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 // Copyright (c) 1991-1999 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 _gp_Parab_HeaderFile
 #define _gp_Parab_HeaderFile
 
 #include <gp_Ax1.hxx>
 #include <gp_Lin.hxx>
 #include <gp_Pnt.hxx>
 #include <Standard_ConstructionError.hxx>
 
 //! Describes a parabola in 3D space.
 //! A parabola is defined by its focal length (that is, the
 //! distance between its focus and apex) and positioned in
 //! space with a coordinate system (a gp_Ax2 object)
 //! where:
 //! -   the origin of the coordinate system is on the apex of
 //! the parabola,
 //! -   the "X Axis" of the coordinate system is the axis of
 //! symmetry; the parabola is on the positive side of this axis, and
 //! -   the origin, "X Direction" and "Y Direction" of the
 //! coordinate system define the plane of the parabola.
 //! The equation of the parabola in this coordinate system,
 //! which is the "local coordinate system" of the parabola, is:
 //! @code
 //! Y**2 = (2*P) * X.
 //! @endcode
 //! where P, referred to as the parameter of the parabola, is
 //! the distance between the focus and the directrix (P is
 //! twice the focal length).
 //! The "main Direction" of the local coordinate system gives
 //! the normal vector to the plane of the parabola.
 //! See Also
 //! gce_MakeParab which provides functions for more
 //! complex parabola constructions
 //! Geom_Parabola which provides additional functions for
 //! constructing parabolas and works, in particular, with the
 //! parametric equations of parabolas
 class gp_Parab 
 {
 public:
 
   DEFINE_STANDARD_ALLOC
 
   //! Creates an indefinite Parabola.
   gp_Parab()
   : focalLength (RealLast())
   {}
 
   //! Creates a parabola with its local coordinate system "theA2"
   //! and it's focal length "Focal".
   //! The XDirection of theA2 defines the axis of symmetry of the
   //! parabola. The YDirection of theA2 is parallel to the directrix
   //! of the parabola. The Location point of theA2 is the vertex of
   //! the parabola
   //! Raises ConstructionError if theFocal < 0.0
   //! Raised if theFocal < 0.0
   gp_Parab (const gp_Ax2& theA2, const Standard_Real theFocal)
   : pos (theA2),
     focalLength (theFocal)
   {
     Standard_ConstructionError_Raise_if (theFocal < 0.0, "gp_Parab() - focal length should be >= 0");
   }
 
   //! theD is the directrix of the parabola and theF the focus point.
   //! The symmetry axis (XAxis) of the parabola is normal to the
   //! directrix and pass through the focus point theF, but its
   //! location point is the vertex of the parabola.
   //! The YAxis of the parabola is parallel to theD 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.
   gp_Parab (const gp_Ax1& theD, const gp_Pnt& theF);
 
   //! Modifies this parabola by redefining its local coordinate system so that
   //! -   its origin and "main Direction" become those of the
   //! axis theA1 (the "X Direction" and "Y Direction" are then
   //! recomputed in the same way as for any gp_Ax2)
   //! Raises ConstructionError if the direction of theA1 is parallel to the previous
   //! XAxis of the parabola.
   void SetAxis (const gp_Ax1& theA1) { pos.SetAxis (theA1); }
 
   //! Changes the focal distance of the parabola.
   //! Raises ConstructionError if theFocal < 0.0
   void SetFocal (const Standard_Real theFocal)
   {
     Standard_ConstructionError_Raise_if (theFocal < 0.0, "gp_Parab::SetFocal() - focal length should be >= 0");
     focalLength = theFocal;
   }
 
   //! Changes the location of the parabola. It is the vertex of
   //! the parabola.
   void SetLocation (const gp_Pnt& theP) { pos.SetLocation (theP); }
 
   //! Changes the local coordinate system of the parabola.
   void SetPosition (const gp_Ax2& theA2) { pos = theA2; }
 
   //! Returns the main axis of the parabola.
   //! It is the axis normal to the plane of the parabola passing
   //! through the vertex of the parabola.
   const gp_Ax1& Axis() const { return pos.Axis(); }
 
