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 TColgp_Array2OfPnt &Poles, const TColStd_Array1OfReal &UKnots, const TColStd_Array1OfReal &VKnots, const TColStd_Array1OfInteger &UMults, const TColStd_Array1OfInteger &VMults, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Boolean UPeriodic=Standard_False, const Standard_Boolean VPeriodic=Standard_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 recommanded 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. More...
	Geom_BSplineSurface (const TColgp_Array2OfPnt &Poles, const TColStd_Array2OfReal &Weights, const TColStd_Array1OfReal &UKnots, const TColStd_Array1OfReal &VKnots, const TColStd_Array1OfInteger &UMults, const TColStd_Array1OfInteger &VMults, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Boolean UPeriodic=Standard_False, const Standard_Boolean VPeriodic=Standard_False)
	Creates a non-rational b-spline surface (weights <br> default value is 1.). <br> //! 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 recommanded 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. More...
void	ExchangeUV ()
	Exchanges the u and v parametric directions on <br> this BSpline surface. As a consequence: More...
void	SetUPeriodic ()
	Sets the surface U periodic. More...
void	SetVPeriodic ()
	Modifies this surface to be periodic in the u (or v) <br> 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 (or 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. More...
void	PeriodicNormalization (Standard_Real &U, Standard_Real &V) const
	returns the parameter normalized within the period if the surface is periodic : otherwise does not do anything More...
void	SetUOrigin (const Standard_Integer Index)
	Assigns the knot of index Index in the knots table in <br> 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. More...
void	SetVOrigin (const Standard_Integer Index)
	Assigns the knot of index Index in the knots table in <br> 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. More...
void	SetUNotPeriodic ()
void	SetVNotPeriodic ()
	Modifies this surface to be periodic in the u (or v) parametric direction. <br> 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 (or 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. More...
void	UReverse ()
	Reverses the U direction of parametrization of <me>. The bounds of the surface are not modified. More...
void	VReverse ()
	Changes the orientation of this BSpline surface in the <br> u (or 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. More...
Standard_Real	UReversedParameter (const Standard_Real U) const
	Returns the parameter on the Ureversed surface for <br> the point of parameter U on <me>. <br> me->UReversed()->Value(me->UReversedParameter(U),V) is the same point as me->Value(U,V) More...
Standard_Real	VReversedParameter (const Standard_Real V) const
	Computes the u (or v) parameter on the modified <br> surface, produced by reversing its u (or v) parametric direction, for the point of u parameter U, (or of v parameter V) on this BSpline surface. For a BSpline surface, these functions return respectively: More...
void	IncreaseDegree (const Standard_Integer UDegree, const Standard_Integer VDegree)
	Increases the degrees of this BSpline surface to <br> 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(). More...
void	InsertUKnots (const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, const Standard_Real ParametricTolerance=0.0, const Standard_Boolean Add=Standard_True)
void	InsertVKnots (const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, const Standard_Real ParametricTolerance=0.0, const Standard_Boolean Add=Standard_True)
	Inserts into the knots table for the corresponding <br> parametric direction of this BSpline surface: More...
Standard_Boolean	RemoveUKnot (const Standard_Integer Index, const Standard_Integer M, const Standard_Real Tolerance)
Standard_Boolean	RemoveVKnot (const Standard_Integer Index, const Standard_Integer M, const Standard_Real Tolerance)
	Reduces to M the multiplicity of the knot of index <br> Index in the given 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. More...
void	IncreaseUMultiplicity (const Standard_Integer UIndex, const Standard_Integer 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. More...
void	IncreaseUMultiplicity (const Standard_Integer FromI1, const Standard_Integer ToI2, const Standard_Integer 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. More...
void	IncrementUMultiplicity (const Standard_Integer FromI1, const Standard_Integer ToI2, const Standard_Integer 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. More...
void	IncreaseVMultiplicity (const Standard_Integer VIndex, const Standard_Integer 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. More...
void	IncreaseVMultiplicity (const Standard_Integer FromI1, const Standard_Integer ToI2, const Standard_Integer 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. More...
void	IncrementVMultiplicity (const Standard_Integer FromI1, const Standard_Integer ToI2, const Standard_Integer 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. More...
void	InsertUKnot (const Standard_Real U, const Standard_Integer M, const Standard_Real ParametricTolerance, const Standard_Boolean Add=Standard_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]. More...
void	InsertVKnot (const Standard_Real V, const Standard_Integer M, const Standard_Real ParametricTolerance, const Standard_Boolean Add=Standard_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]. More...
void	Segment (const Standard_Real U1, const Standard_Real U2, const Standard_Real V1, const Standard_Real V2)
	Segments the surface between U1 and U2 in the U-Direction. <br> between V1 and V2 in the V-Direction. <br> The control points are modified, the first and the last point are not the same. 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 More...
void	CheckAndSegment (const Standard_Real U1, const Standard_Real U2, const Standard_Real V1, const Standard_Real V2)
	Segments the surface between U1 and U2 in the U-Direction. <br> between V1 and V2 in the V-Direction. <br> 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 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 More...
