Geom_BSplineSurface Class Reference

Describes a BSpline surface. In each parametric direction, a BSpline surface can be: More...

#include <Geom_BSplineSurface.hxx>

Inheritance diagram for Geom_BSplineSurface:

Public Member Functions
	Geom_BSplineSurface (const NCollection_Array2< gp_Pnt > &Poles, const NCollection_Array1< double > &UKnots, const NCollection_Array1< double > &VKnots, const NCollection_Array1< int > &UMults, const NCollection_Array1< int > &VMults, const int UDegree, const int VDegree, const bool UPeriodic=false, const bool VPeriodic=false)
	Creates a non-rational b-spline surface (weights default value is 1.). The following conditions must be verified. 0 < UDegree <= MaxDegree. UKnots.Length() == UMults.Length() >= 2 UKnots(i) < UKnots(i+1) (Knots are increasing) 1 <= UMults(i) <= UDegree On a non uperiodic surface the first and last umultiplicities may be UDegree+1 (this is even recommended if you want the curve to start and finish on the first and last pole). On a uperiodic surface the first and the last umultiplicities must be the same. on non-uperiodic surfaces Poles.ColLength() == Sum(UMults(i)) - UDegree - 1 >= 2 on uperiodic surfaces Poles.ColLength() == Sum(UMults(i)) except the first or last The previous conditions for U holds also for V, with the RowLength of the poles.
	Geom_BSplineSurface (const NCollection_Array2< gp_Pnt > &Poles, const NCollection_Array2< double > &Weights, const NCollection_Array1< double > &UKnots, const NCollection_Array1< double > &VKnots, const NCollection_Array1< int > &UMults, const NCollection_Array1< int > &VMults, const int UDegree, const int VDegree, const bool UPeriodic=false, const bool VPeriodic=false)
	Creates a non-rational b-spline surface (weights default value is 1.).
	Geom_BSplineSurface (const Geom_BSplineSurface &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.
void	ExchangeUV ()
	Exchanges the u and v parametric directions on this BSpline surface. As a consequence:
void	SetUPeriodic ()
	Sets the surface U periodic. Modifies this surface to be periodic in the U parametric direction. To become periodic in a given parametric direction a surface must be closed in that parametric direction, and the knot sequence relative to that direction must be periodic. To generate this periodic sequence of knots, the functions FirstUKnotIndex and LastUKnotIndex are used to compute I1 and I2. These are the indexes, in the knot array associated with the given parametric direction, of the knots that correspond to the first and last parameters of this BSpline surface in the given parametric direction. Hence the period is: Knots(I1) - Knots(I2) As a result, the knots and poles tables are modified. Exceptions Standard_ConstructionError if the surface is not closed in the given parametric direction.
void	SetVPeriodic ()
	Sets the surface V periodic. Modifies this surface to be periodic in the V parametric direction. To become periodic in a given parametric direction a surface must be closed in that parametric direction, and the knot sequence relative to that direction must be periodic. To generate this periodic sequence of knots, the functions FirstVKnotIndex and LastVKnotIndex are used to compute I1 and I2. These are the indexes, in the knot array associated with the given parametric direction, of the knots that correspond to the first and last parameters of this BSpline surface in the given parametric direction. Hence the period is: Knots(I1) - Knots(I2) As a result, the knots and poles tables are modified. Exceptions Standard_ConstructionError if the surface is not closed in the given parametric direction.
void	PeriodicNormalization (double &U, double &V) const
	returns the parameter normalized within the period if the surface is periodic : otherwise does not do anything
void	SetUOrigin (const int Index)
	Assigns the knot of index Index in the knots table in the corresponding parametric direction to be the origin of this periodic BSpline surface. As a consequence, the knots and poles tables are modified. Exceptions Standard_NoSuchObject if this BSpline surface is not periodic in the given parametric direction. Standard_DomainError if Index is outside the bounds of the knots table in the given parametric direction.
void	SetVOrigin (const int Index)
	Assigns the knot of index Index in the knots table in the corresponding parametric direction to be the origin of this periodic BSpline surface. As a consequence, the knots and poles tables are modified. Exceptions Standard_NoSuchObject if this BSpline surface is not periodic in the given parametric direction. Standard_DomainError if Index is outside the bounds of the knots table in the given parametric direction.
void	SetUNotPeriodic ()
	Sets the surface U not periodic. Changes this BSpline surface into a non-periodic surface along U direction. If this surface is already non-periodic, it is not modified. Note: the poles and knots tables are modified.
void	SetVNotPeriodic ()
	Sets the surface V not periodic. Changes this BSpline surface into a non-periodic surface along V direction. If this surface is already non-periodic, it is not modified. Note: the poles and knots tables are modified.
void	UReverse () final
	Changes the orientation of this BSpline 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. The knots and poles tables are modified.
void	VReverse () final
	Changes the orientation of this BSpline 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. The knots and poles tables are modified.
double	UReversedParameter (const double U) const final
	Computes the u parameter on the modified surface, produced by reversing its U parametric direction, for the point of u parameter U, on this BSpline surface. For a BSpline surface, these functions return respectively:
double	VReversedParameter (const double V) const final
	Computes the v parameter on the modified surface, produced by reversing its V parametric direction, for the point of v parameter V on this BSpline surface. For a BSpline surface, these functions return respectively:
void	IncreaseDegree (const int UDegree, const int VDegree)
	Increases the degrees of this BSpline surface to UDegree and VDegree in the u and v parametric directions respectively. As a result, the tables of poles, weights and multiplicities are modified. The tables of knots is not changed. Note: Nothing is done if the given degree is less than or equal to the current degree in the corresponding parametric direction. Exceptions Standard_ConstructionError if UDegree or VDegree is greater than Geom_BSplineSurface::MaxDegree().
void	InsertUKnots (const NCollection_Array1< double > &Knots, const NCollection_Array1< int > &Mults, const double ParametricTolerance=0.0, const bool Add=true)
	Inserts into the knots table for the U parametric direction of this BSpline surface:
void	InsertVKnots (const NCollection_Array1< double > &Knots, const NCollection_Array1< int > &Mults, const double ParametricTolerance=0.0, const bool Add=true)
	Inserts into the knots table for the V parametric direction of this BSpline surface:
bool	RemoveUKnot (const int Index, const int M, const double Tolerance)
	Reduces to M the multiplicity of the knot of index Index in the U parametric direction. If M is 0, the knot is removed. With a modification of this type, the table of poles is also modified. Two different algorithms are used systematically to compute the new poles of the surface. For each pole, the distance between the pole calculated using the first algorithm and the same pole calculated using the second algorithm, is checked. If this distance is less than Tolerance it ensures that the surface is not modified by more than Tolerance. Under these conditions, the function returns true; otherwise, it returns false. A low tolerance prevents modification of the surface. A high tolerance "smoothes" the surface. Exceptions Standard_OutOfRange if Index is outside the bounds of the knots table of this BSpline surface.
bool	RemoveVKnot (const int Index, const int M, const double Tolerance)
	Reduces to M the multiplicity of the knot of index Index in the V parametric direction. If M is 0, the knot is removed. With a modification of this type, the table of poles is also modified. Two different algorithms are used systematically to compute the new poles of the surface. For each pole, the distance between the pole calculated using the first algorithm and the same pole calculated using the second algorithm, is checked. If this distance is less than Tolerance it ensures that the surface is not modified by more than Tolerance. Under these conditions, the function returns true; otherwise, it returns false. A low tolerance prevents modification of the surface. A high tolerance "smoothes" the surface. Exceptions Standard_OutOfRange if Index is outside the bounds of the knots table of this BSpline surface.
void	IncreaseUMultiplicity (const int UIndex, const int M)
