Open CASCADE Technology  7.5.0

# 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:
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## 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 default value is 1.). More...

void ExchangeUV ()
Exchanges the u and v parametric directions on this BSpline surface. As a consequence: More...

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. More...

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. 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 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 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 ()
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. More...

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. More...

void UReverse () override
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. More...

void VReverse () override
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. More...

Standard_Real UReversedParameter (const Standard_Real U) const override
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: More...

Standard_Real VReversedParameter (const Standard_Real V) const override
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: More...

void IncreaseDegree (const Standard_Integer UDegree, const Standard_Integer 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(). More...

void InsertUKnots (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 U parametric direction of this BSpline surface: More...

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 V parametric direction of this BSpline surface: More...

Standard_Boolean RemoveUKnot (const Standard_Integer Index, const Standard_Integer M, const Standard_Real 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. More...

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 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. 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]. 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. 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. 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. 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. 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. 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. 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. More...

void Segment (const Standard_Real U1, const Standard_Real U2, const Standard_Real V1, const Standard_Real V2, const Standard_Real theUTolerance=Precision::PConfusion(), const Standard_Real 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. More...

void CheckAndSegment (const Standard_Real U1, const Standard_Real U2, const Standard_Real V1, const Standard_Real V2, const Standard_Real theUTolerance=Precision::PConfusion(), const Standard_Real theVTolerance=Precision::PConfusion())
Segments the surface between U1 and U2 in the U-Direction. between V1 and V2 in the V-Direction. More...

void SetUKnot (const Standard_Integer UIndex, const Standard_Real K)
Substitutes the UKnots of range UIndex with K. More...

void SetUKnots (const TColStd_Array1OfReal &UK)
Changes all the U-knots of the surface. The multiplicity of the knots are not modified. 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. More...

void SetVKnot (const Standard_Integer VIndex, const Standard_Real K)
Substitutes the VKnots of range VIndex with K. More...

void SetVKnots (const TColStd_Array1OfReal &VK)
Changes all the V-knots of the surface. The multiplicity of the knots are not modified. 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. 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 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) - 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. 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. 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. 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. 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. 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. 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. More...

void SetWeightCol (const Standard_Integer VIndex, const TColStd_Array1OfReal &CPoleWeights)
Changes a column of weights of a part of this column. More...

void SetWeightRow (const Standard_Integer UIndex, const TColStd_Array1OfReal &CPoleWeights)
Changes a row of weights or a part of this row. 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. 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. More...

Standard_Boolean IsUClosed () const override
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 override
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 override
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 override
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 override
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 override
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 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...

void Bounds (Standard_Real &U1, Standard_Real &U2, Standard_Real &V1, Standard_Real &V2) const override
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. More...

GeomAbs_Shape Continuity () const override
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 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...

const gp_PntPole (const Standard_Integer UIndex, const Standard_Integer VIndex) const
Returns the pole of range (UIndex, VIndex). More...

void Poles (TColgp_Array2OfPnt &P) const
Returns the poles of the B-spline surface. More...

const TColgp_Array2OfPntPoles () const
Returns the poles of the B-spline surface. 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. More...

const TColStd_Array1OfRealUKnots () const
Returns the knots in the U direction. More...

void UKnotSequence (TColStd_Array1OfReal &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}. More...

const TColStd_Array1OfRealUKnotSequence () 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}. 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. More...

const TColStd_Array1OfIntegerUMultiplicities () const
Returns the multiplicities of the 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. Raised if VIndex < 1 or VIndex > NbVKnots. 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. More...

const TColStd_Array1OfRealVKnots () const
Returns the knots in the V direction. More...

void VKnotSequence (TColStd_Array1OfReal &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}. More...

const TColStd_Array1OfRealVKnotSequence () 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}. 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. More...

const TColStd_Array1OfIntegerVMultiplicities () const
Returns the multiplicities of the 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. More...

void Weights (TColStd_Array2OfReal &W) const
Returns the weights of the B-spline surface. More...

const TColStd_Array2OfRealWeights () const
Returns the weights of the B-spline surface. value and derivatives computation. More...

void D0 (const Standard_Real U, const Standard_Real V, gp_Pnt &P) const override
Computes the point of parameter U,V on the surface. More...

void D1 (const Standard_Real U, const Standard_Real V, gp_Pnt &P, gp_Vec &D1U, gp_Vec &D1V) const override
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 override
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 override
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 override
Nu is the order of derivation in the U parametric direction and Nv is the order of derivation in the V parametric direction. 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. 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. 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. 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. 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. 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. More...