void	SetUKnot (const Standard_Integer UIndex, const Standard_Real K)
	Substitutes the UKnots of range UIndex with K. <br> Raised if UIndex < 1 or UIndex > NbUKnots Raised if K >= UKnots(UIndex+1) or K <= UKnots(UIndex-1) More...
void	SetUKnots (const TColStd_Array1OfReal &UK)
	Changes all the U-knots of the surface. <br> 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 More...
void	SetUKnot (const Standard_Integer UIndex, const Standard_Real K, const Standard_Integer 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. More...
void	SetVKnot (const Standard_Integer VIndex, const Standard_Real K)
	Substitutes the VKnots of range VIndex with K. <br> Raised if VIndex < 1 or VIndex > NbVKnots Raised if K >= VKnots(VIndex+1) or K <= VKnots(VIndex-1) More...
void	SetVKnots (const TColStd_Array1OfReal &VK)
	Changes all the V-knots of the surface. <br> 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 More...
void	SetVKnot (const Standard_Integer VIndex, const Standard_Real K, const Standard_Integer 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. More...
void	LocateU (const Standard_Real U, const Standard_Real ParametricTolerance, Standard_Integer &I1, Standard_Integer &I2, const Standard_Boolean WithKnotRepetition=Standard_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) - Abs(ParametricTolerance) . if I2 > NbUKnots => U > UKnots(NbUKnots)+Abs(ParametricTolerance) More...
void	LocateV (const Standard_Real V, const Standard_Real ParametricTolerance, Standard_Integer &I1, Standard_Integer &I2, const Standard_Boolean WithKnotRepetition=Standard_False) const
	Locates the parametric value U 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) - Abs(ParametricTolerance) . if I2 > NbVKnots => V > VKnots(NbVKnots)+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. More...
void	SetPole (const Standard_Integer UIndex, const Standard_Integer 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. More...
void	SetPole (const Standard_Integer UIndex, const Standard_Integer VIndex, const gp_Pnt &P, const Standard_Real 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. More...
void	SetPoleCol (const Standard_Integer VIndex, const TColgp_Array1OfPnt &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. More...
void	SetPoleCol (const Standard_Integer VIndex, const TColgp_Array1OfPnt &CPoles, const TColStd_Array1OfReal &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. More...
void	SetPoleRow (const Standard_Integer UIndex, const TColgp_Array1OfPnt &CPoles, const TColStd_Array1OfReal &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. More...
void	SetPoleRow (const Standard_Integer UIndex, const TColgp_Array1OfPnt &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. More...
void	SetWeight (const Standard_Integer UIndex, const Standard_Integer VIndex, const Standard_Real 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 More...
void	SetWeightCol (const Standard_Integer VIndex, const TColStd_Array1OfReal &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. More...
void	SetWeightRow (const Standard_Integer UIndex, const TColStd_Array1OfReal &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. More...
void	MovePoint (const Standard_Real U, const Standard_Real V, const gp_Pnt &P, const Standard_Integer UIndex1, const Standard_Integer UIndex2, const Standard_Integer VIndex1, const Standard_Integer VIndex2, Standard_Integer &UFirstIndex, Standard_Integer &ULastIndex, Standard_Integer &VFirstIndex, Standard_Integer &VLastIndex)
	Move a point with parameter U and V to P. <br> given u,v as parameters) to reach a new position <br> UIndex1, UIndex2, VIndex1, VIndex2: <br> indicates the poles which can be moved <br> if Problem in BSplineBasis calculation, no change <br> for the curve and <br> UFirstIndex, VLastIndex = 0 <br> VFirstIndex, VLastIndex = 0 <br> 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 More...
Standard_Boolean	IsUClosed () const
	Returns true if the first control points row and the last control points row are identical. The tolerance criterion is Resolution from package gp. More...
Standard_Boolean	IsVClosed () const
	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. More...
Standard_Boolean	IsCNu (const Standard_Integer N) const
	Returns True if the order of continuity of the surface in the U direction is N. //! Raised if N < 0. More...
Standard_Boolean	IsCNv (const Standard_Integer N) const
	Returns True if the order of continuity of the surface in the V direction is N. //! Raised if N < 0. More...
Standard_Boolean	IsUPeriodic () const
	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. More...
Standard_Boolean	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| More...
Standard_Boolean	IsVPeriodic () const
	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. More...
Standard_Boolean	IsVRational () const
	Returns False if for each column of weights all the weights <br> 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| More...
Standard_Boolean	IsCacheValid (const Standard_Real UParameter, const Standard_Real VParameter) const
	Tells whether the Cache is valid for the <br> given parameter <br> Warnings : the parameter must be normalized within the period if the curve is periodic. Otherwise the answer will be false More...
void	Bounds (Standard_Real &U1, Standard_Real &U2, Standard_Real &V1, Standard_Real &V2) const
	Returns the parametric bounds of the surface. <br> 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 More...
GeomAbs_Shape	Continuity () const
	Returns the continuity of the surface : <br> 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 thats 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. More...
Standard_Integer	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. More...
Standard_Integer	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. More...
Standard_Integer	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. More...
Standard_Integer	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. More...
