Describes a rational or non-rational Bezier surface. More...

#include <Geom_BezierSurface.hxx>

Inheritance diagram for Geom_BezierSurface:

[legend]

Public Member Functions
	Geom_BezierSurface (const NCollection_Array2< gp_Pnt > &SurfacePoles)
	Creates a non-rational Bezier surface with a set of poles. Control points representation : SPoles(Uorigin,Vorigin) ...................SPoles(Uorigin,Vend) . . . . SPoles(Uend, Vorigin) .....................SPoles(Uend, Vend) For the double array the row indice corresponds to the parametric U direction and the columns indice corresponds to the parametric V direction. The weights are defaulted to all being 1.

	Geom_BezierSurface (const Geom_BezierSurface &theOther)
	Copy constructor for optimized copying without validation.

bool	HasEvalRepresentation () const
	Returns true if an evaluation representation is attached.

const occ::handle< GeomEval_RepSurfaceDesc::Base > &	EvalRepresentation () const
	Returns the current evaluation representation descriptor (may be null).

void	SetEvalRepresentation (const occ::handle< GeomEval_RepSurfaceDesc::Base > &theDesc)
	Sets a new evaluation representation. Validates descriptor data and ensures no circular references.

void	ClearEvalRepresentation ()
	Removes the evaluation representation.

	Geom_BezierSurface (const NCollection_Array2< gp_Pnt > &SurfacePoles, const NCollection_Array2< double > &PoleWeights)
	—Purpose Creates a rational Bezier surface with a set of poles and a set of weights. For the double array the row indice corresponds to the parametric U direction and the columns indice corresponds to the parametric V direction. If all the weights are identical the surface is considered as non-rational (the tolerance criterion is Resolution from package gp).

void	ExchangeUV ()
	Exchanges the direction U and V on a Bezier surface As a consequence:

void	Increase (const int UDeg, const int VDeg)
	Increases the degree of this Bezier surface in the two parametric directions.

void	InsertPoleColAfter (const int VIndex, const NCollection_Array1< gp_Pnt > &CPoles)
	Inserts a column of poles. If the surface is rational the weights values associated with CPoles are equal defaulted to 1.

void	InsertPoleColAfter (const int VIndex, const NCollection_Array1< gp_Pnt > &CPoles, const NCollection_Array1< double > &CPoleWeights)
	Inserts a column of poles and weights. If the surface was non-rational it can become rational.

void	InsertPoleColBefore (const int VIndex, const NCollection_Array1< gp_Pnt > &CPoles)
	Inserts a column of poles. If the surface is rational the weights values associated with CPoles are equal defaulted to 1.

void	InsertPoleColBefore (const int VIndex, const NCollection_Array1< gp_Pnt > &CPoles, const NCollection_Array1< double > &CPoleWeights)
	Inserts a column of poles and weights. If the surface was non-rational it can become rational.

void	InsertPoleRowAfter (const int UIndex, const NCollection_Array1< gp_Pnt > &CPoles)
	Inserts a row of poles. If the surface is rational the weights values associated with CPoles are equal defaulted to 1.

void	InsertPoleRowAfter (const int UIndex, const NCollection_Array1< gp_Pnt > &CPoles, const NCollection_Array1< double > &CPoleWeights)
	Inserts a row of poles and weights. If the surface was non-rational it can become rational.

void	InsertPoleRowBefore (const int UIndex, const NCollection_Array1< gp_Pnt > &CPoles)
	Inserts a row of poles. If the surface is rational the weights values associated with CPoles are equal defaulted to 1.

void	InsertPoleRowBefore (const int UIndex, const NCollection_Array1< gp_Pnt > &CPoles, const NCollection_Array1< double > &CPoleWeights)
	Inserts a row of poles and weights. If the surface was non-rational it can become rational.

void	RemovePoleCol (const int VIndex)
	Removes a column of poles. If the surface was rational it can become non-rational.

void	RemovePoleRow (const int UIndex)
	Removes a row of poles. If the surface was rational it can become non-rational.

void	Segment (const double U1, const double U2, const double V1, const double V2)
	Modifies this Bezier surface by segmenting it between U1 and U2 in the u parametric direction, and between V1 and V2 in the v parametric direction. U1, U2, V1, and V2 can be outside the bounds of this surface.

void	SetPole (const int UIndex, const int VIndex, const gp_Pnt &P)
	Modifies a pole value. If the surface is rational the weight of range (UIndex, VIndex) is not modified.

void	SetPole (const int UIndex, const int VIndex, const gp_Pnt &P, const double Weight)
	Substitutes the pole and the weight of range UIndex, VIndex. If the surface <me> is not rational it can become rational. if the surface was rational it can become non-rational.

void	SetPoleCol (const int VIndex, const NCollection_Array1< gp_Pnt > &CPoles)
	Modifies a column of poles. The length of CPoles can be lower but not greater than NbUPoles so you can modify just a part of the column. Raised if VIndex < 1 or VIndex > NbVPoles.

void	SetPoleCol (const int VIndex, const NCollection_Array1< gp_Pnt > &CPoles, const NCollection_Array1< double > &CPoleWeights)
	Modifies a column of poles. If the surface was rational it can become non-rational If the surface was non-rational it can become rational. The length of CPoles can be lower but not greater than NbUPoles so you can modify just a part of the column. Raised if VIndex < 1 or VIndex > NbVPoles.

