opennurbs_nurbscurve.h

/* $NoKeywords: $ */
/*
//
// Copyright (c) 1993-2012 Robert McNeel & Associates. All rights reserved.
// OpenNURBS, Rhinoceros, and Rhino3D are registered trademarks of Robert
// McNeel & Associates.
//
// THIS SOFTWARE IS PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY.
// ALL IMPLIED WARRANTIES OF FITNESS FOR ANY PARTICULAR PURPOSE AND OF
// MERCHANTABILITY ARE HEREBY DISCLAIMED.
//              
// For complete openNURBS copyright information see <http://www.opennurbs.org>.
//
////////////////////////////////////////////////////////////////
*/

////////////////////////////////////////////////////////////////
//
//   Definition of NURBS curve
//
////////////////////////////////////////////////////////////////

#if !defined(OPENNURBS_NURBSCURVE_INC_)
#define OPENNURBS_NURBSCURVE_INC_

class ON_CLASS ON_NurbsCurve : public ON_Curve
{
  ON_OBJECT_DECLARE(ON_NurbsCurve);

public:
  ON_NurbsCurve() ON_NOEXCEPT;
  virtual ~ON_NurbsCurve();
  ON_NurbsCurve(const ON_NurbsCurve&);
    ON_NurbsCurve& operator=(const ON_NurbsCurve& src);

#if defined(ON_HAS_RVALUEREF)
  // rvalue copy constructor
  ON_NurbsCurve( ON_NurbsCurve&& ) ON_NOEXCEPT;

  // The rvalue assignment operator calls ON_Object::operator=(ON_Object&&)
  // which could throw exceptions.  See the implementation of
  // ON_Object::operator=(ON_Object&&) for details.
  ON_NurbsCurve& operator=( ON_NurbsCurve&& );
#endif

public:
  /*
  Description:
    Use ON_NurbsCurve::New(...) instead of new ON_NurbsCurve(...)
  Returns:
    Pointer to an ON_NurbsCurve.  Destroy by calling delete.
  Remarks:
    See static ON_Brep* ON_Brep::New() for details.
  */
  static ON_NurbsCurve* New();
  static ON_NurbsCurve* New(
            const ON_NurbsCurve& nurbs_curve 
            );
  static ON_NurbsCurve* New(
            const ON_BezierCurve& bezier_curve 
            );
  static ON_NurbsCurve* New(
            int dimension,
            bool bIsRational,
            int order,
            int cv_count
            );



  // Description:
  //   Create a NURBS curve equal to bezier with domain [0,1].
  // Parameters:
  //   bezier_curve - [in]
  ON_NurbsCurve(
        const ON_BezierCurve& bezier_curve
        );

  // Description:
  //   Create a NURBS curve with knot a cv memory allocated.
  // Parameters:
  //   dimension - [in] (>= 1)
  //   bIsRational - [in] true to make a rational NURBS
  //   order - [in] (>= 2) The order=degree+1
  //   cv_count - [in] (>= order) number of control vertices
  ON_NurbsCurve(
          int dimension,
          bool bIsRational,
          int order,
          int cv_count
          );

  // virtual ON_Object::SizeOf override
  unsigned int SizeOf() const override;

  // virtual ON_Object::DataCRC override
  ON__UINT32 DataCRC(ON__UINT32 current_remainder) const override;

  /*
  Description:
    See if this and other are same NURBS geometry.
  Parameters:
    other - [in] other NURBS curve
    bIgnoreParameterization - [in] if true, parameterization
             and orientaion are ignored.
    tolerance - [in] tolerance to use when comparing
                     control points.
  Returns:
    true if curves are tne same.
  */
  bool IsDuplicate( 
          const ON_NurbsCurve& other, 
          bool bIgnoreParameterization,
          double tolerance = ON_ZERO_TOLERANCE 
          ) const;

  // Description:
  //   Zeros all fields.
  void Initialize(void);

  // Description:
  //   Create a NURBS curve with knot a cv memory allocated.
  // Parameters:
  //   dimension - [in] (>= 1)
  //   bIsRational - [in] true to make a rational NURBS
  //   order - [in] (>= 2) The order=degree+1
  //   cv_count - [in] (>= order) number of control vertices
  bool Create( 
          int dimension,
          bool bIsRational,
          int order,
          int cv_count
          );

  // Description:
  //   Create a clamped uniform NURBS curve from a list
  //   of control points
  // Parameters:
  //   dimension - [in] 1, 2 or 3
  //   order - [in] (>=2) order=degree+1
  //   point_count - [in] (>=order) number of control vertices
  //   point - [in] array of control vertex locations.
  //   knot_delta - [in] (>0.0) knot spacing
  // Returns:
  //   true if successful
  bool CreateClampedUniformNurbs( 
          int dimension,
          int order,
          int point_count,
          const ON_3dPoint* point,
          double knot_delta = 1.0
          );