Standard_Integer	NbUKnots () const
	Returns the number of knots in the U direction. More...
Standard_Integer	NbUPoles () const
	Returns number of poles in the U direction. More...
Standard_Integer	NbVKnots () const
	Returns the number of knots in the V direction. More...
Standard_Integer	NbVPoles () const
	Returns the number of poles in the V direction. More...
gp_Pnt	Pole (const Standard_Integer UIndex, const Standard_Integer VIndex) const
	Returns the pole of range (UIndex, VIndex). Raised if UIndex < 1 or UIndex > NbUPoles or VIndex < 1 or VIndex > NbVPoles. More...
void	Poles (TColgp_Array2OfPnt &P) const
	Returns the poles of the B-spline surface. <br> Raised if the length of P in the U and V direction is not equal to NbUpoles and NbVPoles. More...
Standard_Integer	UDegree () const
	Returns the degree of the normalized B-splines Ni,n in the U direction. More...
Standard_Real	UKnot (const Standard_Integer UIndex) const
	Returns the Knot value of range UIndex. //! Raised if UIndex < 1 or UIndex > NbUKnots More...
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 : More...
void	UKnots (TColStd_Array1OfReal &Ku) const
	Returns the knots in the U direction. <br> Raised if the length of Ku is not equal to the number of knots in the U direction. More...
void	UKnotSequence (TColStd_Array1OfReal &Ku) const
	Returns the uknots sequence. <br> 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 More...
Standard_Integer	UMultiplicity (const Standard_Integer UIndex) const
	Returns the multiplicity value of knot of range UIndex in the u direction. //! Raised if UIndex < 1 or UIndex > NbUKnots. More...
void	UMultiplicities (TColStd_Array1OfInteger &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. More...
Standard_Integer	VDegree () const
	Returns the degree of the normalized B-splines Ni,d in the V direction. More...
Standard_Real	VKnot (const Standard_Integer VIndex) const
	Returns the Knot value of range VIndex. More...
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 : More...
void	VKnots (TColStd_Array1OfReal &Kv) const
	Returns the knots in the V direction. <br> Raised if the length of Kv is not equal to the number of knots in the V direction. More...
void	VKnotSequence (TColStd_Array1OfReal &Kv) const
	Returns the vknots sequence. <br> 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 More...
Standard_Integer	VMultiplicity (const Standard_Integer VIndex) const
	Returns the multiplicity value of knot of range VIndex in the v direction. //! Raised if VIndex < 1 or VIndex > NbVKnots More...
void	VMultiplicities (TColStd_Array1OfInteger &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. More...
Standard_Real	Weight (const Standard_Integer UIndex, const Standard_Integer VIndex) const
	Returns the weight value of range UIndex, VIndex. <br> Raised if UIndex < 1 or UIndex > NbUPoles or VIndex < 1 or VIndex > NbVPoles. More...
void	Weights (TColStd_Array2OfReal &W) const
	Returns the weights of the B-spline surface. <br> Raised if the length of W in the U and V direction is not equal to NbUPoles and NbVPoles. //! value and derivatives computation More...
void	D0 (const Standard_Real U, const Standard_Real V, gp_Pnt &P) const
	Computes the point of parameter U,V on the surface. <br> Raised only for an "OffsetSurface" if it is not possible to compute the current point. More...
void	D1 (const Standard_Real U, const Standard_Real V, gp_Pnt &P, gp_Vec &D1U, gp_Vec &D1V) const
	Raised if the continuity of the surface is not C1. More...
void	D2 (const Standard_Real U, const Standard_Real V, gp_Pnt &P, gp_Vec &D1U, gp_Vec &D1V, gp_Vec &D2U, gp_Vec &D2V, gp_Vec &D2UV) const
	Raised if the continuity of the surface is not C2. More...
void	D3 (const Standard_Real U, const Standard_Real 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
	Raised if the continuity of the surface is not C3. More...
gp_Vec	DN (const Standard_Real U, const Standard_Real V, const Standard_Integer Nu, const Standard_Integer Nv) const
	Nu is the order of derivation in the U parametric direction and Nv is the order of derivation in the V parametric direction. 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. More...
void	LocalD0 (const Standard_Real U, const Standard_Real V, const Standard_Integer FromUK1, const Standard_Integer ToUK2, const Standard_Integer FromVK1, const Standard_Integer ToVK2, gp_Pnt &P) const
	Raised if FromUK1 = ToUK2 or FromVK1 = ToVK2. <br> Raised if FromUK1, ToUK2 are not in the range [FirstUKnotIndex, LastUKnotIndex] or if FromVK1, ToVK2 are not in the range [FirstVKnotIndex, LastVKnotIndex] More...
void	LocalD1 (const Standard_Real U, const Standard_Real V, const Standard_Integer FromUK1, const Standard_Integer ToUK2, const Standard_Integer FromVK1, const Standard_Integer 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. Raised if FromUK1, ToUK2 are not in the range [FirstUKnotIndex, LastUKnotIndex] or if FromVK1, ToVK2 are not in the range [FirstVKnotIndex, LastVKnotIndex] More...
void	LocalD2 (const Standard_Real U, const Standard_Real V, const Standard_Integer FromUK1, const Standard_Integer ToUK2, const Standard_Integer FromVK1, const Standard_Integer 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. Raised if FromUK1, ToUK2 are not in the range [FirstUKnotIndex, LastUKnotIndex] or if FromVK1, ToVK2 are not in the range [FirstVKnotIndex, LastVKnotIndex] More...
void	LocalD3 (const Standard_Real U, const Standard_Real V, const Standard_Integer FromUK1, const Standard_Integer ToUK2, const Standard_Integer FromVK1, const Standard_Integer 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. Raised if FromUK1, ToUK2 are not in the range [FirstUKnotIndex, LastUKnotIndex] or if FromVK1, ToVK2 are not in the range [FirstVKnotIndex, LastVKnotIndex] More...
gp_Vec	LocalDN (const Standard_Real U, const Standard_Real V, const Standard_Integer FromUK1, const Standard_Integer ToUK2, const Standard_Integer FromVK1, const Standard_Integer ToVK2, const Standard_Integer Nu, const Standard_Integer 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. Raised if FromUK1, ToUK2 are not in the range [FirstUKnotIndex, LastUKnotIndex] or if FromVK1, ToVK2 are not in the range [FirstVKnotIndex, LastVKnotIndex] More...
