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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_Parabola_HeaderFile
 #define _Geom_Parabola_HeaderFile
 
 #include <Standard.hxx>
 #include <Standard_Type.hxx>
 
 #include <Geom_Conic.hxx>
 #include <Standard_Integer.hxx>
 class gp_Parab;
 class gp_Ax2;
 class gp_Ax1;
 class gp_Pnt;
 class gp_Vec;
 class gp_Trsf;
 class Geom_Geometry;
 
 
 class Geom_Parabola;
 DEFINE_STANDARD_HANDLE(Geom_Parabola, Geom_Conic)
 
 //! Describes a parabola in 3D space.
 //! A parabola is defined by its focal length (i.e. the
 //! distance between its focus and its apex) and is
 //! positioned in space with a coordinate system
 //! (gp_Ax2 object) where:
 //! - the origin is the apex of the parabola,
 //! - the "X Axis" defines the axis of symmetry; the
 //! parabola is on the positive side of this axis,
 //! - the origin, "X Direction" and "Y Direction" define the
 //! plane of the parabola.
 //! This coordinate system is the local coordinate
 //! system of the parabola.
 //! The "main Direction" of this coordinate system is a
 //! vector normal to the plane of the parabola. The axis,
 //! of which the origin and unit vector are respectively the
 //! origin and "main Direction" of the local coordinate
 //! system, is termed the "Axis" or "main Axis" of the parabola.
 //! The "main Direction" 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 Geom_Parabola : public Geom_Conic
 {
 
 public:
 
   
   //! Creates a parabola from a non transient one.
   Standard_EXPORT Geom_Parabola(const gp_Parab& Prb);
   
 
   //! Creates a parabola with its local coordinate system "A2"
   //! and it's focal length "Focal".
   //! The XDirection of A2 defines the axis of symmetry of the
   //! parabola. The YDirection of A2 is parallel to the directrix
   //! of the parabola. The Location point of A2 is the vertex of
   //! the parabola
   //! Raised if Focal < 0.0
   Standard_EXPORT Geom_Parabola(const gp_Ax2& A2, const Standard_Real 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. The normal to the plane
   //! of the parabola is the cross product between the XAxis and the
   //! YAxis.
   Standard_EXPORT Geom_Parabola(const gp_Ax1& D, const gp_Pnt& F);
   
   //! Assigns the value Focal to the focal distance of this parabola.
   //! Exceptions Standard_ConstructionError if Focal is negative.
   Standard_EXPORT void SetFocal (const Standard_Real Focal);
   
   //! Converts the gp_Parab parabola Prb into this parabola.
   Standard_EXPORT void SetParab (const gp_Parab& Prb);
   
 
   //! Returns the non transient parabola from gp with the same
   //! geometric properties as <me>.
   Standard_EXPORT gp_Parab Parab() 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 Standard_Real ReversedParameter (const Standard_Real U) const Standard_OVERRIDE;
   
   //! Returns the value of the first or last parameter of this
   //! parabola. This is, respectively:
   //! - Standard_Real::RealFirst(), or
   //! - Standard_Real::RealLast().
   Standard_EXPORT Standard_Real FirstParameter() const Standard_OVERRIDE;
   
   //! Returns the value of the first or last parameter of this
   //! parabola. This is, respectively:
   //! - Standard_Real::RealFirst(), or
   //! - Standard_Real::RealLast().
   Standard_EXPORT Standard_Real LastParameter() const Standard_OVERRIDE;
   
   //! Returns False
   Standard_EXPORT Standard_Boolean IsClosed() const Standard_OVERRIDE;
   
   //! Returns False
   Standard_EXPORT Standard_Boolean IsPeriodic() const Standard_OVERRIDE;
   
   //! Computes the directrix of this parabola.
   //! This is a line normal to the axis of symmetry, in the
   //! plane of this parabola, located on the negative side
   //! of its axis of symmetry, at a distance from the apex
   //! equal to the focal length.
   //! The directrix is returned as an axis (gp_Ax1 object),
   //! where the origin is located on the "X Axis" of this parabola.
   Standard_EXPORT gp_Ax1 Directrix() const;
   
   //! Returns 1. (which is the eccentricity of any parabola).
   Standard_EXPORT Standard_Real Eccentricity() const Standard_OVERRIDE;
   
   //! 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_Pnt Focus() const;
   
   //! Computes the focal distance of this parabola
   //! The focal distance is the distance between the apex
   //! and the focus of the parabola.
   Standard_EXPORT Standard_Real 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 Standard_Real 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 void D0 (const Standard_Real U, gp_Pnt& P) const Standard_OVERRIDE;
   
 
   //! Returns the point P of parameter U and the first derivative V1.
   Standard_EXPORT void D1 (const Standard_Real U, gp_Pnt& P, gp_Vec& V1) const Standard_OVERRIDE;
   
 
   //! Returns the point P of parameter U, the first and second
   //! derivatives V1 and V2.
   Standard_EXPORT void D2 (const Standard_Real U, gp_Pnt& P, gp_Vec& V1, gp_Vec& V2) const Standard_OVERRIDE;
   
 
   //! Returns the point P of parameter U, the first second and third
   //! derivatives V1 V2 and V3.
   Standard_EXPORT void D3 (const Standard_Real U, gp_Pnt& P, gp_Vec& V1, gp_Vec& V2, gp_Vec& V3) const Standard_OVERRIDE;
   
   //! 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_Vec DN (const Standard_Real U, const Standard_Integer N) const Standard_OVERRIDE;
   
   //! Applies the transformation T to this parabola.
   Standard_EXPORT void Transform (const gp_Trsf& T) Standard_OVERRIDE;
   
   //! 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> * T.ScaleFactor()
   Standard_EXPORT Standard_Real TransformedParameter (const Standard_Real U, const gp_Trsf& T) const Standard_OVERRIDE;
   
   //! 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 Standard_Real ParametricTransformation (const gp_Trsf& T) const Standard_OVERRIDE;
   
   //! Creates a new object which is a copy of this parabola.
   Standard_EXPORT Handle(Geom_Geometry) Copy() const Standard_OVERRIDE;
 
   //! 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_Parabola,Geom_Conic)
 
 protected:
 
 
 
 
 private:
 
 
   Standard_Real focalLength;
 
 
 };
 
 
 
 
 
 
 
 #endif // _Geom_Parabola_HeaderFile

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