Open CASCADE Technology
6.9.1

Definition of the 1D B_spline curve. More...
#include <Law_BSpline.hxx>
Public Member Functions  
Law_BSpline (const TColStd_Array1OfReal &Poles, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Multiplicities, const Standard_Integer Degree, const Standard_Boolean Periodic=Standard_False)  
Creates a nonrational B_spline curve on the basis <Knots, Multiplicities> of degree <Degree>. More...  
Law_BSpline (const TColStd_Array1OfReal &Poles, const TColStd_Array1OfReal &Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Multiplicities, const Standard_Integer Degree, const Standard_Boolean Periodic=Standard_False)  
Creates a rational B_spline curve on the basis <Knots, Multiplicities> of degree <Degree>. More...  
void  IncreaseDegree (const Standard_Integer Degree) 
Increase the degree to <Degree>. Nothing is done if <Degree> is lower or equal to the current degree. More...  
void  IncreaseMultiplicity (const Standard_Integer Index, const Standard_Integer M) 
Increases the multiplicity of the knot <Index> to <M>. More...  
void  IncreaseMultiplicity (const Standard_Integer I1, const Standard_Integer I2, const Standard_Integer M) 
Increases the multiplicities of the knots in [I1,I2] to <M>. More...  
void  IncrementMultiplicity (const Standard_Integer I1, const Standard_Integer I2, const Standard_Integer M) 
Increment the multiplicities of the knots in [I1,I2] by <M>. More...  
void  InsertKnot (const Standard_Real U, const Standard_Integer M=1, const Standard_Real ParametricTolerance=0.0, const Standard_Boolean Add=Standard_True) 
Inserts a knot value in the sequence of knots. If <U> is an existing knot the multiplicity is increased by <M>. More...  
void  InsertKnots (const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Mults, const Standard_Real ParametricTolerance=0.0, const Standard_Boolean Add=Standard_False) 
Inserts a set of knots values in the sequence of knots. More...  
Standard_Boolean  RemoveKnot (const Standard_Integer Index, const Standard_Integer M, const Standard_Real Tolerance) 
Decrement the knots multiplicity to <M>. If M is 0 the knot is removed. The Poles sequence is modified. More...  
void  Reverse () 
Changes the direction of parametrization of <me>. The Knot sequence is modified, the FirstParameter and the LastParameter are not modified. The StartPoint of the initial curve becomes the EndPoint of the reversed curve and the EndPoint of the initial curve becomes the StartPoint of the reversed curve. More...  
Standard_Real  ReversedParameter (const Standard_Real U) const 
Returns the parameter on the reversed curve for the point of parameter U on <me>. More...  
void  Segment (const Standard_Real U1, const Standard_Real U2) 
Segments the curve between U1 and U2. 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 curve <me> or if the curve makes loop. After the segmentation the length of a curve can be null. raises if U2 < U1. More...  
void  SetKnot (const Standard_Integer Index, const Standard_Real K) 
Changes the knot of range Index. The multiplicity of the knot is not modified. Raised if K >= Knots(Index+1) or K <= Knots(Index1). Raised if Index < 1  Index > NbKnots. More...  
void  SetKnots (const TColStd_Array1OfReal &K) 
Changes all the knots of the curve The multiplicity of the knots are not modified. More...  
void  SetKnot (const Standard_Integer Index, const Standard_Real K, const Standard_Integer M) 
Changes the knot of range Index with its multiplicity. You can increase the multiplicity of a knot but it is not allowed to decrease the multiplicity of an existing knot. More...  
void  PeriodicNormalization (Standard_Real &U) const 
returns the parameter normalized within the period if the curve is periodic : otherwise does not do anything More...  
void  SetPeriodic () 
Makes a closed Bspline into a periodic curve. The curve is periodic if the knot sequence is periodic and if the curve is closed (The tolerance criterion is Resolution from gp). The period T is equal to Knot(LastUKnotIndex)  Knot(FirstUKnotIndex). A periodic Bspline can be uniform or not. Raised if the curve is not closed. More...  
void  SetOrigin (const Standard_Integer Index) 
Set the origin of a periodic curve at Knot(index) KnotVector and poles are modified. Raised if the curve is not periodic Raised if index not in the range [FirstUKnotIndex , LastUKnotIndex]. More...  
void  SetNotPeriodic () 
Makes a non periodic curve. If the curve was non periodic the curve is not modified. More...  
void  SetPole (const Standard_Integer Index, const Standard_Real P) 
Substitutes the Pole of range Index with P. More...  
void  SetPole (const Standard_Integer Index, const Standard_Real P, const Standard_Real Weight) 
Substitutes the pole and the weight of range Index. If the curve <me> is not rational it can become rational If the curve was rational it can become non rational. More...  
void  SetWeight (const Standard_Integer Index, const Standard_Real Weight) 
Changes the weight for the pole of range Index. If the curve was non rational it can become rational. If the curve was rational it can become non rational. More...  