gp_Pnt	LocalValue (const Standard_Real U, const Standard_Real V, const Standard_Integer FromUK1, const Standard_Integer ToUK2, const Standard_Integer FromVK1, const Standard_Integer 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. Raises if FromUK1, ToUK2 are not in the range [FirstUKnotIndex, LastUKnotIndex] or if FromVK1, ToVK2 are not in the range [FirstVKnotIndex, LastVKnotIndex] More...
Handle_Geom_Curve	UIso (const Standard_Real U) const
	Computes the U isoparametric curve. A B-spline curve is returned. More...
Handle_Geom_Curve	VIso (const Standard_Real V) const
	Computes the V isoparametric curve. A B-spline curve is returned. More...
Handle_Geom_Curve	UIso (const Standard_Real U, const Standard_Boolean CheckRational) const
	Computes the U isoparametric curve. If CheckRational=False, no try to make it non-rational. A B-spline curve is returned. More...
Handle_Geom_Curve	VIso (const Standard_Real V, const Standard_Boolean CheckRational) const
	Computes the V isoparametric curve. If CheckRational=False, no try to make it non-rational. A B-spline curve is returned. //! transformations More...
void	Transform (const gp_Trsf &T)
	Applies the transformation T to this BSpline surface. More...
void	Resolution (const Standard_Real Tolerance3D, Standard_Real &UTolerance, Standard_Real &VTolerance)
	Computes two tolerance values for this BSpline <br> surface, based on the given tolerance in 3D space Tolerance3D. The tolerances computed are: More...
Handle_Geom_Geometry	Copy () const
	Creates a new object which is a copy of this BSpline surface. More...
Public Member Functions inherited from Geom_Surface
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. More...
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. More...
virtual void	TransformParameters (Standard_Real &U, Standard_Real &V, const gp_Trsf &T) const
	Computes the parameters on the transformed surface for <br> the transform of the point of parameters U,V on <me>. <br> me->Transformed(T)->Value(U',V') is the same point as me->Value(U,V).Transformed(T) Where U',V' are the new values of U,V after calling me->TranformParameters(U,V,T) This methods does not change <U> and <V> It can be redefined. For example on the Plane, Cylinder, Cone, Revolved and Extruded surfaces. More...
virtual gp_GTrsf2d	ParametricTransformation (const gp_Trsf &T) const
	Returns a 2d transformation used to find the new <br> parameters of a point on the transformed surface. <br> me->Transformed(T)->Value(U',V') is the same point as me->Value(U,V).Transformed(T) Where U',V' are obtained by transforming U,V with th 2d transformation returned by me->ParametricTransformation(T) This methods returns an identity transformation It can be redefined. For example on the Plane, Cylinder, Cone, Revolved and Extruded surfaces. More...
virtual Standard_Real	UPeriod () const
	Returns the period of this surface in the u <br> parametric direction. //! raises if the surface is not uperiodic. More...
virtual Standard_Real	VPeriod () const
	Returns the period of this surface in the v parametric direction. //! raises if the surface is not vperiodic. More...
gp_Pnt	Value (const Standard_Real U, const Standard_Real V) const
	Computes the point of parameter U on the surface. <br> It is implemented with D0 Raised only for an "OffsetSurface" if it is not possible to compute the current point. More...
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. More...
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. More...
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). More...
void	Rotate (const gp_Ax1 &A1, const Standard_Real Ang)
	Rotates a Geometry. A1 is the axis of the rotation. Ang is the angular value of the rotation in radians. More...
void	Scale (const gp_Pnt &P, const Standard_Real S)
	Scales a Geometry. S is the scaling value. More...
void	Translate (const gp_Vec &V)
	Translates a Geometry. V is the vector of the tanslation. More...
void	Translate (const gp_Pnt &P1, const gp_Pnt &P2)
	Translates a Geometry from the point P1 to the point P2. More...
Handle_Geom_Geometry	Mirrored (const gp_Pnt &P) const
Handle_Geom_Geometry	Mirrored (const gp_Ax1 &A1) const
Handle_Geom_Geometry	Mirrored (const gp_Ax2 &A2) const
Handle_Geom_Geometry	Rotated (const gp_Ax1 &A1, const Standard_Real Ang) const
Handle_Geom_Geometry	Scaled (const gp_Pnt &P, const Standard_Real S) const
Handle_Geom_Geometry	Transformed (const gp_Trsf &T) const
Handle_Geom_Geometry	Translated (const gp_Vec &V) const
Handle_Geom_Geometry	Translated (const gp_Pnt &P1, const gp_Pnt &P2) const
Public Member Functions inherited from MMgt_TShared
virtual void	Delete () const
	Memory deallocator for transient classes. More...
Public Member Functions inherited from Standard_Transient
	Standard_Transient ()
	Empty constructor. More...
	Standard_Transient (const Standard_Transient &)
	Copy constructor – does nothing. More...
Standard_Transient &	operator= (const Standard_Transient &)
	Assignment operator, needed to avoid copying reference counter. More...
virtual	~Standard_Transient ()
	Destructor must be virtual. More...
virtual void	ShallowDump (Standard_OStream &) const
virtual const Handle_Standard_Type &	DynamicType () const
	Returns a type information object about this object. More...
Standard_Boolean	IsInstance (const Handle_Standard_Type &theType) const
	Returns a true value if this is an instance of Type. More...
Standard_Boolean	IsInstance (const Standard_CString theTypeName) const
	Returns a true value if this is an instance of TypeName. More...
Standard_Boolean	IsKind (const 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. More...
Standard_Boolean	IsKind (const Standard_CString 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. More...
virtual Handle_Standard_Transient	This () const
	Returns a Handle which references this object. Must never be called to objects created in stack. More...
Standard_Integer	GetRefCount () const
	Get the reference counter of this object. More...