	Increases the multiplicity of the knot of range UIndex in the UKnots sequence. M is the new multiplicity. M must be greater than the previous multiplicity and lower or equal to the degree of the surface in the U parametric direction. Raised if M is not in the range [1, UDegree].
void	IncreaseUMultiplicity (const int FromI1, const int ToI2, const int M)
	Increases until order M the multiplicity of the set of knots FromI1,...., ToI2 in the U direction. This method can be used to make a B_spline surface into a PiecewiseBezier B_spline surface. If <me> was uniform, it can become non uniform.
void	IncrementUMultiplicity (const int FromI1, const int ToI2, const int Step)
	Increments the multiplicity of the consecutives uknots FromI1..ToI2 by step. The multiplicity of each knot FromI1,.....,ToI2 must be lower or equal to the UDegree of the B_spline.
void	IncreaseVMultiplicity (const int VIndex, const int M)
	Increases the multiplicity of a knot in the V direction. M is the new multiplicity.
void	IncreaseVMultiplicity (const int FromI1, const int ToI2, const int M)
	Increases until order M the multiplicity of the set of knots FromI1,...., ToI2 in the V direction. This method can be used to make a BSplineSurface into a PiecewiseBezier B_spline surface. If <me> was uniform, it can become non-uniform.
void	IncrementVMultiplicity (const int FromI1, const int ToI2, const int Step)
	Increments the multiplicity of the consecutives vknots FromI1..ToI2 by step. The multiplicity of each knot FromI1,.....,ToI2 must be lower or equal to the VDegree of the B_spline.
void	InsertUKnot (const double U, const int M, const double ParametricTolerance, const bool Add=true)
	Inserts a knot value in the sequence of UKnots. If U is a knot value this method increases the multiplicity of the knot if the previous multiplicity was lower than M else it does nothing. The tolerance criterion is ParametricTolerance. ParametricTolerance should be greater or equal than Resolution from package gp.
void	InsertVKnot (const double V, const int M, const double ParametricTolerance, const bool Add=true)
	Inserts a knot value in the sequence of VKnots. If V is a knot value this method increases the multiplicity of the knot if the previous multiplicity was lower than M otherwise it does nothing. The tolerance criterion is ParametricTolerance. ParametricTolerance should be greater or equal than Resolution from package gp.
void	Segment (const double U1, const double U2, const double V1, const double V2, const double theUTolerance=Precision::PConfusion(), const double theVTolerance=Precision::PConfusion())
	Segments the surface between U1 and U2 in the U-Direction. between V1 and V2 in the V-Direction. The control points are modified, the first and the last point are not the same.
void	CheckAndSegment (const double U1, const double U2, const double V1, const double V2, const double theUTolerance=Precision::PConfusion(), const double theVTolerance=Precision::PConfusion())
	Segments the surface between U1 and U2 in the U-Direction. between V1 and V2 in the V-Direction.
void	SetUKnot (const int UIndex, const double K)
	Substitutes the UKnots of range UIndex with K.
void	SetUKnots (const NCollection_Array1< double > &UK)
	Changes all the U-knots of the surface. The multiplicity of the knots are not modified.
void	SetUKnot (const int UIndex, const double K, const int M)
	Changes the value of the UKnots of range UIndex and increases its multiplicity.
void	SetVKnot (const int VIndex, const double K)
	Substitutes the VKnots of range VIndex with K.
void	SetVKnots (const NCollection_Array1< double > &VK)
	Changes all the V-knots of the surface. The multiplicity of the knots are not modified.
void	SetVKnot (const int VIndex, const double K, const int M)
	Changes the value of the VKnots of range VIndex and increases its multiplicity.
void	LocateU (const double U, const double ParametricTolerance, int &I1, int &I2, const bool WithKnotRepetition=false) const
	Locates the parametric value U in the sequence of UKnots. If "WithKnotRepetition" is True we consider the knot's representation with repetition of multiple knot value, otherwise we consider the knot's representation with no repetition of multiple knot values. UKnots (I1) <= U <= UKnots (I2) . if I1 = I2 U is a knot value (the tolerance criterion ParametricTolerance is used). . if I1 < 1 => U < UKnots(1) - std::abs(ParametricTolerance) . if I2 > NbUKnots => U > UKnots(NbUKnots)+std::abs(ParametricTolerance).
void	LocateV (const double V, const double ParametricTolerance, int &I1, int &I2, const bool WithKnotRepetition=false) const
	Locates the parametric value V in the sequence of knots. If "WithKnotRepetition" is True we consider the knot's representation with repetition of multiple knot value, otherwise we consider the knot's representation with no repetition of multiple knot values. VKnots (I1) <= V <= VKnots (I2) . if I1 = I2 V is a knot value (the tolerance criterion ParametricTolerance is used). . if I1 < 1 => V < VKnots(1) - std::abs(ParametricTolerance) . if I2 > NbVKnots => V > VKnots(NbVKnots)+std::abs(ParametricTolerance) poles insertion and removing The following methods are available only if the surface is Uniform or QuasiUniform in the considered direction The knot repartition is modified.
void	SetPole (const int UIndex, const int VIndex, const gp_Pnt &P)
	Substitutes the pole of range (UIndex, VIndex) with P. 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) with P and W.
void	SetPoleCol (const int VIndex, const NCollection_Array1< gp_Pnt > &CPoles)
	Changes a column of poles or a part of this column. Raised if Vindex < 1 or VIndex > NbVPoles.
void	SetPoleCol (const int VIndex, const NCollection_Array1< gp_Pnt > &CPoles, const NCollection_Array1< double > &CPoleWeights)
	Changes a column of poles or a part of this column with the corresponding weights. If the surface was rational it can become non rational. If the surface was non rational it can become rational. Raised if Vindex < 1 or VIndex > NbVPoles.
void	SetPoleRow (const int UIndex, const NCollection_Array1< gp_Pnt > &CPoles, const NCollection_Array1< double > &CPoleWeights)
	Changes a row of poles or a part of this row with the corresponding weights. If the surface was rational it can become non rational. If the surface was non rational it can become rational. Raised if Uindex < 1 or UIndex > NbUPoles.
void	SetPoleRow (const int UIndex, const NCollection_Array1< gp_Pnt > &CPoles)
	Changes a row of poles or a part of this row. Raised if Uindex < 1 or UIndex > NbUPoles.
void	SetWeight (const int UIndex, const int VIndex, const double Weight)
	Changes 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)
	Changes a column of weights of a part of this column.
void	SetWeightRow (const int UIndex, const NCollection_Array1< double > &CPoleWeights)
	Changes a row of weights or a part of this row.
void	MovePoint (const double U, const double V, const gp_Pnt &P, const int UIndex1, const int UIndex2, const int VIndex1, const int VIndex2, int &UFirstIndex, int &ULastIndex, int &VFirstIndex, int &VLastIndex)
	Move a point with parameter U and V to P. given u,v as parameters) to reach a new position UIndex1, UIndex2, VIndex1, VIndex2: indicates the poles which can be moved if Problem in BSplineBasis calculation, no change for the curve and UFirstIndex, VLastIndex = 0 VFirstIndex, VLastIndex = 0.
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 last control points column are identical. The tolerance criterion is Resolution from package gp.
bool	IsCNu (const int N) const final
	Returns True if the order of continuity of the surface in the U direction is N. Raised if N < 0.
bool	IsCNv (const int N) const final
	Returns True if the order of continuity of the surface in the V direction is N. Raised if N < 0.
bool	IsUPeriodic () const final
	Returns True if the surface is closed in the U direction and if the B-spline has been turned into a periodic surface using the function SetUPeriodic.
bool	IsURational () const
	Returns False if for each row of weights all the weights are identical. 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	IsVPeriodic () const final
	Returns True if the surface is closed in the V direction and if the B-spline has been turned into a periodic surface using the function SetVPeriodic.
bool	IsVRational () const
	Returns False if for each column of weights all the weights are identical. The tolerance criterion is resolution from package gp. Examples : |1.0, 2.0, 0.5| if Weights = |1.0, 2.0, 0.5| returns False |1.0, 2.0, 0.5|.
void	Bounds (double &U1, double &U2, double &V1, double &V2) const final
	Returns the parametric bounds of the surface. Warnings : These parametric values are the bounds of the array of knots UKnots and VKnots only if the first knots and the last knots have a multiplicity equal to UDegree + 1 or VDegree + 1.
GeomAbs_Shape	Continuity () const final
