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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_Parabola_HeaderFile
 #define _Geom2d_Parabola_HeaderFile
 
 #include <Standard.hxx>
 #include <Standard_Type.hxx>
 
 #include <Geom2d_Conic.hxx>
 class gp_Parab2d;
 class gp_Ax2d;
 class gp_Ax22d;
 class gp_Trsf2d;
 class Geom2d_Geometry;
 
 //! Describes a parabola in the plane (2D space).
 //! A parabola is defined by its focal length (i.e. the
 //! distance between its focus and its apex) and is
 //! positioned in the plane with a coordinate system
 //! (gp_Ax22d object) where:
 //! - the origin is the apex of the parabola, and
 //! - the "X Axis" defines the axis of symmetry; the
 //! parabola is on the positive side of this axis.
 //! This coordinate system is the local coordinate
 //! system of the parabola.
 //! The orientation (direct or indirect) of the local
 //! coordinate system gives an explicit orientation to the
 //! parabola, determining the direction in which the
 //! parameter increases along the parabola.
 //! The Geom_Parabola parabola is parameterized as follows:
 //! P(U) = O + U*U/(4.*F)*XDir + U*YDir, where:
 //! - P is the point of parameter U,
 //! - O, XDir and YDir are respectively the origin, "X
 //! Direction" and "Y Direction" of its local coordinate system,
 //! - F is the focal length of the parabola.
 //! The parameter of the parabola is therefore its Y
 //! coordinate in the local coordinate system, with the "X
 //! Axis" of the local coordinate system defining the
 //! origin of the parameter.
 //! The parameter range is ] -infinite,+infinite [.
 class Geom2d_Parabola : public Geom2d_Conic
 {
 
 public:
   //! Creates a parabola from a non persistent one.
   Standard_EXPORT Geom2d_Parabola(const gp_Parab2d& Prb);
 
   //! Creates a parabola with its "MirrorAxis" and it's focal
   //! length "Focal".
   //! MirrorAxis is the axis of symmetry of the curve, it is the
   //! "XAxis". The "YAxis" is parallel to the directrix of the
   //! parabola and is in the direct sense if Sense is True.
   //! The "Location" point of "MirrorAxis" is the vertex of the parabola
   //! Raised if Focal < 0.0
   Standard_EXPORT Geom2d_Parabola(const gp_Ax2d& MirrorAxis,
                                   const double   Focal,
                                   const bool     Sense = true);
 
   //! Creates a parabola with its Axis and it's focal
   //! length "Focal".
   //! The XDirection of Axis is the axis of symmetry of the curve,
   //! it is the "XAxis". The "YAxis" is parallel to the directrix of the
   //! parabola. The "Location" point of "Axis" is the vertex
   //! of the parabola.
   //! Raised if Focal < 0.0
   Standard_EXPORT Geom2d_Parabola(const gp_Ax22d& Axis, const double Focal);
 
   //! D is the directrix of the parabola and F the focus point.
   //! The symmetry axis "XAxis" of the parabola is normal to the
   //! directrix and pass through the focus point F, but its
   //! "Location" point is the vertex of the parabola.
   //! The "YAxis" of the parabola is parallel to D and its "Location"
   //! point is the vertex of the parabola.
   Standard_EXPORT Geom2d_Parabola(const gp_Ax2d& D, const gp_Pnt2d& F);
 
   //! Assigns the value Focal to the focal length of this parabola.
   //! Exceptions Standard_ConstructionError if Focal is negative.
   Standard_EXPORT void SetFocal(const double Focal);
 
   //! Converts the gp_Parab2d parabola Prb into this parabola.
   Standard_EXPORT void SetParab2d(const gp_Parab2d& Prb);
 
   //! Returns the non persistent parabola from gp with the same
   //! geometric properties as <me>.
   Standard_EXPORT gp_Parab2d Parab2d() const;
 