  // Description:
  //   Create a periodic uniform NURBS curve from a list
  //   of control points
  // Parameters:
  //   dimension - [in] 1, 2 or 3
  //   order - [in] (>=2) order=degree+1
  //   point_count - [in] (>=max(3,order-1)) number of distinct control vertices
  //   point - [in] array of distinct control vertex locations.
  //   knot_delta - [in] (>0.0) knot spacing
  // Returns:
  //   true if successful
  bool CreatePeriodicUniformNurbs( 
          int dimension,
          int order,
          int point_count,
          const ON_3dPoint* point,
          double knot_delta = 1.0
          );

  // Description:
  //   Deallocate knot and cv memory.  Zeros all fields.
  void Destroy();


  // Description:
  //   Call if memory used by ON_NurbsCurve becomes invalid.
  void EmergencyDestroy(); 


  // Description:
  //   Set NURBS curve equal to bezier with domain [0,1].
  // Parameters:
  //   bezier_curve - [in]
    ON_NurbsCurve& operator=(
    const ON_BezierCurve& bezier_curve
    );

  /////////////////////////////////////////////////////////////////
  // ON_Object overrides

  bool IsValid( class ON_TextLog* text_log = nullptr ) const override;

  // Description:
  //   virtual ON_Object::Dump override
  void Dump( 
    ON_TextLog& dump
    ) const override;

  // Description:
  //   virtual ON_Object::Write override
  bool Write(
         ON_BinaryArchive& binary_archive
       ) const override;

  // Description:
  //   virtual ON_Object::Read override
  bool Read(
         ON_BinaryArchive& binary_archive
       ) override;

  /////////////////////////////////////////////////////////////////
  // ON_Geometry overrides

  // Description:
  //   virtual ON_Geometry::Dimension override
  // Returns:
  //   value of m_dim
  int Dimension() const override;

  // virtual ON_Geometry GetBBox override       
  bool GetBBox( double* boxmin, double* boxmax, bool bGrowBox = false ) const override;

  // Description:
  //   virtual ON_Geometry::Transform override.
  //   Transforms the NURBS curve.
  //
  // Parameters:
  //   xform - [in] transformation to apply to object.
  //
  // Remarks:
  //   When overriding this function, be sure to include a call
  //   to ON_Object::TransformUserData() which takes care of 
  //   transforming any ON_UserData that may be attached to 
  //   the object.
  bool Transform( 
         const ON_Xform& xform
         ) override;

  // virtual ON_Geometry::IsDeformable() override
  bool IsDeformable() const override;

  // virtual ON_Geometry::MakeDeformable() override
  bool MakeDeformable() override;

  // Description:
  //   virtual ON_Geometry::SwapCoordinates override.
  //   Swaps control vertex coordinate values with indices i and j.
  // Parameters:
  //   i - [in] coordinate index
  //   j - [in] coordinate index
  bool SwapCoordinates(
        int i, 
        int j
        ) override;


  /////////////////////////////////////////////////////////////////
  // ON_Curve overrides

  // Description:
  //   virtual ON_Curve::Domain override.
  // Returns:
  //   domain of the NURBS curve.
  ON_Interval Domain() const override;

  // Description:
  //   virtual ON_Curve::SetDomain override.
  //   Set the domain of the curve
  // Parameters:
  //   t0 - [in]
  //   t1 - [in] new domain will be [t0,t1]
  // Returns:
  //   true if successful.
  bool SetDomain(
        double t0, 
        double t1 
        ) override;

  /*
  Description:
    If this curve is closed, then modify it so that
    the start/end point is at curve parameter t.
  Parameters:
    t - [in] curve parameter of new start/end point.  The
             returned curves domain will start at t.
  Returns:
    true if successful.
  Remarks:
    Overrides virtual ON_Curve::ChangeClosedCurveSeam
  */
  bool ChangeClosedCurveSeam( 
            double t 
            ) override;

  // Description:
  //   virtual ON_Curve::SpanCount override.
  //   Get number of nonempty smooth (c-infinity) spans in curve
  // Returns:
  //   Number of nonempty smooth (c-infinity) spans.
  // Remarks:
  //   A nonempty span is bracked by knots m_knot[i] < m_knot[i+1]
  //   with m_order-2 <= i < m_cv_count-1.
  int SpanCount() const override;

  // Description:
  //   virtual ON_Curve::GetSpanVector override.
  //   Get number of parameters of distinct knots in NURBS curve's domain.
  // Parameters:
  //   knot_values - [out] an array of length SpanCount()+1 is 
  //       filled in with the distinct knot values in the list
  ///      (m_knot[m_order-2],...,m_knot[m_cv_count-1)
  // Returns:
  //   true if successful
  bool GetSpanVector(
         double* knot_values
         ) const override; // 