   //! Computes the directrix of this parabola.
   //! The directrix is:
   //! -   a line parallel to the "Y Direction" of the local
   //! coordinate system of this parabola, and
   //! -   located on the negative side of the axis of symmetry,
   //! at a distance from the apex which is equal to the focal
   //! length of this parabola.
   //! The directrix is returned as an axis (a gp_Ax1 object),
   //! the origin of which is situated on the "X Axis" of this parabola.
   gp_Ax1 Directrix() const;
 
   //! Returns the distance between the vertex and the focus
   //! of the parabola.
   Standard_Real Focal() const { return focalLength; }
 
   //! -   Computes the focus of the parabola.
   gp_Pnt Focus() const;
 
   //! Returns the vertex of the parabola. It is the "Location"
   //! point of the coordinate system of the parabola.
   const gp_Pnt& Location() const { return pos.Location(); }
 
   //! Computes the parameter of the parabola.
   //! It is the distance between the focus and the directrix of
   //! the parabola. This distance is twice the focal length.
   Standard_Real Parameter() const { return 2.0 * focalLength; }
 
   //! Returns the local coordinate system of the parabola.
   const gp_Ax2& Position() const { return pos; }
 
   //! Returns the symmetry axis of the parabola. The location point
   //! of the axis is the vertex of the parabola.
   gp_Ax1 XAxis() const  { return gp_Ax1 (pos.Location(), pos.XDirection()); }
 
   //! It is an axis parallel to the directrix of the parabola.
   //! The location point of this axis is the vertex of the parabola.
   gp_Ax1 YAxis() const { return gp_Ax1 (pos.Location(), pos.YDirection()); }
 
   Standard_EXPORT void Mirror (const gp_Pnt& theP);
 
   //! Performs the symmetrical transformation of a parabola
   //! with respect to the point theP which is the center of the
   //! symmetry.
   Standard_NODISCARD Standard_EXPORT gp_Parab Mirrored (const gp_Pnt& theP) const;
 
   Standard_EXPORT void Mirror (const gp_Ax1& theA1);
 
   //! Performs the symmetrical transformation of a parabola
   //! with respect to an axis placement which is the axis of
   //! the symmetry.
   Standard_NODISCARD Standard_EXPORT gp_Parab Mirrored (const gp_Ax1& theA1) const;
 
   Standard_EXPORT void Mirror (const gp_Ax2& theA2);
 
   //! Performs the symmetrical transformation of a parabola
   //! with respect to a plane. The axis placement theA2 locates
   //! the plane of the symmetry (Location, XDirection, YDirection).
   Standard_NODISCARD Standard_EXPORT gp_Parab Mirrored (const gp_Ax2& theA2) const;
 
   void Rotate (const gp_Ax1& theA1, const Standard_Real theAng) { pos.Rotate (theA1, theAng); }
 
   //! Rotates a parabola. theA1 is the axis of the rotation.
   //! Ang is the angular value of the rotation in radians.
   Standard_NODISCARD gp_Parab Rotated (const gp_Ax1& theA1, const Standard_Real theAng) const
   {
     gp_Parab aPrb = *this;
     aPrb.pos.Rotate (theA1, theAng);
     return aPrb;
   }
 
   void Scale (const gp_Pnt& theP, const Standard_Real theS);
 
   //! Scales a parabola. theS is the scaling value.
   //! If theS is negative the direction of the symmetry axis
   //! XAxis is reversed and the direction of the YAxis too.
   Standard_NODISCARD gp_Parab Scaled (const gp_Pnt& theP, const Standard_Real theS) const;
 
   void Transform (const gp_Trsf& theT);
 
   //! Transforms a parabola with the transformation theT from class Trsf.
   Standard_NODISCARD gp_Parab Transformed (const gp_Trsf& theT) const;
 
   void Translate (const gp_Vec& theV) { pos.Translate (theV); }
 
   //! Translates a parabola in the direction of the vector theV.
   //! The magnitude of the translation is the vector's magnitude.
   Standard_NODISCARD gp_Parab Translated (const gp_Vec& theV) const
   {
     gp_Parab aPrb = *this;
     aPrb.pos.Translate (theV);
     return aPrb;
   }
 
   void Translate (const gp_Pnt& theP1, const gp_Pnt& theP2)  { pos.Translate (theP1, theP2); }
 
