opennurbs_polycurve.h

Go to the documentation of this file.

/* $NoKeywords: $ */
/*
//
// Copyright (c) 1993-2007 Robert McNeel & Associates. All rights reserved.
// Rhinoceros is a registered trademark of Robert McNeel & Assoicates.
//
// 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 poly curve (composite curve)
//
 
#if !defined(OPENNURBS_POLYCURVE_INC_)
#define OPENNURBS_POLYCURVE_INC_
 
/*
 Description: 
                An ON_PolyCurve is an ON_Curve represented by a sequence of 
        contiguous ON_Curve segments.    A valid polycurve is represented 
        by an array m_segment of Count()>=1 curve objects       and a strictly
        increasing array m_t of Count()+1 parameter values.  The i-th 
        curve segment,  when considered as part of the polycurve, is affinely 
        reparamaterized from m_t[i] to m_t[i+1], i.e., m_segment[i].Domain()[0] 
        is mapped to    m_t[i] and m_segment[i].Domain()[1] is mapped to m_t[i+1]. 
*/
class ON_PolyCurve;
class ON_CLASS ON_PolyCurve : public ON_Curve
{
  ON_OBJECT_DECLARE(ON_PolyCurve);
 
public:
  // virtual ON_Object::DestroyRuntimeCache override
  void DestroyRuntimeCache( bool bDelete = true );
 
public:
  ON_PolyCurve();
  ON_PolyCurve( int ); // int = initial capacity - use when a good estimate
                        // of the number of segments is known.
  ON_PolyCurve(const ON_PolyCurve&);
 
  void Destroy();
 
  virtual ~ON_PolyCurve();
 
  void EmergencyDestroy(); // call if memory used by ON_PolyCurve becomes invalid
 
        ON_PolyCurve& operator=(const ON_PolyCurve&);
  
  // ON_Object overrides
 
  // virtual ON_Object::SizeOf override
  unsigned int SizeOf() const;
 
  // virtual ON_Object::DataCRC override
  ON__UINT32 DataCRC(ON__UINT32 current_remainder) const;
 
  /*
  Description:
    Tests an object to see if its data members are correctly
    initialized.
  Parameters:
    text_log - [in] if the object is not valid and text_log
        is not NULL, then a brief englis description of the
        reason the object is not valid is appened to the log.
        The information appended to text_log is suitable for 
        low-level debugging purposes by programmers and is 
        not intended to be useful as a high level user 
        interface tool.
  Returns:
    @untitled table
    true     object is valid
    false    object is invalid, uninitialized, etc.
  Remarks:
    Overrides virtual ON_Object::IsValid
  */
  ON_BOOL32 IsValid( ON_TextLog* text_log = NULL ) const;
 
  /*
  Description:
    Tests an object to see if its data members are correctly
    initialized.
  Parameters:
    bAllowGaps - [in]
      If true, gaps are allowed between polycurve segments.
      If false, gaps are not allowed between polycurve segments.
    text_log - [in] if the object is not valid and text_log
        is not NULL, then a brief englis description of the
        reason the object is not valid is appened to the log.
        The information appended to text_log is suitable for 
        low-level debugging purposes by programmers and is 
        not intended to be useful as a high level user 
        interface tool.
  Returns:
    @untitled table
    true     object is valid
    false    object is invalid, uninitialized, etc.
  Remarks:
    Overrides virtual ON_Object::IsValid
  */
  bool IsValid( bool bAllowGaps, ON_TextLog* text_log ) const;
 
 
  void Dump( ON_TextLog& ) const; // for debugging
 
  ON_BOOL32 Write(
         ON_BinaryArchive&  // open binary file
       ) const;
 
  ON_BOOL32 Read(
         ON_BinaryArchive&  // open binary file
       );
 
  // ON_Geometry overrides
 
  int Dimension() const;
 
  ON_BOOL32 GetBBox( // returns true if successful
         double*,    // minimum
         double*,    // maximum
         ON_BOOL32 = false  // true means grow box
         ) const;
 