  // Description:
  //   virtual ON_Curve::Degree override.
  // Returns:
  //   m_order-1
  int Degree() const override; 

  // Description:
  //   virtual ON_Curve::GetParameterTolerance override.
  bool GetParameterTolerance( // returns tminus < tplus: parameters tminus <= s <= tplus
         double t,
         double* tminus,
         double* tplus
         ) const override;

  // Description:
  //   virtual ON_Curve::IsLinear override.
  bool IsLinear(
        double tolerance = ON_ZERO_TOLERANCE
        ) const override;

  /*
  Description:
    Several types of ON_Curve can have the form of a polyline including
    a degree 1 ON_NurbsCurve, an ON_PolylineCurve, and an ON_PolyCurve
    all of whose segments are some form of polyline.  IsPolyline tests
    a curve to see if it can be represented as a polyline.
  Parameters:
    pline_points - [out] if not nullptr and true is returned, then the
        points of the polyline form are returned here.
    t - [out] if not nullptr and true is returned, then the parameters of
        the polyline points are returned here.
  Returns:
    @untitled table
    0        curve is not some form of a polyline
    >=2      number of points in polyline form
  */
  int IsPolyline(
        ON_SimpleArray<ON_3dPoint>* pline_points = nullptr,
        ON_SimpleArray<double>* pline_t = nullptr
        ) const override;

  // Description:
  //   virtual ON_Curve::IsArc override.
  bool IsArc(
        const ON_Plane* plane = nullptr,
        ON_Arc* arc = nullptr,
        double tolerance = ON_ZERO_TOLERANCE
        ) const override;

  // Description:
  //   virtual ON_Curve::IsPlanar override.
  bool IsPlanar(
        ON_Plane* plane = nullptr,
        double tolerance = ON_ZERO_TOLERANCE
        ) const override;

  // Description:
  //   virtual ON_Curve::IsInPlane override.
  bool IsInPlane(
        const ON_Plane& test_plane,
        double tolerance = ON_ZERO_TOLERANCE
        ) const override;

  // Description:
  //   virtual ON_Curve::IsClosed override.
  // Returns:
  //   true if NURBS curve is closed. (Either curve has
  //   clamped end knots and euclidean location of start
  //   CV = euclidean location of end CV, or curve is
  //   periodic.)
  bool IsClosed() const override;

  // Description:
  //   virtual ON_Curve::IsPeriodic override.
  // Returns:
  //   true if NURBS curve is periodic (degree > 1,
  //   periodic knot vector, last degree many CVs 
  //   are duplicates of first degree many CVs).
  bool IsPeriodic() const override;
  
  /*
  Description:
    Search for a derivatitive, tangent, or curvature discontinuity.
  Parameters:
    c - [in] type of continity to test for.  If ON::continuity::C1_continuous
    t0 - [in] search begins at t0
    t1 - [in] (t0 < t1) search ends at t1
    t - [out] if a discontinuity is found, the *t reports the
          parameter at the discontinuity.
    hint - [in/out] if GetNextDiscontinuity will be called repeatedly,
       passing a "hint" with initial value *hint=0 will increase the speed
       of the search.       
    dtype - [out] if not nullptr, *dtype reports the kind of discontinuity
        found at *t.  A value of 1 means the first derivative or unit tangent
        was discontinuous.  A value of 2 means the second derivative or
        curvature was discontinuous.
    cos_angle_tolerance - [in] default = cos(1 degree) Used only when
        c is ON::continuity::G1_continuous or ON::continuity::G2_continuous.  If the cosine
        of the angle between two tangent vectors 
        is <= cos_angle_tolerance, then a G1 discontinuity is reported.
    curvature_tolerance - [in] (default = ON_SQRT_EPSILON) Used only when
        c is ON::continuity::G2_continuous or ON::continuity::Gsmooth_continuous.  
        ON::continuity::G2_continuous:
          If K0 and K1 are curvatures evaluated
          from above and below and |K0 - K1| > curvature_tolerance,
          then a curvature discontinuity is reported.
        ON::continuity::Gsmooth_continuous:
          If K0 and K1 are curvatures evaluated from above and below
          and the angle between K0 and K1 is at least twice angle tolerance
          or ||K0| - |K1|| > (max(|K0|,|K1|) > curvature_tolerance,
          then a curvature discontinuity is reported.
  Returns:
    true if a discontinuity was found on the interior of the interval (t0,t1).
  Remarks:
    Overrides ON_Curve::GetNextDiscontinuity.
  */
  bool GetNextDiscontinuity( 
                  ON::continuity c,
                  double t0,
                  double t1,
                  double* t,
                  int* hint=nullptr,
                  int* dtype=nullptr,
                  double cos_angle_tolerance=ON_DEFAULT_ANGLE_TOLERANCE_COSINE,
                  double curvature_tolerance=ON_SQRT_EPSILON
                  ) const override;

