The abstract class BoundedCurve describes the common behavior of bounded curves in 2D space. A bounded curve is limited by two finite values of the parameter, termed respectively "first parameter" and "last parameter". The "first parameter" gives the "start point" of the bounded curve, and the "last parameter" gives the "end point" of the bounded curve. The length of a bounded curve is finite. The Geom2d package provides three concrete classes of bounded curves: More...

#include <Geom2d_BoundedCurve.hxx>

Inheritance diagram for Geom2d_BoundedCurve:

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Public Member Functions
virtual gp_Pnt2d	EndPoint () const =0
	Returns the end point of the curve. The end point is the value of the curve for the "LastParameter" of the curve.

virtual gp_Pnt2d	StartPoint () const =0
	Returns the start point of the curve. The start point is the value of the curve for the "FirstParameter" of the curve.

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 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
	Computes the parameter on the reversed curve for the point of parameter U on this curve. Note: The point of parameter U on this curve is identical to the point of parameter ReversedParameter(U) on the reversed 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 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_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.

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 BoundedCurve describes the common behavior of bounded curves in 2D space. A bounded curve is limited by two finite values of the parameter, termed respectively "first parameter" and "last parameter". The "first parameter" gives the "start point" of the bounded curve, and the "last parameter" gives the "end point" of the bounded curve. The length of a bounded curve is finite. The Geom2d package provides three concrete classes of bounded curves:

two frequently used mathematical formulations of complex curves:
Geom2d_BezierCurve,
Geom2d_BSplineCurve, and
Geom2d_TrimmedCurve to trim a curve, i.e. to only take part of the curve limited by two values of the parameter of the basis curve.