  /*
        Description:
    Get tight bounding box.
        Parameters:
                tight_bbox - [in/out] tight bounding box
                bGrowBox -[in]  (default=false)                 
      If true and the input tight_bbox is valid, then returned
      tight_bbox is the union of the input tight_bbox and the 
      curve's tight bounding box.
                xform -[in] (default=NULL)
      If not NULL, the tight bounding box of the transformed
      curve is calculated.  The curve is not modified.
        Returns:
    True if a valid tight_bbox is returned.
  */
        bool GetTightBoundingBox( 
                        ON_BoundingBox& tight_bbox, 
      int bGrowBox = false,
                        const ON_Xform* xform = 0
      ) const;
 
  ON_BOOL32 Transform( 
         const ON_Xform&
         );
 
  // virtual ON_Geometry::IsDeformable() override
  bool IsDeformable() const;
 
  // virtual ON_Geometry::MakeDeformable() override
  bool MakeDeformable();
 
  ON_BOOL32 SwapCoordinates(
        int, int        // indices of coords to swap
        );
 
 
  // virtual ON_Geometry override
  bool Morph( const ON_SpaceMorph& morph );
 
  // virtual ON_Geometry override
  bool IsMorphable() const;
 
  // virtual ON_Geometry override
  bool EvaluatePoint( const class ON_ObjRef& objref, ON_3dPoint& P ) const;
 
  // ON_Curve overrides
 
  ON_Curve* DuplicateCurve() const;
 
  ON_Interval Domain() const;
 
  // 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.
  ON_BOOL32 SetDomain(
        double t0, 
        double t1 
        );
 
  bool ChangeDimension(
          int desired_dimension
          );
 
  /*
  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
  */
  ON_BOOL32 ChangeClosedCurveSeam( 
            double t 
            );
 
  int SpanCount() const; // number of smooth spans in curve
 
  ON_BOOL32 GetSpanVector( // span "knots" 
         double* // array of length SpanCount() + 1 
         ) const; // 
 
  int Degree( // returns maximum algebraic degree of any span 
                  // ( or a good estimate if curve spans are not algebraic )
    ) const; 
 
  ON_BOOL32 IsLinear( // true if curve locus is a line segment between
                 // between specified points
        double = ON_ZERO_TOLERANCE // tolerance to use when checking linearity
        ) const;
 
  /*
  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 NULL and true is returned, then the
        points of the polyline form are returned here.
    t - [out] if not NULL 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 = NULL,
        ON_SimpleArray<double>* pline_t = NULL
        ) const;
 
  ON_BOOL32 IsArc( // ON_Arc.m_angle > 0 if curve locus is an arc between
              // specified points
        const ON_Plane* = NULL, // if not NULL, test is performed in this plane
        ON_Arc* = NULL, // if not NULL and true is returned, then arc parameters
                         // are filled in
        double = ON_ZERO_TOLERANCE    // tolerance to use when checking
        ) const;
 
  ON_BOOL32 IsPlanar(
        ON_Plane* = NULL, // if not NULL and true is returned, then plane parameters
                           // are filled in
        double = ON_ZERO_TOLERANCE    // tolerance to use when checking
        ) const;
 
  ON_BOOL32 IsInPlane(
        const ON_Plane&, // plane to test
        double = ON_ZERO_TOLERANCE    // tolerance to use when checking
        ) const;
 
  ON_BOOL32 IsClosed(  // true if curve is closed (either curve has
        void      // clamped end knots and euclidean location of start
        ) const;  // CV = euclidean location of end CV, or curve is
                  // periodic.)
 
  ON_BOOL32 IsPeriodic(  // true if curve is a single periodic segment
        void 
        ) const;
  
  /*
  Description:
    Search for a derivatitive, tangent, or curvature discontinuity.
  Parameters:
    c - [in] type of continity to test for.  If ON::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 NULL, *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::G1_continuous or ON::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::G2_continuous.  If K0 and K1 are curvatures evaluated
        from above and below and |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=NULL,
                  int* dtype=NULL,
                  double cos_angle_tolerance=0.99984769515639123915701155881391,
                  double curvature_tolerance=ON_SQRT_EPSILON
                  ) const;
 
