TKG3d--Package Geom

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Geom_BSplineCurve Class Reference

Definition of the B_spline curve. 
A B-spline curve can be 
Uniform or non-uniform 
Rational or non-rational 
Periodic or non-periodic 

a b-spline curve is defined by : 
its degree; the degree for a 
Geom_BSplineCurve is limited to a value (25) 
which is defined and controlled by the system. 
This value is returned by the function MaxDegree; 

• its periodic or non-periodic nature; 
  
• a table of poles (also called control points), with 
  their associated weights if the BSpline curve is 
  rational. The poles of the curve are "control <br> points" used to deform the curve. If the curve is 
  non-periodic, the first pole is the start point of 
  the curve, and the last pole is the end point of 
  the curve. The segment which joins the first pole 
  to the second pole is the tangent to the curve at 
  its start point, and the segment which joins the 
  last pole to the second-from-last pole is the 
  tangent to the curve at its end point. If the curve 
  is periodic, these geometric properties are not 
  verified. It is more difficult to give a geometric 
  signification to the weights but are useful for 
  providing exact representations of the arcs of a 
  circle or ellipse. Moreover, if the weights of all the 
  poles are equal, the curve has a polynomial 
  equation; it is therefore a non-rational curve. 
  
• a table of knots with their multiplicities. For a 
  Geom_BSplineCurve, the table of knots is an 
  increasing sequence of reals without repetition; 
  the multiplicities define the repetition of the knots. 
  A BSpline curve is a piecewise polynomial or 
  rational curve. The knots are the parameters of 
  junction points between two pieces. The 
  multiplicity Mult(i) of the knot Knot(i) of 
  the BSpline curve is related to the degree of 
  continuity of the curve at the knot Knot(i), 
  which is equal to Degree - Mult(i) 
  where Degree is the degree of the BSpline curve. 
  If the knots are regularly spaced (i.e. the difference 
  between two consecutive knots is a constant), three 
  specific and frequently used cases of knot 
  distribution can be identified: 
  
• "uniform" if all multiplicities are equal to 1, 
  
• "quasi-uniform" if all multiplicities are equal to 1, 
  except the first and the last knot which have a 
  multiplicity of Degree + 1, where Degree is 
  the degree of the BSpline curve, 
  
• "Piecewise Bezier" if all multiplicities are equal to 
  Degree except the first and last knot which 
  have a multiplicity of Degree + 1, where 
  Degree is the degree of the BSpline curve. A 
  curve of this type is a concatenation of arcs of Bezier curves. 
  If the BSpline curve is not periodic: 
  
• the bounds of the Poles and Weights tables are 1 
  and NbPoles, where NbPoles is the number 
  of poles of the BSpline curve, 
  
• the bounds of the Knots and Multiplicities tables 
  are 1 and NbKnots, where NbKnots is the 
  number of knots of the BSpline curve. 
  If the BSpline curve is periodic, and if there are k 
  periodic knots and p periodic poles, the period is: 
  period = Knot(k + 1) - Knot(1) 
  and the poles and knots tables can be considered 
  as infinite tables, verifying: 
  
• Knot(i+k) = Knot(i) + period 
  
• Pole(i+p) = Pole(i) 
  Note: data structures of a periodic BSpline curve 
  are more complex than those of a non-periodic one. 
  Warning 
  In this class, weight value is considered to be zero if 
  the weight is less than or equal to gp::Resolution(). 
  
  References : 
  . A survey of curve and surface methods in CADG Wolfgang BOHM 
  CAGD 1 (1984) 
  . On de Boor-like algorithms and blossoming Wolfgang BOEHM 
  cagd 5 (1988) 
  . Blossoming and knot insertion algorithms for B-spline curves 
  Ronald N. GOLDMAN 
  . Modelisation des surfaces en CAO, Henri GIAUME Peugeot SA 
  . Curves and Surfaces for Computer Aided Geometric Design, 
  a practical guide Gerald Farin 
  

#include <Geom_BSplineCurve.hxx>

Inheritance diagram for Geom_BSplineCurve:

[legend]

