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 // Created on: 1993-03-24
 // 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 _Geom2d_Curve_HeaderFile
 #define _Geom2d_Curve_HeaderFile
 
 #include <Standard.hxx>
 #include <Standard_Type.hxx>
 
 #include <Geom2d_Geometry.hxx>
 #include <gp_Pnt2d.hxx>
 #include <gp_Vec2d.hxx>
 #include <Geom2d_UndefinedDerivative.hxx>
 #include <Geom2d_UndefinedValue.hxx>
 #include <GeomAbs_Shape.hxx>
 
 class gp_Trsf2d;
 
 //! The abstract class Curve describes the common
 //! behavior of curves in 2D space. The Geom2d
 //! 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 Geom2d_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
 //! explicitly states so.
 //! Warning
 //! The Geom2d package does not prevent the
 //! construction of curves with null length or curves which
 //! self-intersect.
 class Geom2d_Curve : public Geom2d_Geometry
 {
 
 public:
   //! Result of D1 evaluation: point and first derivative.
   struct ResD1
   {
     gp_Pnt2d Point;
     gp_Vec2d D1;
   };
 
   //! Result of D2 evaluation: point and first two derivatives.
   struct ResD2
   {
     gp_Pnt2d Point;
     gp_Vec2d D1;
     gp_Vec2d D2;
   };
 
   //! Result of D3 evaluation: point and first three derivatives.
   struct ResD3
   {
     gp_Pnt2d Point;
     gp_Vec2d D1;
     gp_Vec2d D2;
     gp_Vec2d D3;
   };
 
   //! 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;
 
   //! Computes the parameter on the reversed curve for
   //! the point of parameter U on this curve.
   //! Note: The point of parameter U on this curve is
   //! identical to the point of parameter
   //! ReversedParameter(U) on the reversed curve.
   Standard_EXPORT virtual double ReversedParameter(const double U) const = 0;
 
   //! Computes the parameter on the curve transformed by
   //! T for the point of parameter U on this curve.
   //! Note: this function generally returns U but it can be
   //! redefined (for example, on a line).
   Standard_EXPORT virtual double TransformedParameter(const double U, const gp_Trsf2d& T) const;
 
   //! Returns the coefficient required to compute the
   //! parametric transformation of this curve when
   //! transformation T is applied. This coefficient is the
   //! ratio between the parameter of a point on this curve
   //! and the parameter of the transformed point on the
   //! new curve transformed by T.
   //! Note: this function generally returns 1. but it can be
   //! redefined (for example, on a line).
   Standard_EXPORT virtual double ParametricTransformation(const gp_Trsf2d& T) const;
 
   //! Creates a reversed duplicate Changes the orientation of this curve. The first and
   //! last parameters are not changed, but the parametric
   //! direction of the curve is reversed.
   //! If the curve is bounded:
   //! - the start point of the initial curve becomes the end
   //! point of the reversed curve, and
   //! - the end point of the initial curve becomes the start
   //! point of the reversed curve.
   //! - Reversed creates a new curve.
   [[nodiscard]] Standard_EXPORT occ::handle<Geom2d_Curve> Reversed() const;
 
   //! Returns the value of the first parameter.
   //! Warnings :
   //! It can be RealFirst or RealLast from package Standard
   //! if the curve is infinite
   Standard_EXPORT virtual double FirstParameter() const = 0;
 
   //! Value of the last parameter.
   //! Warnings :
   //! It can be RealFirst or RealLast from package Standard
   //! if the curve is infinite
   Standard_EXPORT virtual double LastParameter() const = 0;
 
   //! Returns true if the curve is closed.
   //! Examples :
   //! 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 which is a fixed criterion independent of the
   //! application.
   Standard_EXPORT virtual bool IsClosed() const = 0;
 
   //! Returns true if the parameter of the curve is 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 bool IsPeriodic() const = 0;
 
   //! Returns the period of this curve.
   //! raises if the curve is not periodic
   Standard_EXPORT virtual double 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 bool IsCN(const int N) const = 0;
 
   //! Computes the point of parameter U.
   //! Raises an exception on failure.
   [[nodiscard]] Standard_EXPORT virtual gp_Pnt2d EvalD0(const double U) const = 0;
 
   //! Computes the point and first derivative at parameter U.
   //! Raises an exception if the curve continuity is not C1.
   [[nodiscard]] Standard_EXPORT virtual ResD1 EvalD1(const double U) const = 0;
 
   //! Computes the point and first two derivatives at parameter U.
   //! Raises an exception if the curve continuity is not C2.
   [[nodiscard]] Standard_EXPORT virtual ResD2 EvalD2(const double U) const = 0;
 
   //! Computes the point and first three derivatives at parameter U.
   //! Raises an exception if the curve continuity is not C3.
   [[nodiscard]] Standard_EXPORT virtual ResD3 EvalD3(const double U) const = 0;
 
   //! Computes the Nth derivative at parameter U.
   //! Raises an exception if the curve continuity is not CN, or N < 1.
   [[nodiscard]] Standard_EXPORT virtual gp_Vec2d EvalDN(const double U, const int N) const = 0;
 
   //! Returns in P the point of parameter U.
   inline void D0(const double U, gp_Pnt2d& P) const { P = EvalD0(U); }
 
   //! Returns the point P of parameter U and the first derivative V1.
   inline void D1(const double U, gp_Pnt2d& P, gp_Vec2d& V1) const
   {
     const ResD1 aR = EvalD1(U);
     P              = aR.Point;
     V1             = aR.D1;
   }
 
   //! Returns the point P of parameter U, the first and second derivatives V1 and V2.
   inline void D2(const double U, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2) const
   {
     const ResD2 aR = EvalD2(U);
     P              = aR.Point;
     V1             = aR.D1;
     V2             = aR.D2;
   }
 
   //! Returns the point P of parameter U, the first, the second and the third derivative.
   inline void D3(const double U, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2, gp_Vec2d& V3) const
   {
     const ResD3 aR = EvalD3(U);
     P              = aR.Point;
     V1             = aR.D1;
     V2             = aR.D2;
     V3             = aR.D3;
   }
 
   //! Computes the Nth derivative vector.
   inline gp_Vec2d DN(const double U, const int N) const { return EvalDN(U, N); }
 
   //! Computes the point of parameter U on <me>. Implemented with D0.
   Standard_EXPORT gp_Pnt2d Value(const double U) const;
 
   //! Dumps the content of me into the stream
   Standard_EXPORT void DumpJson(Standard_OStream& theOStream, int theDepth = -1) const override;
 
   DEFINE_STANDARD_RTTIEXT(Geom2d_Curve, Geom2d_Geometry)
 };
 
 #endif // _Geom2d_Curve_HeaderFile

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