3D Trigonometric Bezier curve. Uses a trigonometric Bernstein-like basis over the space {1, sin(alpha*t), cos(alpha*t), ..., sin(n*alpha*t), cos(n*alpha*t)}. More...

#include <GeomEval_TBezierCurve.hxx>

Inheritance diagram for GeomEval_TBezierCurve:

[legend]

Public Member Functions
	GeomEval_TBezierCurve (const NCollection_Array1< gp_Pnt > &thePoles, double theAlpha)
	Constructs a non-rational T-Bezier curve from poles and alpha.

	GeomEval_TBezierCurve (const NCollection_Array1< gp_Pnt > &thePoles, const NCollection_Array1< double > &theWeights, double theAlpha)
	Constructs a rational T-Bezier curve.

const NCollection_Array1< gp_Pnt > &	Poles () const
	Returns the poles array.

const NCollection_Array1< double > &	Weights () const
	Returns the weights array (empty if non-rational).

double	Alpha () const
	Returns the frequency parameter alpha.

int	NbPoles () const
	Returns the number of poles.

int	Order () const
	Returns the trigonometric order n (NbPoles = 2*n + 1).

bool	IsRational () const
	Returns true if the curve is rational.

gp_Pnt	StartPoint () const final
	Returns the start point C(0).

gp_Pnt	EndPoint () const final
	Returns the end point C(Pi/alpha).

void	Reverse () final
	Reversal is not supported for this eval curve.

double	ReversedParameter (const double U) const final
	Reversal is not supported for this eval curve.

double	FirstParameter () const final
	Returns the first parameter value: 0.0.

double	LastParameter () const final
	Returns the last parameter value: Pi/alpha.

bool	IsClosed () const final
	Returns true if StartPoint and EndPoint coincide.

bool	IsPeriodic () const final
	Returns false. T-Bezier curves are not periodic.

GeomAbs_Shape	Continuity () const final
	Returns GeomAbs_CN. T-Bezier curves are infinitely differentiable.

bool	IsCN (const int N) const final
	Returns true for all N. T-Bezier curves are infinitely differentiable.

gp_Pnt	EvalD0 (const double U) const final
	Computes the point C(U).

Geom_Curve::ResD1	EvalD1 (const double U) const final
	Computes the point and first derivative at U.

Geom_Curve::ResD2	EvalD2 (const double U) const final
	Computes the point and first two derivatives at U.

Geom_Curve::ResD3	EvalD3 (const double U) const final
	Computes the point and first three derivatives at U.

gp_Vec	EvalDN (const double U, const int N) const final
	Computes the N-th derivative at U.

void	Transform (const gp_Trsf &T) final
	Transformation is not supported for this eval geometry.

occ::handle< Geom_Geometry >	Copy () const final
	Creates a new object which is a copy of this T-Bezier curve.

void	DumpJson (Standard_OStream &theOStream, int theDepth=-1) const final
	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	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.

Detailed Description

3D Trigonometric Bezier curve. Uses a trigonometric Bernstein-like basis over the space {1, sin(alpha*t), cos(alpha*t), ..., sin(n*alpha*t), cos(n*alpha*t)}.

The parameter domain is [0, Pi/alpha]. The number of control points is 2*n + 1 for order n.

The alpha parameter controls the frequency of the trigonometric basis. A T-Bezier curve of order n with poles P_0, P_1, ..., P_{2n} is:

C(t) = P_0 * T_0(t) + P_1 * T_1(t) + ... + P_{2n} * T_{2n}(t)

t

GLdouble GLdouble t

Definition OpenGl_glext.h:330

NCollection_ForwardRangeIterator

STL input iterator that wraps an OCCT More()/Next() iterator.

Definition NCollection_ForwardRange.hxx:142

where:

T_0(t) = 1
T_{2k-1}(t) = sin(k * alpha * t), for k = 1..n
T_{2k}(t) = cos(k * alpha * t), for k = 1..n

For rational curves, each pole is weighted:

C(t) = sum(w_i * P_i * T_i(t)) / sum(w_i * T_i(t))

Constructor & Destructor Documentation

◆ GeomEval_TBezierCurve() [1/2]

GeomEval_TBezierCurve::GeomEval_TBezierCurve	(	const NCollection_Array1< gp_Pnt > &	thePoles,
		double	theAlpha )

Constructs a non-rational T-Bezier curve from poles and alpha.

Parameters

[in]	thePoles	control points (1-based, size must be odd >= 3)
[in]	theAlpha	frequency parameter (must be > 0)

Exceptions

Standard_ConstructionError if NbPoles is not odd or < 3 or theAlpha <= 0

◆ GeomEval_TBezierCurve() [2/2]

GeomEval_TBezierCurve::GeomEval_TBezierCurve	(	const NCollection_Array1< gp_Pnt > &	thePoles,
		const NCollection_Array1< double > &	theWeights,
		double	theAlpha )

Constructs a rational T-Bezier curve.