  /*
  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::G1_continuous or ON::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::G2_continuous.  If K0 and K1 are curvatures evaluated
        from above and below and |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 = NULL,
    double point_tolerance=ON_ZERO_TOLERANCE,
    double d1_tolerance=ON_ZERO_TOLERANCE,
    double d2_tolerance=ON_ZERO_TOLERANCE,
    double cos_angle_tolerance=0.99984769515639123915701155881391,
    double curvature_tolerance=ON_SQRT_EPSILON
    ) const;
 
  ON_BOOL32 Reverse();       // reverse parameterizatrion
                        // Domain changes from [a,b] to [-b,-a]
 
  /*
  Description:
    Force the curve to start at a specified point.
  Parameters:
    start_point - [in]
  Returns:
    true if successful.
  Remarks:
    Some start points cannot be moved.  Be sure to check return
    code.
  See Also:
    ON_Curve::SetEndPoint
    ON_Curve::PointAtStart
    ON_Curve::PointAtEnd
  */
  // virtual
  ON_BOOL32 SetStartPoint(
          ON_3dPoint start_point
          );
 
  /*
  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
  ON_BOOL32 SetEndPoint(
          ON_3dPoint end_point
          );
 
  ON_BOOL32 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;
 
  // Find parameter of the point on a curve that is closest to test_point.
  // If the maximum_distance parameter is > 0, then only points whose distance
  // to the given point is <= maximum_distance will be returned.  Using a 
  // positive value of maximum_distance can substantially speed up the search.
  // If the sub_domain parameter is not NULL, then the search is restricted
  // to the specified portion of the curve.
  //
  // true if returned if the search is successful.  false is returned if
  // the search fails.
  bool GetClosestPoint( const ON_3dPoint&, // test_point
          double*,       // parameter of local closest point returned here
          double = 0.0,  // maximum_distance
          const ON_Interval* = NULL // sub_domain
          ) const;
 
  // Find parameter of the point on a curve that is locally closest to 
  // the test_point.  The search for a local close point starts at 
  // seed_parameter. If the sub_domain parameter is not NULL, then
  // the search is restricted to the specified portion of the curve.
  //
  // true if returned if the search is successful.  false is returned if
  // the search fails.
  ON_BOOL32 GetLocalClosestPoint( const ON_3dPoint&, // test_point
          double,    // seed_parameter
          double*,   // parameter of local closest point returned here
          const ON_Interval* = NULL // sub_domain
          ) const;
 
  // Length of curve.
  // true if returned if the length calculation is successful.
  // false is returned if the length is not calculated.
  //
  // The arc length will be computed so that
  // (returned length - real length)/(real length) <= fractional_tolerance
  // More simply, if you want N significant figures in the answer, set the
  // fractional_tolerance to 1.0e-N.  For "nice" curves, 1.0e-8 works
  // fine.  For very high degree nurbs and nurbs with bad parameterizations,
  // use larger values of fractional_tolerance.
  ON_BOOL32 GetLength( // returns true if length successfully computed
          double*,                   // length returned here
          double = 1.0e-8,           // fractional_tolerance
          const ON_Interval* = NULL  // (optional) sub_domain
          ) const;
 
  /*
  Description:
    Used to quickly find short curves.
  Parameters:
    tolerance - [in] (>=0)
    sub_domain - [in] If not NULL, the test is performed
      on the interval that is the intersection of 
      sub_domain with Domain().
  Returns:
    True if the length of the curve is <= tolerance.
  Remarks:
    Faster than calling Length() and testing the
    result.
  */
  bool IsShort(
    double tolerance,
    const ON_Interval* sub_domain = NULL
    ) const;
 
  /*
  Description:
    Looks for segments that are shorter than tolerance
    that can be removed. If bRemoveShortSegments is true,
    then the short segments are removed. Does not change the 
    domain, but it will change the relative parameterization.
  Parameters:
    tolerance - [in]
    bRemoveShortSegments - [in] If true, then short segments
                                are removed.
  Returns:
    True if removable short segments can were found.
    False if no removable short segments can were found.
  */
  bool RemoveShortSegments(
    double tolerance,
    bool bRemoveShortSegments = true
    );
 