void	SetPoleRow (const int UIndex, const NCollection_Array1< gp_Pnt > &CPoles)
	Modifies a row of poles. The length of CPoles can be lower but not greater than NbVPoles so you can modify just a part of the row. Raised if UIndex < 1 or UIndex > NbUPoles.

void	SetPoleRow (const int UIndex, const NCollection_Array1< gp_Pnt > &CPoles, const NCollection_Array1< double > &CPoleWeights)
	Modifies a row of poles and weights. If the surface was rational it can become non-rational. If the surface was non-rational it can become rational. The length of CPoles can be lower but not greater than NbVPoles so you can modify just a part of the row. Raised if UIndex < 1 or UIndex > NbUPoles.

void	SetWeight (const int UIndex, const int VIndex, const double Weight)
	Modifies the weight of the pole of range UIndex, VIndex. If the surface was non-rational it can become rational. If the surface was rational it can become non-rational.

void	SetWeightCol (const int VIndex, const NCollection_Array1< double > &CPoleWeights)
	Modifies a column of weights. If the surface was rational it can become non-rational. If the surface was non-rational it can become rational. The length of CPoleWeights can be lower but not greater than NbUPoles. Raised if VIndex < 1 or VIndex > NbVPoles.

void	SetWeightRow (const int UIndex, const NCollection_Array1< double > &CPoleWeights)
	Modifies a row of weights. If the surface was rational it can become non-rational. If the surface was non-rational it can become rational. The length of CPoleWeights can be lower but not greater than NbVPoles. Raised if UIndex < 1 or UIndex > NbUPoles.

void	UReverse () final
	Changes the orientation of this Bezier surface in the u parametric direction. The bounds of the surface are not changed, but the given parametric direction is reversed. Hence, the orientation of the surface is reversed.

double	UReversedParameter (const double U) const final
	Computes the u (or v) parameter on the modified surface, produced by reversing its u (or v) parametric direction, for any point of u parameter U (or of v parameter V) on this Bezier surface. In the case of a Bezier surface, these functions return respectively:

void	VReverse () final
	Changes the orientation of this Bezier surface in the v parametric direction. The bounds of the surface are not changed, but the given parametric direction is reversed. Hence, the orientation of the surface is reversed.

double	VReversedParameter (const double V) const final
	Computes the u (or v) parameter on the modified surface, produced by reversing its u (or v) parametric direction, for any point of u parameter U (or of v parameter V) on this Bezier surface. In the case of a Bezier surface, these functions return respectively:

void	Bounds (double &U1, double &U2, double &V1, double &V2) const final
	Returns the parametric bounds U1, U2, V1 and V2 of this Bezier surface. In the case of a Bezier surface, this function returns U1 = 0, V1 = 0, U2 = 1, V2 = 1.

GeomAbs_Shape	Continuity () const final
	Returns the continuity of the surface CN : the order of continuity is infinite.

gp_Pnt	EvalD0 (const double U, const double V) const final
	Computes the point of parameter (U, V) on the surface. Raises an exception on failure.

Geom_Surface::ResD1	EvalD1 (const double U, const double V) const final
	Computes the point and first partial derivatives at (U, V). Raises an exception if the surface continuity is not C1.

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). Raises an exception if the surface continuity is not C2.

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). Note: The parameters U and V can be outside the bounds of the surface. Raises an exception if the surface continuity is not C3.

gp_Vec	EvalDN (const double U, const double V, const int Nu, const int Nv) const final
	Computes the derivative of order Nu in the u parametric direction, and Nv in the v parametric direction, at the point of parameters (U, V) of this Bezier surface. Note: The parameters U and V can be outside the bounds of the surface. Raises an exception on failure. Exceptions Standard_RangeError if:

int	NbUPoles () const
	Returns the number of poles in the U direction.

int	NbVPoles () const
	Returns the number of poles in the V direction.

const gp_Pnt &	Pole (const int UIndex, const int VIndex) const
	Returns the pole of range UIndex, VIndex Raised if UIndex < 1 or UIndex > NbUPoles, or VIndex < 1 or VIndex > NbVPoles.

void	Poles (NCollection_Array2< gp_Pnt > &P) const
	Returns the poles of the Bezier surface.

const NCollection_Array2< gp_Pnt > &	Poles () const
	Returns the poles of the Bezier surface.

int	UDegree () const
	Returns the degree of the surface in the U direction it is NbUPoles - 1.

occ::handle< Geom_Curve >	UIso (const double U) const final
	Computes the U isoparametric curve. For a Bezier surface the UIso curve is a Bezier curve.

int	VDegree () const
	Returns the degree of the surface in the V direction it is NbVPoles - 1.

occ::handle< Geom_Curve >	VIso (const double V) const final
	Computes the V isoparametric curve. For a Bezier surface the VIso curve is a Bezier curve.

double	Weight (const int UIndex, const int VIndex) const
	Returns the weight of range UIndex, VIndex.

void	Weights (NCollection_Array2< double > &W) const
	Returns the weights of the Bezier surface.

const NCollection_Array2< double > *	Weights () const
	Returns the weights of the Bezier surface.