	Returns the continuity of the surface : C0 : only geometric continuity, C1 : continuity of the first derivative all along the Surface, C2 : continuity of the second derivative all along the Surface, C3 : continuity of the third derivative all along the Surface, CN : the order of continuity is infinite. A B-spline surface is infinitely continuously differentiable for the couple of parameters U, V such that U != UKnots(i) and V != VKnots(i). The continuity of the surface at a knot value depends on the multiplicity of this knot. Example : If the surface is C1 in the V direction and C2 in the U direction this function returns Shape = C1.
int	FirstUKnotIndex () const
	Computes the Index of the UKnots which gives the first parametric value of the surface in the U direction. The UIso curve corresponding to this value is a boundary curve of the surface.
int	FirstVKnotIndex () const
	Computes the Index of the VKnots which gives the first parametric value of the surface in the V direction. The VIso curve corresponding to this knot is a boundary curve of the surface.
int	LastUKnotIndex () const
	Computes the Index of the UKnots which gives the last parametric value of the surface in the U direction. The UIso curve corresponding to this knot is a boundary curve of the surface.
int	LastVKnotIndex () const
	Computes the Index of the VKnots which gives the last parametric value of the surface in the V direction. The VIso curve corresponding to this knot is a boundary curve of the surface.
int	NbUKnots () const
	Returns the number of knots in the U direction.
int	NbUPoles () const
	Returns number of poles in the U direction.
int	NbVKnots () const
	Returns the number of knots in the V 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).
void	Poles (NCollection_Array2< gp_Pnt > &P) const
	Returns the poles of the B-spline surface.
const NCollection_Array2< gp_Pnt > &	Poles () const
	Returns the poles of the B-spline surface.
int	UDegree () const
	Returns the degree of the normalized B-splines Ni,n in the U direction.
double	UKnot (const int UIndex) const
	Returns the Knot value of range UIndex. Raised if UIndex < 1 or UIndex > NbUKnots.
GeomAbs_BSplKnotDistribution	UKnotDistribution () const
	Returns NonUniform or Uniform or QuasiUniform or PiecewiseBezier. If all the knots differ by a positive constant from the preceding knot in the U direction the B-spline surface can be :
void	UKnots (NCollection_Array1< double > &Ku) const
	Returns the knots in the U direction.
const NCollection_Array1< double > &	UKnots () const
	Returns the knots in the U direction.
void	UKnotSequence (NCollection_Array1< double > &Ku) const
	Returns the uknots sequence. In this sequence the knots with a multiplicity greater than 1 are repeated. Example : Ku = {k1, k1, k1, k2, k3, k3, k4, k4, k4}.
const NCollection_Array1< double > &	UKnotSequence () const
	Returns the uknots sequence. In this sequence the knots with a multiplicity greater than 1 are repeated. Example : Ku = {k1, k1, k1, k2, k3, k3, k4, k4, k4}.
int	UMultiplicity (const int UIndex) const
	Returns the multiplicity value of knot of range UIndex in the u direction. Raised if UIndex < 1 or UIndex > NbUKnots.
void	UMultiplicities (NCollection_Array1< int > &Mu) const
	Returns the multiplicities of the knots in the U direction.
const NCollection_Array1< int > &	UMultiplicities () const
	Returns the multiplicities of the knots in the U direction.
int	VDegree () const
	Returns the degree of the normalized B-splines Ni,d in the V direction.
double	VKnot (const int VIndex) const
	Returns the Knot value of range VIndex. Raised if VIndex < 1 or VIndex > NbVKnots.
GeomAbs_BSplKnotDistribution	VKnotDistribution () const
	Returns NonUniform or Uniform or QuasiUniform or PiecewiseBezier. If all the knots differ by a positive constant from the preceding knot in the V direction the B-spline surface can be :
void	VKnots (NCollection_Array1< double > &Kv) const
	Returns the knots in the V direction.
const NCollection_Array1< double > &	VKnots () const
	Returns the knots in the V direction.
void	VKnotSequence (NCollection_Array1< double > &Kv) const
	Returns the vknots sequence. In this sequence the knots with a multiplicity greater than 1 are repeated. Example : Kv = {k1, k1, k1, k2, k3, k3, k4, k4, k4}.
const NCollection_Array1< double > &	VKnotSequence () const
	Returns the vknots sequence. In this sequence the knots with a multiplicity greater than 1 are repeated. Example : Ku = {k1, k1, k1, k2, k3, k3, k4, k4, k4}.
int	VMultiplicity (const int VIndex) const
	Returns the multiplicity value of knot of range VIndex in the v direction. Raised if VIndex < 1 or VIndex > NbVKnots.
void	VMultiplicities (NCollection_Array1< int > &Mv) const
	Returns the multiplicities of the knots in the V direction.
const NCollection_Array1< int > &	VMultiplicities () const
	Returns the multiplicities of the knots in the V direction.
double	Weight (const int UIndex, const int VIndex) const
	Returns the weight value of range UIndex, VIndex.
void	Weights (NCollection_Array2< double > &W) const
	Returns the weights of the B-spline 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().
const NCollection_Array2< double > *	Weights () const
	Returns the weights of the B-spline surface. value and derivatives computation.
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). 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 U and Nv in V at (U, V). Raises an exception on failure.
void	LocalD0 (const double U, const double V, const int FromUK1, const int ToUK2, const int FromVK1, const int ToVK2, gp_Pnt &P) const
	Raised if FromUK1 = ToUK2 or FromVK1 = ToVK2.
void	LocalD1 (const double U, const double V, const int FromUK1, const int ToUK2, const int FromVK1, const int ToVK2, gp_Pnt &P, gp_Vec &D1U, gp_Vec &D1V) const
	Raised if the local continuity of the surface is not C1 between the knots FromUK1, ToUK2 and FromVK1, ToVK2. Raised if FromUK1 = ToUK2 or FromVK1 = ToVK2.
void	LocalD2 (const double U, const double V, const int FromUK1, const int ToUK2, const int FromVK1, const int ToVK2, gp_Pnt &P, gp_Vec &D1U, gp_Vec &D1V, gp_Vec &D2U, gp_Vec &D2V, gp_Vec &D2UV) const
	Raised if the local continuity of the surface is not C2 between the knots FromUK1, ToUK2 and FromVK1, ToVK2. Raised if FromUK1 = ToUK2 or FromVK1 = ToVK2.
void	LocalD3 (const double U, const double V, const int FromUK1, const int ToUK2, const int FromVK1, const int ToVK2, 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
	Raised if the local continuity of the surface is not C3 between the knots FromUK1, ToUK2 and FromVK1, ToVK2. Raised if FromUK1 = ToUK2 or FromVK1 = ToVK2.
gp_Vec	LocalDN (const double U, const double V, const int FromUK1, const int ToUK2, const int FromVK1, const int ToVK2, const int Nu, const int Nv) const
	Raised if the local continuity of the surface is not CNu between the knots FromUK1, ToUK2 and CNv between the knots FromVK1, ToVK2. Raised if FromUK1 = ToUK2 or FromVK1 = ToVK2.
gp_Pnt	LocalValue (const double U, const double V, const int FromUK1, const int ToUK2, const int FromVK1, const int ToVK2) const
	Computes the point of parameter U, V on the BSpline surface patch defines between the knots UK1 UK2, VK1, VK2. U can be out of the bounds [Knot UK1, Knot UK2] and V can be outof the bounds [Knot VK1, Knot VK2] but for the computation we only use the definition of the surface between these knot values. Raises if FromUK1 = ToUK2 or FromVK1 = ToVK2.
occ::handle< Geom_Curve >	UIso (const double U) const final
	Computes the U isoparametric curve. A B-spline curve is returned.
occ::handle< Geom_Curve >	VIso (const double V) const final
	Computes the V isoparametric curve. A B-spline curve is returned.
occ::handle< Geom_Curve >	UIso (const double U, const bool CheckRational) const
	Computes the U isoparametric curve. If CheckRational=False, no try to make it non-rational. A B-spline curve is returned.
occ::handle< Geom_Curve >	VIso (const double V, const bool CheckRational) const
	Computes the V isoparametric curve. If CheckRational=False, no try to make it non-rational. A B-spline curve is returned. transformations.
void	Transform (const gp_Trsf &T) final
	Applies the transformation T to this BSpline surface.
void	Resolution (const double Tolerance3D, double &UTolerance, double &VTolerance)
	Computes two tolerance values for this BSpline 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 BSpline 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.
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 degree of the normalized B-spline basis functions in the u and v directions.
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	segment (const double U1, const double U2, const double V1, const double V2, const double EpsU, const double EpsV, const bool SegmentInU, const bool SegmentInV)
	Segments the surface between U1 and U2 in the U-Direction. between V1 and V2 in the V-Direction. The control points are modified, the first and the last point are not the same.
void	updateUKnots ()
	Recompute the flatknots, the knotsdistribution, the continuity for U.
void	updateVKnots ()
	Recompute the flatknots, the knotsdistribution, the continuity for V.

