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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_Elips_HeaderFile
 #define _gp_Elips_HeaderFile
 
 #include <gp.hxx>
 #include <gp_Ax1.hxx>
 #include <gp_Ax2.hxx>
 #include <gp_Pnt.hxx>
 #include <Standard_ConstructionError.hxx>
 
 //! Describes an ellipse in 3D space.
 //! An ellipse is defined by its major and minor radii and
 //! positioned in space with a coordinate system (a gp_Ax2 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.
 //! Together, the origin, "X Direction" and "Y Direction" of
 //! this coordinate system define the plane of the ellipse.
 //! This coordinate system is the "local coordinate system"
 //! of the ellipse. In this coordinate system, the equation of
 //! the ellipse is:
 //! @code
 //! X*X / (MajorRadius**2) + Y*Y / (MinorRadius**2) = 1.0
 //! @endcode
 //! The "main Direction" of the local coordinate system gives
 //! the normal vector to the plane of the ellipse. This vector
 //! gives an implicit orientation to the ellipse (definition of the
 //! trigonometric sense). We refer to the "main Axis" of the
 //! local coordinate system as the "Axis" of the ellipse.
 //! See Also
 //! gce_MakeElips which provides functions for more
 //! complex ellipse constructions
 //! Geom_Ellipse which provides additional functions for
 //! constructing ellipses and works, in particular, with the
 //! parametric equations of ellipses
 class gp_Elips 
 {
 public:
 
   DEFINE_STANDARD_ALLOC
 
   //! Creates an indefinite ellipse.
   gp_Elips()
   : majorRadius (RealLast()),
     minorRadius (RealSmall())
   {}
 
   //! The major radius of the ellipse is on the "XAxis" and the
   //! minor radius is on the "YAxis" of the ellipse. The "XAxis"
   //! is defined with the "XDirection" of theA2 and the "YAxis" is
   //! defined with the "YDirection" of theA2.
   //! Warnings :
   //! It is not forbidden to create an ellipse with theMajorRadius =
   //! theMinorRadius.
   //! Raises ConstructionError if theMajorRadius < theMinorRadius or theMinorRadius < 0.
   gp_Elips (const gp_Ax2& theA2, const Standard_Real theMajorRadius, const Standard_Real theMinorRadius)
   : pos (theA2),
     majorRadius (theMajorRadius),
     minorRadius (theMinorRadius)
   {
     Standard_ConstructionError_Raise_if (theMinorRadius < 0.0 || theMajorRadius < theMinorRadius,
       "gp_Elips() - invalid construction parameters");
   }
 
   //! Changes the axis normal to the plane of the ellipse.
   //! It modifies the definition of this plane.
   //! The "XAxis" and the "YAxis" are recomputed.
   //! The local coordinate system is redefined 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), or
   //! Raises ConstructionError if the direction of theA1
   //! is parallel to the direction of the "XAxis" of the ellipse.
   void SetAxis (const gp_Ax1& theA1) { pos.SetAxis (theA1); }
 
   //! Modifies this ellipse, by redefining its local coordinate
   //! so that its origin becomes theP.
   void SetLocation (const gp_Pnt& theP) { pos.SetLocation (theP); }
 
   //! The major radius of the ellipse is on the "XAxis" (major axis)
   //! of the ellipse.
   //! Raises ConstructionError if theMajorRadius < MinorRadius.
   void SetMajorRadius (const Standard_Real theMajorRadius)
   {
     Standard_ConstructionError_Raise_if (theMajorRadius < minorRadius,
        "gp_Elips::SetMajorRadius() - major radius should be greater or equal to minor radius");
     majorRadius = theMajorRadius;
   }
 
   //! The minor radius of the ellipse is on the "YAxis" (minor axis)
   //! of the ellipse.
   //! Raises ConstructionError if theMinorRadius > MajorRadius or MinorRadius < 0.
   void SetMinorRadius (const Standard_Real theMinorRadius)
   {
     Standard_ConstructionError_Raise_if (theMinorRadius < 0.0 || majorRadius < theMinorRadius,
       "gp_Elips::SetMinorRadius() - minor radius should be a positive number lesser or equal to major radius");
     minorRadius = theMinorRadius;
   }
 
   //! Modifies this ellipse, by redefining its local coordinate
   //! so that it becomes theA2.
   void SetPosition (const gp_Ax2& theA2) { pos = theA2; }
 
   //! Computes the area of the Ellipse.
   Standard_Real Area() const { return M_PI * majorRadius * minorRadius; }
 
   //! Computes the axis normal to the plane of the ellipse.
   const gp_Ax1& Axis() const { return pos.Axis(); }
 