const NCollection_Array2< double > &	WeightsArray () const
	Returns a const reference to the weights array. For rational surfaces: the internal owning weights array. For non-rational surfaces: a non-owning view of unit weights from BSplSLib. The array is always sized to match NbUPoles() x NbVPoles().

bool	IsUClosed () const final
	Returns True if the first control points row and the last control points row are identical. The tolerance criterion is Resolution from package gp.

bool	IsVClosed () const final
	Returns True if the first control points column and the last control points column are identical. The tolerance criterion is Resolution from package gp.

bool	IsCNu (const int N) const final
	Returns True, a Bezier surface is always CN.

bool	IsCNv (const int N) const final
	Returns True, a BezierSurface is always CN.

bool	IsUPeriodic () const final
	Returns False.

bool	IsVPeriodic () const final
	Returns False.

bool	IsURational () const
	Returns False if the weights are identical in the U direction, The tolerance criterion is Resolution from package gp. Example : \|1.0, 1.0, 1.0\| if Weights = \|0.5, 0.5, 0.5\| returns False \|2.0, 2.0, 2.0\|.

bool	IsVRational () const
	Returns False if the weights are identical in the V direction, The tolerance criterion is Resolution from package gp. Example : \|1.0, 2.0, 0.5\| if Weights = \|1.0, 2.0, 0.5\| returns False \|1.0, 2.0, 0.5\|.

void	Transform (const gp_Trsf &T) final
	Applies the transformation T to this Bezier surface.

void	Resolution (const double Tolerance3D, double &UTolerance, double &VTolerance)
	Computes two tolerance values for this Bezier surface, based on the given tolerance in 3D space Tolerance3D. The tolerances computed are:

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

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

const NCollection_Array1< double > &	UKnots () const
	Returns Bezier knots {0.0, 1.0} as a static array.

const NCollection_Array1< double > &	VKnots () const
	Returns Bezier knots {0.0, 1.0} as a static array.

const NCollection_Array1< int > &	UMultiplicities () const
	Returns Bezier multiplicities for the U degree.

const NCollection_Array1< int > &	VMultiplicities () const
	Returns Bezier multiplicities for the V degree.

const NCollection_Array1< double > &	UKnotSequence () const
	Returns Bezier flat knots for the U degree.

const NCollection_Array1< double > &	VKnotSequence () const
	Returns Bezier flat knots for the V degree.

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.

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.

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.

Static Public Member Functions
static int	MaxDegree ()
	Returns the value of the maximum polynomial degree of a Bezier surface. This value is 25.

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.

Protected Member Functions
void	init (const NCollection_Array2< gp_Pnt > &thePoles, const NCollection_Array2< double > *theWeights)
	Set poles to thePoles, weights to theWeights. If theWeights is null the surface is non rational. Update rational flags.

Additional Inherited Members
Public Types inherited from Standard_Transient
typedef void	base_type
	Returns a type descriptor about this object.

Detailed Description

Describes a rational or non-rational Bezier surface.

A non-rational Bezier surface is defined by a table of poles (also known as control points).
A rational Bezier surface is defined by a table of poles with varying associated weights. This data is manipulated using two associative 2D arrays:
the poles table, which is a 2D array of gp_Pnt, and
the weights table, which is a 2D array of reals. The bounds of these arrays are:
1 and NbUPoles for the row bounds, where NbUPoles is the number of poles of the surface in the u parametric direction, and
1 and NbVPoles for the column bounds, where NbVPoles is the number of poles of the surface in the v parametric direction. The poles of the surface, the "control points", are the points used to shape and reshape the surface. They comprise a rectangular network of points:
The points (1, 1), (NbUPoles, 1), (1, NbVPoles) and (NbUPoles, NbVPoles) are the four parametric "corners" of the surface.
The first column of poles and the last column of poles define two Bezier curves which delimit the surface in the v parametric direction. These are the v isoparametric curves corresponding to values 0 and 1 of the v parameter.
The first row of poles and the last row of poles define two Bezier curves which delimit the surface in the u parametric direction. These are the u isoparametric curves corresponding to values 0 and 1 of the u parameter. It is more difficult to define a geometrical significance for the weights. However they are useful for representing a quadric surface precisely. Moreover, if the weights of all the poles are equal, the surface has a polynomial equation, and hence is a "non-rational surface". The non-rational surface is a special, but frequently used, case, where all poles have identical weights. The weights are defined and used only in the case of a rational surface. This rational characteristic is defined in each parametric direction. Hence, a surface can be rational in the u parametric direction, and non-rational in the v parametric direction. Likewise, the degree of a surface is defined in each parametric direction. The degree of a Bezier surface in a given parametric direction is equal to the number of poles of the surface in that parametric direction, minus 1. This must be greater than or equal to 1. However, the degree for a Geom_BezierSurface is limited to a value of (25) which is defined and controlled by the system. This value is returned by the function MaxDegree. The parameter range for a Bezier surface is [ 0, 1 ] in the two parametric directions. A Bezier surface can also be closed, or open, in each parametric direction. If the first row of poles is identical to the last row of poles, the surface is closed in the u parametric direction. If the first column of poles is identical to the last column of poles, the surface is closed in the v parametric direction. The continuity of a Bezier surface is infinite in the u parametric direction and the in v parametric direction. Note: It is not possible to build a Bezier surface with negative weights. Any weight value that is less than, or equal to, gp::Resolution() is considered to be zero. Two weight values, W1 and W2, are considered equal if: |W2-W1| <= gp::Resolution()

Constructor & Destructor Documentation

◆ Geom_BezierSurface() [1/3]

Geom_BezierSurface::Geom_BezierSurface ( const NCollection_Array2< gp_Pnt > & SurfacePoles )

Creates a non-rational Bezier surface with a set of poles. Control points representation : SPoles(Uorigin,Vorigin) ...................SPoles(Uorigin,Vend) . . . . SPoles(Uend, Vorigin) .....................SPoles(Uend, Vend) For the double array the row indice corresponds to the parametric U direction and the columns indice corresponds to the parametric V direction. The weights are defaulted to all being 1.

