GeomEval_TBezierSurface Class Reference

Tensor-product Trigonometric Bezier surface. Uses trigonometric Bernstein-like bases in both U and V directions over the space {1, sin(alpha*t), cos(alpha*t), ..., sin(n*alpha*t), cos(n*alpha*t)}. More...

#include <GeomEval_TBezierSurface.hxx>

Inheritance diagram for GeomEval_TBezierSurface:

Public Member Functions
	GeomEval_TBezierSurface (const NCollection_Array2< gp_Pnt > &thePoles, double theAlphaU, double theAlphaV)
	Constructs a non-rational T-Bezier surface from poles and alpha parameters.
	GeomEval_TBezierSurface (const NCollection_Array2< gp_Pnt > &thePoles, const NCollection_Array2< double > &theWeights, double theAlphaU, double theAlphaV)
	Constructs a rational T-Bezier surface.
const NCollection_Array2< gp_Pnt > &	Poles () const
	Returns the poles grid.
const NCollection_Array2< double > &	Weights () const
	Returns the weights grid (empty if non-rational).
double	AlphaU () const
	Returns the frequency parameter alpha in the U direction.
double	AlphaV () const
	Returns the frequency parameter alpha in the V direction.
int	NbUPoles () const
	Returns the number of poles in the U direction.
int	NbVPoles () const
	Returns the number of poles in the V direction.
int	OrderU () const
	Returns the trigonometric order in U (NbUPoles = 2*nU + 1).
int	OrderV () const
	Returns the trigonometric order in V (NbVPoles = 2*nV + 1).
bool	IsRational () const
	Returns true if the surface is rational.
void	UReverse () final
	Reversal is not supported for this eval surface.
double	UReversedParameter (const double U) const final
	Reversal is not supported for this eval surface.
void	VReverse () final
	Reversal is not supported for this eval surface.
double	VReversedParameter (const double V) const final
	Reversal is not supported for this eval surface.
void	Bounds (double &U1, double &U2, double &V1, double &V2) const final
	Returns the parametric bounds.
bool	IsUClosed () const final
	Returns true if the surface is closed in U.
bool	IsVClosed () const final
	Returns true if the surface is closed in V.
bool	IsUPeriodic () const final
	Returns false. T-Bezier surfaces are not periodic in U.
bool	IsVPeriodic () const final
	Returns false. T-Bezier surfaces are not periodic in V.
GeomAbs_Shape	Continuity () const final
	Returns GeomAbs_CN. T-Bezier surfaces are infinitely differentiable.
bool	IsCNu (const int N) const final
	Returns true for all N. T-Bezier surfaces are infinitely differentiable in U.
bool	IsCNv (const int N) const final
	Returns true for all N. T-Bezier surfaces are infinitely differentiable in V.
occ::handle< Geom_Curve >	UIso (const double U) const final
	Isoparametric curve extraction is not supported for this eval surface.
occ::handle< Geom_Curve >	VIso (const double V) const final
	Isoparametric curve extraction is not supported for this eval surface.
gp_Pnt	EvalD0 (const double U, const double V) const final
	Computes the point S(U, V).
Geom_Surface::ResD1	EvalD1 (const double U, const double V) const final
	Computes the point and first partial derivatives at (U, V).
Geom_Surface::ResD2	EvalD2 (const double U, const double V) const final
	Computes the point and partial derivatives up to 2nd order at (U, V).
Geom_Surface::ResD3	EvalD3 (const double U, const double V) const final
	Computes the point and partial derivatives up to 3rd order at (U, V).
gp_Vec	EvalDN (const double U, const double V, const int Nu, const int Nv) const final
	Computes the derivative of order Nu in U and Nv in V.
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 surface.
void	DumpJson (Standard_OStream &theOStream, int theDepth=-1) const final
	Dumps the content of me into the stream.
Public Member Functions inherited from Geom_Surface
occ::handle< Geom_Surface >	UReversed () const
	Reverses the U direction of parametrization of <me>. The bounds of the surface are not modified. A copy of <me> is returned.
occ::handle< Geom_Surface >	VReversed () const
	Reverses the V direction of parametrization of <me>. The bounds of the surface are not modified. A copy of <me> is returned.
virtual void	TransformParameters (double &U, double &V, const gp_Trsf &T) const
	Computes the parameters on the transformed surface for the transform of the point of parameters U,V on <me>.
virtual gp_GTrsf2d	ParametricTransformation (const gp_Trsf &T) const
	Returns a 2d transformation used to find the new parameters of a point on the transformed surface.
virtual double	UPeriod () const
	Returns the period of this surface in the u parametric direction. Raises if the surface is not uperiodic.
virtual double	VPeriod () const
	Returns the period of this surface in the v parametric direction. raises if the surface is not vperiodic.
void	D0 (const double U, const double V, gp_Pnt &P) const
	Computes the point of parameter (U, V).
void	D1 (const double U, const double V, gp_Pnt &P, gp_Vec &D1U, gp_Vec &D1V) const
	Computes the point and first partial derivatives.
void	D2 (const double U, const double V, gp_Pnt &P, gp_Vec &D1U, gp_Vec &D1V, gp_Vec &D2U, gp_Vec &D2V, gp_Vec &D2UV) const
	Computes the point and partial derivatives up to 2nd order.
void	D3 (const double U, const double V, gp_Pnt &P, gp_Vec &D1U, gp_Vec &D1V, gp_Vec &D2U, gp_Vec &D2V, gp_Vec &D2UV, gp_Vec &D3U, gp_Vec &D3V, gp_Vec &D3UUV, gp_Vec &D3UVV) const
	Computes the point and partial derivatives up to 3rd order.
gp_Vec	DN (const double U, const double V, const int Nu, const int Nv) const
	Computes the derivative of order Nu in U and Nv in V.
gp_Pnt	Value (const double U, const double V) const
	Computes the point of parameter (U, V) on the surface.
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