Standard_Boolean  IsCN (const Standard_Integer N) const 
Returns the continuity of the curve, the curve is at least C0. Raised if N < 0. More...  
Standard_Boolean  IsClosed () const 
Returns true if the distance between the first point and the last point of the curve is lower or equal to Resolution from package gp. Warnings : The first and the last point can be different from the first pole and the last pole of the curve. More...  
Standard_Boolean  IsPeriodic () const 
Returns True if the curve is periodic. More...  
Standard_Boolean  IsRational () const 
Returns True if the weights are not identical. The tolerance criterion is Epsilon of the class Real. More...  
GeomAbs_Shape  Continuity () const 
Returns the global continuity of the curve : C0 : only geometric continuity, C1 : continuity of the first derivative all along the Curve, C2 : continuity of the second derivative all along the Curve, C3 : continuity of the third derivative all along the Curve, CN : the order of continuity is infinite. For a Bspline curve of degree d if a knot Ui has a multiplicity p the Bspline curve is only Cdp continuous at Ui. So the global continuity of the curve can't be greater than Cdp where p is the maximum multiplicity of the interior Knots. In the interior of a knot span the curve is infinitely continuously differentiable. More...  
Standard_Integer  Degree () const 
Computation of value and derivatives. More...  
Standard_Real  Value (const Standard_Real U) const 
void  D0 (const Standard_Real U, Standard_Real &P) const 
void  D1 (const Standard_Real U, Standard_Real &P, Standard_Real &V1) const 
void  D2 (const Standard_Real U, Standard_Real &P, Standard_Real &V1, Standard_Real &V2) const 
void  D3 (const Standard_Real U, Standard_Real &P, Standard_Real &V1, Standard_Real &V2, Standard_Real &V3) const 
Standard_Real  DN (const Standard_Real U, const Standard_Integer N) const 
The following functions computes the point of parameter U and the derivatives at this point on the Bspline curve arc defined between the knot FromK1 and the knot ToK2. U can be out of bounds [Knot (FromK1), Knot (ToK2)] but for the computation we only use the definition of the curve between these two knots. This method is useful to compute local derivative, if the order of continuity of the whole curve is not greater enough. Inside the parametric domain Knot (FromK1), Knot (ToK2) the evaluations are the same as if we consider the whole definition of the curve. Of course the evaluations are different outside this parametric domain. More...  
Standard_Real  LocalValue (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2) const 
void  LocalD0 (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2, Standard_Real &P) const 
void  LocalD1 (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2, Standard_Real &P, Standard_Real &V1) const 
void  LocalD2 (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2, Standard_Real &P, Standard_Real &V1, Standard_Real &V2) const 
void  LocalD3 (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2, Standard_Real &P, Standard_Real &V1, Standard_Real &V2, Standard_Real &V3) const 
Standard_Real  LocalDN (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2, const Standard_Integer N) const 
Standard_Real  EndPoint () const 
Returns the last point of the curve. Warnings : The last point of the curve is different from the last pole of the curve if the multiplicity of the last knot is lower than Degree. More...  
Standard_Integer  FirstUKnotIndex () const 
For a Bspline curve the first parameter (which gives the start point of the curve) is a knot value but if the multiplicity of the first knot index is lower than Degree + 1 it is not the first knot of the curve. This method computes the index of the knot corresponding to the first parameter. More...  
Standard_Real  FirstParameter () const 
Computes the parametric value of the start point of the curve. It is a knot value. More...  
Standard_Real  Knot (const Standard_Integer Index) const 
Returns the knot of range Index. When there is a knot with a multiplicity greater than 1 the knot is not repeated. The method Multiplicity can be used to get the multiplicity of the Knot. Raised if Index < 1 or Index > NbKnots. More...  
void  Knots (TColStd_Array1OfReal &K) const 
returns the knot values of the Bspline curve; More...  
void  KnotSequence (TColStd_Array1OfReal &K) const 
Returns the knots sequence. In this sequence the knots with a multiplicity greater than 1 are repeated. Example : K = {k1, k1, k1, k2, k3, k3, k4, k4, k4}. More...  