Raised if the number of poles of the surface is lower than 2 or greater than MaxDegree + 1 in one of the two directions U or V.

◆ Geom_BezierSurface() [2/3]

Geom_BezierSurface::Geom_BezierSurface ( const Geom_BezierSurface & theOther )

Copy constructor for optimized copying without validation.

Parameters

[in] theOther the Bezier surface to copy from

◆ Geom_BezierSurface() [3/3]

Geom_BezierSurface::Geom_BezierSurface	(	const NCollection_Array2< gp_Pnt > &	SurfacePoles,
		const NCollection_Array2< double > &	PoleWeights )

—Purpose Creates a rational Bezier surface with a set of poles and a set of weights. For the double array the row indice corresponds to the parametric U direction and the columns indice corresponds to the parametric V direction. If all the weights are identical the surface is considered as non-rational (the tolerance criterion is Resolution from package gp).

Raised if SurfacePoles and PoleWeights have not the same Rowlength or have not the same ColLength. Raised if PoleWeights (i, j) <= Resolution from gp; Raised if the number of poles of the surface is lower than 2 or greater than MaxDegree + 1 in one of the two directions U or V.

Member Function Documentation

◆ Bounds()

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

finalvirtual

Returns the parametric bounds U1, U2, V1 and V2 of this Bezier surface. In the case of a Bezier surface, this function returns U1 = 0, V1 = 0, U2 = 1, V2 = 1.

Implements Geom_Surface.

◆ ClearEvalRepresentation()

void Geom_BezierSurface::ClearEvalRepresentation ( )

inline

Removes the evaluation representation.

◆ Continuity()

GeomAbs_Shape Geom_BezierSurface::Continuity ( ) const

finalvirtual

Returns the continuity of the surface CN : the order of continuity is infinite.

Implements Geom_Surface.

◆ Copy()

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

finalvirtual

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

Implements Geom_Geometry.

◆ DumpJson()

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

finalvirtual

Dumps the content of me into the stream.

Reimplemented from Geom_Geometry.

◆ EvalD0()

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

finalvirtual

Computes the point of parameter (U, V) on the surface. Raises an exception on failure.

Implements Geom_Surface.

◆ EvalD1()

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

finalvirtual

Computes the point and first partial derivatives at (U, V). Raises an exception if the surface continuity is not C1.

Implements Geom_Surface.

◆ EvalD2()

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

finalvirtual

Computes the point and partial derivatives up to 2nd order at (U, V). Raises an exception if the surface continuity is not C2.

Implements Geom_Surface.

◆ EvalD3()

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

finalvirtual

Computes the point and partial derivatives up to 3rd order at (U, V). Note: The parameters U and V can be outside the bounds of the surface. Raises an exception if the surface continuity is not C3.

Implements Geom_Surface.

◆ EvalDN()

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

finalvirtual

Computes the derivative of order Nu in the u parametric direction, and Nv in the v parametric direction, at the point of parameters (U, V) of this Bezier surface. Note: The parameters U and V can be outside the bounds of the surface. Raises an exception on failure. Exceptions Standard_RangeError if:

Nu + Nv is less than 1, or Nu or Nv is negative.

Implements Geom_Surface.

◆ EvalRepresentation()

const occ::handle< GeomEval_RepSurfaceDesc::Base > & Geom_BezierSurface::EvalRepresentation ( ) const

inline

Returns the current evaluation representation descriptor (may be null).

◆ ExchangeUV()

void Geom_BezierSurface::ExchangeUV ( )

Exchanges the direction U and V on a Bezier surface As a consequence:

the poles and weights tables are transposed,
degrees, rational characteristics and so on are exchanged between the two parametric directions, and
the orientation of the surface is reversed.

◆ HasEvalRepresentation()

bool Geom_BezierSurface::HasEvalRepresentation ( ) const

inline

Returns true if an evaluation representation is attached.

◆ Increase()

void Geom_BezierSurface::Increase	(	const int	UDeg,
		const int	VDeg )

Increases the degree of this Bezier surface in the two parametric directions.

Raised if UDegree < UDegree <me> or VDegree < VDegree <me> Raised if the degree of the surface is greater than MaxDegree in one of the two directions U or V.

◆ init()

void Geom_BezierSurface::init	(	const NCollection_Array2< gp_Pnt > &	thePoles,
		const NCollection_Array2< double > *	theWeights )

protected

Set poles to thePoles, weights to theWeights. If theWeights is null the surface is non rational. Update rational flags.