  /*
  Description:
    Test continuity at a curve parameter value.
  Parameters:
    c - [in] continuity to test for
    t - [in] parameter to test
    hint - [in] evaluation hint
    point_tolerance - [in] if the distance between two points is
        greater than point_tolerance, then the curve is not C0.
    d1_tolerance - [in] if the difference between two first derivatives is
        greater than d1_tolerance, then the curve is not C1.
    d2_tolerance - [in] if the difference between two second derivatives is
        greater than d2_tolerance, then the curve is not C2.
    cos_angle_tolerance - [in] default = cos(1 degree) Used only when
        c is ON::continuity::G1_continuous or ON::continuity::G2_continuous.  If the cosine
        of the angle between two tangent vectors 
        is <= cos_angle_tolerance, then a G1 discontinuity is reported.
    curvature_tolerance - [in] (default = ON_SQRT_EPSILON) Used only when
        c is ON::continuity::G2_continuous or ON::continuity::Gsmooth_continuous.  
        ON::continuity::G2_continuous:
          If K0 and K1 are curvatures evaluated
          from above and below and |K0 - K1| > curvature_tolerance,
          then a curvature discontinuity is reported.
        ON::continuity::Gsmooth_continuous:
          If K0 and K1 are curvatures evaluated from above and below
          and the angle between K0 and K1 is at least twice angle tolerance
          or ||K0| - |K1|| > (max(|K0|,|K1|) > curvature_tolerance,
          then a curvature discontinuity is reported.
  Returns:
    true if the curve has at least the c type continuity at the parameter t.
  Remarks:
    Overrides ON_Curve::IsContinuous.
  */
  bool IsContinuous(
    ON::continuity c,
    double t, 
    int* hint = nullptr,
    double point_tolerance=ON_ZERO_TOLERANCE,
    double d1_tolerance=ON_ZERO_TOLERANCE,
    double d2_tolerance=ON_ZERO_TOLERANCE,
    double cos_angle_tolerance=ON_DEFAULT_ANGLE_TOLERANCE_COSINE,
    double curvature_tolerance=ON_SQRT_EPSILON
    ) const override;

  /*
  Description:
    Force the curve to start at a specified point.
  Parameters:
    start_point - [in]
  Returns:
    true if successful.
  Remarks:
    Some end points cannot be moved.  Be sure to check return
    code.
  See Also:
    ON_Curve::SetEndPoint
    ON_Curve::PointAtStart
    ON_Curve::PointAtEnd
  */
  //virtual
  bool SetStartPoint(
          ON_3dPoint start_point
          ) override;

  /*
  Description:
    Force the curve to end at a specified point.
  Parameters:
    end_point - [in]
  Returns:
    true if successful.
  Remarks:
    Some end points cannot be moved.  Be sure to check return
    code.
  See Also:
    ON_Curve::SetStartPoint
    ON_Curve::PointAtStart
    ON_Curve::PointAtEnd
  */
  //virtual
  bool SetEndPoint(
          ON_3dPoint end_point
          ) override;

  // Description:
  //   virtual ON_Curve::Reverse override.
  //   Reverse parameterizatrion by negating all knots
  //   and reversing the order of the control vertices.
  // Remarks:
  //   Domain changes from [a,b] to [-b,-a]
  bool Reverse() override;       

  // Description:
  //   virtual ON_Curve::Evaluate override.
  bool Evaluate( // returns false if unable to evaluate
         double,         // evaluation parameter
         int,            // number of derivatives (>=0)
         int,            // array stride (>=Dimension())
         double*,        // array of length stride*(ndir+1)
         int = 0,        // optional - determines which side to evaluate from
                         //         0 = default
                         //      <  0 to evaluate from below, 
                         //      >  0 to evaluate from above
         int* = 0        // optional - evaluation hint (int) used to speed
                         //            repeated evaluations
         ) const override;


  /*
  Parameters:
    span_index - [in]
      (0 <= span_index <= m_cv_count-m_order)
    min_length -[in]
      minimum length of a linear span
    tolerance -[in]
      distance tolerance to use when checking control points
      between the span ends
  Returns 
    true if the span is a non-degenrate line.  This means:
    - dimension = 2 or 3
    - There are full multiplicity knots at each end of the span.
    - The length of the the line segment from the span's initial 
      control point to the span's final control point is 
      >= min_length.
    - The distance from the line segment to the interior control points
      is <= tolerance and the projections of these points onto
      the line increases monotonically.
  */
  bool SpanIsLinear( 
    int span_index, 
    double min_length,
    double tolerance
    ) const;

  bool SpanIsLinear( 
    int span_index, 
    double min_length,
    double tolerance,
    ON_Line* line
    ) const;


