

gp_Vec Geom_Curve::DN	(	const double	U,
		const int	N ) const

inline

The returned vector gives the value of the derivative for the order of derivation N.

◆ DumpJson()

void Geom_Curve::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, Geom_Line, Geom_OffsetCurve, Geom_Parabola, Geom_TrimmedCurve, GeomEval_AHTBezierCurve, GeomEval_CircularHelixCurve, GeomEval_SineWaveCurve, and GeomEval_TBezierCurve.

◆ EvalD0()

virtual gp_Pnt Geom_Curve::EvalD0 ( const double U ) const

pure virtual

Computes the point of parameter U. Raises an exception on failure (e.g. OffsetCurve at singular point).

Implemented in Geom_BezierCurve, Geom_BSplineCurve, Geom_Circle, Geom_Ellipse, Geom_Hyperbola, Geom_Line, Geom_OffsetCurve, Geom_Parabola, Geom_TrimmedCurve, GeomEval_AHTBezierCurve, GeomEval_CircularHelixCurve, GeomEval_SineWaveCurve, GeomEval_TBezierCurve, and ShapeExtend_ComplexCurve.

◆ EvalD1()

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

pure virtual

Computes the point and first derivative at parameter U. Raises an exception if the curve continuity is not C1.

Implemented in Geom_BezierCurve, Geom_BSplineCurve, Geom_Circle, Geom_Ellipse, Geom_Hyperbola, Geom_Line, Geom_OffsetCurve, Geom_Parabola, Geom_TrimmedCurve, GeomEval_AHTBezierCurve, GeomEval_CircularHelixCurve, GeomEval_SineWaveCurve, GeomEval_TBezierCurve, and ShapeExtend_ComplexCurve.

◆ EvalD2()

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

pure virtual

Computes the point and first two derivatives at parameter U. Raises an exception if the curve continuity is not C2.

Implemented in Geom_BezierCurve, Geom_BSplineCurve, Geom_Circle, Geom_Ellipse, Geom_Hyperbola, Geom_Line, Geom_OffsetCurve, Geom_Parabola, Geom_TrimmedCurve, GeomEval_AHTBezierCurve, GeomEval_CircularHelixCurve, GeomEval_SineWaveCurve, GeomEval_TBezierCurve, and ShapeExtend_ComplexCurve.

◆ EvalD3()

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

pure virtual

Computes the point and first three derivatives at parameter U. Raises an exception if the curve continuity is not C3.

Implemented in Geom_BezierCurve, Geom_BSplineCurve, Geom_Circle, Geom_Ellipse, Geom_Hyperbola, Geom_Line, Geom_OffsetCurve, Geom_Parabola, Geom_TrimmedCurve, GeomEval_AHTBezierCurve, GeomEval_CircularHelixCurve, GeomEval_SineWaveCurve, GeomEval_TBezierCurve, and ShapeExtend_ComplexCurve.

◆ EvalDN()

virtual gp_Vec Geom_Curve::EvalDN	(	const double	U,
		const int	N ) const

pure virtual

Computes the Nth derivative at parameter U. Raises an exception if the curve continuity is not CN, or N < 1.

Implemented in Geom_BezierCurve, Geom_BSplineCurve, Geom_Circle, Geom_Ellipse, Geom_Hyperbola, Geom_Line, Geom_OffsetCurve, Geom_Parabola, Geom_TrimmedCurve, GeomEval_AHTBezierCurve, GeomEval_CircularHelixCurve, GeomEval_SineWaveCurve, GeomEval_TBezierCurve, and ShapeExtend_ComplexCurve.

◆ FirstParameter()

virtual double Geom_Curve::FirstParameter ( ) const

pure virtual

Returns the value of the first parameter. Warnings : It can be RealFirst from package Standard if the curve is infinite.

Implemented in Geom_BezierCurve, Geom_BSplineCurve, Geom_Circle, Geom_Ellipse, Geom_Hyperbola, Geom_Line, Geom_OffsetCurve, Geom_Parabola, Geom_TrimmedCurve, GeomEval_AHTBezierCurve, GeomEval_CircularHelixCurve, GeomEval_SineWaveCurve, GeomEval_TBezierCurve, and ShapeExtend_ComplexCurve.

◆ IsClosed()

virtual bool Geom_Curve::IsClosed ( ) const

pure virtual

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.

Implemented in Geom_BezierCurve, Geom_BSplineCurve, Geom_Circle, Geom_Ellipse, Geom_Hyperbola, Geom_Line, Geom_OffsetCurve, Geom_Parabola, Geom_TrimmedCurve, GeomEval_AHTBezierCurve, GeomEval_CircularHelixCurve, GeomEval_SineWaveCurve, GeomEval_TBezierCurve, and ShapeExtend_ComplexCurve.