   //! Translates a parabola from the point theP1 to the point theP2.
   Standard_NODISCARD gp_Parab Translated (const gp_Pnt& theP1, const gp_Pnt& theP2) const
   {
     gp_Parab aPrb = *this;
     aPrb.pos.Translate (theP1, theP2);
     return aPrb;
   }
 
 private:
 
   gp_Ax2 pos;
   Standard_Real focalLength;
 
 };
 
 //=======================================================================
 //function : gp_Parab
 // purpose :
 //=======================================================================
 inline gp_Parab::gp_Parab (const gp_Ax1& theD,
                            const gp_Pnt& theF)
 {
   gp_Lin aDroite (theD);
   focalLength = aDroite.Distance (theF) / 2.;
   gp_Ax1 anAx = aDroite.Normal (theF).Position();
   gp_Ax1 anAy = aDroite.Position();     
   const gp_Dir& aDD = anAx.Direction();
   pos = gp_Ax2 (gp_Pnt (theF.X() - focalLength * aDD.X(),
                         theF.Y() - focalLength * aDD.Y(),
                         theF.Z() - focalLength * aDD.Z()),
                 anAx.Direction().Crossed (anAy.Direction()),
                 anAx.Direction());
 }
 
 //=======================================================================
 //function : Directrix
 // purpose :
 //=======================================================================
 inline gp_Ax1 gp_Parab::Directrix() const
 {
   const gp_Pnt& aPP = pos.Location  ();
   const gp_Dir& aDD = pos.XDirection();
   gp_Pnt aP (aPP.X() - focalLength * aDD.X(),
              aPP.Y() - focalLength * aDD.Y(),
              aPP.Z() - focalLength * aDD.Z());
   return gp_Ax1 (aP, pos.YDirection());
 }
 
 //=======================================================================
 //function : Focus
 // purpose :
 //=======================================================================
 inline gp_Pnt gp_Parab::Focus() const
 {
   const gp_Pnt& aPP = pos.Location  ();
   const gp_Dir& aDD = pos.XDirection();
   return gp_Pnt (aPP.X() + focalLength * aDD.X(),
                  aPP.Y() + focalLength * aDD.Y(),
                  aPP.Z() + focalLength * aDD.Z());
 }
 
 //=======================================================================
 //function : Scale
 // purpose :
 //=======================================================================
 inline void gp_Parab::Scale (const gp_Pnt& theP, const Standard_Real theS)
 {
   focalLength *= theS;
   if (focalLength < 0)
   {
     focalLength = -focalLength;
   }
   pos.Scale (theP, theS);
 }
 
 //=======================================================================
 //function : Scaled
 // purpose :
 //=======================================================================
 inline gp_Parab gp_Parab::Scaled (const gp_Pnt& theP, const Standard_Real theS) const
 {
   gp_Parab aPrb = *this;
   aPrb.focalLength *= theS;
   if (aPrb.focalLength < 0)
   {
     aPrb.focalLength = -aPrb.focalLength;
   }
   aPrb.pos.Scale (theP, theS);
   return aPrb;
 }
 
 //=======================================================================
 //function : Transform
 // purpose :
 //=======================================================================
 inline void gp_Parab::Transform (const gp_Trsf& theT)
 {
   focalLength *= theT.ScaleFactor();
   if (focalLength < 0)
   {
     focalLength = -focalLength;
   }
   pos.Transform (theT);
 }
 
 //=======================================================================
 //function : Transformed
 // purpose :
 //=======================================================================
 inline gp_Parab gp_Parab::Transformed (const gp_Trsf& theT) const
 {
   gp_Parab aPrb = *this;
   aPrb.focalLength *= theT.ScaleFactor();
   if (aPrb.focalLength < 0)
   {
     aPrb.focalLength = -aPrb.focalLength;
   }
   aPrb.pos.Transform (theT);
   return aPrb;
 }
 
 #endif // _gp_Parab_HeaderFile

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