Handle< Geom_CurveUIso (const Standard_Real U) const override
Computes the U isoparametric curve. A B-spline curve is returned. More...

Handle< Geom_CurveVIso (const Standard_Real V) const override
Computes the V isoparametric curve. A B-spline curve is returned. More...

Handle< Geom_CurveUIso (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_CurveVIso (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) override
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 surface, based on the given tolerance in 3D space Tolerance3D. The tolerances computed are: More...

Handle< Geom_GeometryCopy () const override
Creates a new object which is a copy of this BSpline surface. More...

virtual void DumpJson (Standard_OStream &theOStream, Standard_Integer theDepth=-1) const override
Dumps the content of me into the stream. More...

Public Member Functions inherited from Geom_Surface
Handle< Geom_SurfaceUReversed () 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_SurfaceVReversed () 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 the transform of the point of parameters U,V on <me>. More...

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. More...

virtual Standard_Real UPeriod () const
Returns the period of this surface in the u 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. 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_GeometryMirrored (const gp_Pnt &P) const

Handle< Geom_GeometryMirrored (const gp_Ax1 &A1) const

Handle< Geom_GeometryMirrored (const gp_Ax2 &A2) const

Handle< Geom_GeometryRotated (const gp_Ax1 &A1, const Standard_Real Ang) const

Handle< Geom_GeometryScaled (const gp_Pnt &P, const Standard_Real S) const

Handle< Geom_GeometryTransformed (const gp_Trsf &T) const

Handle< Geom_GeometryTranslated (const gp_Vec &V) const

Handle< Geom_GeometryTranslated (const gp_Pnt &P1, const gp_Pnt &P2) const

Public Member Functions inherited from Standard_Transient
Standard_Transient ()
Empty constructor. More...

Standard_Transient (const Standard_Transient &)
Copy constructor – does nothing. More...

Standard_Transientoperator= (const Standard_Transient &)
Assignment operator, needed to avoid copying reference counter. More...

virtual ~Standard_Transient ()
Destructor must be virtual. More...

virtual void Delete () const
Memory deallocator for transient classes. More...

virtual const opencascade::handle< Standard_Type > & DynamicType () const

Standard_Boolean IsInstance (const opencascade::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 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. 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...

Standard_TransientThis () 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. More...

Standard_Integer GetRefCount () const
Get the reference counter of this object. More...

void IncrementRefCounter () const
Increments the reference counter of this object. More...

Standard_Integer DecrementRefCounter () const
Decrements the reference counter of this object; returns the decremented value. 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...

Static Public Member Functions inherited from Standard_Transient
static const char * get_type_name ()

static const opencascade::handle< Standard_Type > & get_type_descriptor ()
Returns type descriptor of Standard_Transient class. More...

## Protected Member Functions

void segment (const Standard_Real U1, const Standard_Real U2, const Standard_Real V1, const Standard_Real V2, const Standard_Real EpsU, const Standard_Real EpsV, const Standard_Boolean SegmentInU, const Standard_Boolean 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. More...

## Additional Inherited Members

Public Types inherited from Standard_Transient
typedef void base_type

## 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

## ◆ Geom_BSplineSurface() [1/2]

 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() [2/2]

 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 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.

## ◆ Bounds()

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

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 Standard_Real U1, const Standard_Real U2, const Standard_Real V1, const Standard_Real V2, const Standard_Real theUTolerance = `Precision::PConfusion()`, const Standard_Real 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 correponding 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()).

## ◆ Continuity()

 GeomAbs_Shape Geom_BSplineSurface::Continuity ( ) const
overridevirtual

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 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.

## ◆ Copy()

 Handle< Geom_Geometry > Geom_BSplineSurface::Copy ( ) const
overridevirtual

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

Implements Geom_Geometry.

## ◆ D0()

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

Computes the point of parameter U,V on the surface.

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

Implements Geom_Surface.

## ◆ D1()

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

Raised if the continuity of the surface is not C1.

Implements Geom_Surface.

## ◆ D2()

 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
overridevirtual

Raised if the continuity of the surface is not C2.

Implements Geom_Surface.