Public Member Functions
	Geom_BSplineCurve (const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Multiplicities, const Standard_Integer Degree, constStandard_Boolean Periodic=Standard_False)
	Creates a non-rational B_spline curve on the  basis <Knots, Multiplicities> of degree <Degree>.
	Geom_BSplineCurve (const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &Weights, const TColStd_Array1OfReal &Knots, const TColStd_Array1OfInteger &Multiplicities, constStandard_Integer Degree, const Standard_Boolean Periodic=Standard_False, const Standard_Boolean CheckRational=Standard_True)
	Creates a rational B_spline curve on the basis  <Knots, Multiplicities> of degree <Degree>.  Raises ConstructionError subject to the following conditions  0 < Degree <= MaxDegree.  Weights.Length() == Poles.Length()  Knots.Length() == Mults.Length() >= 2  Knots(i) < Knots(i+1) (Knots are increasing)  1 <= Mults(i) <= Degree  On a non periodic curve the first and last multiplicities  may be Degree+1 (this is even recommanded if you want the  curve to start and finish on the first and last pole).  On a periodic curve the first and the last multicities  must be the same.  on non-periodic curves  Poles.Length() == Sum(Mults(i)) - Degree - 1 >= 2  on periodic curves  Poles.Length() == Sum(Mults(i)) except the first or last
void	IncreaseDegree (const Standard_Integer Degree)
	Increases the degree of this BSpline curve to  Degree. As a result, the poles, weights and  multiplicities tables are modified; the knots table is  not changed. Nothing is done if Degree is less than  or equal to the current degree.  Exceptions  Standard_ConstructionError if Degree is greater than  Geom_BSplineCurve::MaxDegree().
void	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	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	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	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	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	RemoveKnot (const Standard_Integer Index, const Standard_Integer M, const Standard_Real Tolerance)
	Reduces the multiplicity of the knot of index Index  to M. If M is equal to 0, the knot is removed.  With a modification of this type, the array of poles is also modified.  Two different algorithms are systematically used to  compute the new poles of the curve. If, for each  pole, the distance between the pole calculated  using the first algorithm and the same pole  calculated using the second algorithm, is less than  Tolerance, this ensures that the curve is not  modified by more than Tolerance. Under these  conditions, true is returned; otherwise, false is returned.  A low tolerance is used to prevent modification of  the curve. A high tolerance is used to "smooth" the curve.  Exceptions  Standard_OutOfRange if Index is outside the  bounds of the knots table.  //! 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	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	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	Segment (const Standard_Real U1, const Standard_Real U2)
	Modifies this BSpline curve by segmenting it between  U1 and U2. Either of these values can be outside the  bounds of the curve, but U2 must be greater than U1.  All data structure tables of this BSpline curve are  modified, but the knots located between U1 and U2  are retained. The degree of the curve is not modified.  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	SetKnot (const Standard_Integer Index, const Standard_Real K)
	Modifies this BSpline curve by assigning the value K  to the knot of index Index in the knots table. This is a  relatively local modification because K must be such that:  Knots(Index - 1) < K < Knots(Index + 1)  The second syntax allows you also to increase the  multiplicity of the knot to M (but it is not possible to  decrease the multiplicity of the knot with this function).  Standard_ConstructionError if:  K is not such that:  Knots(Index - 1) < K < Knots(Index + 1)  M is greater than the degree of this BSpline curve  or lower than the previous multiplicity of knot of  index Index in the knots table.  Standard_OutOfRange if Index is outside the bounds of the knots table.
void	SetKnots (const TColStd_Array1OfReal &K)
	Modifies this BSpline curve by assigning the array  K to its knots table. The multiplicity of the knots is not modified.  Exceptions  Standard_ConstructionError if the values in the  array K are not in ascending order.  Standard_OutOfRange if the bounds of the array  K are not respectively 1 and the number of knots of this BSpline curve.