Static Public Member Functions
static Standard_Integer	MaxDegree ()
	Returns the value of the maximum degree of the normalized B-spline basis functions in the u and v directions. More...

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::Geom_BSplineSurface	(	const TColgp_Array2OfPnt &	Poles,
		const TColStd_Array1OfReal &	UKnots,
		const TColStd_Array1OfReal &	VKnots,
		const TColStd_Array1OfInteger &	UMults,
		const TColStd_Array1OfInteger &	VMults,
		const Standard_Integer	UDegree,
		const Standard_Integer	VDegree,
		const Standard_Boolean	UPeriodic = Standard_False,
		const Standard_Boolean	VPeriodic = Standard_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
recommanded 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::Geom_BSplineSurface	(	const TColgp_Array2OfPnt &	Poles,
		const TColStd_Array2OfReal &	Weights,
		const TColStd_Array1OfReal &	UKnots,
		const TColStd_Array1OfReal &	VKnots,
		const TColStd_Array1OfInteger &	UMults,
		const TColStd_Array1OfInteger &	VMults,
		const Standard_Integer	UDegree,
		const Standard_Integer	VDegree,
		const Standard_Boolean	UPeriodic = Standard_False,
		const Standard_Boolean	VPeriodic = Standard_False
	)

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

//! 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
recommanded 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.

Member Function Documentation

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

virtual

Returns the parametric bounds of the surface. <br>

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.

void Geom_BSplineSurface::CheckAndSegment	(	const Standard_Real	U1,
		const Standard_Real	U2,
		const Standard_Real	V1,
		const Standard_Real	V2
	)

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

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

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

GeomAbs_Shape Geom_BSplineSurface::Continuity ( ) const

virtual

Returns the continuity of the surface : <br>

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 thats 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.

Handle_Geom_Geometry Geom_BSplineSurface::Copy ( ) const

virtual

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

Implements Geom_Geometry.

void Geom_BSplineSurface::D0 ( const Standard_Real  U, const Standard_Real  V, gp_Pnt &  P  ) const

virtual

Computes the point of parameter U,V on the surface. <br>

Raised only for an "OffsetSurface" if it is not possible to
compute the current point.

Implements Geom_Surface.

void Geom_BSplineSurface::D1 ( const Standard_Real  U, const Standard_Real  V, gp_Pnt &  P, gp_Vec &  D1U, gp_Vec &  D1V  ) const

virtual

Raised if the continuity of the surface is not C1.

Implements Geom_Surface.

void Geom_BSplineSurface::D2 ( const Standard_Real  U, const Standard_Real  V, gp_Pnt &  P, gp_Vec &  D1U, gp_Vec &  D1V, gp_Vec &  D2U, gp_Vec &  D2V, gp_Vec &  D2UV  ) const

virtual

Raised if the continuity of the surface is not C2.

Implements Geom_Surface.

void Geom_BSplineSurface::D3 ( const Standard_Real  U, const Standard_Real  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

virtual

Raised if the continuity of the surface is not C3.

Implements Geom_Surface.

gp_Vec Geom_BSplineSurface::DN ( const Standard_Real  U, const Standard_Real  V, const Standard_Integer  Nu, const Standard_Integer  Nv  ) const

virtual

Nu is the order of derivation in the U parametric direction and
Nv is the order of derivation in the V parametric direction.
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.

void Geom_BSplineSurface::ExchangeUV

(

)

 Exchanges the u and v parametric directions on <br>

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.
  

Standard_Integer 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.

Standard_Integer 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.

