path: root/src/Law/Law_BSpline.cdl

-- File:	Law_BSpline.cdl
-- Created:	Fri Oct 20 11:52:40 1995
-- Author:	Laurent BOURESCHE
--		<lbo@phylox>
---Copyright:	 Matra Datavision 1995

class BSpline from Law inherits TShared from MMgt

    ---Purpose : Definition of the 1D B_spline curve.
    --         
    --         Uniform  or non-uniform
    --         Rational or non-rational
    --         Periodic or non-periodic
    --  
    --  a b-spline 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 :
    --             
    --              - Uniform if all multiplicities are 1.
    --              
    --              -  Quasi-uniform if  all multiplicities are  1
    --              but the first and the last which are Degree+1.
    --              
    --              -   PiecewiseBezier if  all multiplicites  are
    --              Degree but the   first and the  last which are
    --              Degree+1. 
    --              
    --         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 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

uses  
    Array1OfInteger      from TColStd,
    Array1OfReal         from TColStd,
    HArray1OfInteger     from TColStd,
    HArray1OfReal        from TColStd,
    BSplKnotDistribution from GeomAbs,
    Shape                from GeomAbs

raises 
    ConstructionError   from Standard,
    DimensionError      from Standard,
    DomainError         from Standard,
    OutOfRange          from Standard,
    RangeError          from Standard,
    NoSuchObject        from Standard

is


    Create (Poles          : Array1OfReal    from TColStd; 
            Knots          : Array1OfReal    from TColStd; 
            Multiplicities : Array1OfInteger from TColStd; 
            Degree         : Integer;
    	    Periodic       : Boolean = Standard_False)
	  
    returns mutable BSpline from Law

    ---Purpose :  Creates a  non-rational B_spline curve   on  the
    --         basis <Knots, Multiplicities> of degree <Degree>.

    raises ConstructionError;

    -- The following conditions must be verified.
    
    --  0 < Degree <= MaxDegree.
    --  
    --  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


    Create (Poles          : Array1OfReal    from TColStd;
    	    Weights        : Array1OfReal    from TColStd;
            Knots          : Array1OfReal    from TColStd; 
            Multiplicities : Array1OfInteger from TColStd; 
            Degree         : Integer;
    	    Periodic       : Boolean = Standard_False)
	  
    returns mutable BSpline from Law

    ---Purpose : Creates  a rational B_spline  curve  on the basis
    --         <Knots, Multiplicities> of degree <Degree>.

    raises ConstructionError;

    -- The following conditions must be verified.
    
    --  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


    IncreaseDegree (me : mutable; Degree : Integer)
  
    ---Purpose: Increase the degree to  <Degree>. Nothing is  done
    --          if  <Degree>   is lower or  equal  to the  current
    --          degree.  

    raises ConstructionError;

    --  Raised if Degree is greater than MaxDegree.


    IncreaseMultiplicity (me : mutable; Index : Integer; M : Integer)
 
    ---Purpose :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.

    raises OutOfRange;
    	
    ---Purpose: If <Index> is not in [FirstUKnotIndex, LastUKnotIndex]


    IncreaseMultiplicity (me : mutable; I1, I2 : Integer; M : Integer) 
  
    ---Purpose :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.

    raises OutOfRange;
    	
    ---Purpose: If <I1,I2> are not in [FirstUKnotIndex, LastUKnotIndex]


    IncrementMultiplicity (me : mutable; I1, I2 : Integer; M : Integer) 
  
    ---Purpose :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.

    raises OutOfRange;
    	
    ---Purpose: If <I1,I2> are not in [FirstUKnotIndex, LastUKnotIndex]


    InsertKnot (me  : mutable; 
        	U   : Real; 
    	        M   : Integer = 1; 
    	        ParametricTolerance : Real = 0.0;
    	        Add : Boolean = Standard_True); 
  
    ---Purpose: 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.
    
    
    InsertKnots (me : mutable; Knots : Array1OfReal    from TColStd; 
    	    	    	       Mults : Array1OfInteger from TColStd;
    	    	    	     ParametricTolerance : Real = 0.0;
      	    	    	     Add : Boolean = Standard_False);
			     
    ---Purpose: 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.


    RemoveKnot(me : mutable; Index     : Integer; 
    	    	    	     M         : Integer;
    	    	    	     Tolerance : Real) returns Boolean
			   
    ---Purpose : 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.
    --         
    raises OutOfRange;
    ---Purpose :
    --  Raised if Index is not in the range
    --  [FirstUKnotIndex, LastUKnotIndex]
    
    
    ---Purpose : 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.
    
    
    Reverse (me : mutable);
    ---Purpose :
    --  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.


    ReversedParameter(me; U : Real) returns Real;
    ---Purpose: Returns the  parameter on the  reversed  curve for
    --          the point of parameter U on <me>.
    --          
    --          returns UFirst + ULast - U


    Segment (me : mutable; U1, U2 : Real)
    ---Purpose :
    --  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 DomainError from Standard;

    ---Purpose: raises if U2 < U1.