  /*
  Description:
    virtual ON_Curve::GetNormalizedArcLengthPoint override.
    Get the parameter of the point on the line that is a 
    prescribed distance from the start of the line
  Parameters:
    s - [in] normalized arc length parameter.  E.g., 0 = start
         of curve, 1/2 = midpoint of curve, 1 = end of curve.
    t - [out] parameter such that the length of the line
       from its start to t is arc_length.
    fractional_tolerance - [in] desired fractional precision.
        fabs(("exact" length from start to t) - arc_length)/arc_length <= fractional_tolerance
    sub_domain - [in] If not NULL, the calculation is performed on
        the specified sub-domain of the curve.
  Returns:
    true if successful
  */
  ON_BOOL32 GetNormalizedArcLengthPoint(
          double s,
          double* t,
          double fractional_tolerance = 1.0e-8,
          const ON_Interval* sub_domain = NULL
          ) const;
 
  /*
  Description:
    virtual ON_Curve::GetNormalizedArcLengthPoints override.
    Get the parameter of the point on the curve that is a 
    prescribed arc length from the start of the curve.
  Parameters:
    count - [in] number of parameters in s.
    s - [in] array of normalized arc length parameters. E.g., 0 = start
         of curve, 1/2 = midpoint of curve, 1 = end of curve.
    t - [out] array of curve parameters such that the length of the 
       curve from its start to t[i] is s[i]*curve_length.
    absolute_tolerance - [in] if absolute_tolerance > 0, then the difference
        between (s[i+1]-s[i])*curve_length and the length of the curve
        segment from t[i] to t[i+1] will be <= absolute_tolerance.
    fractional_tolerance - [in] desired fractional precision for each segment.
        fabs("true" length - actual length)/(actual length) <= fractional_tolerance
    sub_domain - [in] If not NULL, the calculation is performed on
        the specified sub-domain of the curve.  A 0.0 s value corresponds to
        sub_domain->Min() and a 1.0 s value corresponds to sub_domain->Max().
  Returns:
    true if successful
  */
  ON_BOOL32 GetNormalizedArcLengthPoints(
          int count,
          const double* s,
          double* t,
          double absolute_tolerance = 0.0,
          double fractional_tolerance = 1.0e-8,
          const ON_Interval* sub_domain = NULL
          ) const;
 
  // Description:
  //   virtual ON_Curve::Trim override.
  //   Removes portions of the curve outside the specified interval.
  // Parameters:
  //   domain - [in] interval of the curve to keep.  Portions of the
  //      curve before curve(domain[0]) and after curve(domain[1]) are
  //      removed.
  // Returns:
  //   true if successful.
  ON_BOOL32 Trim(
    const ON_Interval& domain
    );
 
  // 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
    );
 
  // Description:
  //   virtual ON_Curve::Split override.
  //   Divide the curve at the specified parameter.  The parameter
  //   must be in the interior of the curve's domain.  The pointers
  //   passed to Split must either be NULL or point to an ON_Curve
  //   object of the same of the same type.  If the pointer is NULL,
  //   then a curve will be created in Split().  You may pass "this"
  //   as one of the pointers to Split().
  // Parameters:
  //   t - [in] parameter in interval Domain().
  //   left_side - [out] left portion of curve
  //   right_side - [out] right portion of curve
  // Example:
  //   For example, if crv were an ON_NurbsCurve, then
  //
  //     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.
  ON_BOOL32 Split(
      double t,    // t = curve parameter to split curve at
      ON_Curve*& left_side, // left portion returned here
      ON_Curve*& right_side // right portion returned here
    ) const;
 
  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&,
        double = 0.0,
        const ON_Interval* = NULL     // OPTIONAL subdomain of polycurve
        ) const;
 
  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;
 
  // virtual ON_Curve::GetCurveParameterFromNurbFormParameter override
  ON_BOOL32 GetCurveParameterFromNurbFormParameter(
        double, // nurbs_t
        double* // curve_t
        ) const;
 
  // virtual ON_Curve::GetNurbFormParameterFromCurveParameter override
  ON_BOOL32 GetNurbFormParameterFromCurveParameter(
        double, // curve_t
        double* // nurbs_t
        ) const;
 
