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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_Elips2d_HeaderFile
 #define _gp_Elips2d_HeaderFile
 
 #include <gp.hxx>
 #include <gp_Ax22d.hxx>
 #include <gp_Ax2d.hxx>
 #include <gp_Pnt2d.hxx>
 #include <Standard_ConstructionError.hxx>
 
 //! Describes an ellipse in the plane (2D space).
 //! An ellipse is defined by its major and minor radii and
 //! positioned in the plane with a coordinate system (a
 //! gp_Ax22d object) as follows:
 //! -   the origin of the coordinate system is the center of the ellipse,
 //! -   its "X Direction" defines the major axis of the ellipse, and
 //! -   its "Y Direction" defines the minor axis of the ellipse.
 //! This coordinate system is the "local coordinate system"
 //! of the ellipse. Its orientation (direct or indirect) gives an
 //! implicit orientation to the ellipse. In this coordinate
 //! system, the equation of the ellipse is:
 //! @code
 //! X*X / (MajorRadius**2) + Y*Y / (MinorRadius**2) = 1.0
 //! @endcode
 //! See Also
 //! gce_MakeElips2d which provides functions for more
 //! complex ellipse constructions
 //! Geom2d_Ellipse which provides additional functions for
 //! constructing ellipses and works, in particular, with the
 //! parametric equations of ellipses
 class gp_Elips2d 
 {
 public:
 
   DEFINE_STANDARD_ALLOC
 
   //! Creates an indefinite ellipse.
   gp_Elips2d()
   : majorRadius (RealLast()),
     minorRadius (RealSmall())
   {}
 
   //! Creates an ellipse with the major axis, the major and the
   //! minor radius. The location of the theMajorAxis is the center
   //! of the  ellipse.
   //! The sense of parametrization is given by theIsSense.
   //! Warnings :
   //! It is possible to create an ellipse with
   //! theMajorRadius = theMinorRadius.
   //! Raises ConstructionError if theMajorRadius < theMinorRadius or theMinorRadius < 0.0
   gp_Elips2d (const gp_Ax2d& theMajorAxis, const Standard_Real theMajorRadius,
               const Standard_Real theMinorRadius, const Standard_Boolean theIsSense = Standard_True)
   : majorRadius (theMajorRadius),
     minorRadius (theMinorRadius)
   {
     pos = gp_Ax22d (theMajorAxis, theIsSense);
     Standard_ConstructionError_Raise_if (theMinorRadius < 0.0 || theMajorRadius < theMinorRadius,
       "gp_Elips2d() - invalid construction parameters");
   }
 
   //! Creates an ellipse with radii MajorRadius and
   //! MinorRadius, positioned in the plane by coordinate system theA where:
   //! -   the origin of theA is the center of the ellipse,
   //! -   the "X Direction" of theA defines the major axis of
   //! the ellipse, that is, the major radius MajorRadius
   //! is measured along this axis, and
   //! -   the "Y Direction" of theA defines the minor axis of
   //! the ellipse, that is, the minor radius theMinorRadius
   //! is measured along this axis, and
   //! -   the orientation (direct or indirect sense) of theA
   //! gives the orientation of the ellipse.
   //! Warnings :
   //! It is possible to create an ellipse with
   //! theMajorRadius = theMinorRadius.
   //! Raises ConstructionError if theMajorRadius < theMinorRadius or theMinorRadius < 0.0
   gp_Elips2d (const gp_Ax22d& theA, const Standard_Real theMajorRadius, const Standard_Real theMinorRadius)
   : pos (theA),
     majorRadius (theMajorRadius),
     minorRadius (theMinorRadius)
   {
     Standard_ConstructionError_Raise_if (theMinorRadius < 0.0 || theMajorRadius < theMinorRadius,
       "gp_Elips2d() - invalid construction parameters");
   }
 
   //! Modifies this ellipse, by redefining its local coordinate system so that
   //! -   its origin becomes theP.
   void SetLocation (const gp_Pnt2d& theP) { pos.SetLocation (theP); }
 
   //! Changes the value of the major radius.
   //! Raises ConstructionError if theMajorRadius < MinorRadius.
   void SetMajorRadius (const Standard_Real theMajorRadius)
   {
     Standard_ConstructionError_Raise_if (theMajorRadius < minorRadius,
       "gp_Elips2d::SetMajorRadius() - major radius should be greater or equal to minor radius");
     majorRadius = theMajorRadius;
   }
   