    SetKnot (me : mutable; Index : Integer; K : Real)
    ---Purpose :  Changes the knot of range Index.
    --  The multiplicity of the knot is not modified.
    raises ConstructionError,
    ---Purpose : Raised if K >= Knots(Index+1) or K <= Knots(Index-1).
           OutOfRange;
    ---Purpose : Raised if Index < 1 || Index > NbKnots


    SetKnots (me : mutable; K : Array1OfReal from TColStd)
    ---Purpose :  Changes all the knots of the curve
    --  The multiplicity of the knots are not modified.
    raises ConstructionError,
    ---Purpose : 
    --  Raised if there is an index such that K (Index+1) <= K (Index).
           OutOfRange;
    ---Purpose : 
    --  Raised if  K.Lower() < 1 or K.Upper() > NbKnots


    SetKnot (me : mutable; Index : Integer; K : Real; M : Integer)
    ---Purpose :
    --  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.
    raises ConstructionError,
    ---Purpose :
    --  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. 
	    OutOfRange;
    ---Purpose : Raised if Index < 1 || Index > NbKnots


    PeriodicNormalization(me ;  U : in out Real) ; 
       
    ---Purpose : returns the parameter normalized within
    --         the period if the curve is periodic : otherwise
    --         does not do anything


    SetPeriodic (me : mutable)
    ---Purpose :
    --  Makes a closed B-spline 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 B-spline can be uniform 
    --   or not.
    raises ConstructionError;
    ---Purpose : Raised if the curve is not closed.


    SetOrigin (me : mutable; Index : Integer)
    ---Purpose: Set the origin of a periodic curve at Knot(index)
    --          KnotVector and poles are modified.
    raises NoSuchObject,
    ---Purpose: Raised if the curve is not periodic
    	   DomainError;
    ---Purpose: Raised if index not in the range 
    --          [FirstUKnotIndex , LastUKnotIndex]


    SetNotPeriodic (me : mutable);
    ---Purpose :
    --  Makes a non periodic curve. If the curve was non periodic
    --  the curve is not modified.
	        
 
    SetPole (me : mutable; Index : Integer; P : Real)
    ---Purpose : Substitutes the Pole of range Index with P.
    raises OutOfRange;
    ---Purpose:
    --  Raised if Index < 1 || Index > NbPoles


    SetPole (me : mutable; Index : Integer; P : Real; Weight : Real)
    ---Purpose:
    --  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
    raises OutOfRange,
    ---Purpose:
    --  Raised if Index < 1 || Index > NbPoles
           ConstructionError;
    ---Purpose : Raised if Weight <= 0.0


    SetWeight (me : mutable; Index : Integer; Weight : Real)
    ---Purpose :
    --  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.
    raises OutOfRange,
    ---Purpose:
    --  Raised if Index < 1 || Index > NbPoles
           ConstructionError;
    ---Purpose : Raised if Weight <= 0.0


    IsCN (me; N : Integer)   returns Boolean
    ---Purpose :
    --  Returns the continuity of the curve, the curve is at least C0.
    raises RangeError;
    ---Purpose : Raised if N < 0.


    IsClosed (me)  returns Boolean;
    ---Purpose :
    --  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.


    IsPeriodic (me)  returns Boolean;
    ---Purpose : Returns True if the curve is periodic.


    IsRational (me)  returns Boolean;
    ---Purpose :
    --  Returns True if the weights are not identical.
    --  The tolerance criterion is Epsilon of the class Real.
    
    IsCacheValid(me;  Parameter : Real) returns Boolean
  
    ---Purpose :
    --           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
    -- 
    is static private;
  
    Continuity (me)  returns Shape from GeomAbs;
    ---Purpose :
    --  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.


    Degree (me)  returns Integer;


    -------------------------------------------------
    ---Purpose : Computation of value and derivatives
    -------------------------------------------------

    Value(me ; U : Real) returns Real from Standard;

    D0 (me ; U : Real; P : out Real);

    D1 (me; U : Real; P : out Real; V1 : out Real);

    D2 (me; U : Real; P : out Real; V1, V2 : out Real);

    D3 (me; U : Real; P : out Real; V1, V2, V3 : out Real);

    DN (me; U : Real; N : Integer)  returns Real;


    ------------------------------------------------------------------
    ---Purpose  :
    --  The following functions computes 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.
    ------------------------------------------------------------------
    
    LocalValue (me; U : Real; FromK1, ToK2 : Integer) returns Real;

    LocalD0 (me; U : Real; FromK1, ToK2 : Integer; P : out Real);

    LocalD1 (me; U : Real; FromK1, ToK2 : Integer; P, V1 : out Real);

    LocalD2 (me; U : Real; FromK1, ToK2 : Integer; P, V1, V2 : out Real);

    LocalD3 (me; U : Real; FromK1, ToK2 : Integer; P, V1, V2, V3 : out Real);

    LocalDN (me; U : Real; FromK1, ToK2 : Integer; N : Integer)  returns Real;


    EndPoint (me)   returns Real;
    ---Purpose :
    --  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.