  // Interface
 
  int Count() const; // number of segment curves
 
  // These operator[] functions return NULL if index is out of range
  ON_Curve* operator[](int) const;
 
  /*
  Description:
    Returns a pointer to a segment curve.
  Parameters:
    segment_index - [in] 0 based index  (0 <= segment_index < Count() )
  Returns:
    A pointer to the segment curve.  Returns NULL if segment_index < 0
    or segment_index >= Count().
  */
  ON_Curve* SegmentCurve(
    int segment_index
    ) const;
 
  /*
  Description:
    Converts a polycurve parameter to a segment curve parameter.
  Parameters:
    polycurve_parameter - [in] 
  Returns:
    Segment curve evaluation parameter or ON_UNSET_VALUE if the
    segment curve parameter cannot be computed.
  See Also:
    ON_PolyCurve::PolyCurveParameter
  */
  double SegmentCurveParameter(
    double polycurve_parameter
    ) const;
 
  /*
  Description:
    Converts a segment curve parameter to a polycurve parameter.
  Parameters:
    segment_index - [in]
    segmentcurve_parameter - [in] 
  Returns:
    Polycurve evaluation parameter or ON_UNSET_VALUE if the
    polycurve curve parameter cannot be computed.
  See Also:
    ON_PolyCurve::SegmentCurveParameter
  */
  double PolyCurveParameter(
    int segment_index,
    double segmentcurve_parameter
    ) const;
 
  /*
  Description:
    Returns the polycurve subdomain assigned to a segment curve.
  Parameters:
    segment_index - [in] 0 based index  (0 <= segment_index < Count() )
  Returns:
    The polycurve subdomain assigned to a segment curve.
    Returns ([ON_UNSET_VALUE,ON_UNSET_VALUE) if segment_index < 0  
    or segment_index >= Count().
  */
  ON_Interval SegmentDomain( 
    int segment_index
    ) const;
 
  /*
  Description:
    Find the segment used for evaluation at polycurve_parameter.
  Parameters:
    polycurve_parameter - [in]
  Returns:
    index of the segment used for evaluation at polycurve_parameter.
    If polycurve_parameter < Domain.Min(), then 0 is returned.
    If polycurve_parameter > Domain.Max(), then Count()-1 is returned.
  */
  int SegmentIndex(
    double polycurve_parameter
    ) const;
 
  /*
  Description:
    Find the segments with support on sub_domain.
  Parameters:
    sub_domain - [in] increasing interval
    segment_index0 - [out] 
    segment_index1 - [out] segments with index i where
      *segment_index0 <= i < *segment_index1 are the segments
      with support on the sub_domain
  Returns:
    number of segments with support on sub_domain.
  */
  int SegmentIndex(
    ON_Interval sub_domain,
    int* segment_index0,
    int* segment_index1
    ) const;
 
  ON_Curve* FirstSegmentCurve() const; // returns NULL if count = 0
 
  ON_Curve* LastSegmentCurve() const;  // returns NULL if count = 0
 
  /*
  Description:
    This is a quick way to see if the curve has 
    gaps between the sub curve segments.  
    The test is fairly severe (ON_ComparePoint).
  Returns:
    0:     The ends adjacent polycuve segments are coincident.
    i > 0: The end of polycuve segment (i-1) is not coincident
           with the start of polycurve segment i.
  */
  int HasGap() const;
 
  void Reserve( int ); // make sure capacity is at least the specified count
 
  // ON_Curve pointers added with Prepend(), Append(), PrependAndMatch(), AppendANdMatch(),and Insert() are deleted
  // by ~ON_PolyCurve(). Use ON_CurveProxy( ON_Curve*) if you want
  // the original curve segment to survive ~ON_PolyCurve().
  ON_BOOL32 Prepend( ON_Curve* ); // Prepend curve.
  ON_BOOL32 Append( ON_Curve* );  // Append curve.
  ON_BOOL32 Insert( 
           int, // segment_index,
           ON_Curve*
           );
 