   //! Changes the value of the minor radius.
   //! Raises ConstructionError if MajorRadius < theMinorRadius or MinorRadius < 0.0
   void SetMinorRadius (const Standard_Real theMinorRadius)
   {
     Standard_ConstructionError_Raise_if (theMinorRadius < 0.0 || majorRadius < theMinorRadius,
       "gp_Elips2d::SetMinorRadius() - minor radius should be a positive number lesser or equal to major radius");
     minorRadius = theMinorRadius;
   }
 
   //! Modifies this ellipse, by redefining its local coordinate system so that
   //! it becomes theA.
   void SetAxis (const gp_Ax22d& theA) { pos.SetAxis (theA); }
 
   //! Modifies this ellipse, by redefining its local coordinate system so that
   //! its origin and its "X Direction"  become those
   //! of the axis theA. The "Y  Direction"  is then
   //! recomputed. The orientation of the local coordinate
   //! system is not modified.
   void SetXAxis (const gp_Ax2d& theA) { pos.SetXAxis (theA); }
 
   //! Modifies this ellipse, by redefining its local coordinate system so that
   //! its origin and its "Y Direction"  become those
   //! of the axis theA. The "X  Direction"  is then
   //! recomputed. The orientation of the local coordinate
   //! system is not modified.
   void SetYAxis (const gp_Ax2d& theA) { pos.SetYAxis (theA); }
 
   //! Computes the area of the ellipse.
   Standard_Real Area() const { return M_PI * majorRadius * minorRadius; }
 
   //! Returns the coefficients of the implicit equation of the ellipse.
   //! theA * (X**2) + theB * (Y**2) + 2*theC*(X*Y) + 2*theD*X + 2*theE*Y + theF = 0.
   Standard_EXPORT void Coefficients (Standard_Real& theA, Standard_Real& theB, Standard_Real& theC,
                                      Standard_Real& theD, Standard_Real& theE, Standard_Real& theF) const;
 
   //! This directrix is the line normal to the XAxis of the ellipse
   //! in the local plane (Z = 0) at a distance d = MajorRadius / e
   //! from the center of the ellipse, where e is the eccentricity of
   //! the ellipse.
   //! This line is parallel to the "YAxis". The intersection point
   //! between directrix1 and the "XAxis" is the location point of the
   //! directrix1. This point is on the positive side of the "XAxis".
   //!
   //! Raised if Eccentricity = 0.0. (The ellipse degenerates into a
   //! circle)
   gp_Ax2d Directrix1() const;
 
   //! This line is obtained by the symmetrical transformation
   //! of "Directrix1" with respect to the minor axis of the ellipse.
   //!
   //! Raised if Eccentricity = 0.0. (The ellipse degenerates into a
   //! circle).
   gp_Ax2d Directrix2() const;
 
   //! Returns the eccentricity of the ellipse  between 0.0 and 1.0
   //! If f is the distance between the center of the ellipse and
   //! the Focus1 then the eccentricity e = f / MajorRadius.
   //! Returns 0 if MajorRadius = 0.
   Standard_Real Eccentricity() const;
 
   //! Returns the distance between the center of the ellipse
   //! and focus1 or focus2.
   Standard_Real Focal() const
   {
     return 2.0 * sqrt (majorRadius * majorRadius - minorRadius * minorRadius);
   }
 
   //! Returns the first focus of the ellipse. This focus is on the
   //! positive side of the major axis of the ellipse.
   gp_Pnt2d Focus1() const;
 
   //! Returns the second focus of the ellipse. This focus is on the
   //! negative side of the major axis of the ellipse.
   gp_Pnt2d Focus2() const;
 
   //! Returns the center of the ellipse.
   const gp_Pnt2d& Location() const { return pos.Location(); }
 
   //! Returns the major radius of the Ellipse.
   Standard_Real MajorRadius() const { return majorRadius; }
 
   //! Returns the minor radius of the Ellipse.
   Standard_Real MinorRadius() const { return minorRadius; }
 
   //! Returns p = (1 - e * e) * MajorRadius where e is the eccentricity
   //! of the ellipse.
   //! Returns 0 if MajorRadius = 0
   Standard_Real Parameter() const;
 
   //! Returns the major axis of the ellipse.
   const gp_Ax22d& Axis() const { return pos; }
 
   //! Returns the major axis of the ellipse.
   gp_Ax2d XAxis() const { return pos.XAxis(); }
 