Tensor-product Trigonometric Bezier surface. Uses trigonometric Bernstein-like bases in both U and V directions over the space {1, sin(alpha*t), cos(alpha*t), ..., sin(n*alpha*t), cos(n*alpha*t)}.

Parameter domain: U in [0, Pi/alphaU], V in [0, Pi/alphaV]. Number of control points: (2*nU + 1) x (2*nV + 1) for orders nU, nV.

The surface is:

S(u,v) = sum_i sum_j P_ij * Bu_i(u) * Bv_j(v)

where Bu_i and Bv_j are trigonometric basis functions in U and V respectively.

For rational surfaces:

S(u,v) = sum_i sum_j (w_ij * P_ij * Bu_i(u) * Bv_j(v))
       / sum_i sum_j (w_ij * Bu_i(u) * Bv_j(v))

Constructor & Destructor Documentation

GeomEval_TBezierSurface() [1/2]

GeomEval_TBezierSurface::GeomEval_TBezierSurface	(	const NCollection_Array2< gp_Pnt > &	thePoles,
		double	theAlphaU,
		double	theAlphaV )

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

Parameters

[in]	thePoles	control points grid (row count and col count must be odd >= 3)
[in]	theAlphaU	frequency parameter in U direction (must be > 0)
[in]	theAlphaV	frequency parameter in V direction (must be > 0)

Exceptions

Standard_ConstructionError

if validation fails

GeomEval_TBezierSurface() [2/2]

GeomEval_TBezierSurface::GeomEval_TBezierSurface	(	const NCollection_Array2< gp_Pnt > &	thePoles,
		const NCollection_Array2< double > &	theWeights,
		double	theAlphaU,
		double	theAlphaV )

Constructs a rational T-Bezier surface.

Parameters

[in]	thePoles	control points grid
[in]	theWeights	weights grid (same dimensions as poles, all > 0)
[in]	theAlphaU	frequency parameter in U direction (must be > 0)
[in]	theAlphaV	frequency parameter in V direction (must be > 0)

Exceptions

Standard_ConstructionError

if validation fails

Member Function Documentation

AlphaU()

double GeomEval_TBezierSurface::AlphaU

(

)

const

Returns the frequency parameter alpha in the U direction.

AlphaV()

double GeomEval_TBezierSurface::AlphaV

(

)

const

Returns the frequency parameter alpha in the V direction.

Bounds()

void GeomEval_TBezierSurface::Bounds ( double & U1, double & U2, double & V1, double & V2 ) const

finalvirtual

Returns the parametric bounds.

Parameters

[out]	U1	lower U bound (0)
[out]	U2	upper U bound (Pi/alphaU)
[out]	V1	lower V bound (0)
[out]	V2	upper V bound (Pi/alphaV)

Implements Geom_Surface.

Continuity()

GeomAbs_Shape GeomEval_TBezierSurface::Continuity ( ) const

finalvirtual

Returns GeomAbs_CN. T-Bezier surfaces are infinitely differentiable.

Implements Geom_Surface.

Copy()

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

finalvirtual

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

Implements Geom_Geometry.

DumpJson()

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

finalvirtual

Dumps the content of me into the stream.

Reimplemented from Geom_Surface.

EvalD0()

gp_Pnt GeomEval_TBezierSurface::EvalD0 ( const double U, const double V ) const

finalvirtual

Computes the point S(U, V).

Implements Geom_Surface.

EvalD1()

Geom_Surface::ResD1 GeomEval_TBezierSurface::EvalD1 ( const double U, const double V ) const

finalvirtual

Computes the point and first partial derivatives at (U, V).

Implements Geom_Surface.