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.  Raised if K >= Knots(Index+1) or K <= Knots(Index-1).  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	PeriodicNormalization (Standard_Real &U) const
	returns the parameter normalized within  the period if the curve is periodic : otherwise  does not do anything
void	SetPeriodic ()
	Changes this BSpline curve into a periodic curve.  To become periodic, the curve must first be closed.  Next, the knot sequence must be periodic. For this,  FirstUKnotIndex and LastUKnotIndex are used  to compute I1 and I2, the indexes in the knots  array of the knots corresponding to the first and  last parameters of this BSpline curve.  The period is therefore: Knots(I2) - Knots(I1).  Consequently, the knots and poles tables are modified.  Exceptions  Standard_ConstructionError if this BSpline curve is not closed.
void	SetOrigin (const Standard_Integer Index)
	Assigns the knot of index Index in the knots table as  the origin of this periodic BSpline curve. As a  consequence, the knots and poles tables are modified.  Exceptions  Standard_NoSuchObject if this curve is not periodic.  Standard_DomainError if Index is outside the bounds of the knots table.
void	SetOrigin (const Standard_Real U, const Standard_Real Tol)
	Set the origin of a periodic curve at Knot U. If U  is not a knot of the BSpline a new knot is  inseted. KnotVector and poles are modified.  //! Raised if the curve is not periodic
void	SetNotPeriodic ()
	Changes this BSpline curve into a non-periodic  curve. If this curve is already non-periodic, it is not modified.  Note: the poles and knots tables are modified.  Warning  If this curve is periodic, as the multiplicity of the first  and last knots is not modified, and is not equal to  Degree + 1, where Degree is the degree of  this BSpline curve, the start and end points of the  curve are not its first and last poles.
void	SetPole (const Standard_Integer Index, const gp_Pnt &P)
	Modifies this BSpline curve by assigning P to the pole  of index Index in the poles table.  Exceptions  Standard_OutOfRange if Index is outside the  bounds of the poles table.  Standard_ConstructionError if Weight is negative or null.
void	SetPole (const Standard_Integer Index, const gp_Pnt &P, const Standard_Real Weight)
	Modifies this BSpline curve by assigning P to the pole  of index Index in the poles table.  This syntax also allows you to modify the  weight of the modified pole, which becomes Weight.  In this case, if this BSpline curve is non-rational, it  can become rational and vice versa.  Exceptions  Standard_OutOfRange if Index is outside the  bounds of the poles table.  Standard_ConstructionError if Weight is negative or null.
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.  Raised if Index < 1 || Index > NbPoles  //! Raised if Weight <= 0.0
void	MovePoint (const Standard_Real U, const gp_Pnt &P, const Standard_Integer Index1, const Standard_Integer Index2, Standard_Integer &FirstModifiedPole, Standard_Integer&LastModifiedPole)
	Moves the point of parameter U of this BSpline curve  to P. Index1 and Index2 are the indexes in the table  of poles of this BSpline curve of the first and last  poles designated to be moved.  FirstModifiedPole and LastModifiedPole are the  indexes of the first and last poles which are effectively modified.  In the event of incompatibility between Index1, Index2 and the value U:  no change is made to this BSpline curve, and  the FirstModifiedPole and LastModifiedPole are returned null.  Exceptions  Standard_OutOfRange if:  Index1 is greater than or equal to Index2, or  Index1 or Index2 is less than 1 or greater than the  number of poles of this BSpline curve.
void	MovePointAndTangent (const Standard_Real U, const gp_Pnt &P, const gp_Vec &Tangent, const Standard_Real Tolerance, const Standard_Integer StartingCondition, const Standard_IntegerEndingCondition, Standard_Integer &ErrorStatus)
	Move a point with parameter U to P.  and makes it tangent at U be Tangent.  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
Standard_Boolean	IsCN (const Standard_Integer N) const
	Returns the continuity of the curve, the curve is at least C0.  //! Raised if N < 0.
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.
Standard_Boolean	IsPeriodic () const
	Returns True if the curve is periodic.
Standard_Boolean	IsRational () const
	Returns True if the weights are not identical.  The tolerance criterion is Epsilon of the class Real.