GeomAbs_BSplKnotDistribution  KnotDistribution () const 
Returns NonUniform or Uniform or QuasiUniform or PiecewiseBezier. If all the knots differ by a positive constant from the preceding knot the BSpline Curve can be : More...  
Standard_Integer  LastUKnotIndex () const 
For a BSpline curve the last parameter (which gives the end point of the curve) is a knot value but if the multiplicity of the last knot index is lower than Degree + 1 it is not the last knot of the curve. This method computes the index of the knot corresponding to the last parameter. More...  
Standard_Real  LastParameter () const 
Computes the parametric value of the end point of the curve. It is a knot value. 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 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. Knots (I1) <= U <= Knots (I2) . if I1 = I2 U is a knot value (the tolerance criterion ParametricTolerance is used). . if I1 < 1 => U < Knots (1)  Abs(ParametricTolerance) . if I2 > NbKnots => U > Knots (NbKnots) + Abs(ParametricTolerance) More...  
Standard_Integer  Multiplicity (const Standard_Integer Index) const 
Returns the multiplicity of the knots of range Index. Raised if Index < 1 or Index > NbKnots. More...  
void  Multiplicities (TColStd_Array1OfInteger &M) const 
Returns the multiplicity of the knots of the curve. More...  
Standard_Integer  NbKnots () const 
Returns the number of knots. This method returns the number of knot without repetition of multiple knots. More...  
Standard_Integer  NbPoles () const 
Returns the number of poles. More...  
Standard_Real  Pole (const Standard_Integer Index) const 
Returns the pole of range Index. Raised if Index < 1 or Index > NbPoles. More...  
void  Poles (TColStd_Array1OfReal &P) const 
Returns the poles of the Bspline curve;. More...  
Standard_Real  StartPoint () const 
Returns the start point of the curve. Warnings : This point is different from the first pole of the curve if the multiplicity of the first knot is lower than Degree. More...  
Standard_Real  Weight (const Standard_Integer Index) const 
Returns the weight of the pole of range Index . Raised if Index < 1 or Index > NbPoles. More...  
void  Weights (TColStd_Array1OfReal &W) const 
Returns the weights of the Bspline curve;. More...  
void  MovePointAndTangent (const Standard_Real U, const Standard_Real NewValue, const Standard_Real Derivative, const Standard_Real Tolerance, const Standard_Integer StartingCondition, const Standard_Integer EndingCondition, Standard_Integer &ErrorStatus) 
Changes the value of the Law at parameter U to NewValue. and makes its derivative at U be derivative. StartingCondition = 1 means first can move EndingCondition = 1 means last point can move StartingCondition = 0 means the first point cannot move EndingCondition = 0 means the last point cannot move StartingCondition = 1 means the first point and tangent cannot move EndingCondition = 1 means the last point and tangent cannot move and so forth ErrorStatus != 0 means that there are not enought degree of freedom with the constrain to deform the curve accordingly. More...  
void  Resolution (const Standard_Real Tolerance3D, Standard_Real &UTolerance) const 
given Tolerance3D returns UTolerance such that if f(t) is the curve we have  t1  t0 < Utolerance ===> f(t1)  f(t0) < Tolerance3D More...  
Handle< Law_BSpline >  Copy () 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 this package. More...  
Definition of the 1D B_spline curve.
Uniform or nonuniform Rational or nonrational Periodic or nonperiodic
a bspline curve is defined by :
The Degree (up to 25)
The Poles (and the weights if it is rational)
The Knots and Multiplicities
The knot vector is an increasing sequence of reals without repetition. The multiplicities are the repetition of the knots.
If the knots are regularly spaced (the difference of two consecutive knots is a constant), the knots repartition is :
The curve may be periodic.