◆ InsertPoleColAfter() [1/2]

void Geom_BezierSurface::InsertPoleColAfter	(	const int	VIndex,
		const NCollection_Array1< gp_Pnt > &	CPoles )

Inserts a column of poles. If the surface is rational the weights values associated with CPoles are equal defaulted to 1.

Raised if Vindex < 1 or VIndex > NbVPoles.

raises if VDegree is greater than MaxDegree. raises if the Length of CPoles is not equal to NbUPoles

◆ InsertPoleColAfter() [2/2]

void Geom_BezierSurface::InsertPoleColAfter	(	const int	VIndex,
		const NCollection_Array1< gp_Pnt > &	CPoles,
		const NCollection_Array1< double > &	CPoleWeights )

Inserts a column of poles and weights. If the surface was non-rational it can become rational.

Raised if Vindex < 1 or VIndex > NbVPoles. Raised if . VDegree is greater than MaxDegree. . the Length of CPoles is not equal to NbUPoles . a weight value is lower or equal to Resolution from package gp

◆ InsertPoleColBefore() [1/2]

void Geom_BezierSurface::InsertPoleColBefore	(	const int	VIndex,
		const NCollection_Array1< gp_Pnt > &	CPoles )

Inserts a column of poles. If the surface is rational the weights values associated with CPoles are equal defaulted to 1.

Raised if Vindex < 1 or VIndex > NbVPoles.

Raised if VDegree is greater than MaxDegree. Raised if the Length of CPoles is not equal to NbUPoles

◆ InsertPoleColBefore() [2/2]

void Geom_BezierSurface::InsertPoleColBefore	(	const int	VIndex,
		const NCollection_Array1< gp_Pnt > &	CPoles,
		const NCollection_Array1< double > &	CPoleWeights )

Inserts a column of poles and weights. If the surface was non-rational it can become rational.

Raised if Vindex < 1 or VIndex > NbVPoles. Raised if : . VDegree is greater than MaxDegree. . the Length of CPoles is not equal to NbUPoles . a weight value is lower or equal to Resolution from package gp

◆ InsertPoleRowAfter() [1/2]

void Geom_BezierSurface::InsertPoleRowAfter	(	const int	UIndex,
		const NCollection_Array1< gp_Pnt > &	CPoles )

Inserts a row of poles. If the surface is rational the weights values associated with CPoles are equal defaulted to 1.

Raised if Uindex < 1 or UIndex > NbUPoles.

Raised if UDegree is greater than MaxDegree. Raised if the Length of CPoles is not equal to NbVPoles

◆ InsertPoleRowAfter() [2/2]

void Geom_BezierSurface::InsertPoleRowAfter	(	const int	UIndex,
		const NCollection_Array1< gp_Pnt > &	CPoles,
		const NCollection_Array1< double > &	CPoleWeights )

Inserts a row of poles and weights. If the surface was non-rational it can become rational.

Raised if Uindex < 1 or UIndex > NbUPoles. Raised if : . UDegree is greater than MaxDegree. . the Length of CPoles is not equal to NbVPoles . a weight value is lower or equal to Resolution from package gp

◆ InsertPoleRowBefore() [1/2]

void Geom_BezierSurface::InsertPoleRowBefore	(	const int	UIndex,
		const NCollection_Array1< gp_Pnt > &	CPoles )

Inserts a row of poles. If the surface is rational the weights values associated with CPoles are equal defaulted to 1.

Raised if Uindex < 1 or UIndex > NbUPoles.

Raised if UDegree is greater than MaxDegree. Raised if the Length of CPoles is not equal to NbVPoles

◆ InsertPoleRowBefore() [2/2]

void Geom_BezierSurface::InsertPoleRowBefore	(	const int	UIndex,
		const NCollection_Array1< gp_Pnt > &	CPoles,
		const NCollection_Array1< double > &	CPoleWeights )

Inserts a row of poles and weights. If the surface was non-rational it can become rational.

Raised if Uindex < 1 or UIndex > NbUPoles. Raised if : . UDegree is greater than MaxDegree. . the Length of CPoles is not equal to NbVPoles . a weight value is lower or equal to Resolution from package gp

◆ IsCNu()

bool Geom_BezierSurface::IsCNu ( const int N ) const

finalvirtual

Returns True, a Bezier surface is always CN.

Implements Geom_Surface.

◆ IsCNv()

bool Geom_BezierSurface::IsCNv ( const int N ) const

finalvirtual

Returns True, a BezierSurface is always CN.

Implements Geom_Surface.

◆ IsUClosed()

bool Geom_BezierSurface::IsUClosed ( ) const

finalvirtual

Returns True if the first control points row and the last control points row are identical. The tolerance criterion is Resolution from package gp.

Implements Geom_Surface.

◆ IsUPeriodic()

bool Geom_BezierSurface::IsUPeriodic ( ) const

finalvirtual

Returns False.

Implements Geom_Surface.

◆ IsURational()

bool Geom_BezierSurface::IsURational ( ) const

Returns False if the weights are identical in the U direction, The tolerance criterion is Resolution from package gp. Example : |1.0, 1.0, 1.0| if Weights = |0.5, 0.5, 0.5| returns False |2.0, 2.0, 2.0|.

◆ IsVClosed()

bool Geom_BezierSurface::IsVClosed ( ) const

finalvirtual

Returns True if the first control points column and the last control points column are identical. The tolerance criterion is Resolution from package gp.