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 B-spline curve of degree d if a knot Ui has a  multiplicity p the B-spline curve is only Cd-p continuous  at Ui. So the global continuity of the curve can't be greater  than Cd-p where p is the maximum multiplicity of the interior  Knots. In the interior of a knot span the curve is infinitely  continuously differentiable.
Standard_Integer	Degree () const
	Returns the degree of this BSpline curve.  The degree of a Geom_BSplineCurve curve cannot  be greater than Geom_BSplineCurve::MaxDegree().  //! Computation of value and derivatives
void	D0 (const Standard_Real U, gp_Pnt &P) const
	Returns in P the point of parameter U.
void	D1 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1) const
	Raised if the continuity of the curve is not C1.
void	D2 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2) const
	Raised if the continuity of the curve is not C2.
void	D3 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2, gp_Vec &V3) const
	Raised if the continuity of the curve is not C3.
gp_Vec	DN (const Standard_Real U, const Standard_Integer N) const
	For the point of parameter U of this BSpline curve,  computes the vector corresponding to the Nth derivative.  Warning  On a point where the continuity of the curve is not the  one requested, this function impacts the part defined  by the parameter with a value greater than U, i.e. the  part of the curve to the "right" of the singularity.  Exceptions  Standard_RangeError if N is less than 1.  The following functions compute the point of parameter U  and the derivatives at this point on the B-spline 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.
gp_Pnt	LocalValue (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2) const
	Raised if FromK1 = ToK2.  Raised if FromK1 and ToK2 are not in the range  [FirstUKnotIndex, LastUKnotIndex].
void	LocalD0 (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2, gp_Pnt &P) const
	Raised if FromK1 = ToK2.  Raised if FromK1 and ToK2 are not in the range  [FirstUKnotIndex, LastUKnotIndex].
void	LocalD1 (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2, gp_Pnt &P, gp_Vec &V1) const
	Raised if the local continuity of the curve is not C1  between the knot K1 and the knot K2.  //! Raised if FromK1 = ToK2.  Raised if FromK1 and ToK2 are not in the range  [FirstUKnotIndex, LastUKnotIndex].
void	LocalD2 (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2) const
	Raised if the local continuity of the curve is not C2  between the knot K1 and the knot K2.  //! Raised if FromK1 = ToK2.  Raised if FromK1 and ToK2 are not in the range  [FirstUKnotIndex, LastUKnotIndex].
void	LocalD3 (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2, gp_Vec &V3) const
	Raised if the local continuity of the curve is not C3  between the knot K1 and the knot K2.  //! Raised if FromK1 = ToK2.  Raised if FromK1 and ToK2 are not in the range  [FirstUKnotIndex, LastUKnotIndex].
gp_Vec	LocalDN (const Standard_Real U, const Standard_Integer FromK1, const Standard_Integer ToK2, const Standard_Integer N) const
	Raised if the local continuity of the curve is not CN  between the knot K1 and the knot K2.  //! Raised if FromK1 = ToK2.  //! Raised if N < 1.  Raises if FromK1 and ToK2 are not in the range  [FirstUKnotIndex, LastUKnotIndex].
gp_Pnt	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_Integer	FirstUKnotIndex () const
	Returns the index in the knot array of the knot  corresponding to the first or last parameter of this BSpline curve.  For a BSpline curve, the first (or last) parameter  (which gives the start (or end) point of the curve) is a  knot value. However, if the multiplicity of the first (or  last) knot is less than Degree + 1, where  Degree is the degree of the curve, it is not the first  (or last) knot of the curve.
Standard_Real	FirstParameter () const
	Returns the value of the first parameter of this  BSpline curve. This is a knot value.  The first parameter is the one of the start point of the BSpline curve.
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
void	Knots (TColStd_Array1OfReal &K) const
	returns the knot values of the B-spline curve;  Warning  A knot with a multiplicity greater than 1 is not  repeated in the knot table. The Multiplicity function  can be used to obtain the multiplicity of each knot.  Raised if the length of K is not equal to the number of knots.
void	KnotSequence (TColStd_Array1OfReal &K) const