EvalD2()

Geom_Surface::ResD2 GeomEval_TBezierSurface::EvalD2 ( const double U, const double V ) const

finalvirtual

Computes the point and partial derivatives up to 2nd order at (U, V).

Implements Geom_Surface.

EvalD3()

Geom_Surface::ResD3 GeomEval_TBezierSurface::EvalD3 ( const double U, const double V ) const

finalvirtual

Computes the point and partial derivatives up to 3rd order at (U, V).

Implements Geom_Surface.

EvalDN()

gp_Vec GeomEval_TBezierSurface::EvalDN ( const double U, const double V, const int Nu, const int Nv ) const

finalvirtual

Computes the derivative of order Nu in U and Nv in V.

Parameters

[in]	U	the u parameter
[in]	V	the v parameter
[in]	Nu	derivative order in U (must be >= 0)
[in]	Nv	derivative order in V (must be >= 0)

Returns

the derivative vector

Exceptions

Standard_RangeError

if Nu + Nv < 1 or Nu < 0 or Nv < 0

Implements Geom_Surface.

IsCNu()

bool GeomEval_TBezierSurface::IsCNu ( const int N ) const

finalvirtual

Returns true for all N. T-Bezier surfaces are infinitely differentiable in U.

Implements Geom_Surface.

IsCNv()

bool GeomEval_TBezierSurface::IsCNv ( const int N ) const

finalvirtual

Returns true for all N. T-Bezier surfaces are infinitely differentiable in V.

Implements Geom_Surface.

IsRational()

bool GeomEval_TBezierSurface::IsRational

(

)

const

Returns true if the surface is rational.

IsUClosed()

bool GeomEval_TBezierSurface::IsUClosed ( ) const

finalvirtual

Returns true if the surface is closed in U.

Implements Geom_Surface.

IsUPeriodic()

bool GeomEval_TBezierSurface::IsUPeriodic ( ) const

finalvirtual

Returns false. T-Bezier surfaces are not periodic in U.

Implements Geom_Surface.

IsVClosed()

bool GeomEval_TBezierSurface::IsVClosed ( ) const

finalvirtual

Returns true if the surface is closed in V.

Implements Geom_Surface.

IsVPeriodic()

bool GeomEval_TBezierSurface::IsVPeriodic ( ) const

finalvirtual

Returns false. T-Bezier surfaces are not periodic in V.

Implements Geom_Surface.

NbUPoles()

int GeomEval_TBezierSurface::NbUPoles

(

)

const

Returns the number of poles in the U direction.

NbVPoles()

int GeomEval_TBezierSurface::NbVPoles

(

)

const

Returns the number of poles in the V direction.

OrderU()

int GeomEval_TBezierSurface::OrderU

(

)

const

Returns the trigonometric order in U (NbUPoles = 2*nU + 1).

OrderV()

int GeomEval_TBezierSurface::OrderV

(

)

const

Returns the trigonometric order in V (NbVPoles = 2*nV + 1).

Poles()

const NCollection_Array2< gp_Pnt > & GeomEval_TBezierSurface::Poles

(

)

const

Returns the poles grid.

Transform()

void GeomEval_TBezierSurface::Transform ( const gp_Trsf & T )

finalvirtual

Transformation is not supported for this eval geometry.

Exceptions

Standard_NotImplemented

Implements Geom_Geometry.

UIso()

occ::handle< Geom_Curve > GeomEval_TBezierSurface::UIso ( const double U ) const

finalvirtual

Isoparametric curve extraction is not supported for this eval surface.

Exceptions

Standard_NotImplemented

Implements Geom_Surface.

UReverse()

void GeomEval_TBezierSurface::UReverse ( )

finalvirtual

Reversal is not supported for this eval surface.

Exceptions

Standard_NotImplemented

Implements Geom_Surface.

UReversedParameter()

double GeomEval_TBezierSurface::UReversedParameter ( const double U ) const

finalvirtual

Reversal is not supported for this eval surface.

Exceptions

Standard_NotImplemented

Implements Geom_Surface.

VIso()

occ::handle< Geom_Curve > GeomEval_TBezierSurface::VIso ( const double V ) const

finalvirtual

Isoparametric curve extraction is not supported for this eval surface.

Exceptions

Standard_NotImplemented

Implements Geom_Surface.

VReverse()

void GeomEval_TBezierSurface::VReverse ( )

finalvirtual

Reversal is not supported for this eval surface.

Exceptions

Standard_NotImplemented

Implements Geom_Surface.

VReversedParameter()

double GeomEval_TBezierSurface::VReversedParameter ( const double V ) const

finalvirtual

Reversal is not supported for this eval surface.

Exceptions

Standard_NotImplemented

Implements Geom_Surface.

Weights()

const NCollection_Array2< double > & GeomEval_TBezierSurface::Weights

(

)

const

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

---

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

• GeomEval_TBezierSurface.hxx