  //PrependAndMatch() and AppendAndMatch() return false if this->IsCLosed() or 
  //this->Count() > 0 and curve is closed
  ON_BOOL32 PrependAndMatch(ON_Curve*); //Prepend and match end of curve to start of polycurve
  ON_BOOL32 AppendAndMatch(ON_Curve*);  //Append and match start of curve to end of polycurve
 
  ON_BOOL32 Remove(); // delete last segment and reduce count by 1
  ON_BOOL32 Remove( int ); // delete specified segment and reduce count by 1
 
  // Use the HarvestSegment() function when you want to prevent a
  // segment from being destroyed by ~ON_PolyCurve().  HarvestSegment()
  // replaces the polycurve segment with a NULL.  Count() and parameter
  // information remains unchanged.
  ON_Curve* HarvestSegment( int );
 
        /*
  Returns:
    True if a curve in the m_segment[] array is an ON_PolyCurve.
  */
  bool IsNested() const;
 
        /*
  Description:
    Same as RemoveNestingEx().
  Remarks:
    RemoveNestingEx was added to avoid breaking the SDK.
  */
        void RemoveNesting();
 
  /* 
  Description:
    Removes the nested of polycurves. The result will have not
    have an  ON_PolyCurve  as a segment but will have identical
    locus and parameterization.
  Returns:
    True if a nested polycurve was removed.  False
    if no nested polycurves were found.
  */
        bool RemoveNestingEx();
 
  /* 
  Returns:
    True if the domains of the curves in the m_segment[] array exactly
    match the domains of the segments specified in the m_t[] array.
    Put another way, returns true if SegmentDomain(i) = SegmentCurve(i).Domain()
    for every segment index.
  */
        bool HasSynchronizedSegmentDomains() const;
 
  /* 
  Description:
    Sets the domain of the curve int the m_segment[] array to exactly
    match the domain defined in the m_t[] array.  This is not required,
    but can simplify some coding situations.
  Returns:
    True if at least one segment was reparameterized. False if no
    changes were made.
  */
        bool SynchronizeSegmentDomains();
 
 
 
 
        // Expert user function  
        //   Sets the m_segment[index] to crv. 
        void SetSegment(int index, ON_Curve* crv);
 
  /*
  Description:
          Expert user function to set the m_t[] array.
  Parameters:
    t - [in] increasing array of SegmentCount()+1 parameters.
  Returns
    True if successful.
  */
  bool SetParameterization( const double* t );
 
/*
        Description:
                Lookup a parameter in the m_t array, optionally using a built in snap tolerance to 
                snap a parameter value to an element of m_t.
        Parameters:
                t    - [in]             parameter
                index -[out]    index into m_t such that if the function returns true then t is equal 
                                                                        to, or is within tolerance of m_t[index]. 
                                                                if function returns false then the value of index is
 
                                                                         @table  
                                                                                                condition                                                                       value of index
                                                                        t<m_t[0] or m_t is empty                                -1
                                                                                m_t[i] < t < m_t[i+1]                           i for 0<=i<=m_t.Count()-2
                                                                                t>m_t[ m_t.Count()-1]                           m_t.Count()-1
                                                                        
                bEnableSnap -[in]  if true use tolerance when comparing to m_t values 
        Returns         
                true if the t is exactly equal to, or within tolerance of
                (only if bEnableSnap==true) m_t[index]. 
*/ 
        bool ParameterSearch(double t, int& index, bool bEnableSnap) const;
 
  /*
  Returns:
    Reference to m_segment.
  */
  const ON_CurveArray& SegmentCurves() const;
 
  /*
  Returns:
    Reference to m_t.
  */
  const ON_SimpleArray<double>& SegmentParameters() const;
 
  // Implementation
private:
  // The curves in this array are deleted by ~ON_PolyCurve().
  // Use ON_CurveProxy classes if you don't want ON_PolyCurve()
  // to destroy the curve.
 
  ON_CurveArray m_segment;  // array of pointers to curves
                             // all have the same dimension
                             // and are contiguous to tolerance
 
  ON_SimpleArray<double> m_t; // ON_PolyCurve segment parameterizations
};
 
 
#endif