	Returns K, the knots sequence of this BSpline curve.  In this sequence, knots with a multiplicity greater than 1 are repeated.  In the case of a non-periodic curve the length of the  sequence must be equal to the sum of the NbKnots  multiplicities of the knots of the curve (where  NbKnots is the number of knots of this BSpline  curve). This sum is also equal to : NbPoles + Degree + 1  where NbPoles is the number of poles and  Degree the degree of this BSpline curve.  In the case of a periodic curve, if there are k periodic  knots, the period is Knot(k+1) - Knot(1).  The initial sequence is built by writing knots 1 to k+1,  which are repeated according to their corresponding multiplicities.  If Degree is the degree of the curve, the degree of  continuity of the curve at the knot of index 1 (or k+1)  is equal to c = Degree + 1 - Mult(1). c  knots are then inserted at the beginning and end of  the initial sequence:  the c values of knots preceding the first item  Knot(k+1) in the initial sequence are inserted  at the beginning; the period is subtracted from these c values;  the c values of knots following the last item  Knot(1) in the initial sequence are inserted at  the end; the period is added to these c values.  The length of the sequence must therefore be equal to:  NbPoles + 2*Degree - Mult(1) + 2.  Example  For a non-periodic BSpline curve of degree 2 where:  the array of knots is: { k1 k2 k3 k4 },  with associated multiplicities: { 3 1 2 3 },  the knot sequence is:  K = { k1 k1 k1 k2 k3 k3 k4 k4 k4 }  For a periodic BSpline curve of degree 4 , which is  "C1" continuous at the first knot, and where :  the periodic knots are: { k1 k2 k3 (k4) }  (3 periodic knots: the points of parameter k1 and k4  are identical, the period is p = k4 - k1),  with associated multiplicities: { 3 1 2 (3) },  the degree of continuity at knots k1 and k4 is:  Degree + 1 - Mult(i) = 2.  2 supplementary knots are added at the beginning  and end of the sequence:  at the beginning: the 2 knots preceding k4 minus  the period; in this example, this is k3 - p both times;  at the end: the 2 knots following k1 plus the period;  in this example, this is k2 + p and k3 + p.  The knot sequence is therefore:  K = { k3-p k3-p k1 k1 k1 k2 k3 k3  k4 k4 k4 k2+p k3+p }  Exceptions  Standard_DimensionError if the array K is not of  the appropriate length.Returns the knots sequence.
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 :  Uniform if all the knots are of multiplicity 1,  QuasiUniform if all the knots are of multiplicity 1 except for  the first and last knot which are of multiplicity Degree + 1,  PiecewiseBezier if the first and last knots have multiplicity  Degree + 1 and if interior knots have multiplicity Degree  A piecewise Bezier with only two knots is a BezierCurve.  else the curve is non uniform.  The tolerance criterion is Epsilon from class Real.
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.
Standard_Real	LastParameter () const
	Computes the parametric value of the end point of the curve.  It is a knot value.
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)
Standard_Integer	Multiplicity (const Standard_Integer Index) const
	Returns the multiplicity of the knots of range Index.  //! Raised if Index < 1 or Index > NbKnots
void	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	NbKnots () const
	Returns the number of knots. This method returns the number of  knot without repetition of multiple knots.
Standard_Integer	NbPoles () const
	Returns the number of poles
gp_Pnt	Pole (const Standard_Integer Index) const
	Returns the pole of range Index.  //! Raised if Index < 1 or Index > NbPoles.
void	Poles (TColgp_Array1OfPnt &P) const
	Returns the poles of the B-spline curve;  Raised if the length of P is not equal to the number of poles.
gp_Pnt	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	Weight (const Standard_Integer Index) const
	Returns the weight of the pole of range Index .  //! Raised if Index < 1 or Index > NbPoles.
void	Weights (TColStd_Array1OfReal &W) const
	Returns the weights of the B-spline curve;  Raised if the length of W is not equal to NbPoles.
void	Transform (const gp_Trsf &T)
	Applies the transformation T to this BSpline curve.
void	Resolution (const Standard_Real Tolerance3D, Standard_Real &UTolerance)
	Computes for this BSpline curve the parametric  tolerance UTolerance for a given 3D tolerance Tolerance3D.  If f(t) is the equation of this BSpline curve,  UTolerance ensures that:  | t1 - t0| < Utolerance ===>  |f(t1) - f(t0)| < Tolerance3D
Handle_Geom_Geometry	Copy () const
	Creates a new object which is a copy of this BSpline curve.
Static Public Member Functions
static Standard_Integer	MaxDegree ()
	Returns the value of the maximum degree of the normalized  B-spline basis functions in this package.

