Open CASCADE Technology
6.9.1

Describes a BSpline surface. In each parametric direction, a BSpline surface can be: More...
#include <Geom_BSplineSurface.hxx>
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 nonrational bspline 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 nonuperiodic 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 nonrational bspline 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. More...  
void  SetVPeriodic () 
Modifies this surface to be periodic in the u (or 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 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 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 () 
void  SetVNotPeriodic () 
Modifies this surface to be periodic in the u (or 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 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 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 the point of parameter U on <me>. More...  
Standard_Real  VReversedParameter (const Standard_Real V) const 
Computes the u (or v) parameter on the modified 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 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 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 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]. 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 nonuniform. 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) 
Segments the surface between U1 and U2 in the UDirection. between V1 and V2 in the VDirection. 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 UDirection. between V1 and V2 in the VDirection. 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 Uknots 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 Vknots 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 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. 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 
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 Bspline 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 Bspline 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...  
Standard_Boolean  IsCacheValid (const Standard_Real UParameter, const Standard_Real VParameter) const 
Tells whether the Cache is valid for the given parameter 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. 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 : 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 Bspline 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). More...  
void  Poles (TColgp_Array2OfPnt &P) const 
Returns the poles of the Bspline surface. More...  
const TColgp_Array2OfPnt &  Poles () const 
Returns the poles of the Bspline surface. More...  
Standard_Integer  UDegree () const 
Returns the degree of the normalized Bsplines 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 Bspline surface can be : More...  
void  UKnots (TColStd_Array1OfReal &Ku) const 
Returns the knots in the U direction. More...  
const TColStd_Array1OfReal &  UKnots () 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_Array1OfReal &  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}. 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_Array1OfInteger &  UMultiplicities () const 
Returns the multiplicities of the knots in the U direction. More...  
Standard_Integer  VDegree () const 
Returns the degree of the normalized Bsplines 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 Bspline surface can be : More...  
void  VKnots (TColStd_Array1OfReal &Kv) const 
Returns the knots in the V direction. More...  
const TColStd_Array1OfReal &  VKnots () 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_Array1OfReal &  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}. 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_Array1OfInteger &  VMultiplicities () 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 Bspline surface. More...  
const TColStd_Array2OfReal &  Weights () const 
Returns the weights of the Bspline surface. 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. 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. 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_Curve >  UIso (const Standard_Real U) const 
Computes the U isoparametric curve. A Bspline curve is returned. More...  
Handle< Geom_Curve >  VIso (const Standard_Real V) const 
Computes the V isoparametric curve. A Bspline 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 nonrational. A Bspline 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 nonrational. A Bspline 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 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 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_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 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 Bspline basis functions in the u and v directions. More...  
Describes a BSpline surface. In each parametric direction, a BSpline surface can be:
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 nonrational bspline 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 nonuperiodic 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 nonrational bspline 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 nonuperiodic 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.

virtual 
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.
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 UDirection. between V1 and V2 in the VDirection.
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

virtual 
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 Bspline 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.

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

virtual 
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.

virtual 
Raised if the continuity of the surface is not C1.
Implements Geom_Surface.

virtual 
Raised if the continuity of the surface is not C2.
Implements Geom_Surface.

virtual 
Raised if the continuity of the surface is not C3.
Implements Geom_Surface.

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 Bspline 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 this BSpline surface. As a consequence:
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 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 nonuniform.
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 parametric direction of this BSpline surface:
Standard_Boolean Geom_BSplineSurface::IsCacheValid  (  const Standard_Real  UParameter, 
const Standard_Real  VParameter  
)  const 
Tells whether the Cache is valid for the given parameter Warnings : the parameter must be normalized within the period if the curve is periodic. Otherwise the answer will be false.

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

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

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.

virtual 
Returns True if the surface is closed in the U direction and if the Bspline 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.

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.

virtual 
Returns True if the surface is closed in the V direction and if the Bspline 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 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.
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 
Returns the value of the maximum degree of the normalized Bspline 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. 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
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 Bspline surface.
Raised if the length of P in the U and V direction is not equal to NbUpoles and NbVPoles.
const TColgp_Array2OfPnt& Geom_BSplineSurface::Poles  (  )  const 
Returns the poles of the Bspline surface.
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 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 surface, based on the given tolerance in 3D space Tolerance3D. The tolerances computed are:
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 UDirection. between V1 and V2 in the VDirection. 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.
Raised if UIndex < 1 or UIndex > NbUKnots
Raised if K >= UKnots(UIndex+1) or K <= UKnots(UIndex1)
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(UIndex1) 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 Uknots 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
void Geom_BSplineSurface::SetUNotPeriodic  (  ) 
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.
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.
Raised if VIndex < 1 or VIndex > NbVKnots
Raised if K >= VKnots(VIndex+1) or K <= VKnots(VIndex1)
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(VIndex1) 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 Vknots 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
void Geom_BSplineSurface::SetVNotPeriodic  (  ) 
Modifies this surface to be periodic in the u (or 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 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 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) 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.

virtual 
Applies the transformation T to this BSpline surface.
Implements Geom_Geometry.
Standard_Integer Geom_BSplineSurface::UDegree  (  )  const 
Returns the degree of the normalized Bsplines Ni,n in the U direction.

virtual 
Computes the U isoparametric curve. A Bspline 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 nonrational. A Bspline 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 Bspline surface can be :
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.
const TColStd_Array1OfReal& Geom_BSplineSurface::UKnots  (  )  const 
Returns the knots in the U direction.
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
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}.
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.
const TColStd_Array1OfInteger& Geom_BSplineSurface::UMultiplicities  (  )  const 
Returns the multiplicities of the 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.

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

virtual 
Returns the parameter on the Ureversed surface for the point of parameter U on <me>.
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 Bsplines Ni,d in the V direction.

virtual 
Computes the V isoparametric curve. A Bspline 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 nonrational. A Bspline 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 Bspline surface can be :
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.
const TColStd_Array1OfReal& Geom_BSplineSurface::VKnots  (  )  const 
Returns the knots in the V direction.
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
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}.
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.
const TColStd_Array1OfInteger& Geom_BSplineSurface::VMultiplicities  (  )  const 
Returns the multiplicities of the 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.

virtual 
Changes the orientation of this BSpline surface in the 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.

virtual 
Computes the u (or v) parameter on the modified 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:
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.
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 Bspline surface.
Raised if the length of W in the U and V direction is not equal to NbUPoles and NbVPoles.
const TColStd_Array2OfReal& Geom_BSplineSurface::Weights  (  )  const 
Returns the weights of the Bspline surface. value and derivatives computation.