Implements Geom_Surface.

◆ IsVPeriodic()

bool Geom_BezierSurface::IsVPeriodic ( ) const

finalvirtual

Returns False.

Implements Geom_Surface.

◆ IsVRational()

bool Geom_BezierSurface::IsVRational ( ) const

Returns False if the weights are identical in the V direction, The tolerance criterion is Resolution from package gp. Example : |1.0, 2.0, 0.5| if Weights = |1.0, 2.0, 0.5| returns False |1.0, 2.0, 0.5|.

◆ MaxDegree()

static int Geom_BezierSurface::MaxDegree ( )

static

Returns the value of the maximum polynomial degree of a Bezier surface. This value is 25.

◆ NbUPoles()

int Geom_BezierSurface::NbUPoles ( ) const

Returns the number of poles in the U direction.

◆ NbVPoles()

int Geom_BezierSurface::NbVPoles ( ) const

Returns the number of poles in the V direction.

◆ Pole()

const gp_Pnt & Geom_BezierSurface::Pole	(	const int	UIndex,
		const int	VIndex ) const

Returns the pole of range UIndex, VIndex Raised if UIndex < 1 or UIndex > NbUPoles, or VIndex < 1 or VIndex > NbVPoles.

◆ Poles() [1/2]

const NCollection_Array2< gp_Pnt > & Geom_BezierSurface::Poles ( ) const

inline

Returns the poles of the Bezier surface.

◆ Poles() [2/2]

void Geom_BezierSurface::Poles ( NCollection_Array2< gp_Pnt > & P ) const

Returns the poles of the Bezier surface.

Raised if the length of P in the U an V direction is not equal to NbUPoles and NbVPoles.

Deprecated: ("use Poles() returning const reference instead")

◆ RemovePoleCol()

void Geom_BezierSurface::RemovePoleCol ( const int VIndex )

Removes a column of poles. If the surface was rational it can become non-rational.

Raised if NbVPoles <= 2 after removing, a Bezier surface must have at least two columns of poles. Raised if Vindex < 1 or VIndex > NbVPoles

◆ RemovePoleRow()

void Geom_BezierSurface::RemovePoleRow ( const int UIndex )

Removes a row of poles. If the surface was rational it can become non-rational.

Raised if NbUPoles <= 2 after removing, a Bezier surface must have at least two rows of poles. Raised if Uindex < 1 or UIndex > NbUPoles

◆ Resolution()

void Geom_BezierSurface::Resolution	(	const double	Tolerance3D,
		double &	UTolerance,
		double &	VTolerance )

Computes two tolerance values for this Bezier surface, based on the given tolerance in 3D space Tolerance3D. The tolerances computed are:

UTolerance in the u parametric direction, and
VTolerance in the v parametric direction. If f(u,v) is the equation of this Bezier surface, UTolerance and VTolerance guarantee that: | u1 - u0 | < UTolerance and | v1 - v0 | < VTolerance ====> |f (u1,v1) - f (u0,v0)| < Tolerance3D

◆ Segment()

void Geom_BezierSurface::Segment	(	const double	U1,
		const double	U2,
		const double	V1,
		const double	V2 )

Modifies this Bezier surface by segmenting it between U1 and U2 in the u parametric direction, and between V1 and V2 in the v parametric direction. U1, U2, V1, and V2 can be outside the bounds of this surface.

U1 and U2 isoparametric Bezier curves, segmented between V1 and V2, become the two bounds of the surface in the v parametric direction (0. and 1. u isoparametric curves).
V1 and V2 isoparametric Bezier curves, segmented between U1 and U2, become the two bounds of the surface in the u parametric direction (0. and 1. v isoparametric curves). The poles and weights tables are modified, but the degree of this surface in the u and v parametric directions does not change. U1 can be greater than U2, and V1 can be greater than V2. In these cases, the corresponding parametric direction is inverted. The orientation of the surface is inverted if one (and only one) parametric direction is inverted.

◆ SetEvalRepresentation()

void Geom_BezierSurface::SetEvalRepresentation ( const occ::handle< GeomEval_RepSurfaceDesc::Base > & theDesc )

Sets a new evaluation representation. Validates descriptor data and ensures no circular references.

◆ SetPole() [1/2]

void Geom_BezierSurface::SetPole	(	const int	UIndex,
		const int	VIndex,
		const gp_Pnt &	P )

Modifies a pole value. If the surface is rational the weight of range (UIndex, VIndex) is not modified.

Raised if UIndex < 1 or UIndex > NbUPoles or VIndex < 1 or VIndex > NbVPoles.

◆ SetPole() [2/2]

void Geom_BezierSurface::SetPole	(	const int	UIndex,
		const int	VIndex,
		const gp_Pnt &	P,
		const double	Weight )

Substitutes the pole and the weight of range UIndex, VIndex. If the surface <me> is not rational it can become rational. if the surface was rational it can become non-rational.

raises if UIndex < 1 or UIndex > NbUPoles or VIndex < 1 or VIndex > NbVPoles. Raised if Weight <= Resolution from package gp.

◆ SetPoleCol() [1/2]

void Geom_BezierSurface::SetPoleCol	(	const int	VIndex,
		const NCollection_Array1< gp_Pnt > &	CPoles )

Modifies a column of poles. The length of CPoles can be lower but not greater than NbUPoles so you can modify just a part of the column. Raised if VIndex < 1 or VIndex > NbVPoles.