Constructor & Destructor Documentation

Geom_BSplineCurve::Geom_BSplineCurve	(	const TColgp_Array1OfPnt &	Poles,
		const TColStd_Array1OfReal &	Knots,
		const TColStd_Array1OfInteger &	Multiplicities,
		const Standard_Integer	Degree,
		const Standard_Boolean	Periodic = Standard_False
	)

Geom_BSplineCurve::Geom_BSplineCurve	(	const TColgp_Array1OfPnt &	Poles,
		const TColStd_Array1OfReal &	Weights,
		const TColStd_Array1OfReal &	Knots,
		const TColStd_Array1OfInteger &	Multiplicities,
		const Standard_Integer	Degree,
		const Standard_Boolean	Periodic = Standard_False,
		const Standard_Boolean	CheckRational = Standard_True
	)

Member Function Documentation

GeomAbs_Shape Geom_BSplineCurve::Continuity

(

)

const [virtual]

Implements Geom_Curve.

Handle_Geom_Geometry Geom_BSplineCurve::Copy

(

)

const [virtual]

Implements Geom_Geometry.

void Geom_BSplineCurve::D0	(	const Standard_Real	U,
		gp_Pnt &	P
	)			const [virtual]

Implements Geom_Curve.

void Geom_BSplineCurve::D1	(	const Standard_Real	U,
		gp_Pnt &	P,
		gp_Vec &	V1
	)			const [virtual]

Implements Geom_Curve.

void Geom_BSplineCurve::D2	(	const Standard_Real	U,
		gp_Pnt &	P,
		gp_Vec &	V1,
		gp_Vec &	V2
	)			const [virtual]

Implements Geom_Curve.

void Geom_BSplineCurve::D3	(	const Standard_Real	U,
		gp_Pnt &	P,
		gp_Vec &	V1,
		gp_Vec &	V2,
		gp_Vec &	V3
	)			const [virtual]

Implements Geom_Curve.

Standard_Integer Geom_BSplineCurve::Degree

(

)

const

gp_Vec Geom_BSplineCurve::DN	(	const Standard_Real	U,
		const Standard_Integer	N
	)			const [virtual]

Implements Geom_Curve.

gp_Pnt Geom_BSplineCurve::EndPoint

(

)

const [virtual]

Implements Geom_BoundedCurve.

Standard_Real Geom_BSplineCurve::FirstParameter

(

)

const [virtual]

Implements Geom_Curve.

Standard_Integer Geom_BSplineCurve::FirstUKnotIndex

(

)

const

void Geom_BSplineCurve::IncreaseDegree

(

const Standard_Integer

Degree

)

void Geom_BSplineCurve::IncreaseMultiplicity	(	const Standard_Integer	I1,
		const Standard_Integer	I2,
		const Standard_Integer	M
	)

void Geom_BSplineCurve::IncreaseMultiplicity	(	const Standard_Integer	Index,
		const Standard_Integer	M
	)

void Geom_BSplineCurve::IncrementMultiplicity	(	const Standard_Integer	I1,
		const Standard_Integer	I2,
		const Standard_Integer	M
	)

void Geom_BSplineCurve::InsertKnot	(	const Standard_Real	U,
		const Standard_Integer	M = 1,
		const Standard_Real	ParametricTolerance = 0.0,
		const Standard_Boolean	Add = Standard_True
	)

void Geom_BSplineCurve::InsertKnots	(	const TColStd_Array1OfReal &	Knots,
		const TColStd_Array1OfInteger &	Mults,
		const Standard_Real	ParametricTolerance = 0.0,
		const Standard_Boolean	Add = Standard_False
	)

Standard_Boolean Geom_BSplineCurve::IsClosed

(

)

const [virtual]

Implements Geom_Curve.

Standard_Boolean Geom_BSplineCurve::IsCN

(

const Standard_Integer

N

)

const [virtual]

Implements Geom_Curve.

Standard_Boolean Geom_BSplineCurve::IsPeriodic

(

)

const [virtual]

Implements Geom_Curve.

Standard_Boolean Geom_BSplineCurve::IsRational

(

)

const

Standard_Real Geom_BSplineCurve::Knot

(

const Standard_Integer

Index

)

const

GeomAbs_BSplKnotDistribution Geom_BSplineCurve::KnotDistribution

(

)

const

void Geom_BSplineCurve::Knots

(

TColStd_Array1OfReal &

K

)

const

void Geom_BSplineCurve::KnotSequence

(

TColStd_Array1OfReal &

K

)

const

Standard_Real Geom_BSplineCurve::LastParameter

(

)

const [virtual]

Implements Geom_Curve.

Standard_Integer Geom_BSplineCurve::LastUKnotIndex

(

)

const

void Geom_BSplineCurve::LocalD0	(	const Standard_Real	U,
		const Standard_Integer	FromK1,
		const Standard_Integer	ToK2,
		gp_Pnt &	P
	)			const

void Geom_BSplineCurve::LocalD1	(	const Standard_Real	U,
		const Standard_Integer	FromK1,
		const Standard_Integer	ToK2,
		gp_Pnt &	P,
		gp_Vec &	V1
	)			const

void Geom_BSplineCurve::LocalD2	(	const Standard_Real	U,
		const Standard_Integer	FromK1,
		const Standard_Integer	ToK2,
		gp_Pnt &	P,
		gp_Vec &	V1,
		gp_Vec &	V2
	)			const

void Geom_BSplineCurve::LocalD3	(	const Standard_Real	U,
		const Standard_Integer	FromK1,
		const Standard_Integer	ToK2,
		gp_Pnt &	P,
		gp_Vec &	V1,
		gp_Vec &	V2,
		gp_Vec &	V3
	)			const

