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 // 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 <gp_Pnt.hxx>
 #include <gp_Vec.hxx>
 #include <GeomAbs_Shape.hxx>
 #include <Geom_UndefinedDerivative.hxx>
 #include <Geom_UndefinedValue.hxx>
 
 class gp_Trsf;
 
 //! 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:
   //! Result of D1 evaluation: point and first derivative.
   struct ResD1
   {
     gp_Pnt Point;
     gp_Vec D1;
   };
 
   //! Result of D2 evaluation: point and first two derivatives.
   struct ResD2
   {
     gp_Pnt Point;
     gp_Vec D1;
     gp_Vec D2;
   };
 
   //! Result of D3 evaluation: point and first three derivatives.
   struct ResD3
   {
     gp_Pnt Point;
     gp_Vec D1;
     gp_Vec D2;
     gp_Vec 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;
 
   //! 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 double ReversedParameter(const double 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 double TransformedParameter(const double 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 double ParametricTransformation(const gp_Trsf& T) const;
 
   //! Returns a copy of <me> reversed.
   [[nodiscard]] Standard_EXPORT occ::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 double 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 double 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 which is a fixed criterion independent of the
   //! application.
   Standard_EXPORT virtual bool 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 bool IsPeriodic() const = 0;
 
   //! Returns the period of this curve.
   //! Exceptions Standard_NoSuchObject if this 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 (e.g. OffsetCurve at singular point).
   [[nodiscard]] Standard_EXPORT virtual gp_Pnt 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_Vec EvalDN(const double U, const int N) const = 0;
 
   //! Returns in P the point of parameter U.
   inline void D0(const double U, gp_Pnt& P) const { P = EvalD0(U); }
 
   //! Returns the point P of parameter U and the first derivative V1.
   inline void D1(const double U, gp_Pnt& P, gp_Vec& 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_Pnt& P, gp_Vec& V1, gp_Vec& 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_Pnt& P, gp_Vec& V1, gp_Vec& V2, gp_Vec& V3) const
   {
     const ResD3 aR = EvalD3(U);
     P              = aR.Point;
     V1             = aR.D1;
     V2             = aR.D2;
     V3             = aR.D3;
   }
 
   //! The returned vector gives the value of the derivative for the order of derivation N.
   inline gp_Vec DN(const double U, const int N) const { return EvalDN(U, N); }
 
   //! Computes the point of parameter U on <me>.
   gp_Pnt Value(const double U) const { return EvalD0(U); }
 
   //! Dumps the content of me into the stream
   Standard_EXPORT void DumpJson(Standard_OStream& theOStream, int theDepth = -1) const override;
 
   DEFINE_STANDARD_RTTIEXT(Geom_Curve, Geom_Geometry)
 };
 
 #endif // _Geom_Curve_HeaderFile

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