## ◆ D3()

 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
overridevirtual

Raised if the continuity of the surface is not C3.

Implements Geom_Surface.

## ◆ DN()

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

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.

## ◆ DumpJson()

 virtual void Geom_BSplineSurface::DumpJson ( Standard_OStream & theOStream, Standard_Integer theDepth = `-1` ) const
overridevirtual

Dumps the content of me into the stream.

Reimplemented from Geom_Surface.

## ◆ 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()

 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.

## ◆ FirstVKnotIndex()

 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.

## ◆ IncreaseDegree()

 void Geom_BSplineSurface::IncreaseDegree ( const Standard_Integer UDegree, const Standard_Integer 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 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.

## ◆ IncreaseUMultiplicity() [2/2]

 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.

## ◆ IncreaseVMultiplicity() [1/2]

 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.

## ◆ IncreaseVMultiplicity() [2/2]

 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.

## ◆ IncrementUMultiplicity()

 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.

## ◆ IncrementVMultiplicity()

 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.

## ◆ InsertUKnot()

 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].

## ◆ InsertUKnots()

 void Geom_BSplineSurface::InsertUKnots ( 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 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 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.

## ◆ InsertVKnot()

 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].

## ◆ InsertVKnots()

 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 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 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.

## ◆ IsCNu()

 Standard_Boolean Geom_BSplineSurface::IsCNu ( const Standard_Integer N ) const
overridevirtual

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

Implements Geom_Surface.

## ◆ IsCNv()

 Standard_Boolean Geom_BSplineSurface::IsCNv ( const Standard_Integer N ) const
overridevirtual

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

Implements Geom_Surface.

## ◆ IsUClosed()

 Standard_Boolean Geom_BSplineSurface::IsUClosed ( ) const
overridevirtual

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()

 Standard_Boolean Geom_BSplineSurface::IsUPeriodic ( ) const
overridevirtual

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()

 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|.

## ◆ IsVClosed()

 Standard_Boolean Geom_BSplineSurface::IsVClosed ( ) const
overridevirtual

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()

 Standard_Boolean Geom_BSplineSurface::IsVPeriodic ( ) const
overridevirtual

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()

 Standard_Boolean 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()

 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.

## ◆ LastVKnotIndex()

 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.

## ◆ LocalD0()

 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.

## ◆ LocalD1()

 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.

## ◆ LocalD2()

 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.

## ◆ LocalD3()

 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.

## ◆ LocalDN()

 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.

## ◆ LocalValue()

 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.

## ◆ LocateU()

 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)

## ◆ LocateV()

 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 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) - 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.

## ◆ MaxDegree()

 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.

## ◆ MovePoint()

 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. 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()

 Standard_Integer Geom_BSplineSurface::NbUKnots ( ) const

Returns the number of knots in the U direction.

## ◆ NbUPoles()

 Standard_Integer Geom_BSplineSurface::NbUPoles ( ) const

Returns number of poles in the U direction.

## ◆ NbVKnots()

 Standard_Integer Geom_BSplineSurface::NbVKnots ( ) const

Returns the number of knots in the V direction.

## ◆ NbVPoles()

 Standard_Integer Geom_BSplineSurface::NbVPoles ( ) const

Returns the number of poles in the V direction.

## ◆ PeriodicNormalization()

 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

## ◆ Pole()

 const 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.

## ◆ Poles() [1/2]

 void Geom_BSplineSurface::Poles ( TColgp_Array2OfPnt & 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.

## ◆ Poles() [2/2]

 const TColgp_Array2OfPnt& Geom_BSplineSurface::Poles ( ) const

Returns the poles of the B-spline surface.

## ◆ RemoveUKnot()

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

 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 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 Standard_Real Tolerance3D, Standard_Real & UTolerance, Standard_Real & 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 Standard_Real U1, const Standard_Real U2, const Standard_Real V1, const Standard_Real V2, const Standard_Real theUTolerance = `Precision::PConfusion()`, const Standard_Real 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 correponding 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 Standard_Real U1, const Standard_Real U2, const Standard_Real V1, const Standard_Real V2, const Standard_Real EpsU, const Standard_Real EpsV, const Standard_Boolean SegmentInU, const Standard_Boolean 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.

## ◆ SetPole() [1/2]

 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.

## ◆ SetPole() [2/2]

 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.