gp_Vec Geom_BSplineCurve::LocalDN	(	const Standard_Real	U,
		const Standard_Integer	FromK1,
		const Standard_Integer	ToK2,
		const Standard_Integer	N
	)			const

gp_Pnt Geom_BSplineCurve::LocalValue	(	const Standard_Real	U,
		const Standard_Integer	FromK1,
		const Standard_Integer	ToK2
	)			const

void Geom_BSplineCurve::LocateU	(	const Standard_Real	U,
		const Standard_Real	ParametricTolerance,
		Standard_Integer &	I1,
		Standard_Integer &	I2,
		const Standard_Boolean	WithKnotRepetition = Standard_False
	)			const

static Standard_Integer Geom_BSplineCurve::MaxDegree

(

)

[static]

void Geom_BSplineCurve::MovePoint	(	const Standard_Real	U,
		const gp_Pnt &	P,
		const Standard_Integer	Index1,
		const Standard_Integer	Index2,
		Standard_Integer &	FirstModifiedPole,
		Standard_Integer &	LastModifiedPole
	)

void Geom_BSplineCurve::MovePointAndTangent	(	const Standard_Real	U,
		const gp_Pnt &	P,
		const gp_Vec &	Tangent,
		const Standard_Real	Tolerance,
		const Standard_Integer	StartingCondition,
		const Standard_Integer	EndingCondition,
		Standard_Integer &	ErrorStatus
	)

void Geom_BSplineCurve::Multiplicities

(

TColStd_Array1OfInteger &

M

)

const

Standard_Integer Geom_BSplineCurve::Multiplicity

(

const Standard_Integer

Index

)

const

Standard_Integer Geom_BSplineCurve::NbKnots

(

)

const

Standard_Integer Geom_BSplineCurve::NbPoles

(

)

const

void Geom_BSplineCurve::PeriodicNormalization

(

Standard_Real &

U

)

const

gp_Pnt Geom_BSplineCurve::Pole

(

const Standard_Integer

Index

)

const

void Geom_BSplineCurve::Poles

(

TColgp_Array1OfPnt &

P

)

const

Standard_Boolean Geom_BSplineCurve::RemoveKnot	(	const Standard_Integer	Index,
		const Standard_Integer	M,
		const Standard_Real	Tolerance
	)

void Geom_BSplineCurve::Resolution	(	const Standard_Real	Tolerance3D,
		Standard_Real &	UTolerance
	)

void Geom_BSplineCurve::Reverse

(

)

[virtual]

Implements Geom_Curve.

Standard_Real Geom_BSplineCurve::ReversedParameter

(

const Standard_Real

U

)

const [virtual]

Implements Geom_Curve.

void Geom_BSplineCurve::Segment	(	const Standard_Real	U1,
		const Standard_Real	U2
	)

void Geom_BSplineCurve::SetKnot	(	const Standard_Integer	Index,
		const Standard_Real	K,
		const Standard_Integer	M
	)

void Geom_BSplineCurve::SetKnot	(	const Standard_Integer	Index,
		const Standard_Real	K
	)

void Geom_BSplineCurve::SetKnots

(

const TColStd_Array1OfReal &

K

)

void Geom_BSplineCurve::SetNotPeriodic

(

)

void Geom_BSplineCurve::SetOrigin	(	const Standard_Real	U,
		const Standard_Real	Tol
	)

void Geom_BSplineCurve::SetOrigin

(

const Standard_Integer

Index

)

void Geom_BSplineCurve::SetPeriodic

(

)

void Geom_BSplineCurve::SetPole	(	const Standard_Integer	Index,
		const gp_Pnt &	P,
		const Standard_Real	Weight
	)

void Geom_BSplineCurve::SetPole	(	const Standard_Integer	Index,
		const gp_Pnt &	P
	)

void Geom_BSplineCurve::SetWeight	(	const Standard_Integer	Index,
		const Standard_Real	Weight
	)

gp_Pnt Geom_BSplineCurve::StartPoint

(

)

const [virtual]

Implements Geom_BoundedCurve.

void Geom_BSplineCurve::Transform

(

const gp_Trsf &

T

)

[virtual]

Implements Geom_Geometry.

Standard_Real Geom_BSplineCurve::Weight

(

const Standard_Integer

Index

)

const

void Geom_BSplineCurve::Weights

(

TColStd_Array1OfReal &

W

)

const