text: // Created on: 1993-03-10
  // Created by: JCV
  // Copyright (c) 1993-1999 Matra Datavision
  // Copyright (c) 1999-2014 OPEN CASCADE SAS
  //
  // This file is part of Open CASCADE Technology software library.
  //
  // This library is free software; you can redistribute it and/or modify it under
  // the terms of the GNU Lesser General Public License version 2.1 as published
  // by the Free Software Foundation, with special exception defined in the file
  // OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
  // distribution for complete text of the license and disclaimer of any warranty.
  //
  // Alternatively, this file may be used under the terms of Open CASCADE
  // commercial license or contractual agreement.
  
  #ifndef _Geom_Curve_HeaderFile
  #define _Geom_Curve_HeaderFile
  
  #include <Standard.hxx>
  #include <Standard_Type.hxx>
  
  #include <Geom_Geometry.hxx>
  #include <Standard_Real.hxx>
  #include <Standard_Boolean.hxx>
  #include <GeomAbs_Shape.hxx>
  #include <Standard_Integer.hxx>
  class Standard_RangeError;
  class Standard_NoSuchObject;
  class Geom_UndefinedDerivative;
  class Geom_UndefinedValue;
  class gp_Trsf;
  class gp_Pnt;
  class gp_Vec;
  
  
  class Geom_Curve;
  DEFINE_STANDARD_HANDLE(Geom_Curve, Geom_Geometry)
  
  //! The abstract class Curve describes the common
  //! behavior of curves in 3D space. The Geom package
  //! provides numerous concrete classes of derived
  //! curves, including lines, circles, conics, Bezier or
  //! BSpline curves, etc.
  //! The main characteristic of these curves is that they
  //! are parameterized. The Geom_Curve class shows:
  //! - how to work with the parametric equation of a curve
  //! in order to calculate the point of parameter u,
  //! together with the vector tangent and the derivative
  //! vectors of order 2, 3,..., N at this point;
  //! - how to obtain general information about the curve
  //! (for example, level of continuity, closed
  //! characteristics, periodicity, bounds of the parameter field);
  //! - how the parameter changes when a geometric
  //! transformation is applied to the curve or when the
  //! orientation of the curve is inverted.
  //! All curves must have a geometric continuity: a curve is
  //! at least "C0". Generally, this property is checked at
  //! the time of construction or when the curve is edited.
  //! Where this is not the case, the documentation states so explicitly.
  //! Warning
  //! The Geom package does not prevent the
  //! construction of curves with null length or curves which
  //! self-intersect.
  class Geom_Curve : public Geom_Geometry
  {
  
  public:
  
    
  
    //! Changes the direction of parametrization of <me>.
    //! The "FirstParameter" and the "LastParameter" are not changed
    //! but the orientation  of the curve is modified. If the curve
    //! is bounded the StartPoint of the initial curve becomes the
    //! EndPoint of the reversed curve  and the EndPoint of the initial
    //! curve becomes the StartPoint of the reversed curve.
    Standard_EXPORT virtual void Reverse() = 0;
    
    //! Returns the  parameter on the  reversed  curve for
    //! the point of parameter U on <me>.
    //!
    //! me->Reversed()->Value(me->ReversedParameter(U))
    //!
    //! is the same point as
    //!
    //! me->Value(U)
    Standard_EXPORT virtual Standard_Real ReversedParameter (const Standard_Real U) const = 0;
    
    //! Returns the  parameter on the  transformed  curve for
    //! the transform of the point of parameter U on <me>.
    //!
    //! me->Transformed(T)->Value(me->TransformedParameter(U,T))
    //!
    //! is the same point as
    //!
    //! me->Value(U).Transformed(T)
    //!
    //! This methods returns <U>
    //!
    //! It can be redefined. For example on the Line.
    Standard_EXPORT virtual Standard_Real TransformedParameter (const Standard_Real U, const gp_Trsf& T) const;
    
    //! Returns a  coefficient to compute the parameter on
    //! the transformed  curve  for  the transform  of the
    //! point on <me>.
    //!
    //! Transformed(T)->Value(U * ParametricTransformation(T))
    //!
    //! is the same point as
    //!
    //! Value(U).Transformed(T)
    //!
    //! This methods returns 1.
    //!
    //! It can be redefined. For example on the Line.
    Standard_EXPORT virtual Standard_Real ParametricTransformation (const gp_Trsf& T) const;
    
    //! Returns a copy of <me> reversed.
    Standard_NODISCARD Standard_EXPORT Handle(Geom_Curve) Reversed() const;
    
    //! Returns the value of the first parameter.
    //! Warnings :
    //! It can be RealFirst from package Standard
    //! if the curve is infinite
    Standard_EXPORT virtual Standard_Real FirstParameter() const = 0;
    
    //! Returns the value of the last parameter.
    //! Warnings :
    //! It can be RealLast from package Standard
    //! if the curve is infinite
    Standard_EXPORT virtual Standard_Real LastParameter() const = 0;
    