   //! Computes the parameter on the reversed parabola
   //! for the point of parameter U on this parabola.
   //! For a parabola, the returned value is -U.
   Standard_EXPORT double ReversedParameter(const double U) const final;
 
   //! Returns RealFirst from Standard.
   Standard_EXPORT double FirstParameter() const final;
 
   //! Returns RealLast from Standard.
   Standard_EXPORT double LastParameter() const final;
 
   //! Returns False
   Standard_EXPORT bool IsClosed() const final;
 
   //! Returns False
   Standard_EXPORT bool IsPeriodic() const final;
 
   //! The directrix is parallel to the "YAxis" of the parabola.
   //! The "Location" point of the directrix is the intersection
   //! point between the directrix and the symmetry axis ("XAxis") of the parabola.
   Standard_EXPORT gp_Ax2d Directrix() const;
 
   //! Returns the eccentricity e = 1.0
   Standard_EXPORT double Eccentricity() const final;
 
   //! Computes the focus of this parabola The focus is on the
   //! positive side of the "X Axis" of the local coordinate system of the parabola.
   Standard_EXPORT gp_Pnt2d Focus() const;
 
   //! Computes the focal length of this parabola.
   //! The focal length is the distance between the apex and the focus of the parabola.
   Standard_EXPORT double Focal() const;
 
   //! Computes the parameter of this parabola, which is
   //! the distance between its focus and its directrix. This
   //! distance is twice the focal length.
   //! If P is the parameter of the parabola, the equation of
   //! the parabola in its local coordinate system is: Y**2 = 2.*P*X.
   Standard_EXPORT double Parameter() const;
 
   //! Returns in P the point of parameter U.
   //! If U = 0 the returned point is the origin of the XAxis and
   //! the YAxis of the parabola and it is the vertex of the parabola.
   //! P = S + F * (U * U * XDir + * U * YDir)
   //! where S is the vertex of the parabola, XDir the XDirection and
   //! YDir the YDirection of the parabola's local coordinate system.
   Standard_EXPORT gp_Pnt2d EvalD0(const double U) const final;
 
   //! Returns the point P of parameter U and the first derivative V1.
   Standard_EXPORT Geom2d_Curve::ResD1 EvalD1(const double U) const final;
 
   //! Returns the point P of parameter U, the first and second
   //! derivatives V1 and V2.
   Standard_EXPORT Geom2d_Curve::ResD2 EvalD2(const double U) const final;
 
   //! Returns the point P of parameter U, the first second and third
   //! derivatives V1 V2 and V3.
   Standard_EXPORT Geom2d_Curve::ResD3 EvalD3(const double U) const final;
 
   //! For the point of parameter U of this parabola,
   //! computes the vector corresponding to the Nth derivative.
   //! Exceptions Standard_RangeError if N is less than 1.
   Standard_EXPORT gp_Vec2d EvalDN(const double U, const int N) const final;
 
   //! Applies the transformation T to this parabola.
   Standard_EXPORT void Transform(const gp_Trsf2d& T) final;
 
   //! Computes the parameter on the transformed
   //! parabola, for the point of parameter U on this parabola.
   //! For a parabola, the returned value is equal to U
   //! multiplied by the scale factor of transformation T.
   Standard_EXPORT double TransformedParameter(const double U, const gp_Trsf2d& T) const final;
 
   //! 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 T.ScaleFactor()
   Standard_EXPORT double ParametricTransformation(const gp_Trsf2d& T) const final;
 
   //! Creates a new object, which is a copy of this parabola.
   Standard_EXPORT occ::handle<Geom2d_Geometry> Copy() const final;
 
   //! Dumps the content of me into the stream
   Standard_EXPORT void DumpJson(Standard_OStream& theOStream, int theDepth = -1) const final;
 
   DEFINE_STANDARD_RTTIEXT(Geom2d_Parabola, Geom2d_Conic)
 
 private:
   double focalLength;
 };
 
 #endif // _Geom2d_Parabola_HeaderFile

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