Raised if CPoles.Lower() < 1 or CPoles.Upper() > NbUPoles

◆ SetPoleCol() [2/2]

void Geom_BezierSurface::SetPoleCol	(	const int	VIndex,
		const NCollection_Array1< gp_Pnt > &	CPoles,
		const NCollection_Array1< double > &	CPoleWeights )

Modifies a column of poles. If the surface was rational it can become non-rational If the surface was non-rational it can become rational. The length of CPoles can be lower but not greater than NbUPoles so you can modify just a part of the column. Raised if VIndex < 1 or VIndex > NbVPoles.

Raised if CPoles.Lower() < 1 or CPoles.Upper() > NbUPoles Raised if CPoleWeights and CPoles have not the same bounds. Raised if one of the weight value CPoleWeights (i) is lower or equal to Resolution from package gp.

◆ SetPoleRow() [1/2]

void Geom_BezierSurface::SetPoleRow	(	const int	UIndex,
		const NCollection_Array1< gp_Pnt > &	CPoles )

Modifies a row of poles. The length of CPoles can be lower but not greater than NbVPoles so you can modify just a part of the row. Raised if UIndex < 1 or UIndex > NbUPoles.

Raised if CPoles.Lower() < 1 or CPoles.Upper() > NbVPoles

◆ SetPoleRow() [2/2]

void Geom_BezierSurface::SetPoleRow	(	const int	UIndex,
		const NCollection_Array1< gp_Pnt > &	CPoles,
		const NCollection_Array1< double > &	CPoleWeights )

Modifies a row of poles and weights. If the surface was rational it can become non-rational. If the surface was non-rational it can become rational. The length of CPoles can be lower but not greater than NbVPoles so you can modify just a part of the row. Raised if UIndex < 1 or UIndex > NbUPoles.

Raised if CPoles.Lower() < 1 or CPoles.Upper() > NbVPoles Raised if CPoleWeights and CPoles have not the same bounds. Raised if one of the weight value CPoleWeights (i) is lower or equal to Resolution from gp.

◆ SetWeight()

void Geom_BezierSurface::SetWeight	(	const int	UIndex,
		const int	VIndex,
		const double	Weight )

Modifies the weight of the pole of range UIndex, VIndex. If the surface was non-rational it can become rational. If the surface was rational it can become non-rational.

Raised if UIndex < 1 or UIndex > NbUPoles or VIndex < 1 or VIndex > NbVPoles. Raised if Weight <= Resolution from package gp.

◆ SetWeightCol()

void Geom_BezierSurface::SetWeightCol	(	const int	VIndex,
		const NCollection_Array1< double > &	CPoleWeights )

Modifies a column of weights. If the surface was rational it can become non-rational. If the surface was non-rational it can become rational. The length of CPoleWeights can be lower but not greater than NbUPoles. Raised if VIndex < 1 or VIndex > NbVPoles.

Raised if CPoleWeights.Lower() < 1 or CPoleWeights.Upper() > NbUPoles Raised if one of the weight value CPoleWeights (i) is lower or equal to Resolution from package gp.

◆ SetWeightRow()

void Geom_BezierSurface::SetWeightRow	(	const int	UIndex,
		const NCollection_Array1< double > &	CPoleWeights )

Modifies a row of weights. If the surface was rational it can become non-rational. If the surface was non-rational it can become rational. The length of CPoleWeights can be lower but not greater than NbVPoles. Raised if UIndex < 1 or UIndex > NbUPoles.

Raised if CPoleWeights.Lower() < 1 or CPoleWeights.Upper() > NbVPoles Raised if one of the weight value CPoleWeights (i) is lower or equal to Resolution from package gp.

◆ Transform()

void Geom_BezierSurface::Transform ( const gp_Trsf & T )

finalvirtual

Applies the transformation T to this Bezier surface.

Implements Geom_Geometry.

◆ UDegree()

int Geom_BezierSurface::UDegree ( ) const

Returns the degree of the surface in the U direction it is NbUPoles - 1.

◆ UIso()

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

finalvirtual

Computes the U isoparametric curve. For a Bezier surface the UIso curve is a Bezier curve.

Implements Geom_Surface.

◆ UKnots()

const NCollection_Array1< double > & Geom_BezierSurface::UKnots ( ) const

Returns Bezier knots {0.0, 1.0} as a static array.

◆ UKnotSequence()

const NCollection_Array1< double > & Geom_BezierSurface::UKnotSequence ( ) const

Returns Bezier flat knots for the U degree.

◆ UMultiplicities()

const NCollection_Array1< int > & Geom_BezierSurface::UMultiplicities ( ) const

Returns Bezier multiplicities for the U degree.

◆ UReverse()

void Geom_BezierSurface::UReverse ( )

finalvirtual

Changes the orientation of this Bezier surface in the u parametric direction. The bounds of the surface are not changed, but the given parametric direction is reversed. Hence, the orientation of the surface is reversed.

Implements Geom_Surface.