Additional Inherited Members
typedef void	base_type
	Returns a type descriptor about this object.

Detailed Description

Describes a BSpline surface. In each parametric direction, a BSpline surface can be:

• uniform or non-uniform,
• rational or non-rational,
• periodic or non-periodic. A BSpline surface is defined by:
• its degrees, in the u and v parametric directions,
• its periodic characteristic, in the u and v parametric directions,
• a table of poles, also called control points (together with the associated weights if the surface is rational), and
• a table of knots, together with the associated multiplicities. The degree of a Geom_BSplineSurface is limited to a value (25) which is defined and controlled by the system. This value is returned by the function MaxDegree. Poles and Weights Poles and Weights are manipulated using two associative double arrays:
• the poles table, which is a double array of gp_Pnt points, and
• the weights table, which is a double array of reals. The bounds of the poles and weights arrays are:
• 1 and NbUPoles for the row bounds (provided that the BSpline surface is not periodic in the u parametric direction), where NbUPoles is the number of poles of the surface in the u parametric direction, and
• 1 and NbVPoles for the column bounds (provided that the BSpline surface is not periodic in the v parametric direction), where NbVPoles is the number of poles of the surface in the v parametric direction. The poles of the surface are the points used to shape and reshape the surface. They comprise a rectangular network. If the surface is not periodic:
• 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 BSpline curves which delimit the surface in the v parametric direction. These are the v isoparametric curves corresponding to the two bounds of the v parameter.
• The first row of poles and the last row of poles define two BSpline curves which delimit the surface in the u parametric direction. These are the u isoparametric curves corresponding to the two bounds of the u parameter. If the surface is periodic, these geometric properties are not verified. 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. The rational characteristic is defined in each parametric direction. A surface can be rational in the u parametric direction, and non-rational in the v parametric direction. Knots and Multiplicities For a Geom_BSplineSurface the table of knots is made up of two increasing sequences of reals, without repetition, one for each parametric direction. The multiplicities define the repetition of the knots. A BSpline surface comprises multiple contiguous patches, which are themselves polynomial or rational surfaces. The knots are the parameters of the isoparametric curves which limit these contiguous patches. The multiplicity of a knot on a BSpline surface (in a given parametric direction) is related to the degree of continuity of the surface at that knot in that parametric direction: Degree of continuity at knot(i) = Degree - Multi(i) where:
• Degree is the degree of the BSpline surface in the given parametric direction, and
• Multi(i) is the multiplicity of knot number i in the given parametric direction. There are some special cases, where the knots are regularly spaced in one parametric direction (i.e. the difference between two consecutive knots is a constant).
• "Uniform": all the multiplicities are equal to 1.
• "Quasi-uniform": all the multiplicities are equal to 1, except for the first and last knots in this parametric direction, and these are equal to Degree + 1.
• "Piecewise Bezier": all the multiplicities are equal to Degree except for the first and last knots, which are equal to Degree + 1. This surface is a concatenation of Bezier patches in the given parametric direction. If the BSpline surface is not periodic in a given parametric direction, the bounds of the knots and multiplicities tables are 1 and NbKnots, where NbKnots is the number of knots of the BSpline surface in that parametric direction. If the BSpline surface is periodic in a given parametric direction, and there are k periodic knots and p periodic poles in that parametric direction:
• the period is such that: period = Knot(k+1) - Knot(1), and
• the poles and knots tables in that parametric direction can be considered as infinite tables, such that: Knot(i+k) = Knot(i) + period, and Pole(i+p) = Pole(i) Note: The data structure tables for a periodic BSpline surface are more complex than those of a non-periodic one. References : . A survey of curve and surface methods in CADG Wolfgang BOHM CAGD 1 (1984) . On de Boor-like algorithms and blossoming Wolfgang BOEHM cagd 5 (1988) . Blossoming and knot insertion algorithms for B-spline curves Ronald N. GOLDMAN . Modelisation des surfaces en CAO, Henri GIAUME Peugeot SA . Curves and Surfaces for Computer Aided Geometric Design, a practical guide Gerald Farin

Constructor & Destructor Documentation

Geom_BSplineSurface() [1/3]

Geom_BSplineSurface::Geom_BSplineSurface	(	const NCollection_Array2< gp_Pnt > &	Poles,
		const NCollection_Array1< double > &	UKnots,
		const NCollection_Array1< double > &	VKnots,
		const NCollection_Array1< int > &	UMults,
		const NCollection_Array1< int > &	VMults,
		const int	UDegree,
		const int	VDegree,
		const bool	UPeriodic = false,
		const bool	VPeriodic = false )

Creates a non-rational b-spline surface (weights default value is 1.). The following conditions must be verified. 0 < UDegree <= MaxDegree. UKnots.Length() == UMults.Length() >= 2 UKnots(i) < UKnots(i+1) (Knots are increasing) 1 <= UMults(i) <= UDegree On a non uperiodic surface the first and last umultiplicities may be UDegree+1 (this is even recommended if you want the curve to start and finish on the first and last pole). On a uperiodic surface the first and the last umultiplicities must be the same. on non-uperiodic surfaces Poles.ColLength() == Sum(UMults(i)) - UDegree - 1 >= 2 on uperiodic surfaces Poles.ColLength() == Sum(UMults(i)) except the first or last The previous conditions for U holds also for V, with the RowLength of the poles.

Geom_BSplineSurface() [2/3]

Geom_BSplineSurface::Geom_BSplineSurface	(	const NCollection_Array2< gp_Pnt > &	Poles,
		const NCollection_Array2< double > &	Weights,
		const NCollection_Array1< double > &	UKnots,
		const NCollection_Array1< double > &	VKnots,
		const NCollection_Array1< int > &	UMults,
		const NCollection_Array1< int > &	VMults,
		const int	UDegree,
		const int	VDegree,
		const bool	UPeriodic = false,
		const bool	VPeriodic = false )

Creates a non-rational b-spline surface (weights default value is 1.).

The following conditions must be verified. 0 < UDegree <= MaxDegree.

UKnots.Length() == UMults.Length() >= 2

UKnots(i) < UKnots(i+1) (Knots are increasing) 1 <= UMults(i) <= UDegree

On a non uperiodic surface the first and last umultiplicities may be UDegree+1 (this is even recommended if you want the curve to start and finish on the first and last pole).

On a uperiodic surface the first and the last umultiplicities must be the same.

on non-uperiodic surfaces

Poles.ColLength() == Sum(UMults(i)) - UDegree - 1 >= 2

on uperiodic surfaces

Poles.ColLength() == Sum(UMults(i)) except the first or last

The previous conditions for U holds also for V, with the RowLength of the poles.

Geom_BSplineSurface() [3/3]

Geom_BSplineSurface::Geom_BSplineSurface

(

const Geom_BSplineSurface &

theOther

)

Copy constructor for optimized copying without validation.

Parameters

[in]

theOther

the BSpline surface to copy from

Member Function Documentation

Bounds()

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

finalvirtual

Returns the parametric bounds of the surface. Warnings : These parametric values are the bounds of the array of knots UKnots and VKnots only if the first knots and the last knots have a multiplicity equal to UDegree + 1 or VDegree + 1.

Implements Geom_Surface.

CheckAndSegment()

void Geom_BSplineSurface::CheckAndSegment	(	const double	U1,
		const double	U2,
		const double	V1,
		const double	V2,
		const double	theUTolerance = Precision::PConfusion(),
		const double	theVTolerance = Precision::PConfusion() )

Segments the surface between U1 and U2 in the U-Direction. between V1 and V2 in the V-Direction.

same as Segment but do nothing if U1 and U2 (resp. V1 and V2) are equal to the bounds in U (resp. in V) of <me>. For example, if <me> is periodic in V, it will be always periodic in V after the segmentation if the bounds in V are unchanged

Parameters theUTolerance, theVTolerance define the possible proximity along the corresponding direction of the segment boundaries and B-spline knots to treat them as equal.

Warnings : Even if <me> is not closed it can become closed after the segmentation for example if U1 or U2 are out of the bounds of the surface <me> or if the surface makes loop. raises if U2 < U1 or V2 < V1. Standard_DomainError if U2 - U1 exceeds the uperiod for uperiodic surfaces. i.e. ((U2 - U1) - UPeriod) > Precision::PConfusion(). Standard_DomainError if V2 - V1 exceeds the vperiod for vperiodic surfaces. i.e. ((V2 - V1) - VPeriod) > Precision::PConfusion()).

ClearEvalRepresentation()

void Geom_BSplineSurface::ClearEvalRepresentation ( )

inline

Removes the evaluation representation.

Continuity()

GeomAbs_Shape Geom_BSplineSurface::Continuity ( ) const

finalvirtual

Returns the continuity of the surface : C0 : only geometric continuity, C1 : continuity of the first derivative all along the Surface, C2 : continuity of the second derivative all along the Surface, C3 : continuity of the third derivative all along the Surface, CN : the order of continuity is infinite. A B-spline surface is infinitely continuously differentiable for the couple of parameters U, V such that U != UKnots(i) and V != VKnots(i). The continuity of the surface at a knot value depends on the multiplicity of this knot. Example : If the surface is C1 in the V direction and C2 in the U direction this function returns Shape = C1.

Implements Geom_Surface.

Copy()

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

finalvirtual

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

Implements Geom_Geometry.

DumpJson()

void Geom_BSplineSurface::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_BSplineSurface::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_BSplineSurface::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_BSplineSurface::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_BSplineSurface::EvalD3 ( const double U, const double V ) const

finalvirtual

Computes the point and partial derivatives up to 3rd order at (U, V). Raises an exception if the surface continuity is not C3.

Implements Geom_Surface.

EvalDN()

gp_Vec Geom_BSplineSurface::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 at (U, V). Raises an exception on failure.

Raised if the continuity of the surface is not CNu in the U direction and CNv in the V direction.

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

The following functions computes the point for the parametric values (U, V) and the derivatives at this point on the B-spline surface patch delimited with the knots FromUK1, FromVK1 and the knots ToUK2, ToVK2. (U, V) can be out of these parametric bounds but for the computation we only use the definition of the surface between these knots. This method is useful to compute local derivative, if the order of continuity of the whole surface is not greater enough. Inside the parametric knot's domain previously defined the evaluations are the same as if we consider the whole definition of the surface. Of course the evaluations are different outside this parametric domain.

Implements Geom_Surface.