  /*
  Description:
    Looks for problems caused by knots that are close together
    or have mulitplicity >= order. If bRepair is true, the problems
    are fixed.  Does not change the domain.
  Parameters:
    knot_tolerance - [in] >= 0  When in doubt, use zero.
    bRepair - [in] If true, then problems are repaired.
      Otherwise this function looks for problemsn that
      can be repaired, but does not modify the curve.
  Returns:
    True if bad knots were found and can be repaired.
  See Also:
    ON_NurbsCurve::RemoveShortSegments
  */
  bool RepairBadKnots(
    double knot_tolerance=0.0,
    bool bRepair = true
    );

  // Description:
  //   virtual ON_Curve::Trim override.
  bool Trim( const ON_Interval& ) override;



  // Description:
  //   Where possible, analytically extends curve to include domain.
  // Parameters:
  //   domain - [in] if domain is not included in curve domain, 
  //   curve will be extended so that its domain includes domain.  
  //   Will not work if curve is closed. Original curve is identical
  //   to the restriction of the resulting curve to the original curve domain, 
  // Returns:
  //   true if successful.
  bool Extend(
    const ON_Interval& domain
    ) override;

  // Description:
  //   virtual ON_Curve::Split override.
  //
  // Split() divides the curve at the specified parameter.  The parameter
  // must be in the interior of the curve's domain.  The pointers passed
  // to ON_NurbsCurve::Split must either be nullptr or point to an ON_NurbsCurve.
  // If the pointer is nullptr, then a curve will be created
  // in Split().  You may pass "this" as one of the pointers to Split().
  // For example, 
  //
  //   ON_NurbsCurve right_side;
  //   crv.Split( crv.Domain().Mid() &crv, &right_side );
  //
  // would split crv at the parametric midpoint, put the left side in crv,
  // and return the right side in right_side.
  bool Split(
      double split_param,    // t = curve parameter to split curve at
      ON_Curve*& left_result, // left portion returned here (must be an ON_NurbsCurve)
      ON_Curve*& right_result // right portion returned here (must be an ON_NurbsCurve)
    ) const override;

  // Description:
  //   virtual ON_Curve::GetNurbForm override.
  int GetNurbForm( // returns 0: unable to create NURBS representation
                   //            with desired accuracy.
                   //         1: success - returned NURBS parameterization
                   //            matches the curve's to wthe desired accuracy
                   //         2: success - returned NURBS point locus matches
                   //            the curve's to the desired accuracy but, on
                   //            the interior of the curve's domain, the 
                   //            curve's parameterization and the NURBS
                   //            parameterization may not match to the 
                   //            desired accuracy.
        ON_NurbsCurve& nurbsform,
        double tolerance = 0.0,
        const ON_Interval* subdomain = nullptr     // OPTIONAL subdomain of curve
        ) const override;

  // Description:
  //   virtual ON_Curve::HasNurbForm override.
  int HasNurbForm( // returns 0: unable to create NURBS representation
                   //            with desired accuracy.
                   //         1: success - returned NURBS parameterization
                   //            matches the curve's to wthe desired accuracy
                   //         2: success - returned NURBS point locus matches
                   //            the curve's to the desired accuracy but, on
                   //            the interior of the curve's domain, the 
                   //            curve's parameterization and the NURBS
                   //            parameterization may not match to the 
                   //            desired accuracy.
        ) const override;

  // Description:
  //   virtual ON_Curve::GetCurveParameterFromNurbFormParameter override
  bool GetCurveParameterFromNurbFormParameter(
        double  nurbs_t,
        double* curve_t
        ) const override;

  // Description:
  //   virtual ON_Curve::GetNurbFormParameterFromCurveParameter override
  bool GetNurbFormParameterFromCurveParameter(
        double  curve_t,
        double* nurbs_t
        ) const override;

public:

  /////////////////////////////////////////////////////////////////
  // Interface

  bool IsRational(  // true if NURBS curve is rational
        void
        ) const;
  
  int CVSize(       // number of doubles per control vertex 
        void        // = IsRational() ? Dim()+1 : Dim()
        ) const;
  
  int Order(        // order = degree + 1
        void
        ) const;
    
  int CVCount(      // number of control vertices
        void 
        ) const;

  int KnotCount(    // total number of knots in knot vector
        void
        ) const;
  