    //! Returns true if the curve is closed.
    //! Some curves such as circle are always closed, others such as line
    //! are never closed (by definition).
    //! Some Curves such as OffsetCurve can be closed or not. These curves
    //! are considered as closed if the distance between the first point
    //! and the last point of the curve is lower or equal to the Resolution
    //! from package gp wich is a fixed criterion independant of the
    //! application.
    Standard_EXPORT virtual Standard_Boolean IsClosed() const = 0;
    
    //! Is the parametrization of the curve periodic ?
    //! It is possible only if the curve is closed and if the
    //! following relation is satisfied :
    //! for each parametric value U the distance between the point
    //! P(u) and the point P (u + T) is lower or equal to Resolution
    //! from package gp, T is the period and must be a constant.
    //! There are three possibilities :
    //! . the curve is never periodic by definition (SegmentLine)
    //! . the curve is always periodic by definition (Circle)
    //! . the curve can be defined as periodic (BSpline). In this case
    //! a function SetPeriodic allows you to give the shape of the
    //! curve.  The general rule for this case is : if a curve can be
    //! periodic or not the default periodicity set is non periodic
    //! and you have to turn (explicitly) the curve into a periodic
    //! curve  if you want the curve to be periodic.
    Standard_EXPORT virtual Standard_Boolean IsPeriodic() const = 0;
    
    //! Returns the period of this curve.
    //! Exceptions Standard_NoSuchObject if this curve is not periodic.
    Standard_EXPORT virtual Standard_Real Period() const;
    
    //! It is 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,
    //! G1 : tangency continuity all along the Curve,
    //! G2 : curvature continuity all along the Curve,
    //! CN : the order of continuity is infinite.
    Standard_EXPORT virtual GeomAbs_Shape Continuity() const = 0;
    
    //! Returns true if the degree of continuity of this curve is at least N.
    //! Exceptions -  Standard_RangeError if N is less than 0.
    Standard_EXPORT virtual Standard_Boolean IsCN (const Standard_Integer N) const = 0;
    
    //! Returns in P the point of parameter U.
    //! If the curve is periodic  then the returned point is P(U) with
    //! U = Ustart + (U - Uend)  where Ustart and Uend are the
    //! parametric bounds of the curve.
    //!
    //! Raised only for the "OffsetCurve" if it is not possible to
    //! compute the current point. For example when the first
    //! derivative on the basis curve and the offset direction
    //! are parallel.
    Standard_EXPORT virtual void D0 (const Standard_Real U, gp_Pnt& P) const = 0;
    
  
    //! Returns the point P of parameter U and the first derivative V1.
    //! Raised if the continuity of the curve is not C1.
    Standard_EXPORT virtual void D1 (const Standard_Real U, gp_Pnt& P, gp_Vec& V1) const = 0;
    
  
    //! Returns the point P of parameter U, the first and second
    //! derivatives V1 and V2.
    //! Raised if the continuity of the curve is not C2.
    Standard_EXPORT virtual void D2 (const Standard_Real U, gp_Pnt& P, gp_Vec& V1, gp_Vec& V2) const = 0;
    
  
    //! Returns the point P of parameter U, the first, the second
    //! and the third derivative.
    //! Raised if the continuity of the curve is not C3.
    Standard_EXPORT virtual void D3 (const Standard_Real U, gp_Pnt& P, gp_Vec& V1, gp_Vec& V2, gp_Vec& V3) const = 0;
    
  
    //! The returned vector gives the value of the derivative for the
    //! order of derivation N.
    //! Raised if the continuity of the curve is not CN.
    //!
    //! Raised if the   derivative  cannot  be  computed
    //! easily. e.g. rational bspline and n > 3.
    //! Raised if N < 1.
    Standard_EXPORT virtual gp_Vec DN (const Standard_Real U, const Standard_Integer N) const = 0;
    
    //! Computes the point of parameter U on <me>.
    //! If the curve is periodic  then the returned point is P(U) with
    //! U = Ustart + (U - Uend)  where Ustart and Uend are the
    //! parametric bounds of the curve.
    //! it is implemented with D0.
    //!
    //! Raised only for the "OffsetCurve" if it is not possible to
    //! compute the current point. For example when the first
    //! derivative on the basis curve and the offset direction are parallel.
    Standard_EXPORT gp_Pnt Value (const Standard_Real U) const;
  
    //! Dumps the content of me into the stream
    Standard_EXPORT virtual void DumpJson (Standard_OStream& theOStream, Standard_Integer theDepth = -1) const Standard_OVERRIDE;
  
  
  
  
    DEFINE_STANDARD_RTTIEXT(Geom_Curve,Geom_Geometry)
  
  protected:
  
  
  
  
  private:
  
  
  
  
  };
  
  
  
  
  
  
  
  #endif // _Geom_Curve_HeaderFile
  