EvalRepresentation()

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

inline

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

ExchangeUV()

void Geom_BSplineSurface::ExchangeUV

(

)

Exchanges the u and v parametric directions on this BSpline surface. As a consequence:

• the poles and weights tables are transposed,
• the knots and multiplicities tables are exchanged,
• degrees of continuity, and rational, periodic and uniform characteristics are exchanged, and
• the orientation of the surface is inverted.

FirstUKnotIndex()

int Geom_BSplineSurface::FirstUKnotIndex

(

)

const

Computes the Index of the UKnots which gives the first parametric value of the surface in the U direction. The UIso curve corresponding to this value is a boundary curve of the surface.

FirstVKnotIndex()

int Geom_BSplineSurface::FirstVKnotIndex

(

)

const

Computes the Index of the VKnots which gives the first parametric value of the surface in the V direction. The VIso curve corresponding to this knot is a boundary curve of the surface.

HasEvalRepresentation()

bool Geom_BSplineSurface::HasEvalRepresentation ( ) const

inline

Returns true if an evaluation representation is attached.

IncreaseDegree()

void Geom_BSplineSurface::IncreaseDegree	(	const int	UDegree,
		const int	VDegree )

Increases the degrees of this BSpline surface to UDegree and VDegree in the u and v parametric directions respectively. As a result, the tables of poles, weights and multiplicities are modified. The tables of knots is not changed. Note: Nothing is done if the given degree is less than or equal to the current degree in the corresponding parametric direction. Exceptions Standard_ConstructionError if UDegree or VDegree is greater than Geom_BSplineSurface::MaxDegree().

IncreaseUMultiplicity() [1/2]

void Geom_BSplineSurface::IncreaseUMultiplicity	(	const int	FromI1,
		const int	ToI2,
		const int	M )

Increases until order M the multiplicity of the set of knots FromI1,...., ToI2 in the U direction. This method can be used to make a B_spline surface into a PiecewiseBezier B_spline surface. If <me> was uniform, it can become non uniform.

Raised if FromI1 or ToI2 is out of the range [FirstUKnotIndex, LastUKnotIndex].

M should be greater than the previous multiplicity of the all the knots FromI1,..., ToI2 and lower or equal to the Degree of the surface in the U parametric direction.

IncreaseUMultiplicity() [2/2]

void Geom_BSplineSurface::IncreaseUMultiplicity	(	const int	UIndex,
		const int	M )

Increases the multiplicity of the knot of range UIndex in the UKnots sequence. M is the new multiplicity. M must be greater than the previous multiplicity and lower or equal to the degree of the surface in the U parametric direction. Raised if M is not in the range [1, UDegree].

Raised if UIndex is not in the range [FirstUKnotIndex, LastUKnotIndex] given by the methods with the same name.

IncreaseVMultiplicity() [1/2]

void Geom_BSplineSurface::IncreaseVMultiplicity	(	const int	FromI1,
		const int	ToI2,
		const int	M )

Increases until order M the multiplicity of the set of knots FromI1,...., ToI2 in the V direction. This method can be used to make a BSplineSurface into a PiecewiseBezier B_spline surface. If <me> was uniform, it can become non-uniform.

Raised if FromI1 or ToI2 is out of the range [FirstVKnotIndex, LastVKnotIndex] given by the methods with the same name.

M should be greater than the previous multiplicity of the all the knots FromI1,..., ToI2 and lower or equal to the Degree of the surface in the V parametric direction.

IncreaseVMultiplicity() [2/2]

void Geom_BSplineSurface::IncreaseVMultiplicity	(	const int	VIndex,
		const int	M )

Increases the multiplicity of a knot in the V direction. M is the new multiplicity.

M should be greater than the previous multiplicity and lower than the degree of the surface in the V parametric direction.

Raised if VIndex is not in the range [FirstVKnotIndex, LastVKnotIndex] given by the methods with the same name.

IncrementUMultiplicity()

void Geom_BSplineSurface::IncrementUMultiplicity	(	const int	FromI1,
		const int	ToI2,
		const int	Step )

Increments the multiplicity of the consecutives uknots FromI1..ToI2 by step. The multiplicity of each knot FromI1,.....,ToI2 must be lower or equal to the UDegree of the B_spline.

Raised if FromI1 or ToI2 is not in the range [FirstUKnotIndex, LastUKnotIndex]

Raised if one knot has a multiplicity greater than UDegree.

IncrementVMultiplicity()

void Geom_BSplineSurface::IncrementVMultiplicity	(	const int	FromI1,
		const int	ToI2,
		const int	Step )

Increments the multiplicity of the consecutives vknots FromI1..ToI2 by step. The multiplicity of each knot FromI1,.....,ToI2 must be lower or equal to the VDegree of the B_spline.

Raised if FromI1 or ToI2 is not in the range [FirstVKnotIndex, LastVKnotIndex]

Raised if one knot has a multiplicity greater than VDegree.

InsertUKnot()

void Geom_BSplineSurface::InsertUKnot	(	const double	U,
		const int	M,
		const double	ParametricTolerance,
		const bool	Add = true )

Inserts a knot value in the sequence of UKnots. If U is a knot value this method increases the multiplicity of the knot if the previous multiplicity was lower than M else it does nothing. The tolerance criterion is ParametricTolerance. ParametricTolerance should be greater or equal than Resolution from package gp.

Raised if U is out of the bounds [U1, U2] given by the methods Bounds, the criterion ParametricTolerance is used. Raised if M is not in the range [1, UDegree].

InsertUKnots()

void Geom_BSplineSurface::InsertUKnots	(	const NCollection_Array1< double > &	Knots,
		const NCollection_Array1< int > &	Mults,
		const double	ParametricTolerance = 0.0,
		const bool	Add = true )

Inserts into the knots table for the U parametric direction of this BSpline surface:

• the values of the array Knots, with their respective multiplicities, Mults. If the knot value to insert already exists in the table, its multiplicity is:
• increased by M, if Add is true (the default), or
• increased to M, if Add is false. The tolerance criterion used to check the equality of the knots is the larger of the values ParametricTolerance and double::Epsilon(val), where val is the knot value to be inserted. Warning
• If a given multiplicity coefficient is null, or negative, nothing is done.
• The new multiplicity of a knot is limited to the degree of this BSpline surface in the corresponding parametric direction. Exceptions Standard_ConstructionError if a knot value to insert is outside the bounds of this BSpline surface in the specified parametric direction. The comparison uses the precision criterion ParametricTolerance.

InsertVKnot()

void Geom_BSplineSurface::InsertVKnot	(	const double	V,
		const int	M,
		const double	ParametricTolerance,
		const bool	Add = true )

Inserts a knot value in the sequence of VKnots. If V is a knot value this method increases the multiplicity of the knot if the previous multiplicity was lower than M otherwise it does nothing. The tolerance criterion is ParametricTolerance. ParametricTolerance should be greater or equal than Resolution from package gp.

raises if V is out of the Bounds [V1, V2] given by the methods Bounds, the criterion ParametricTolerance is used. raises if M is not in the range [1, VDegree].

InsertVKnots()

void Geom_BSplineSurface::InsertVKnots	(	const NCollection_Array1< double > &	Knots,
		const NCollection_Array1< int > &	Mults,
		const double	ParametricTolerance = 0.0,
		const bool	Add = true )

Inserts into the knots table for the V parametric direction of this BSpline surface:

• the values of the array Knots, with their respective multiplicities, Mults. If the knot value to insert already exists in the table, its multiplicity is:
• increased by M, if Add is true (the default), or
• increased to M, if Add is false. The tolerance criterion used to check the equality of the knots is the larger of the values ParametricTolerance and double::Epsilon(val), where val is the knot value to be inserted. Warning
• If a given multiplicity coefficient is null, or negative, nothing is done.
• The new multiplicity of a knot is limited to the degree of this BSpline surface in the corresponding parametric direction. Exceptions Standard_ConstructionError if a knot value to insert is outside the bounds of this BSpline surface in the specified parametric direction. The comparison uses the precision criterion ParametricTolerance.

IsCNu()

bool Geom_BSplineSurface::IsCNu ( const int N ) const

finalvirtual

Returns True if the order of continuity of the surface in the U direction is N. Raised if N < 0.

Implements Geom_Surface.

IsCNv()

bool Geom_BSplineSurface::IsCNv ( const int N ) const

finalvirtual

Returns True if the order of continuity of the surface in the V direction is N. Raised if N < 0.

Implements Geom_Surface.

IsUClosed()

bool Geom_BSplineSurface::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_BSplineSurface::IsUPeriodic ( ) const

finalvirtual

Returns True if the surface is closed in the U direction and if the B-spline has been turned into a periodic surface using the function SetUPeriodic.

Implements Geom_Surface.

IsURational()

bool Geom_BSplineSurface::IsURational

(

)

const

Returns False if for each row of weights all the weights are identical. 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_BSplineSurface::IsVClosed ( ) const

finalvirtual

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

Implements Geom_Surface.