   //! Returns the minor axis of the ellipse.
   //! Reverses the direction of the circle.
   gp_Ax2d YAxis() const { return pos.YAxis(); }
 
   void Reverse()
   {
     gp_Dir2d aTemp = pos.YDirection();
     aTemp.Reverse();
     pos.SetAxis (gp_Ax22d (pos.Location(), pos.XDirection(), aTemp));
   }
 
   Standard_NODISCARD gp_Elips2d Reversed() const;
 
   //! Returns true if the local coordinate system is direct
   //! and false in the other case.
   Standard_Boolean IsDirect() const { return (pos.XDirection().Crossed (pos.YDirection())) >= 0.0; }
 
   Standard_EXPORT void Mirror (const gp_Pnt2d& theP);
 
   //! Performs the symmetrical transformation of a ellipse with respect
   //! to the point theP which is the center of the symmetry
   Standard_NODISCARD Standard_EXPORT gp_Elips2d Mirrored (const gp_Pnt2d& theP) const;
 
   Standard_EXPORT void Mirror (const gp_Ax2d& theA);
 
   //! Performs the symmetrical transformation of a ellipse with respect
   //! to an axis placement which is the axis of the symmetry.
   Standard_NODISCARD Standard_EXPORT gp_Elips2d Mirrored (const gp_Ax2d& theA) const;
 
   void Rotate (const gp_Pnt2d& theP, const Standard_Real theAng) { pos.Rotate (theP, theAng); }
 
   Standard_NODISCARD gp_Elips2d Rotated (const gp_Pnt2d& theP, const Standard_Real theAng) const
   {
     gp_Elips2d anE = *this;
     anE.pos.Rotate (theP, theAng);
     return anE;
   }
 
   void Scale (const gp_Pnt2d& theP, const Standard_Real theS);
 
   //! Scales a ellipse. theS is the scaling value.
   Standard_NODISCARD gp_Elips2d Scaled (const gp_Pnt2d& theP, const Standard_Real theS) const;
 
   void Transform (const gp_Trsf2d& theT);
 
   //! Transforms an ellipse with the transformation theT from class Trsf2d.
   Standard_NODISCARD gp_Elips2d Transformed (const gp_Trsf2d& theT) const;
 
   void Translate (const gp_Vec2d& theV) { pos.Translate (theV); }
 
   //! Translates a ellipse in the direction of the vector theV.
   //! The magnitude of the translation is the vector's magnitude.
   Standard_NODISCARD gp_Elips2d Translated (const gp_Vec2d& theV) const
   {
     gp_Elips2d anE = *this;
     anE.pos.Translate (theV);
     return anE;
   }
 
   void Translate (const gp_Pnt2d& theP1, const gp_Pnt2d& theP2) { pos.Translate (theP1, theP2); }
 
   //! Translates a ellipse from the point theP1 to the point theP2.
   Standard_NODISCARD gp_Elips2d Translated (const gp_Pnt2d& theP1, const gp_Pnt2d& theP2) const
   {
     gp_Elips2d anE = *this;
     anE.pos.Translate (theP1, theP2);
     return anE;
   }
 
 private:
 
   gp_Ax22d pos;
   Standard_Real majorRadius;
   Standard_Real minorRadius;
 
 };
 
 
 // =======================================================================
 // function : Directrix1
 // purpose  :
 // =======================================================================
 inline gp_Ax2d gp_Elips2d::Directrix1() const
 {
   Standard_Real anE = Eccentricity();
   Standard_ConstructionError_Raise_if (anE <= gp::Resolution(), "gp_Elips2d::Directrix1() - zero eccentricity");
   gp_XY anOrig = pos.XDirection().XY();
   anOrig.Multiply (majorRadius / anE);
   anOrig.Add (pos.Location().XY());
   return gp_Ax2d (gp_Pnt2d (anOrig), gp_Dir2d (pos.YDirection()));
 }
 
 // =======================================================================
 // function : Directrix2
 // purpose  :
 // =======================================================================
 inline gp_Ax2d gp_Elips2d::Directrix2() const
 {
   Standard_Real anE = Eccentricity();
   Standard_ConstructionError_Raise_if (anE <= gp::Resolution(), "gp_Elips2d::Directrix2() - zero eccentricity");
   gp_XY anOrig = pos.XDirection().XY();
   anOrig.Multiply (-majorRadius / anE);
   anOrig.Add (pos.Location().XY());
   return gp_Ax2d (gp_Pnt2d (anOrig), gp_Dir2d (pos.YDirection()));
 }
 