Parameters

[in]	thePoles	control points (1-based, size must be odd >= 3)
[in]	theWeights	weights (same size as poles, all > 0)
[in]	theAlpha	frequency parameter (must be > 0)

Exceptions

Standard_ConstructionError if validation fails

Member Function Documentation

◆ Alpha()

double GeomEval_TBezierCurve::Alpha ( ) const

Returns the frequency parameter alpha.

◆ Continuity()

GeomAbs_Shape GeomEval_TBezierCurve::Continuity ( ) const

finalvirtual

Returns GeomAbs_CN. T-Bezier curves are infinitely differentiable.

Implements Geom_Curve.

◆ Copy()

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

finalvirtual

Creates a new object which is a copy of this T-Bezier curve.

Implements Geom_Geometry.

◆ DumpJson()

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

finalvirtual

Dumps the content of me into the stream.

Reimplemented from Geom_BoundedCurve.

◆ EndPoint()

gp_Pnt GeomEval_TBezierCurve::EndPoint ( ) const

finalvirtual

Returns the end point C(Pi/alpha).

Implements Geom_BoundedCurve.

◆ EvalD0()

gp_Pnt GeomEval_TBezierCurve::EvalD0 ( const double U ) const

finalvirtual

Computes the point C(U).

Implements Geom_Curve.

◆ EvalD1()

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

finalvirtual

Computes the point and first derivative at U.

Implements Geom_Curve.

◆ EvalD2()

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

finalvirtual

Computes the point and first two derivatives at U.

Implements Geom_Curve.

◆ EvalD3()

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

finalvirtual

Computes the point and first three derivatives at U.

Implements Geom_Curve.

◆ EvalDN()

gp_Vec GeomEval_TBezierCurve::EvalDN	(	const double	U,
		const int	N ) const

finalvirtual

Computes the N-th derivative at U.

Parameters

[in]	U	parameter value
[in]	N	derivative order (must be >= 1)

Returns: the N-th derivative vector

Exceptions

Standard_RangeError if N < 1

Implements Geom_Curve.

◆ FirstParameter()

double GeomEval_TBezierCurve::FirstParameter ( ) const

finalvirtual

Returns the first parameter value: 0.0.

Implements Geom_Curve.

◆ IsClosed()

bool GeomEval_TBezierCurve::IsClosed ( ) const

finalvirtual

Returns true if StartPoint and EndPoint coincide.

Implements Geom_Curve.

◆ IsCN()

bool GeomEval_TBezierCurve::IsCN ( const int N ) const

finalvirtual

Returns true for all N. T-Bezier curves are infinitely differentiable.

Implements Geom_Curve.

◆ IsPeriodic()

bool GeomEval_TBezierCurve::IsPeriodic ( ) const

finalvirtual

Returns false. T-Bezier curves are not periodic.

Implements Geom_Curve.

◆ IsRational()

bool GeomEval_TBezierCurve::IsRational ( ) const

Returns true if the curve is rational.

◆ LastParameter()

double GeomEval_TBezierCurve::LastParameter ( ) const

finalvirtual

Returns the last parameter value: Pi/alpha.

Implements Geom_Curve.

◆ NbPoles()

int GeomEval_TBezierCurve::NbPoles ( ) const

Returns the number of poles.

◆ Order()

int GeomEval_TBezierCurve::Order ( ) const

Returns the trigonometric order n (NbPoles = 2*n + 1).

◆ Poles()

const NCollection_Array1< gp_Pnt > & GeomEval_TBezierCurve::Poles ( ) const

Returns the poles array.

◆ Reverse()

void GeomEval_TBezierCurve::Reverse ( )

finalvirtual

Reversal is not supported for this eval curve.

Exceptions

Standard_NotImplemented

Implements Geom_Curve.

◆ ReversedParameter()

double GeomEval_TBezierCurve::ReversedParameter ( const double U ) const

finalvirtual

Reversal is not supported for this eval curve.

Exceptions

Standard_NotImplemented

Implements Geom_Curve.

◆ StartPoint()

gp_Pnt GeomEval_TBezierCurve::StartPoint ( ) const

finalvirtual

Returns the start point C(0).

Implements Geom_BoundedCurve.

◆ Transform()

void GeomEval_TBezierCurve::Transform ( const gp_Trsf & T )

finalvirtual

Transformation is not supported for this eval geometry.

Exceptions

Standard_NotImplemented

Implements Geom_Geometry.

◆ Weights()

const NCollection_Array1< double > & GeomEval_TBezierCurve::Weights ( ) const

Returns the weights array (empty if non-rational).

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

GeomEval_TBezierCurve.hxx

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ GeomEval_TBezierCurve() [1/2]

◆ GeomEval_TBezierCurve() [2/2]

Member Function Documentation

◆ Alpha()

◆ Continuity()

◆ Copy()

◆ DumpJson()

◆ EndPoint()

◆ EvalD0()

◆ EvalD1()

◆ EvalD2()

◆ EvalD3()

◆ EvalDN()

◆ FirstParameter()

◆ IsClosed()

◆ IsCN()

◆ IsPeriodic()

◆ IsRational()

◆ LastParameter()

◆ NbPoles()

◆ Order()

◆ Poles()

◆ Reverse()

◆ ReversedParameter()

◆ StartPoint()

◆ Transform()

◆ Weights()