    FirstUKnotIndex (me)   returns Integer;
    ---Purpose :
    --  For a B-spline 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.


    FirstParameter (me)   returns Real;
    ---Purpose :
    --  Computes the parametric value of the start point of the curve.
    --  It is a knot value.


    Knot (me; Index : Integer)   returns Real
    ---Purpose :
    --  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.
    raises OutOfRange;
    ---Purpose : Raised if Index < 1 or Index > NbKnots


    Knots (me; K : out Array1OfReal from TColStd)
    ---Purpose : returns the knot values of the B-spline curve;
    raises DimensionError;
    ---Purpose :
    --  Raised if the length of K is not equal to the number of knots.


    KnotSequence (me; K : out Array1OfReal from TColStd)
    ---Purpose : 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}
    raises DimensionError;
    ---Purpose :
    --  Raised if the length of K is not equal to NbPoles + Degree + 1
    


    KnotDistribution (me)   returns BSplKnotDistribution from GeomAbs;
    ---Purpose :
    --  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.


    LastUKnotIndex (me)  returns Integer;
    ---Purpose :
    --  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.


    LastParameter (me)   returns Real;
    ---Purpose :
    --  Computes the parametric value of the end point of the curve.
    --  It is a knot value.


    LocateU (me;
             U                   : Real; 
             ParametricTolerance : Real; 
             I1, I2              : in out Integer;
             WithKnotRepetition  : Boolean = Standard_False);
    ---Purpose :
    --  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)


    Multiplicity (me; Index : Integer)   returns Integer
    ---Purpose :
    --  Returns the multiplicity of the knots of range Index.
    raises OutOfRange;
    ---Purpose : Raised if Index < 1 or Index > NbKnots


    Multiplicities (me; M : out Array1OfInteger from TColStd)
    ---Purpose :
    --  Returns the multiplicity of the knots of the curve.
    raises DimensionError;
    ---Purpose :
    --  Raised if the length of M is not equal to NbKnots.


    NbKnots (me)  returns Integer;
    ---Purpose :
    --  Returns the number of knots. This method returns the number of 
    --  knot without repetition of multiple knots.


    NbPoles (me)  returns Integer;
    ---Purpose : Returns the number of poles


    Pole (me; Index : Integer)   returns Real
    ---Purpose : Returns the pole of range Index.
    raises OutOfRange;
    ---Purpose : Raised if Index < 1 or Index > NbPoles.


    Poles (me; P : out Array1OfReal from TColStd)
    ---Purpose : Returns the poles of the B-spline curve;
    raises DimensionError;
    ---Purpose : 
    --  Raised if the length of P is not equal to the number of poles.


    StartPoint (me)  returns Real;
    ---Purpose :
    --  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.
    

    Weight (me; Index : Integer)  returns Real  
    ---Purpose : Returns the weight of the pole of range Index .
    raises OutOfRange;
    ---Purpose : Raised if Index < 1 or Index > NbPoles.


    Weights (me; W : out Array1OfReal from TColStd)
    ---Purpose : Returns the weights of the B-spline curve;
    raises DimensionError;
    ---Purpose :
    --  Raised if the length of W is not equal to NbPoles.


    MaxDegree (myclass)  returns Integer;
    ---Purpose :
    --  Returns the value of the maximum degree of the normalized 
    --  B-spline basis functions in this package.

      MovePointAndTangent (me : mutable; 
    	    	       U                 : Real ; 
    	    	       NewValue          : Real ; 
                       Derivative        : Real ;
		       Tolerance         : Real ; 
    	    	       StartingCondition, 
                       EndingCondition   : Integer; 
    	    	       ErrorStatus       : out Integer) 

        ---Purpose : 
        -- 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
        -- 
     raises OutOfRange;

    Resolution(me ; Tolerance3D : Real;
            	    UTolerance  : out Real);
    ---Purpose:  given Tolerance3D returns UTolerance
    --           such that if f(t) is the curve we have
    --           | t1 - t0| < Utolerance ===> 
    --           |f(t1) - f(t0)| < Tolerance3D
    

    Copy (me)  returns mutable like me;


    UpdateKnots(me : mutable)
    ---Purpose : Recompute  the  flatknots,  the knotsdistribution, the
    --          continuity.
    is static private;
  

fields

  rational        : Boolean;
  periodic        : Boolean;
  knotSet         : BSplKnotDistribution from GeomAbs; 
  smooth          : Shape from GeomAbs;
  deg             : Integer;
  poles           : HArray1OfReal    from TColStd;
  weights         : HArray1OfReal    from TColStd;
  flatknots       : HArray1OfReal    from TColStd;
  knots           : HArray1OfReal    from TColStd;
  mults           : HArray1OfInteger from TColStd;
end;