## ◆ SetPoleCol() [1/2]

 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.

## ◆ SetPoleCol() [2/2]

 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.

## ◆ SetPoleRow() [1/2]

 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.

## ◆ SetPoleRow() [2/2]

 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.

## ◆ SetUKnot() [1/2]

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

## ◆ SetUKnots()

 void Geom_BSplineSurface::SetUKnots ( const TColStd_Array1OfReal & 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 Standard_Integer 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 Standard_Integer VIndex, const Standard_Real 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 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.

## ◆ SetVKnots()

 void Geom_BSplineSurface::SetVKnots ( const TColStd_Array1OfReal & 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 Standard_Integer 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 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

## ◆ SetWeightCol()

 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.

## ◆ SetWeightRow()

 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.

## ◆ Transform()

 void Geom_BSplineSurface::Transform ( const gp_Trsf & T )
overridevirtual

Applies the transformation T to this BSpline surface.

Implements Geom_Geometry.

## ◆ UDegree()

 Standard_Integer Geom_BSplineSurface::UDegree ( ) const

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

## ◆ UIso() [1/2]

 Handle< Geom_Curve > Geom_BSplineSurface::UIso ( const Standard_Real U ) const
overridevirtual

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

Implements Geom_Surface.

## ◆ UIso() [2/2]

 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.

## ◆ UKnot()

 Standard_Real Geom_BSplineSurface::UKnot ( const Standard_Integer 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]

 void Geom_BSplineSurface::UKnots ( TColStd_Array1OfReal & 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.

## ◆ UKnots() [2/2]

 const TColStd_Array1OfReal& Geom_BSplineSurface::UKnots ( ) const

Returns the knots in the U direction.

## ◆ UKnotSequence() [1/2]

 void Geom_BSplineSurface::UKnotSequence ( TColStd_Array1OfReal & 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

## ◆ UKnotSequence() [2/2]

 const TColStd_Array1OfReal& 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}.

## ◆ UMultiplicities() [1/2]

 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.

## ◆ UMultiplicities() [2/2]

 const TColStd_Array1OfInteger& Geom_BSplineSurface::UMultiplicities ( ) const

Returns the multiplicities of the knots in the U direction.

## ◆ UMultiplicity()

 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.

## ◆ UReverse()

 void Geom_BSplineSurface::UReverse ( )
overridevirtual

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()

 Standard_Real Geom_BSplineSurface::UReversedParameter ( const Standard_Real U ) const
overridevirtual

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()

 Standard_Integer Geom_BSplineSurface::VDegree ( ) const

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

## ◆ VIso() [1/2]

 Handle< Geom_Curve > Geom_BSplineSurface::VIso ( const Standard_Real V ) const
overridevirtual

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

Implements Geom_Surface.

## ◆ VIso() [2/2]

 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.

## ◆ VKnot()

 Standard_Real Geom_BSplineSurface::VKnot ( const Standard_Integer 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]

 void Geom_BSplineSurface::VKnots ( TColStd_Array1OfReal & 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.

## ◆ VKnots() [2/2]

 const TColStd_Array1OfReal& Geom_BSplineSurface::VKnots ( ) const

Returns the knots in the V direction.

## ◆ VKnotSequence() [1/2]

 void Geom_BSplineSurface::VKnotSequence ( TColStd_Array1OfReal & 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

## ◆ VKnotSequence() [2/2]

 const TColStd_Array1OfReal& 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}.

## ◆ VMultiplicities() [1/2]

 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.

## ◆ VMultiplicities() [2/2]

 const TColStd_Array1OfInteger& Geom_BSplineSurface::VMultiplicities ( ) const

Returns the multiplicities of the knots in the V direction.

## ◆ VMultiplicity()

 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.

## ◆ VReverse()

 void Geom_BSplineSurface::VReverse ( )
overridevirtual

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()

 Standard_Real Geom_BSplineSurface::VReversedParameter ( const Standard_Real V ) const
overridevirtual

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()

 Standard_Real Geom_BSplineSurface::Weight ( const Standard_Integer UIndex, const Standard_Integer 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]

 void Geom_BSplineSurface::Weights ( TColStd_Array2OfReal & 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.

## ◆ Weights() [2/2]

 const TColStd_Array2OfReal* Geom_BSplineSurface::Weights ( ) const

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

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