IsVPeriodic()

bool Geom_BSplineSurface::IsVPeriodic ( ) const

finalvirtual

Returns True if the surface is closed in the V direction and if the B-spline has been turned into a periodic surface using the function SetVPeriodic.

Implements Geom_Surface.

IsVRational()

bool Geom_BSplineSurface::IsVRational

(

)

const

Returns False if for each column of weights all the weights are identical. The tolerance criterion is resolution from package gp. Examples : |1.0, 2.0, 0.5| if Weights = |1.0, 2.0, 0.5| returns False |1.0, 2.0, 0.5|.

LastUKnotIndex()

int Geom_BSplineSurface::LastUKnotIndex

(

)

const

Computes the Index of the UKnots which gives the last parametric value of the surface in the U direction. The UIso curve corresponding to this knot is a boundary curve of the surface.

LastVKnotIndex()

int Geom_BSplineSurface::LastVKnotIndex

(

)

const

Computes the Index of the VKnots which gives the last parametric value of the surface in the V direction. The VIso curve corresponding to this knot is a boundary curve of the surface.

LocalD0()

void Geom_BSplineSurface::LocalD0	(	const double	U,
		const double	V,
		const int	FromUK1,
		const int	ToUK2,
		const int	FromVK1,
		const int	ToVK2,
		gp_Pnt &	P ) const

Raised if FromUK1 = ToUK2 or FromVK1 = ToVK2.

LocalD1()

void Geom_BSplineSurface::LocalD1	(	const double	U,
		const double	V,
		const int	FromUK1,
		const int	ToUK2,
		const int	FromVK1,
		const int	ToVK2,
		gp_Pnt &	P,
		gp_Vec &	D1U,
		gp_Vec &	D1V ) const

Raised if the local continuity of the surface is not C1 between the knots FromUK1, ToUK2 and FromVK1, ToVK2. Raised if FromUK1 = ToUK2 or FromVK1 = ToVK2.

LocalD2()

void Geom_BSplineSurface::LocalD2	(	const double	U,
		const double	V,
		const int	FromUK1,
		const int	ToUK2,
		const int	FromVK1,
		const int	ToVK2,
		gp_Pnt &	P,
		gp_Vec &	D1U,
		gp_Vec &	D1V,
		gp_Vec &	D2U,
		gp_Vec &	D2V,
		gp_Vec &	D2UV ) const

Raised if the local continuity of the surface is not C2 between the knots FromUK1, ToUK2 and FromVK1, ToVK2. Raised if FromUK1 = ToUK2 or FromVK1 = ToVK2.

LocalD3()

void Geom_BSplineSurface::LocalD3	(	const double	U,
		const double	V,
		const int	FromUK1,
		const int	ToUK2,
		const int	FromVK1,
		const int	ToVK2,
		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

Raised if the local continuity of the surface is not C3 between the knots FromUK1, ToUK2 and FromVK1, ToVK2. Raised if FromUK1 = ToUK2 or FromVK1 = ToVK2.

LocalDN()

gp_Vec Geom_BSplineSurface::LocalDN	(	const double	U,
		const double	V,
		const int	FromUK1,
		const int	ToUK2,
		const int	FromVK1,
		const int	ToVK2,
		const int	Nu,
		const int	Nv ) const

Raised if the local continuity of the surface is not CNu between the knots FromUK1, ToUK2 and CNv between the knots FromVK1, ToVK2. Raised if FromUK1 = ToUK2 or FromVK1 = ToVK2.

LocalValue()

gp_Pnt Geom_BSplineSurface::LocalValue	(	const double	U,
		const double	V,
		const int	FromUK1,
		const int	ToUK2,
		const int	FromVK1,
		const int	ToVK2 ) const

Computes the point of parameter U, V on the BSpline surface patch defines between the knots UK1 UK2, VK1, VK2. U can be out of the bounds [Knot UK1, Knot UK2] and V can be outof the bounds [Knot VK1, Knot VK2] but for the computation we only use the definition of the surface between these knot values. Raises if FromUK1 = ToUK2 or FromVK1 = ToVK2.

LocateU()

void Geom_BSplineSurface::LocateU	(	const double	U,
		const double	ParametricTolerance,
		int &	I1,
		int &	I2,
		const bool	WithKnotRepetition = false ) const

Locates the parametric value U in the sequence of UKnots. If "WithKnotRepetition" is True we consider the knot's representation with repetition of multiple knot value, otherwise we consider the knot's representation with no repetition of multiple knot values. UKnots (I1) <= U <= UKnots (I2) . if I1 = I2 U is a knot value (the tolerance criterion ParametricTolerance is used). . if I1 < 1 => U < UKnots(1) - std::abs(ParametricTolerance) . if I2 > NbUKnots => U > UKnots(NbUKnots)+std::abs(ParametricTolerance).

LocateV()

void Geom_BSplineSurface::LocateV	(	const double	V,
		const double	ParametricTolerance,
		int &	I1,
		int &	I2,
		const bool	WithKnotRepetition = false ) const

Locates the parametric value V in the sequence of knots. If "WithKnotRepetition" is True we consider the knot's representation with repetition of multiple knot value, otherwise we consider the knot's representation with no repetition of multiple knot values. VKnots (I1) <= V <= VKnots (I2) . if I1 = I2 V is a knot value (the tolerance criterion ParametricTolerance is used). . if I1 < 1 => V < VKnots(1) - std::abs(ParametricTolerance) . if I2 > NbVKnots => V > VKnots(NbVKnots)+std::abs(ParametricTolerance) poles insertion and removing The following methods are available only if the surface is Uniform or QuasiUniform in the considered direction The knot repartition is modified.

MaxDegree()

int Geom_BSplineSurface::MaxDegree ( )

static

Returns the value of the maximum degree of the normalized B-spline basis functions in the u and v directions.

MovePoint()

void Geom_BSplineSurface::MovePoint	(	const double	U,
		const double	V,
		const gp_Pnt &	P,
		const int	UIndex1,
		const int	UIndex2,
		const int	VIndex1,
		const int	VIndex2,
		int &	UFirstIndex,
		int &	ULastIndex,
		int &	VFirstIndex,
		int &	VLastIndex )

Move a point with parameter U and V to P. given u,v as parameters) to reach a new position UIndex1, UIndex2, VIndex1, VIndex2: indicates the poles which can be moved if Problem in BSplineBasis calculation, no change for the curve and UFirstIndex, VLastIndex = 0 VFirstIndex, VLastIndex = 0.

Raised if UIndex1 < UIndex2 or VIndex1 < VIndex2 or UIndex1 < 1 || UIndex1 > NbUPoles or UIndex2 < 1 || UIndex2 > NbUPoles VIndex1 < 1 || VIndex1 > NbVPoles or VIndex2 < 1 || VIndex2 > NbVPoles characteristics of the surface

NbUKnots()

int Geom_BSplineSurface::NbUKnots

(

)

const

Returns the number of knots in the U direction.

NbUPoles()

int Geom_BSplineSurface::NbUPoles

(

)

const

Returns number of poles in the U direction.

NbVKnots()

int Geom_BSplineSurface::NbVKnots

(

)

const

Returns the number of knots in the V direction.

NbVPoles()

int Geom_BSplineSurface::NbVPoles

(

)

const

Returns the number of poles in the V direction.

PeriodicNormalization()

void Geom_BSplineSurface::PeriodicNormalization	(	double &	U,
		double &	V ) const

returns the parameter normalized within the period if the surface is periodic : otherwise does not do anything

Pole()

const gp_Pnt & Geom_BSplineSurface::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_BSplineSurface::Poles

(

)

const

Returns the poles of the B-spline surface.

Poles() [2/2]

void Geom_BSplineSurface::Poles

(

NCollection_Array2< gp_Pnt > &

P

)

const

Returns the poles of the B-spline surface.

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

Deprecated

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

RemoveUKnot()

bool Geom_BSplineSurface::RemoveUKnot	(	const int	Index,
		const int	M,
		const double	Tolerance )

Reduces to M the multiplicity of the knot of index Index in the U parametric direction. If M is 0, the knot is removed. With a modification of this type, the table of poles is also modified. Two different algorithms are used systematically to compute the new poles of the surface. For each pole, the distance between the pole calculated using the first algorithm and the same pole calculated using the second algorithm, is checked. If this distance is less than Tolerance it ensures that the surface is not modified by more than Tolerance. Under these conditions, the function returns true; otherwise, it returns false. A low tolerance prevents modification of the surface. A high tolerance "smoothes" the surface. Exceptions Standard_OutOfRange if Index is outside the bounds of the knots table of this BSpline surface.