◆ UReversedParameter()

double Geom_BezierSurface::UReversedParameter ( const double U ) const

finalvirtual

Computes the u (or v) parameter on the modified surface, produced by reversing its u (or v) parametric direction, for any point of u parameter U (or of v parameter V) on this Bezier surface. In the case of a Bezier surface, these functions return respectively:

1.-U, or 1.-V.

Implements Geom_Surface.

◆ VDegree()

int Geom_BezierSurface::VDegree ( ) const

Returns the degree of the surface in the V direction it is NbVPoles - 1.

◆ VIso()

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

finalvirtual

Computes the V isoparametric curve. For a Bezier surface the VIso curve is a Bezier curve.

Implements Geom_Surface.

◆ VKnots()

const NCollection_Array1< double > & Geom_BezierSurface::VKnots ( ) const

Returns Bezier knots {0.0, 1.0} as a static array.

◆ VKnotSequence()

const NCollection_Array1< double > & Geom_BezierSurface::VKnotSequence ( ) const

Returns Bezier flat knots for the V degree.

◆ VMultiplicities()

const NCollection_Array1< int > & Geom_BezierSurface::VMultiplicities ( ) const

Returns Bezier multiplicities for the V degree.

◆ VReverse()

void Geom_BezierSurface::VReverse ( )

finalvirtual

Changes the orientation of this Bezier surface in the v parametric direction. The bounds of the surface are not changed, but the given parametric direction is reversed. Hence, the orientation of the surface is reversed.

Implements Geom_Surface.

◆ VReversedParameter()

double Geom_BezierSurface::VReversedParameter ( const double V ) const

finalvirtual

Computes the u (or v) parameter on the modified surface, produced by reversing its u (or v) parametric direction, for any point of u parameter U (or of v parameter V) on this Bezier surface. In the case of a Bezier surface, these functions return respectively:

1.-U, or 1.-V.

Implements Geom_Surface.

◆ Weight()

double Geom_BezierSurface::Weight	(	const int	UIndex,
		const int	VIndex ) const

Returns the weight of range UIndex, VIndex.

Raised if UIndex < 1 or UIndex > NbUPoles, or VIndex < 1 or VIndex > NbVPoles.

◆ Weights() [1/2]

const NCollection_Array2< double > * Geom_BezierSurface::Weights ( ) const

inline

Returns the weights of the Bezier surface.

◆ Weights() [2/2]

void Geom_BezierSurface::Weights ( NCollection_Array2< double > & W ) const

Returns the weights of the Bezier surface.

Raised if the length of W in the U an V direction is not equal to NbUPoles and NbVPoles.

Deprecated: ("use Weights() returning const pointer instead")

◆ WeightsArray()

const NCollection_Array2< double > & Geom_BezierSurface::WeightsArray ( ) const

inline

Returns a const reference to the weights array. For rational surfaces: the internal owning weights array. For non-rational surfaces: a non-owning view of unit weights from BSplSLib. The array is always sized to match NbUPoles() x NbVPoles().

Warning: Do NOT modify elements through the returned reference.

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

Geom_BezierSurface.hxx

Public Member Functions

Static Public Member Functions

Protected Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ Geom_BezierSurface() [1/3]

◆ Geom_BezierSurface() [2/3]

◆ Geom_BezierSurface() [3/3]

Member Function Documentation

◆ Bounds()

◆ ClearEvalRepresentation()

◆ Continuity()

◆ Copy()

◆ DumpJson()

◆ EvalD0()

◆ EvalD1()

◆ EvalD2()

◆ EvalD3()

◆ EvalDN()

◆ EvalRepresentation()

◆ ExchangeUV()

◆ HasEvalRepresentation()

◆ Increase()

◆ init()

◆ InsertPoleColAfter() [1/2]

◆ InsertPoleColAfter() [2/2]

◆ InsertPoleColBefore() [1/2]

◆ InsertPoleColBefore() [2/2]

◆ InsertPoleRowAfter() [1/2]

◆ InsertPoleRowAfter() [2/2]

◆ InsertPoleRowBefore() [1/2]

◆ InsertPoleRowBefore() [2/2]

◆ IsCNu()

◆ IsCNv()

◆ IsUClosed()

◆ IsUPeriodic()

◆ IsURational()

◆ IsVClosed()

◆ IsVPeriodic()

◆ IsVRational()

◆ MaxDegree()

◆ NbUPoles()

◆ NbVPoles()

◆ Pole()

◆ Poles() [1/2]

◆ Poles() [2/2]

◆ RemovePoleCol()

◆ RemovePoleRow()

◆ Resolution()

◆ Segment()

◆ SetEvalRepresentation()

◆ SetPole() [1/2]

◆ SetPole() [2/2]

◆ SetPoleCol() [1/2]

◆ SetPoleCol() [2/2]

◆ SetPoleRow() [1/2]

◆ SetPoleRow() [2/2]

◆ SetWeight()

◆ SetWeightCol()

◆ SetWeightRow()

◆ Transform()

◆ UDegree()

◆ UIso()

◆ UKnots()

◆ UKnotSequence()

◆ UMultiplicities()

◆ UReverse()

◆ UReversedParameter()

◆ VDegree()

◆ VIso()

◆ VKnots()

◆ VKnotSequence()

◆ VMultiplicities()

◆ VReverse()

◆ VReversedParameter()

◆ Weight()

◆ Weights() [1/2]

◆ Weights() [2/2]

◆ WeightsArray()