On a periodic curve if there are k knots and p poles. the period is knot(k)  knot(1)
the poles and knots are infinite vectors with :
knot(i+k) = knot(i) + period
pole(i+p) = pole(i)
References : . A survey of curve and surface methods in CADG Wolfgang BOHM CAGD 1 (1984) . On de Boorlike algorithms and blossoming Wolfgang BOEHM cagd 5 (1988) . Blossoming and knot insertion algorithms for Bspline 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
Law_BSpline::Law_BSpline  (  const TColStd_Array1OfReal &  Poles, 
const TColStd_Array1OfReal &  Knots,  
const TColStd_Array1OfInteger &  Multiplicities,  
const Standard_Integer  Degree,  
const Standard_Boolean  Periodic = Standard_False 

) 
Creates a nonrational B_spline curve on the basis <Knots, Multiplicities> of degree <Degree>.
Law_BSpline::Law_BSpline  (  const TColStd_Array1OfReal &  Poles, 
const TColStd_Array1OfReal &  Weights,  
const TColStd_Array1OfReal &  Knots,  
const TColStd_Array1OfInteger &  Multiplicities,  
const Standard_Integer  Degree,  
const Standard_Boolean  Periodic = Standard_False 

) 
Creates a rational B_spline curve on the basis <Knots, Multiplicities> of degree <Degree>.
GeomAbs_Shape Law_BSpline::Continuity  (  )  const 
Returns the global continuity of the curve : C0 : only geometric continuity, C1 : continuity of the first derivative all along the Curve, C2 : continuity of the second derivative all along the Curve, C3 : continuity of the third derivative all along the Curve, CN : the order of continuity is infinite. For a Bspline curve of degree d if a knot Ui has a multiplicity p the Bspline curve is only Cdp continuous at Ui. So the global continuity of the curve can't be greater than Cdp where p is the maximum multiplicity of the interior Knots. In the interior of a knot span the curve is infinitely continuously differentiable.
Handle< Law_BSpline > Law_BSpline::Copy  (  )  const 
void Law_BSpline::D0  (  const Standard_Real  U, 
Standard_Real &  P  
)  const 
void Law_BSpline::D1  (  const Standard_Real  U, 
Standard_Real &  P,  
Standard_Real &  V1  
)  const 
void Law_BSpline::D2  (  const Standard_Real  U, 
Standard_Real &  P,  
Standard_Real &  V1,  
Standard_Real &  V2  
)  const 
void Law_BSpline::D3  (  const Standard_Real  U, 
Standard_Real &  P,  
Standard_Real &  V1,  
Standard_Real &  V2,  
Standard_Real &  V3  
)  const 
Standard_Integer Law_BSpline::Degree  (  )  const 
Computation of value and derivatives.
Standard_Real Law_BSpline::DN  (  const Standard_Real  U, 
const Standard_Integer  N  
)  const 
The following functions computes the point of parameter U and the derivatives at this point on the Bspline curve arc defined between the knot FromK1 and the knot ToK2. U can be out of bounds [Knot (FromK1), Knot (ToK2)] but for the computation we only use the definition of the curve between these two knots. This method is useful to compute local derivative, if the order of continuity of the whole curve is not greater enough. Inside the parametric domain Knot (FromK1), Knot (ToK2) the evaluations are the same as if we consider the whole definition of the curve. Of course the evaluations are different outside this parametric domain.
Standard_Real Law_BSpline::EndPoint  (  )  const 
Returns the last point of the curve. Warnings : The last point of the curve is different from the last pole of the curve if the multiplicity of the last knot is lower than Degree.
Standard_Real Law_BSpline::FirstParameter  (  )  const 
Computes the parametric value of the start point of the curve. It is a knot value.
Standard_Integer Law_BSpline::FirstUKnotIndex  (  )  const 
For a Bspline curve the first parameter (which gives the start point of the curve) is a knot value but if the multiplicity of the first knot index is lower than Degree + 1 it is not the first knot of the curve. This method computes the index of the knot corresponding to the first parameter.
void Law_BSpline::IncreaseDegree  (  const Standard_Integer  Degree  ) 
Increase the degree to <Degree>. Nothing is done if <Degree> is lower or equal to the current degree.
void Law_BSpline::IncreaseMultiplicity  (  const Standard_Integer  Index, 
const Standard_Integer  M  
) 
Increases the multiplicity of the knot <Index> to <M>.
If <M> is lower or equal to the current multiplicity nothing is done. If <M> is higher than the degree the degree is used. If <Index> is not in [FirstUKnotIndex, LastUKnotIndex]
void Law_BSpline::IncreaseMultiplicity  (  const Standard_Integer  I1, 
const Standard_Integer  I2,  
const Standard_Integer  M  
) 
Increases the multiplicities of the knots in [I1,I2] to <M>.