RemoveVKnot()

bool Geom_BSplineSurface::RemoveVKnot	(	const int	Index,
		const int	M,
		const double	Tolerance )

Reduces to M the multiplicity of the knot of index Index in the V parametric direction. If M is 0, the knot is removed. With a modification of this type, the table of poles is also modified. Two different algorithms are used systematically to compute the new poles of the surface. For each pole, the distance between the pole calculated using the first algorithm and the same pole calculated using the second algorithm, is checked. If this distance is less than Tolerance it ensures that the surface is not modified by more than Tolerance. Under these conditions, the function returns true; otherwise, it returns false. A low tolerance prevents modification of the surface. A high tolerance "smoothes" the surface. Exceptions Standard_OutOfRange if Index is outside the bounds of the knots table of this BSpline surface.

Resolution()

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

Computes two tolerance values for this BSpline 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 BSpline surface, UTolerance and VTolerance guarantee that : | u1 - u0 | < UTolerance and | v1 - v0 | < VTolerance ====> |f (u1,v1) - f (u0,v0)| < Tolerance3D

Segment()

void Geom_BSplineSurface::Segment	(	const double	U1,
		const double	U2,
		const double	V1,
		const double	V2,
		const double	theUTolerance = Precision::PConfusion(),
		const double	theVTolerance = Precision::PConfusion() )

Segments the surface between U1 and U2 in the U-Direction. between V1 and V2 in the V-Direction. The control points are modified, the first and the last point are not the same.

Parameters theUTolerance, theVTolerance define the possible proximity along the corresponding direction of the segment boundaries and B-spline knots to treat them as equal.

Warnings : Even if <me> is not closed it can become closed after the segmentation for example if U1 or U2 are out of the bounds of the surface <me> or if the surface makes loop. raises if U2 < U1 or V2 < V1. Standard_DomainError if U2 - U1 exceeds the uperiod for uperiodic surfaces. i.e. ((U2 - U1) - UPeriod) > Precision::PConfusion(). Standard_DomainError if V2 - V1 exceeds the vperiod for vperiodic surfaces. i.e. ((V2 - V1) - VPeriod) > Precision::PConfusion()).

segment()

void Geom_BSplineSurface::segment ( const double U1, const double U2, const double V1, const double V2, const double EpsU, const double EpsV, const bool SegmentInU, const bool SegmentInV )

protected

Segments the surface between U1 and U2 in the U-Direction. between V1 and V2 in the V-Direction. The control points are modified, the first and the last point are not the same.

Parameters EpsU, EpsV define the proximity along U-Direction and V-Direction respectively.

SetEvalRepresentation()

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

Substitutes the pole of range (UIndex, VIndex) with P. 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_BSplineSurface::SetPole	(	const int	UIndex,
		const int	VIndex,
		const gp_Pnt &	P,
		const double	Weight )

Substitutes the pole and the weight of range (UIndex, VIndex) with P and W.

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

SetPoleCol() [1/2]

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

Changes a column of poles or a part of this column. Raised if Vindex < 1 or VIndex > NbVPoles.

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

SetPoleCol() [2/2]

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

Changes a column of poles or a part of this column with the corresponding weights. If the surface was rational it can become non rational. If the surface was non rational it can become rational. Raised if Vindex < 1 or VIndex > NbVPoles.

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

SetPoleRow() [1/2]

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

Changes a row of poles or a part of this row. Raised if Uindex < 1 or UIndex > NbUPoles.

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

SetPoleRow() [2/2]

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

Changes a row of poles or a part of this row with the corresponding weights. If the surface was rational it can become non rational. If the surface was non rational it can become rational. Raised if Uindex < 1 or UIndex > NbUPoles.

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

SetUKnot() [1/2]

void Geom_BSplineSurface::SetUKnot	(	const int	UIndex,
		const double	K )

Substitutes the UKnots of range UIndex with K.

Raised if UIndex < 1 or UIndex > NbUKnots

Raised if K >= UKnots(UIndex+1) or K <= UKnots(UIndex-1)

SetUKnot() [2/2]

void Geom_BSplineSurface::SetUKnot	(	const int	UIndex,
		const double	K,
		const int	M )

Changes the value of the UKnots of range UIndex and increases its multiplicity.

Raised if UIndex is not in the range [FirstUKnotIndex, LastUKnotIndex] given by the methods with the same name.

Raised if K >= UKnots(UIndex+1) or K <= UKnots(UIndex-1) M must be lower than UDegree and greater than the previous multiplicity of the knot of range UIndex.

SetUKnots()

void Geom_BSplineSurface::SetUKnots

(

const NCollection_Array1< double > &

UK

)

Changes all the U-knots of the surface. The multiplicity of the knots are not modified.

Raised if there is an index such that UK (Index+1) <= UK (Index).

Raised if UK.Lower() < 1 or UK.Upper() > NbUKnots

SetUNotPeriodic()

void Geom_BSplineSurface::SetUNotPeriodic

(

)

Sets the surface U not periodic. Changes this BSpline surface into a non-periodic surface along U direction. If this surface is already non-periodic, it is not modified. Note: the poles and knots tables are modified.

SetUOrigin()

void Geom_BSplineSurface::SetUOrigin

(

const int

Index

)

Assigns the knot of index Index in the knots table in the corresponding parametric direction to be the origin of this periodic BSpline surface. As a consequence, the knots and poles tables are modified. Exceptions Standard_NoSuchObject if this BSpline surface is not periodic in the given parametric direction. Standard_DomainError if Index is outside the bounds of the knots table in the given parametric direction.

SetUPeriodic()

void Geom_BSplineSurface::SetUPeriodic

(

)

Sets the surface U periodic. Modifies this surface to be periodic in the U parametric direction. To become periodic in a given parametric direction a surface must be closed in that parametric direction, and the knot sequence relative to that direction must be periodic. To generate this periodic sequence of knots, the functions FirstUKnotIndex and LastUKnotIndex are used to compute I1 and I2. These are the indexes, in the knot array associated with the given parametric direction, of the knots that correspond to the first and last parameters of this BSpline surface in the given parametric direction. Hence the period is: Knots(I1) - Knots(I2) As a result, the knots and poles tables are modified. Exceptions Standard_ConstructionError if the surface is not closed in the given parametric direction.

SetVKnot() [1/2]

void Geom_BSplineSurface::SetVKnot	(	const int	VIndex,
		const double	K )

Substitutes the VKnots of range VIndex with K.

Raised if VIndex < 1 or VIndex > NbVKnots

Raised if K >= VKnots(VIndex+1) or K <= VKnots(VIndex-1)

SetVKnot() [2/2]

void Geom_BSplineSurface::SetVKnot	(	const int	VIndex,
		const double	K,
		const int	M )

Changes the value of the VKnots of range VIndex and increases its multiplicity.

Raised if VIndex is not in the range [FirstVKnotIndex, LastVKnotIndex] given by the methods with the same name.

Raised if K >= VKnots(VIndex+1) or K <= VKnots(VIndex-1) M must be lower than VDegree and greater than the previous multiplicity of the knot of range VIndex.

SetVKnots()

void Geom_BSplineSurface::SetVKnots

(

const NCollection_Array1< double > &

VK

)

Changes all the V-knots of the surface. The multiplicity of the knots are not modified.

Raised if there is an index such that VK (Index+1) <= VK (Index).

Raised if VK.Lower() < 1 or VK.Upper() > NbVKnots

SetVNotPeriodic()

void Geom_BSplineSurface::SetVNotPeriodic

(

)

Sets the surface V not periodic. Changes this BSpline surface into a non-periodic surface along V direction. If this surface is already non-periodic, it is not modified. Note: the poles and knots tables are modified.

SetVOrigin()

void Geom_BSplineSurface::SetVOrigin

(

const int

Index

)

Assigns the knot of index Index in the knots table in the corresponding parametric direction to be the origin of this periodic BSpline surface. As a consequence, the knots and poles tables are modified. Exceptions Standard_NoSuchObject if this BSpline surface is not periodic in the given parametric direction. Standard_DomainError if Index is outside the bounds of the knots table in the given parametric direction.

SetVPeriodic()

void Geom_BSplineSurface::SetVPeriodic

(

)

Sets the surface V periodic. Modifies this surface to be periodic in the V parametric direction. To become periodic in a given parametric direction a surface must be closed in that parametric direction, and the knot sequence relative to that direction must be periodic. To generate this periodic sequence of knots, the functions FirstVKnotIndex and LastVKnotIndex are used to compute I1 and I2. These are the indexes, in the knot array associated with the given parametric direction, of the knots that correspond to the first and last parameters of this BSpline surface in the given parametric direction. Hence the period is: Knots(I1) - Knots(I2) As a result, the knots and poles tables are modified. Exceptions Standard_ConstructionError if the surface is not closed in the given parametric direction.

SetWeight()

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

Changes 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 is lower or equal to Resolution from package gp

SetWeightCol()

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

Changes a column of weights of a part of this column.

Raised if VIndex < 1 or VIndex > NbVPoles

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

SetWeightRow()

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

Changes a row of weights or a part of this row.