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

 Increases the degrees of this BSpline surface to <br>

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 Geom_BSplineSurface::IncreaseUMultiplicity	(	const Standard_Integer	UIndex,
		const Standard_Integer	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.

void Geom_BSplineSurface::IncreaseUMultiplicity	(	const Standard_Integer	FromI1,
		const Standard_Integer	ToI2,
		const Standard_Integer	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.

void Geom_BSplineSurface::IncreaseVMultiplicity	(	const Standard_Integer	VIndex,
		const Standard_Integer	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.

void Geom_BSplineSurface::IncreaseVMultiplicity	(	const Standard_Integer	FromI1,
		const Standard_Integer	ToI2,
		const Standard_Integer	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.

void Geom_BSplineSurface::IncrementUMultiplicity	(	const Standard_Integer	FromI1,
		const Standard_Integer	ToI2,
		const Standard_Integer	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.

void Geom_BSplineSurface::IncrementVMultiplicity	(	const Standard_Integer	FromI1,
		const Standard_Integer	ToI2,
		const Standard_Integer	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.

void Geom_BSplineSurface::InsertUKnot	(	const Standard_Real	U,
		const Standard_Integer	M,
		const Standard_Real	ParametricTolerance,
		const Standard_Boolean	Add = Standard_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].

void Geom_BSplineSurface::InsertUKnots	(	const TColStd_Array1OfReal &	Knots,
		const TColStd_Array1OfInteger &	Mults,
		const Standard_Real	ParametricTolerance = 0.0,
		const Standard_Boolean	Add = Standard_True
	)

void Geom_BSplineSurface::InsertVKnot	(	const Standard_Real	V,
		const Standard_Integer	M,
		const Standard_Real	ParametricTolerance,
		const Standard_Boolean	Add = Standard_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].

void Geom_BSplineSurface::InsertVKnots	(	const TColStd_Array1OfReal &	Knots,
		const TColStd_Array1OfInteger &	Mults,
		const Standard_Real	ParametricTolerance = 0.0,
		const Standard_Boolean	Add = Standard_True
	)

 Inserts into the knots table for the corresponding <br>

parametric direction of this BSpline surface:

• the value U, or V, with the multiplicity M (defaulted to 1), or
  
• 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
  Standard_Real::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.
  

Standard_Boolean Geom_BSplineSurface::IsCacheValid	(	const Standard_Real	UParameter,
		const Standard_Real	VParameter
	)		const

         Tells whether the Cache is valid for the <br>
      given parameter <br>

Warnings : the parameter must be normalized within
the period if the curve is periodic. Otherwise
the answer will be false

Standard_Boolean Geom_BSplineSurface::IsCNu ( const Standard_Integer  N ) const

virtual

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

Implements Geom_Surface.

Standard_Boolean Geom_BSplineSurface::IsCNv ( const Standard_Integer  N ) const

virtual

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

Implements Geom_Surface.

Standard_Boolean Geom_BSplineSurface::IsUClosed ( ) const

virtual

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.

Standard_Boolean Geom_BSplineSurface::IsUPeriodic ( ) const

virtual

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.

Standard_Boolean 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|

Standard_Boolean Geom_BSplineSurface::IsVClosed ( ) const

virtual

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.

Standard_Boolean Geom_BSplineSurface::IsVPeriodic ( ) const

virtual

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.

Standard_Boolean Geom_BSplineSurface::IsVRational

(

)

const

Returns False if for each column of weights all the weights <br>

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|

Standard_Integer 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.

Standard_Integer 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.

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

Raised if FromUK1 = ToUK2 or FromVK1 = ToVK2. <br>

Raised if FromUK1, ToUK2 are not in the range [FirstUKnotIndex,
LastUKnotIndex] or if FromVK1, ToVK2 are not in the range
[FirstVKnotIndex, LastVKnotIndex]

void Geom_BSplineSurface::LocalD1	(	const Standard_Real	U,
		const Standard_Real	V,
		const Standard_Integer	FromUK1,
		const Standard_Integer	ToUK2,
		const Standard_Integer	FromVK1,
		const Standard_Integer	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.
Raised if FromUK1, ToUK2 are not in the range [FirstUKnotIndex,
LastUKnotIndex] or if FromVK1, ToVK2 are not in the range
[FirstVKnotIndex, LastVKnotIndex]

void Geom_BSplineSurface::LocalD2	(	const Standard_Real	U,
		const Standard_Real	V,
		const Standard_Integer	FromUK1,
		const Standard_Integer	ToUK2,
		const Standard_Integer	FromVK1,
		const Standard_Integer	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.
Raised if FromUK1, ToUK2 are not in the range [FirstUKnotIndex,
LastUKnotIndex] or if FromVK1, ToVK2 are not in the range
[FirstVKnotIndex, LastVKnotIndex]

void Geom_BSplineSurface::LocalD3	(	const Standard_Real	U,
		const Standard_Real	V,
		const Standard_Integer	FromUK1,
		const Standard_Integer	ToUK2,
		const Standard_Integer	FromVK1,
		const Standard_Integer	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.
Raised if FromUK1, ToUK2 are not in the range [FirstUKnotIndex,
LastUKnotIndex] or if FromVK1, ToVK2 are not in the range
[FirstVKnotIndex, LastVKnotIndex]

gp_Vec Geom_BSplineSurface::LocalDN	(	const Standard_Real	U,
		const Standard_Real	V,
		const Standard_Integer	FromUK1,
		const Standard_Integer	ToUK2,
		const Standard_Integer	FromVK1,
		const Standard_Integer	ToVK2,
		const Standard_Integer	Nu,
		const Standard_Integer	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.
Raised if FromUK1, ToUK2 are not in the range [FirstUKnotIndex,
LastUKnotIndex] or if FromVK1, ToVK2 are not in the range
[FirstVKnotIndex, LastVKnotIndex]