For each knot if <M> is lower or equal to the current multiplicity nothing is done. If <M> is higher than the degree the degree is used. If <I1,I2> are not in [FirstUKnotIndex, LastUKnotIndex]
void Law_BSpline::IncrementMultiplicity  (  const Standard_Integer  I1, 
const Standard_Integer  I2,  
const Standard_Integer  M  
) 
Increment the multiplicities of the knots in [I1,I2] by <M>.
If <M> is not positive nithing is done.
For each knot the resulting multiplicity is limited to the Degree. If <I1,I2> are not in [FirstUKnotIndex, LastUKnotIndex]
void Law_BSpline::InsertKnot  (  const Standard_Real  U, 
const Standard_Integer  M = 1 , 

const Standard_Real  ParametricTolerance = 0.0 , 

const Standard_Boolean  Add = Standard_True 

) 
Inserts a knot value in the sequence of knots. If <U> is an existing knot the multiplicity is increased by <M>.
If U is not on the parameter range nothing is done.
If the multiplicity is negative or null nothing is done. The new multiplicity is limited to the degree.
The tolerance criterion for knots equality is the max of Epsilon(U) and ParametricTolerance.
void Law_BSpline::InsertKnots  (  const TColStd_Array1OfReal &  Knots, 
const TColStd_Array1OfInteger &  Mults,  
const Standard_Real  ParametricTolerance = 0.0 , 

const Standard_Boolean  Add = Standard_False 

) 
Inserts a set of knots values in the sequence of knots.
For each U = Knots(i), M = Mults(i)
If <U> is an existing knot the multiplicity is increased by <M> if <Add> is True, increased to <M> if <Add> is False.
If U is not on the parameter range nothing is done.
If the multiplicity is negative or null nothing is done. The new multiplicity is limited to the degree.
The tolerance criterion for knots equality is the max of Epsilon(U) and ParametricTolerance.
Standard_Boolean Law_BSpline::IsClosed  (  )  const 
Returns true if the distance between the first point and the last point of the curve is lower or equal to Resolution from package gp. Warnings : The first and the last point can be different from the first pole and the last pole of the curve.
Standard_Boolean Law_BSpline::IsCN  (  const Standard_Integer  N  )  const 
Returns the continuity of the curve, the curve is at least C0. Raised if N < 0.
Standard_Boolean Law_BSpline::IsPeriodic  (  )  const 
Returns True if the curve is periodic.
Standard_Boolean Law_BSpline::IsRational  (  )  const 
Returns True if the weights are not identical. The tolerance criterion is Epsilon of the class Real.
Standard_Real Law_BSpline::Knot  (  const Standard_Integer  Index  )  const 
Returns the knot of range Index. When there is a knot with a multiplicity greater than 1 the knot is not repeated. The method Multiplicity can be used to get the multiplicity of the Knot. Raised if Index < 1 or Index > NbKnots.
GeomAbs_BSplKnotDistribution Law_BSpline::KnotDistribution  (  )  const 
Returns NonUniform or Uniform or QuasiUniform or PiecewiseBezier. If all the knots differ by a positive constant from the preceding knot the BSpline Curve can be :
void Law_BSpline::Knots  (  TColStd_Array1OfReal &  K  )  const 
returns the knot values of the Bspline curve;
Raised if the length of K is not equal to the number of knots.
void Law_BSpline::KnotSequence  (  TColStd_Array1OfReal &  K  )  const 
Returns the knots sequence. In this sequence the knots with a multiplicity greater than 1 are repeated. Example : K = {k1, k1, k1, k2, k3, k3, k4, k4, k4}.
Raised if the length of K is not equal to NbPoles + Degree + 1
Standard_Real Law_BSpline::LastParameter  (  )  const 
Computes the parametric value of the end point of the curve. It is a knot value.