  /*
  Description:
    Expert user function to get a pointer to control vertex
    memory.  If you are not an expert user, please use
    ON_NurbsCurve::GetCV( ON_3dPoint& ) or 
    ON_NurbsCurve::GetCV( ON_4dPoint& ).
  Parameters:
    cv_index - [in]
  Returns:
    Pointer to control vertex.
  Remarks:
    If the NURBS curve is rational, the format of the 
    returned array is a homogeneos rational point with
    length m_dim+1.  If the NURBS curve is not rational, 
    the format of the returned array is a nonrational 
    euclidean point with length m_dim.
  See Also
    ON_NurbsCurve::CVStyle
    ON_NurbsCurve::GetCV
    ON_NurbsCurve::Weight
  */
  double* CV(
        int cv_index
        ) const;

  /*
  Parameters:
    cv_index - [in]
      zero based control point index
  Returns:
    Control point as an ON_4dPoint.
  Remarks:
    If cv_index or the nurbs curve is not valid, then ON_4dPoint::Nan is returned.
    If dim < 3, unused coordinates are zero.
    If dim >= 4, the first three coordinates are returned.
    If is_rat is false, the weight is 1.
  */
  const ON_4dPoint ControlPoint(
    int cv_index
  ) const;

  /*
  Description:
    Returns the style of control vertices in the m_cv array.
  Returns:
    @untitled table
    ON::not_rational                m_is_rat is false
    ON::homogeneous_rational        m_is_rat is true
  */
  ON::point_style CVStyle() const;


  double Weight(        // get value of control vertex weight
        int             // CV index ( >= 0 and < CVCount() )
        ) const;

  /*
  Description:
    Set value of control vertex weight.
    If curve is non-rational, it will be converted to rational.
    */
  bool SetWeight(
        int,            // CV index ( >= 0 and < CVCount() )
        double          // value of control point weight
        );

  bool SetCV(              // set a single control vertex
        int,              // CV index ( >= 0 and < CVCount() )
        ON::point_style, // style of input point
        const double*     // value of control vertex
        );

  bool SetCV(               // set a single control vertex
        int,               // CV index ( >= 0 and < CVCount() )
        const ON_3dPoint& // value of control vertex
                           // If NURBS is rational, weight
                           // will be set to 1.
        );

  bool SetCV(              // set a single control vertex
        int,              // CV index ( >= 0 and < CVCount() )
        const ON_4dPoint& // value of control vertex
                          // If NURBS is not rational, euclidean
                          // location of homogeneous point will
                          // be used.
        );

  bool GetCV(              // get a single control vertex
        int,              // CV index ( >= 0 and < CVCount() )
        ON::point_style, // style to use for output point
        double*           // array of length >= CVSize()
        ) const;

  bool GetCV(              // get a single control vertex
        int,              // CV index ( >= 0 and < CVCount() )
        ON_3dPoint&      // gets euclidean cv when NURBS is rational
        ) const;

  bool GetCV(              // get a single control vertex
        int,              // CV index ( >= 0 and < CVCount() )
        ON_4dPoint&      // gets homogeneous cv
        ) const;

  // Description:
  //   Set knot value.
  // Parameters:
  //   knot_index - [in] 0 <= knot_index <= KnotCount()-1
  //   knot_value - [in]
  // Remarks:
  //   m_knot[] must exist.  Use ReserveKnotCapacity to
  //   allocate m_knot[].
  // Returns:
  //   true if successful
  // See Also:
  //   ON_NurbsCurve::ReserveKnotCapacity
  bool SetKnot(
        int knot_index,
        double knot_value
        );

  // Description:
  //   Get knot value.
  // Parameters:
  //   knot_index - [in] 0 <= knot_index <= KnotCount()-1
  // Returns:
  //   knot value = m_knot[knot_index]
  // See Also:
  //   ON_NurbsCurve::SetKnot, ON_NurbsCurve::KnotMultiplicity
  double Knot(
        int knot_index
        ) const;

  // Description:
  //   Get knot multiplicity.
  // Parameters:
  //   knot_index - [in] 0 <= knot_index <= KnotCount()-1
  // Returns:
  //   knot multiplicity = m_knot[knot_index]
  // See Also:
  //   ON_NurbsCurve::SetKnot, ON_NurbsCurve::Knot, 
  //   ON_NurbsCurve::InsertKnot
  int KnotMultiplicity(
        int knot_index
        ) const;

  // Description:
  //   Get pointer to knot vector array.
  // Returns:
  //   pointer to knot vector array (m_knot).
  // See Also:
  //   ON_NurbsCurve::SetKnot, ON_NurbsCurve::Knot, 
  //   ON_NurbsCurve::InsertKnot
  const double* Knot() const;