gp_Pnt Geom_BSplineSurface::LocalValue	(	const Standard_Real	U,
		const Standard_Real	V,
		const Standard_Integer	FromUK1,
		const Standard_Integer	ToUK2,
		const Standard_Integer	FromVK1,
		const Standard_Integer	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.
Raises if FromUK1, ToUK2 are not in the range [FirstUKnotIndex,
LastUKnotIndex] or if FromVK1, ToVK2 are not in the range
[FirstVKnotIndex, LastVKnotIndex]

void Geom_BSplineSurface::LocateU	(	const Standard_Real	U,
		const Standard_Real	ParametricTolerance,
		Standard_Integer &	I1,
		Standard_Integer &	I2,
		const Standard_Boolean	WithKnotRepetition = Standard_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) - Abs(ParametricTolerance)
. if I2 > NbUKnots => U > UKnots(NbUKnots)+Abs(ParametricTolerance)

void Geom_BSplineSurface::LocateV	(	const Standard_Real	V,
		const Standard_Real	ParametricTolerance,
		Standard_Integer &	I1,
		Standard_Integer &	I2,
		const Standard_Boolean	WithKnotRepetition = Standard_False
	)		const

Locates the parametric value U 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) - Abs(ParametricTolerance)
. if I2 > NbVKnots => V > VKnots(NbVKnots)+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.

static Standard_Integer Geom_BSplineSurface::MaxDegree ( )

static

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

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

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

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

Standard_Integer Geom_BSplineSurface::NbUKnots

(

)

const

Returns the number of knots in the U direction.

Standard_Integer Geom_BSplineSurface::NbUPoles

(

)

const

Returns number of poles in the U direction.

Standard_Integer Geom_BSplineSurface::NbVKnots

(

)

const

Returns the number of knots in the V direction.

Standard_Integer Geom_BSplineSurface::NbVPoles

(

)

const

Returns the number of poles in the V direction.

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

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

gp_Pnt Geom_BSplineSurface::Pole	(	const Standard_Integer	UIndex,
		const Standard_Integer	VIndex
	)		const

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

void Geom_BSplineSurface::Poles

(

TColgp_Array2OfPnt &

P

)

const

Returns the poles of the B-spline surface. <br>

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

Standard_Boolean Geom_BSplineSurface::RemoveUKnot	(	const Standard_Integer	Index,
		const Standard_Integer	M,
		const Standard_Real	Tolerance
	)

Standard_Boolean Geom_BSplineSurface::RemoveVKnot	(	const Standard_Integer	Index,
		const Standard_Integer	M,
		const Standard_Real	Tolerance
	)

 Reduces to M the multiplicity of the knot of index <br>

Index in the given 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 Geom_BSplineSurface::Resolution	(	const Standard_Real	Tolerance3D,
		Standard_Real &	UTolerance,
		Standard_Real &	VTolerance
	)

 Computes two tolerance values for this BSpline <br>

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
  

void Geom_BSplineSurface::Segment	(	const Standard_Real	U1,
		const Standard_Real	U2,
		const Standard_Real	V1,
		const Standard_Real	V2
	)

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

The control points are modified, the first and the last point
are not the same.
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

void Geom_BSplineSurface::SetPole	(	const Standard_Integer	UIndex,
		const Standard_Integer	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.

void Geom_BSplineSurface::SetPole	(	const Standard_Integer	UIndex,
		const Standard_Integer	VIndex,
		const gp_Pnt &	P,
		const Standard_Real	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.

void Geom_BSplineSurface::SetPoleCol	(	const Standard_Integer	VIndex,
		const TColgp_Array1OfPnt &	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.

void Geom_BSplineSurface::SetPoleCol	(	const Standard_Integer	VIndex,
		const TColgp_Array1OfPnt &	CPoles,
		const TColStd_Array1OfReal &	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.

void Geom_BSplineSurface::SetPoleRow	(	const Standard_Integer	UIndex,
		const TColgp_Array1OfPnt &	CPoles,
		const TColStd_Array1OfReal &	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.

void Geom_BSplineSurface::SetPoleRow	(	const Standard_Integer	UIndex,
		const TColgp_Array1OfPnt &	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.

void Geom_BSplineSurface::SetUKnot	(	const Standard_Integer	UIndex,
		const Standard_Real	K
	)

 Substitutes the UKnots of range UIndex with K. <br>

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

void Geom_BSplineSurface::SetUKnot	(	const Standard_Integer	UIndex,
		const Standard_Real	K,
		const Standard_Integer	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.

void Geom_BSplineSurface::SetUKnots

(

const TColStd_Array1OfReal &

UK

)

 Changes all the U-knots of the surface. <br>

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

void Geom_BSplineSurface::SetUNotPeriodic

(

)

void Geom_BSplineSurface::SetUOrigin

(

const Standard_Integer

Index

)

 Assigns the knot of index Index in the knots table in <br>

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 Geom_BSplineSurface::SetUPeriodic

(

)

Sets the surface U periodic.