Standard_Integer Law_BSpline::LastUKnotIndex  (  )  const 
For a BSpline curve the last parameter (which gives the end point of the curve) is a knot value but if the multiplicity of the last knot index is lower than Degree + 1 it is not the last knot of the curve. This method computes the index of the knot corresponding to the last parameter.
void Law_BSpline::LocalD0  (  const Standard_Real  U, 
const Standard_Integer  FromK1,  
const Standard_Integer  ToK2,  
Standard_Real &  P  
)  const 
void Law_BSpline::LocalD1  (  const Standard_Real  U, 
const Standard_Integer  FromK1,  
const Standard_Integer  ToK2,  
Standard_Real &  P,  
Standard_Real &  V1  
)  const 
void Law_BSpline::LocalD2  (  const Standard_Real  U, 
const Standard_Integer  FromK1,  
const Standard_Integer  ToK2,  
Standard_Real &  P,  
Standard_Real &  V1,  
Standard_Real &  V2  
)  const 
void Law_BSpline::LocalD3  (  const Standard_Real  U, 
const Standard_Integer  FromK1,  
const Standard_Integer  ToK2,  
Standard_Real &  P,  
Standard_Real &  V1,  
Standard_Real &  V2,  
Standard_Real &  V3  
)  const 
Standard_Real Law_BSpline::LocalDN  (  const Standard_Real  U, 
const Standard_Integer  FromK1,  
const Standard_Integer  ToK2,  
const Standard_Integer  N  
)  const 
Standard_Real Law_BSpline::LocalValue  (  const Standard_Real  U, 
const Standard_Integer  FromK1,  
const Standard_Integer  ToK2  
)  const 
void Law_BSpline::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 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. Knots (I1) <= U <= Knots (I2) . if I1 = I2 U is a knot value (the tolerance criterion ParametricTolerance is used). . if I1 < 1 => U < Knots (1)  Abs(ParametricTolerance) . if I2 > NbKnots => U > Knots (NbKnots) + Abs(ParametricTolerance)

static 
Returns the value of the maximum degree of the normalized Bspline basis functions in this package.
void Law_BSpline::MovePointAndTangent  (  const Standard_Real  U, 
const Standard_Real  NewValue,  
const Standard_Real  Derivative,  
const Standard_Real  Tolerance,  
const Standard_Integer  StartingCondition,  
const Standard_Integer  EndingCondition,  
Standard_Integer &  ErrorStatus  
) 
Changes the value of the Law at parameter U to NewValue. and makes its derivative at U be derivative. StartingCondition = 1 means first can move EndingCondition = 1 means last point can move StartingCondition = 0 means the first point cannot move EndingCondition = 0 means the last point cannot move StartingCondition = 1 means the first point and tangent cannot move EndingCondition = 1 means the last point and tangent cannot move and so forth ErrorStatus != 0 means that there are not enought degree of freedom with the constrain to deform the curve accordingly.
void Law_BSpline::Multiplicities  (  TColStd_Array1OfInteger &  M  )  const 
Returns the multiplicity of the knots of the curve.
Raised if the length of M is not equal to NbKnots.
Standard_Integer Law_BSpline::Multiplicity  (  const Standard_Integer  Index  )  const 
Returns the multiplicity of the knots of range Index. Raised if Index < 1 or Index > NbKnots.
Standard_Integer Law_BSpline::NbKnots  (  )  const 
Returns the number of knots. This method returns the number of knot without repetition of multiple knots.
Standard_Integer Law_BSpline::NbPoles  (  )  const 
Returns the number of poles.
void Law_BSpline::PeriodicNormalization  (  Standard_Real &  U  )  const 
returns the parameter normalized within the period if the curve is periodic : otherwise does not do anything
Standard_Real Law_BSpline::Pole  (  const Standard_Integer  Index  )  const 
Returns the pole of range Index. Raised if Index < 1 or Index > NbPoles.
void Law_BSpline::Poles  (  TColStd_Array1OfReal &  P  )  const 
Returns the poles of the Bspline curve;.
Raised if the length of P is not equal to the number of poles.
Standard_Boolean Law_BSpline::RemoveKnot  (  const Standard_Integer  Index, 
const Standard_Integer  M,  
const Standard_Real  Tolerance  
) 
Decrement the knots multiplicity to <M>. If M is 0 the knot is removed. The Poles sequence is modified.
As there are two ways to compute the new poles the average is computed if the distance is lower than the <Tolerance>, else False is returned.
A low tolerance is used to prevent the modification of the curve.
A high tolerance is used to "smooth" the curve.