  // Description:
  //   Make knot vector a clamped uniform knot vector
  //   based on the current values of m_order and m_cv_count.
  //   Does not change values of control vertices.
  // Parameters:
  //   delta - [in] (>0.0) knot spacing.
  // Returns:
  //   true if successful.
  // Remarks:
  //   Allocates m_knot[] if it is not big enough.
  // See Also:
  //   ON_MakeClampedUniformKnotVector
  bool MakeClampedUniformKnotVector( 
    double delta = 1.0 
    );

  // Description:
  //   Make knot vector a periodic uniform knot vector
  //   based on the current values of m_order and m_cv_count.
  //   Does not change values of control vertices.
  // Parameters:
  //   delta - [in] (>0.0) knot spacing.
  // Returns:
  //   true if successful.
  // Remarks:
  //   Allocates m_knot[] if it is not big enough.
  // See Also:
  //   ON_MakePeriodicUniformKnotVector
  bool MakePeriodicUniformKnotVector( 
    double delta = 1.0 
    );

  bool IsClamped( // determine if knot vector is clamped
        int = 2 // end to check: 0 = start, 1 = end, 2 = start and end
        ) const;
  
  double SuperfluousKnot(
           int // 0 = start, 1 = end
           ) const;

  double GrevilleAbcissa(
           int   // index (0 <= index < CVCount(dir)
           ) const;

  bool GetGrevilleAbcissae( // see ON_GetGrevilleAbcissae() for details
           double*   // g[cv_count]
           ) const;

  bool ZeroCVs(); // zeros control vertices and, if rational, sets weights to 1

  // Description:
  //   Clamp end knots.  Does not modify control points.
  // Parameters:
  //   end - [in] 0 = clamp start, 1 = clamp end, 2 = clamp start and end
  // Returns:
  //   true if successful
  bool ClampEnd(
            int end
            );

  // Description:
  //   Insert a knot and update cv locations.
  // Parameters:
  //   knot_value - [in] m_knot[order-2] < knot_value < m_knot[m_cv_count-1]
  //   knot_multiplicity - [in] 1 to degree - includes multiplicity of existing knots.
  // Remarks:
  //   Does not change parameterization or locus of curve.
  // Returns:
  //   true if successful
  bool InsertKnot( 
            double knot_value,
            int knot_multiplicity
            );

  bool MakeRational();

  bool MakeNonRational();

  bool IncreaseDegree(
          int desired_degree
          );

  bool ChangeDimension(
          int desired_dimension
          ) override;

  bool Append( const ON_NurbsCurve& );

  /////////////////////////////////////////////////////////////////
  // Tools for managing CV and knot memory
  bool ReserveCVCapacity(
    int // number of doubles to reserve
    );
  bool ReserveKnotCapacity(
    int // number of doubles to reserve
    );

  //////////
  // returns the length of the control polygon
  double ControlPolygonLength() const;

  ////////
  // Converts a span of the NURBS curve into a bezier.  If
  // the span is empty 
  // (m_knot[span_index+m_order-2] == m_knot[span_index+m_order-1]),
  // then false is returned.
  bool ConvertSpanToBezier(
      int,            // span_index (0 <= span_index <= m_cv_count-m_order)
      ON_BezierCurve& // bezier returned here
      ) const;

  /*
  Paramaters:
    span_index - [in]
      The index of a non-empty span to test.
        span_index >= 0
        span_index <= m_cv_count-m_order
        m_knot[span_index+m_order-2] < m_knot[span_index+m_order-1]
  Returns:
    true if the span_index parameter is valid and the span is singular
    (collapsed to a point).
    false if the span is not singular or span_index does not identify
    a non-empty span.
  */
  bool SpanIsSingular( 
    int span_index 
    ) const;

  /*
  Returns:
    True if every span in the NURBS curve is singular.
  See Also:
    ON_NurbsCurve::RepairBadKnots()
    ON_NurbsCurve::RemoveShortSegments()
  */
  bool IsSingular() const;

  /*
  Paramaters:
    span_index - [in]
      The index of a non-empty span to remove.
        span_index >= 0
        span_index <= m_cv_count-m_order
        m_knot[span_index+m_order-2] < m_knot[span_index+m_order-1]
  Returns:
    True if the span was successfully removed.
  Remarks:
    The NURBS curve must have 2 or more spans (m_cv_count > m_order).
    Set m0 = mulitiplicity of the knot at m_knot[span_index+m_order-2]
    and m1 = mulitiplicity of the knot at m_knot[span_index+m_order-1].
    If (m0 + m1) < degree, then the degree-(m0+m1) cvs will be added
    to the NURBS curve. If (m0+m1) > degree, then (m0+m1)-degree cvs will
    be removed from the curve.
  See Also:
    ON_NurbsCurve::RepairBadKnots()
    ON_NurbsCurve::RemoveShortSegments()
  */
  bool RemoveSpan(
    int span_index 
    );

  /*
  Returns:
    Number of spans removed.
  */
  int RemoveSingularSpans();