void Geom_BSplineSurface::SetVKnot	(	const Standard_Integer	VIndex,
		const Standard_Real	K
	)

 Substitutes the VKnots of range VIndex with K. <br>

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

void Geom_BSplineSurface::SetVKnot	(	const Standard_Integer	VIndex,
		const Standard_Real	K,
		const Standard_Integer	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.

void Geom_BSplineSurface::SetVKnots

(

const TColStd_Array1OfReal &

VK

)

 Changes all the V-knots of the surface. <br>

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

void Geom_BSplineSurface::SetVNotPeriodic

(

)

 Modifies this surface to be periodic in the u (or v) parametric direction. <br>

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 (or
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 Geom_BSplineSurface::SetVOrigin

(

const Standard_Integer

Index

)

 Assigns the knot of index Index in the knots table in <br>

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 Geom_BSplineSurface::SetVPeriodic

(

)

  Modifies this surface to be periodic in the u (or v) <br>

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 (or
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 Geom_BSplineSurface::SetWeight	(	const Standard_Integer	UIndex,
		const Standard_Integer	VIndex,
		const Standard_Real	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

void Geom_BSplineSurface::SetWeightCol	(	const Standard_Integer	VIndex,
		const TColStd_Array1OfReal &	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.

void Geom_BSplineSurface::SetWeightRow	(	const Standard_Integer	UIndex,
		const TColStd_Array1OfReal &	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.

void Geom_BSplineSurface::Transform ( const gp_Trsf &  T )

virtual

Applies the transformation T to this BSpline surface.

Implements Geom_Geometry.

Standard_Integer Geom_BSplineSurface::UDegree

(

)

const

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

Handle_Geom_Curve Geom_BSplineSurface::UIso ( const Standard_Real  U ) const

virtual

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

Implements Geom_Surface.

Handle_Geom_Curve Geom_BSplineSurface::UIso	(	const Standard_Real	U,
		const Standard_Boolean	CheckRational
	)		const

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

Standard_Real Geom_BSplineSurface::UKnot

(

const Standard_Integer

UIndex

)

const

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

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.
  

void Geom_BSplineSurface::UKnots

(

TColStd_Array1OfReal &

Ku

)

const

Returns the knots in the U direction. <br>

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

void Geom_BSplineSurface::UKnotSequence

(

TColStd_Array1OfReal &

Ku

)

const

 Returns the uknots sequence. <br>

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

void Geom_BSplineSurface::UMultiplicities

(

TColStd_Array1OfInteger &

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.

Standard_Integer Geom_BSplineSurface::UMultiplicity

(

const Standard_Integer

UIndex

)

const

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

void Geom_BSplineSurface::UReverse ( )

virtual

Reverses the U direction of parametrization of <me>.
The bounds of the surface are not modified.

Implements Geom_Surface.

Standard_Real Geom_BSplineSurface::UReversedParameter ( const Standard_Real  U ) const

virtual

 Returns the  parameter on the  Ureversed surface for <br>
     the point of parameter U on <me>. <br>

me->UReversed()->Value(me->UReversedParameter(U),V)

is the same point as

me->Value(U,V)

Implements Geom_Surface.

Standard_Integer Geom_BSplineSurface::VDegree

(

)

const

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

Handle_Geom_Curve Geom_BSplineSurface::VIso ( const Standard_Real  V ) const

virtual

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

Implements Geom_Surface.

Handle_Geom_Curve Geom_BSplineSurface::VIso	(	const Standard_Real	V,
		const Standard_Boolean	CheckRational
	)		const

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

Standard_Real Geom_BSplineSurface::VKnot

(

const Standard_Integer

VIndex

)

const

Returns the Knot value of range VIndex.

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.
  

void Geom_BSplineSurface::VKnots

(

TColStd_Array1OfReal &

Kv

)

const

Returns the knots in the V direction. <br>

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

void Geom_BSplineSurface::VKnotSequence

(

TColStd_Array1OfReal &

Kv

)

const

 Returns the vknots sequence. <br>

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

void Geom_BSplineSurface::VMultiplicities

(

TColStd_Array1OfInteger &

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.

Standard_Integer Geom_BSplineSurface::VMultiplicity

(

const Standard_Integer

VIndex

)

const

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

void Geom_BSplineSurface::VReverse ( )

virtual

 Changes the orientation of this BSpline surface in the <br>

u (or 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.

Standard_Real Geom_BSplineSurface::VReversedParameter ( const Standard_Real  V ) const

virtual

 Computes the u (or v) parameter on the modified <br>

surface, produced by reversing its u (or v) parametric
direction, for the point of u parameter U, (or of v
parameter V) on this BSpline surface.
For a BSpline surface, these functions return respectively:

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

Implements Geom_Surface.

Standard_Real Geom_BSplineSurface::Weight	(	const Standard_Integer	UIndex,
		const Standard_Integer	VIndex
	)		const

Returns the weight value of range UIndex, VIndex. <br>

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

void Geom_BSplineSurface::Weights

(

TColStd_Array2OfReal &

W

)

const

Returns the weights of the B-spline surface. <br>

Raised if the length of W in the U and V direction is
not equal to NbUPoles and NbVPoles.
//! value and derivatives computation

---

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

• Geom_BSplineSurface.hxx