Raised if Index is not in the range [FirstUKnotIndex, LastUKnotIndex] pole insertion and pole removing this operation is limited to the Uniform or QuasiUniform BSplineCurve. The knot values are modified . If the BSpline is NonUniform or Piecewise Bezier an exception Construction error is raised.
void Law_BSpline::Resolution  (  const Standard_Real  Tolerance3D, 
Standard_Real &  UTolerance  
)  const 
given Tolerance3D returns UTolerance such that if f(t) is the curve we have  t1  t0 < Utolerance ===> f(t1)  f(t0) < Tolerance3D
void Law_BSpline::Reverse  (  ) 
Changes the direction of parametrization of <me>. The Knot sequence is modified, the FirstParameter and the LastParameter are not modified. The StartPoint of the initial curve becomes the EndPoint of the reversed curve and the EndPoint of the initial curve becomes the StartPoint of the reversed curve.
Standard_Real Law_BSpline::ReversedParameter  (  const Standard_Real  U  )  const 
Returns the parameter on the reversed curve for the point of parameter U on <me>.
returns UFirst + ULast  U
void Law_BSpline::Segment  (  const Standard_Real  U1, 
const Standard_Real  U2  
) 
Segments the curve between U1 and U2. 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 curve <me> or if the curve makes loop. After the segmentation the length of a curve can be null. raises if U2 < U1.
void Law_BSpline::SetKnot  (  const Standard_Integer  Index, 
const Standard_Real  K  
) 
Changes the knot of range Index. The multiplicity of the knot is not modified. Raised if K >= Knots(Index+1) or K <= Knots(Index1). Raised if Index < 1  Index > NbKnots.
void Law_BSpline::SetKnot  (  const Standard_Integer  Index, 
const Standard_Real  K,  
const Standard_Integer  M  
) 
Changes the knot of range Index with its multiplicity. You can increase the multiplicity of a knot but it is not allowed to decrease the multiplicity of an existing knot.
Raised if K >= Knots(Index+1) or K <= Knots(Index1). Raised if M is greater than Degree or lower than the previous multiplicity of knot of range Index. Raised if Index < 1  Index > NbKnots
void Law_BSpline::SetKnots  (  const TColStd_Array1OfReal &  K  ) 
Changes all the knots of the curve The multiplicity of the knots are not modified.
Raised if there is an index such that K (Index+1) <= K (Index).
Raised if K.Lower() < 1 or K.Upper() > NbKnots
void Law_BSpline::SetNotPeriodic  (  ) 
Makes a non periodic curve. If the curve was non periodic the curve is not modified.
void Law_BSpline::SetOrigin  (  const Standard_Integer  Index  ) 
Set the origin of a periodic curve at Knot(index) KnotVector and poles are modified. Raised if the curve is not periodic Raised if index not in the range [FirstUKnotIndex , LastUKnotIndex].
void Law_BSpline::SetPeriodic  (  ) 
Makes a closed Bspline into a periodic curve. The curve is periodic if the knot sequence is periodic and if the curve is closed (The tolerance criterion is Resolution from gp). The period T is equal to Knot(LastUKnotIndex)  Knot(FirstUKnotIndex). A periodic Bspline can be uniform or not. Raised if the curve is not closed.
void Law_BSpline::SetPole  (  const Standard_Integer  Index, 
const Standard_Real  P  
) 
Substitutes the Pole of range Index with P.
Raised if Index < 1  Index > NbPoles
void Law_BSpline::SetPole  (  const Standard_Integer  Index, 
const Standard_Real  P,  
const Standard_Real  Weight  
) 
Substitutes the pole and the weight of range Index. If the curve <me> is not rational it can become rational If the curve was rational it can become non rational.
Raised if Index < 1  Index > NbPoles Raised if Weight <= 0.0
void Law_BSpline::SetWeight  (  const Standard_Integer  Index, 
const Standard_Real  Weight  
) 
Changes the weight for the pole of range Index. If the curve was non rational it can become rational. If the curve was rational it can become non rational.
Raised if Index < 1  Index > NbPoles Raised if Weight <= 0.0
Standard_Real Law_BSpline::StartPoint  (  )  const 
Returns the start point of the curve. Warnings : This point is different from the first pole of the curve if the multiplicity of the first knot is lower than Degree.
Standard_Real Law_BSpline::Value  (  const Standard_Real  U  )  const 
Standard_Real Law_BSpline::Weight  (  const Standard_Integer  Index  )  const 
Returns the weight of the pole of range Index . Raised if Index < 1 or Index > NbPoles.
void Law_BSpline::Weights  (  TColStd_Array1OfReal &  W  )  const 
Returns the weights of the Bspline curve;.
Raised if the length of W is not equal to NbPoles.