Raised if UIndex < 1 or UIndex > NbUPoles

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

Transform()

void Geom_BSplineSurface::Transform ( const gp_Trsf & T )

finalvirtual

Applies the transformation T to this BSpline surface.

Implements Geom_Geometry.

UDegree()

int Geom_BSplineSurface::UDegree

(

)

const

Returns the degree of the normalized B-splines Ni,n in the U direction.

UIso() [1/2]

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

finalvirtual

Computes the U isoparametric curve. A B-spline curve is returned.

Implements Geom_Surface.

UIso() [2/2]

occ::handle< Geom_Curve > Geom_BSplineSurface::UIso	(	const double	U,
		const bool	CheckRational ) const

Computes the U isoparametric curve. If CheckRational=False, no try to make it non-rational. A B-spline curve is returned.

UKnot()

double Geom_BSplineSurface::UKnot

(

const int

UIndex

)

const

Returns the Knot value of range UIndex. Raised if UIndex < 1 or UIndex > NbUKnots.

UKnotDistribution()

GeomAbs_BSplKnotDistribution Geom_BSplineSurface::UKnotDistribution

(

)

const

Returns NonUniform or Uniform or QuasiUniform or PiecewiseBezier. If all the knots differ by a positive constant from the preceding knot in the U direction the B-spline surface can be :

• Uniform if all the knots are of multiplicity 1,
• QuasiUniform if all the knots are of multiplicity 1 except for the first and last knot which are of multiplicity Degree + 1,
• PiecewiseBezier if the first and last knots have multiplicity Degree + 1 and if interior knots have multiplicity Degree otherwise the surface is non uniform in the U direction The tolerance criterion is Resolution from package gp.

UKnots() [1/2]

const NCollection_Array1< double > & Geom_BSplineSurface::UKnots

(

)

const

Returns the knots in the U direction.

UKnots() [2/2]

void Geom_BSplineSurface::UKnots

(

NCollection_Array1< double > &

Ku

)

const

Returns the knots in the U direction.

Raised if the length of Ku is not equal to the number of knots in the U direction.

Deprecated

("use UKnots() returning const reference instead")

UKnotSequence() [1/2]

const NCollection_Array1< double > & Geom_BSplineSurface::UKnotSequence

(

)

const

Returns the uknots sequence. In this sequence the knots with a multiplicity greater than 1 are repeated. Example : Ku = {k1, k1, k1, k2, k3, k3, k4, k4, k4}.

UKnotSequence() [2/2]

void Geom_BSplineSurface::UKnotSequence

(

NCollection_Array1< double > &

Ku

)

const

Returns the uknots sequence. In this sequence the knots with a multiplicity greater than 1 are repeated. Example : Ku = {k1, k1, k1, k2, k3, k3, k4, k4, k4}.

Raised if the length of Ku is not equal to NbUPoles + UDegree + 1

Deprecated

("use UKnotSequence() returning const reference instead")

UMultiplicities() [1/2]

const NCollection_Array1< int > & Geom_BSplineSurface::UMultiplicities

(

)

const

Returns the multiplicities of the knots in the U direction.

UMultiplicities() [2/2]

void Geom_BSplineSurface::UMultiplicities

(

NCollection_Array1< int > &

Mu

)

const

Returns the multiplicities of the knots in the U direction.

Raised if the length of Mu is not equal to the number of knots in the U direction.

Deprecated

("use UMultiplicities() returning const reference instead")

UMultiplicity()

int Geom_BSplineSurface::UMultiplicity

(

const int

UIndex

)

const

Returns the multiplicity value of knot of range UIndex in the u direction. Raised if UIndex < 1 or UIndex > NbUKnots.

updateUKnots()

void Geom_BSplineSurface::updateUKnots ( )

protected

Recompute the flatknots, the knotsdistribution, the continuity for U.

updateVKnots()

void Geom_BSplineSurface::updateVKnots ( )

protected

Recompute the flatknots, the knotsdistribution, the continuity for V.

UReverse()

void Geom_BSplineSurface::UReverse ( )

finalvirtual

Changes the orientation of this BSpline 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. The knots and poles tables are modified.

Implements Geom_Surface.

UReversedParameter()

double Geom_BSplineSurface::UReversedParameter ( const double U ) const

finalvirtual

Computes the u parameter on the modified surface, produced by reversing its U parametric direction, for the point of u parameter U, on this BSpline surface. For a BSpline surface, these functions return respectively:

• UFirst + ULast - U, where UFirst, ULast are the values of the first and last parameters of this BSpline surface, in the u parametric directions.

Implements Geom_Surface.

VDegree()

int Geom_BSplineSurface::VDegree

(

)

const

Returns the degree of the normalized B-splines Ni,d in the V direction.

VIso() [1/2]

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

finalvirtual

Computes the V isoparametric curve. A B-spline curve is returned.

Implements Geom_Surface.

VIso() [2/2]

occ::handle< Geom_Curve > Geom_BSplineSurface::VIso	(	const double	V,
		const bool	CheckRational ) const

Computes the V isoparametric curve. If CheckRational=False, no try to make it non-rational. A B-spline curve is returned. transformations.

VKnot()

double Geom_BSplineSurface::VKnot

(

const int

VIndex

)

const

Returns the Knot value of range VIndex. Raised if VIndex < 1 or VIndex > NbVKnots.

VKnotDistribution()

GeomAbs_BSplKnotDistribution Geom_BSplineSurface::VKnotDistribution

(

)

const

Returns NonUniform or Uniform or QuasiUniform or PiecewiseBezier. If all the knots differ by a positive constant from the preceding knot in the V direction the B-spline surface can be :

• Uniform if all the knots are of multiplicity 1,
• QuasiUniform if all the knots are of multiplicity 1 except for the first and last knot which are of multiplicity Degree + 1,
• PiecewiseBezier if the first and last knots have multiplicity Degree + 1 and if interior knots have multiplicity Degree otherwise the surface is non uniform in the V direction. The tolerance criterion is Resolution from package gp.

VKnots() [1/2]

const NCollection_Array1< double > & Geom_BSplineSurface::VKnots

(

)

const

Returns the knots in the V direction.

VKnots() [2/2]

void Geom_BSplineSurface::VKnots

(

NCollection_Array1< double > &

Kv

)

const

Returns the knots in the V direction.

Raised if the length of Kv is not equal to the number of knots in the V direction.

Deprecated

("use VKnots() returning const reference instead")

VKnotSequence() [1/2]

const NCollection_Array1< double > & Geom_BSplineSurface::VKnotSequence

(

)

const

Returns the vknots sequence. In this sequence the knots with a multiplicity greater than 1 are repeated. Example : Ku = {k1, k1, k1, k2, k3, k3, k4, k4, k4}.

VKnotSequence() [2/2]

void Geom_BSplineSurface::VKnotSequence

(

NCollection_Array1< double > &

Kv

)

const

Returns the vknots sequence. In this sequence the knots with a multiplicity greater than 1 are repeated. Example : Kv = {k1, k1, k1, k2, k3, k3, k4, k4, k4}.

Raised if the length of Kv is not equal to NbVPoles + VDegree + 1

Deprecated

("use VKnotSequence() returning const reference instead")

VMultiplicities() [1/2]

const NCollection_Array1< int > & Geom_BSplineSurface::VMultiplicities

(

)

const

Returns the multiplicities of the knots in the V direction.

VMultiplicities() [2/2]

void Geom_BSplineSurface::VMultiplicities

(

NCollection_Array1< int > &

Mv

)

const

Returns the multiplicities of the knots in the V direction.

Raised if the length of Mv is not equal to the number of knots in the V direction.

Deprecated

("use VMultiplicities() returning const reference instead")

VMultiplicity()

int Geom_BSplineSurface::VMultiplicity

(

const int

VIndex

)

const

Returns the multiplicity value of knot of range VIndex in the v direction. Raised if VIndex < 1 or VIndex > NbVKnots.

VReverse()

void Geom_BSplineSurface::VReverse ( )

finalvirtual

Changes the orientation of this BSpline 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. The knots and poles tables are modified.

Implements Geom_Surface.

VReversedParameter()

double Geom_BSplineSurface::VReversedParameter ( const double V ) const

finalvirtual

Computes the v parameter on the modified surface, produced by reversing its V parametric direction, for the point of v parameter V on this BSpline surface. For a BSpline surface, these functions return respectively:

• VFirst + VLast - V, VFirst and VLast are the values of the first and last parameters of this BSpline surface, in the v pametric directions.

Implements Geom_Surface.

Weight()

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

Returns the weight value 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_BSplineSurface::Weights

(

)

const

Returns the weights of the B-spline surface. value and derivatives computation.

Weights() [2/2]

void Geom_BSplineSurface::Weights

(

NCollection_Array2< double > &

W

)

const

Returns the weights of the B-spline surface.

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

Deprecated

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

WeightsArray()

const NCollection_Array2< double > & Geom_BSplineSurface::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_BSplineSurface.hxx