 // =======================================================================
 // function : Eccentricity
 // purpose  :
 // =======================================================================
 inline Standard_Real gp_Elips2d::Eccentricity() const
 {
   if (majorRadius == 0.0)
   {
     return 0.0;
   }
   else
   {
     return sqrt (majorRadius * majorRadius - minorRadius * minorRadius) / majorRadius;
   }
 }
 
 // =======================================================================
 // function : Focus1
 // purpose  :
 // =======================================================================
 inline gp_Pnt2d gp_Elips2d::Focus1() const
 {
   Standard_Real aC = sqrt (majorRadius * majorRadius - minorRadius * minorRadius);
   const gp_Pnt2d& aPP = pos.Location();
   const gp_Dir2d& aDD = pos.XDirection();
   return gp_Pnt2d (aPP.X() + aC * aDD.X(),
                    aPP.Y() + aC * aDD.Y());
 }
 
 // =======================================================================
 // function : Focus2
 // purpose  :
 // =======================================================================
 inline gp_Pnt2d gp_Elips2d::Focus2() const
 {
   Standard_Real aC = sqrt (majorRadius * majorRadius - minorRadius * minorRadius);
   const gp_Pnt2d& aPP = pos.Location();
   const gp_Dir2d& aDD = pos.XDirection();
   return gp_Pnt2d (aPP.X() - aC * aDD.X(),
                    aPP.Y() - aC * aDD.Y());
 }
 
 // =======================================================================
 // function : Scale
 // purpose  :
 // =======================================================================
 inline void gp_Elips2d::Scale (const gp_Pnt2d& theP, const Standard_Real theS)
 {
   majorRadius *= theS;
   if (majorRadius < 0)
   {
     majorRadius = -majorRadius;
   }
   minorRadius *= theS;
   if (minorRadius < 0)
   {
     minorRadius = -minorRadius;
   }
   pos.Scale (theP, theS);
 }
 
 // =======================================================================
 // function : Scaled
 // purpose  :
 // =======================================================================
 inline gp_Elips2d gp_Elips2d::Scaled (const gp_Pnt2d& theP, const Standard_Real theS) const
 {
   gp_Elips2d anE = *this;
   anE.majorRadius *= theS;
   if (anE.majorRadius < 0)
   {
     anE.majorRadius = -anE.majorRadius;
   }
   anE.minorRadius *= theS;
   if (anE.minorRadius < 0)
   {
     anE.minorRadius = -anE.minorRadius;
   }
   anE.pos.Scale (theP, theS);
   return anE; 
 }
 
 // =======================================================================
 // function : Parameter
 // purpose  :
 // =======================================================================
 inline Standard_Real gp_Elips2d::Parameter() const
 { 
   if (majorRadius == 0.0)
   {
     return 0.0;
   }
   else
   {
     return (minorRadius * minorRadius) / majorRadius;
   }
 }
 
 // =======================================================================
 // function : Reversed
 // purpose  :
 // =======================================================================
 inline gp_Elips2d gp_Elips2d::Reversed() const
 {
   gp_Elips2d anE = *this;
   gp_Dir2d aTemp = pos.YDirection ();
   aTemp.Reverse ();
   anE.pos.SetAxis (gp_Ax22d (pos.Location(),pos.XDirection(), aTemp));
   return anE;
 }
 
 // =======================================================================
 // function : Transform
 // purpose  :
 // =======================================================================
 inline void gp_Elips2d::Transform (const gp_Trsf2d& theT)
 {
   Standard_Real aTSca = theT.ScaleFactor();
   if (aTSca < 0.0)
   {
     aTSca = -aTSca;
   }
   majorRadius *=  aTSca;
   minorRadius *=  aTSca;
   pos.Transform (theT);
 }
 
 // =======================================================================
 // function : Transformed
 // purpose  :
 // =======================================================================
 inline gp_Elips2d gp_Elips2d::Transformed (const gp_Trsf2d& theT) const  
 {
   gp_Elips2d anE = *this;
   anE.majorRadius *= theT.ScaleFactor();
   if (anE.majorRadius < 0)
   {
     anE.majorRadius = -anE.majorRadius;
   }
   anE.minorRadius *= theT.ScaleFactor();
   if (anE.minorRadius < 0)
   {
     anE.minorRadius = -anE.minorRadius;
   }
   anE.pos.Transform (theT);
   return anE;
 }
 
 #endif // _gp_Elips2d_HeaderFile

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