  ////////
  // Returns true if the NURBS curve has bezier spans 
  // (all distinct knots have multiplitity = degree)
  bool HasBezierSpans() const;

  /*
  Description:
    Clamps ends and adds knots so the NURBS curve has bezier spans 
   (all distinct knots have multiplitity = degree).
  Paremeters:
    bSetEndWeightsToOne - [in] If true and the first or last weight is
       not one, then the first and last spans are reparameterized so 
       that the end weights are one.
  Returns:
    true if successful.
  */      
  bool MakePiecewiseBezier( 
        bool bSetEndWeightsToOne = false
        );

  /*
  Description:
    Use a combination of scaling and reparameterization to change
    the end weights to the specified values.
  Parameters:
    w0 - [in] weight for first cv
    w1 - [in] weight for last cv
  Returns:
    true if successful.
  See Also:
    ON_ChangeRationalNurbsCurveEndWeights
  Remarks:
    The domain, eucleanean locations of the control points,
    and locus of the curve do not change, but the weights,
    homogeneous cv values and internal knot values may change.
    If w0 and w1 are 1 and the curve is not rational, the 
    curve is not changed.
  */
  bool ChangeEndWeights( double w0, double w1 );

  /*
  Description:
    Use a linear fractional transformation to reparameterize 
    the NURBS curve.  This does not change the curve's domain.
  Parameters:
    c - [in]
      reparameterization constant (generally speaking, c should be > 0).
      The control points and knots are adjusted so that 
      output_nurbs(t) = input_nurbs(lambda(t)), where
      lambda(t) = c*t/( (c-1)*t + 1 ).
      Note that lambda(0) = 0, lambda(1) = 1, lambda'(t) > 0, 
      lambda'(0) = c and lambda'(1) = 1/c.
  Returns:
    true if successful.  
  Remarks:
    The cv and knot values are values are changed so that
    output_nurbs(t) = input_nurbs(lambda(t)).
  See Also:
    ON_ReparameterizeRationalNurbsCurve
  */
  bool Reparameterize( double c );



  /////////////////////////////////////////////////////////////////
  // Implementation
public:
  // NOTE: These members are left "public" so that expert users may efficiently
  //       create NURBS curves using the default constructor and borrow the
  //       knot and CV arrays from their native NURBS representation.
  //       No technical support will be provided for users who access these
  //       members directly.  If you can't get your stuff to work, then use
  //       the constructor with the arguments and the SetKnot() and SetCV()
  //       functions to fill in the arrays.

  int     m_dim;            // (>=1)

  int     m_is_rat;         // 1 for rational B-splines.
                            //   Rational control vertices use homogeneous form
                            //   and explicit weight values are in m_cv[] array.
                            // 0 for non-rational B-splines.
                            //   Control verticies have an implicit weight value
                            //   of 1.0.  An explicit weight value is not
                            //   set in the m_cv[] array.

  int     m_order;          // order = degree+1 ( order >=2 )

  int     m_cv_count;       // number of control vertices ( >= order )

  // knot vector memory

  int     m_knot_capacity;  // If m_knot_capacity > 0, then m_knot[]
                            // is an array of at least m_knot_capacity
                            // doubles whose memory is managed by the
                            // ON_NurbsCurve class using onmalloc(),
                            // onrealloc(), and onfree().
                            // If m_knot_capacity is 0 and m_knot is
                            // not nullptr, then  m_knot[] is assumed to
                            // be big enough for any requested operation
                            // and m_knot[] is not deleted by the
                            // destructor.

  double* m_knot;           // Knot vector. ( The knot vector has length
                            // m_order+m_cv_count-2. )
  
  // control vertex net memory

  int     m_cv_stride;      // The pointer to start of "CV[i]" is
                            //   m_cv + i*m_cv_stride.

  int     m_cv_capacity;    // If m_cv_capacity > 0, then m_cv[] is an array
                            // of at least m_cv_capacity doubles whose
                            // memory is managed by the ON_NurbsCurve
                            // class using onmalloc(), onrealloc(), and onfree().
                            // If m_cv_capacity is 0 and m_cv is not
                            // nullptr, then m_cv[] is assumed to be big enough
                            // for any requested operation and m_cv[] is not
                            // deleted by the destructor.

  double* m_cv;             // Control points.
                            //   - The i-th control point begins at
                            //     CV(i) = m_cv + (i*m_cv_stride).
                            //   - If m_is_rat is false, then the i-th control
                            //     point is ( CV(i)[0], ..., CV(i)[m_dim-1] ).
                            //   - If m_is_rat is true, then the i-th control
                            //     point is stored in HOMOGENEOUS form and is
                            //     [ CV(i)[0], ..., CV(i)[m_dim] ].
};

#endif