◆ IsCN()

virtual bool Geom_Curve::IsCN ( const int N ) const

pure virtual

Returns true if the degree of continuity of this curve is at least N. Exceptions - Standard_RangeError if N is less than 0.

Implemented in Geom_BezierCurve, Geom_BSplineCurve, Geom_Line, Geom_OffsetCurve, Geom_TrimmedCurve, GeomEval_AHTBezierCurve, GeomEval_CircularHelixCurve, GeomEval_SineWaveCurve, GeomEval_TBezierCurve, ShapeExtend_ComplexCurve, and Geom_Conic.

◆ IsPeriodic()

virtual bool Geom_Curve::IsPeriodic ( ) const

pure virtual

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.

Implemented in Geom_BezierCurve, Geom_BSplineCurve, Geom_Circle, Geom_Ellipse, Geom_Hyperbola, Geom_Line, Geom_OffsetCurve, Geom_Parabola, Geom_TrimmedCurve, GeomEval_AHTBezierCurve, GeomEval_CircularHelixCurve, GeomEval_SineWaveCurve, GeomEval_TBezierCurve, and ShapeExtend_ComplexCurve.

◆ LastParameter()

virtual double Geom_Curve::LastParameter ( ) const

pure virtual

Returns the value of the last parameter. Warnings : It can be RealLast from package Standard if the curve is infinite.

Implemented in Geom_BezierCurve, Geom_BSplineCurve, Geom_Circle, Geom_Ellipse, Geom_Hyperbola, Geom_Line, Geom_OffsetCurve, Geom_Parabola, Geom_TrimmedCurve, GeomEval_AHTBezierCurve, GeomEval_CircularHelixCurve, GeomEval_SineWaveCurve, GeomEval_TBezierCurve, and ShapeExtend_ComplexCurve.

◆ ParametricTransformation()

virtual double Geom_Curve::ParametricTransformation ( const gp_Trsf & T ) const

virtual

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 1.

It can be redefined. For example on the Line.

Reimplemented in Geom_Line, Geom_OffsetCurve, Geom_Parabola, and Geom_TrimmedCurve.

◆ Period()

virtual double Geom_Curve::Period ( ) const

virtual

Returns the period of this curve. Exceptions Standard_NoSuchObject if this curve is not periodic.

Reimplemented in Geom_OffsetCurve, and Geom_TrimmedCurve.

◆ Reverse()

virtual void Geom_Curve::Reverse ( )

pure virtual

Changes the direction of parametrization of <me>. The "FirstParameter" and the "LastParameter" are not changed but the orientation of the curve is modified. If the curve is bounded the StartPoint of the initial curve becomes the EndPoint of the reversed curve and the EndPoint of the initial curve becomes the StartPoint of the reversed curve.

Implemented in Geom_BezierCurve, Geom_BSplineCurve, Geom_Line, Geom_OffsetCurve, Geom_TrimmedCurve, GeomEval_AHTBezierCurve, GeomEval_CircularHelixCurve, GeomEval_SineWaveCurve, GeomEval_TBezierCurve, and Geom_Conic.

◆ Reversed()

occ::handle< Geom_Curve > Geom_Curve::Reversed ( ) const

Returns a copy of <me> reversed.

◆ ReversedParameter()

virtual double Geom_Curve::ReversedParameter ( const double U ) const

pure virtual

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

me->Reversed()->Value(me->ReversedParameter(U))

is the same point as

me->Value(U)

Implemented in Geom_BezierCurve, Geom_BSplineCurve, Geom_Circle, Geom_Ellipse, Geom_Hyperbola, Geom_Line, Geom_OffsetCurve, Geom_Parabola, Geom_TrimmedCurve, GeomEval_AHTBezierCurve, GeomEval_CircularHelixCurve, GeomEval_SineWaveCurve, GeomEval_TBezierCurve, ShapeExtend_ComplexCurve, and Geom_Conic.

◆ TransformedParameter()

virtual double Geom_Curve::TransformedParameter	(	const double	U,
		const gp_Trsf &	T ) const

virtual

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

It can be redefined. For example on the Line.

Reimplemented in Geom_Line, Geom_OffsetCurve, Geom_Parabola, and Geom_TrimmedCurve.

◆ Value()

gp_Pnt Geom_Curve::Value ( const double U ) const

inline

Computes the point of parameter U on <me>.

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

Geom_Curve.hxx

Data Structures

Public Member Functions

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ Continuity()

◆ D0()

◆ D1()

◆ D2()

◆ D3()

◆ DN()

◆ DumpJson()

◆ EvalD0()

◆ EvalD1()

◆ EvalD2()

◆ EvalD3()

◆ EvalDN()

◆ FirstParameter()

◆ IsClosed()

◆ IsCN()

◆ IsPeriodic()

◆ LastParameter()

◆ ParametricTransformation()

◆ Period()

◆ Reverse()

◆ Reversed()

◆ ReversedParameter()

◆ TransformedParameter()

◆ Value()