   //! Computes the first or second directrix of this ellipse.
   //! These are the lines, in the plane of the ellipse, normal to
   //! the major axis, at a distance equal to
   //! MajorRadius/e from the center of the ellipse, where
   //! e is the eccentricity of the ellipse.
   //! The first directrix (Directrix1) is on the positive side of
   //! the major axis. The second directrix (Directrix2) is on
   //! the negative side.
   //! The directrix is returned as an axis (gp_Ax1 object), the
   //! origin of which is situated on the "X Axis" of the local
   //! coordinate system of this ellipse.
   //! Exceptions
   //! Standard_ConstructionError if the eccentricity is null
   //! (the ellipse has degenerated into a circle).
   gp_Ax1 Directrix1() const;
 
   //! This line is obtained by the symmetrical transformation
   //! of "Directrix1" with respect to the "YAxis" of the ellipse.
   //! Exceptions
   //! Standard_ConstructionError if the eccentricity is null
   //! (the ellipse has degenerated into a circle).
   gp_Ax1 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.
   //! Raises ConstructionError if MajorRadius = 0.0
   Standard_Real Eccentricity() const;
 
   //! Computes the focal distance. It is the distance between the
   //! two focus focus1 and focus2 of the ellipse.
   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 "XAxis" of the ellipse.
   gp_Pnt Focus1() const;
 
   //! Returns the second focus of the ellipse. This focus is on the
   //! negative side of the "XAxis" of the ellipse.
   gp_Pnt Focus2() const;
 
   //! Returns the center of the ellipse. It is the "Location"
   //! point of the coordinate system of the ellipse.
   const gp_Pnt& 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 coordinate system of the ellipse.
   const gp_Ax2& Position() const { return pos; }
 
   //! Returns the "XAxis" of the ellipse whose origin
   //! is the center of this ellipse. It is the major axis of the
   //! ellipse.
   gp_Ax1 XAxis() const { return gp_Ax1 (pos.Location(), pos.XDirection()); }
 
   //! Returns the "YAxis" of the ellipse whose unit vector is the "X Direction" or the "Y Direction"
   //! of the local coordinate system of this ellipse.
   //! This is the minor axis of the ellipse.
   gp_Ax1 YAxis() const { return gp_Ax1 (pos.Location(), pos.YDirection()); }
 
   Standard_EXPORT void Mirror (const gp_Pnt& theP);
 
   //! Performs the symmetrical transformation of an ellipse with
   //! respect to the point theP which is the center of the symmetry.
   Standard_NODISCARD Standard_EXPORT gp_Elips Mirrored (const gp_Pnt& theP) const;
 
   Standard_EXPORT void Mirror (const gp_Ax1& theA1);
 
   //! Performs the symmetrical transformation of an ellipse with
   //! respect to an axis placement which is the axis of the symmetry.
   Standard_NODISCARD Standard_EXPORT gp_Elips Mirrored (const gp_Ax1& theA1) const;
 
   Standard_EXPORT void Mirror (const gp_Ax2& theA2);
 
   //! Performs the symmetrical transformation of an ellipse with
   //! respect to a plane. The axis placement theA2 locates the plane
   //! of the symmetry (Location, XDirection, YDirection).
   Standard_NODISCARD Standard_EXPORT gp_Elips Mirrored (const gp_Ax2& theA2) const;
 
   void Rotate (const gp_Ax1& theA1, const Standard_Real theAng) { pos.Rotate (theA1, theAng); }
 
   //! Rotates an ellipse. theA1 is the axis of the rotation.
   //! theAng is the angular value of the rotation in radians.
   Standard_NODISCARD gp_Elips Rotated (const gp_Ax1& theA1, const Standard_Real theAng) const
   {
     gp_Elips anE = *this;
     anE.pos.Rotate (theA1, theAng);
     return anE;
   }
 
   void Scale (const gp_Pnt& theP, const Standard_Real theS);
 
   //! Scales an ellipse. theS is the scaling value.
   Standard_NODISCARD gp_Elips Scaled (const gp_Pnt& theP, const Standard_Real theS) const;
 
   void Transform (const gp_Trsf& theT);
 
   //! Transforms an ellipse with the transformation theT from class Trsf.
   Standard_NODISCARD gp_Elips Transformed (const gp_Trsf& theT) const;
 
   void Translate (const gp_Vec& theV) { pos.Translate (theV); }
 
   //! Translates an ellipse in the direction of the vector theV.
   //! The magnitude of the translation is the vector's magnitude.
   Standard_NODISCARD gp_Elips Translated (const gp_Vec& theV) const
   {
     gp_Elips anE = *this;
     anE.pos.Translate (theV);
     return anE;
   }
 
   void Translate (const gp_Pnt& theP1, const gp_Pnt& theP2) { pos.Translate (theP1, theP2); }
 
   //! Translates an ellipse from the point theP1 to the point theP2.
   Standard_NODISCARD gp_Elips Translated (const gp_Pnt& theP1, const gp_Pnt& theP2) const
   {
     gp_Elips anE = *this;
     anE.pos.Translate (theP1, theP2);
     return anE;
   }
 
 private:
 
   gp_Ax2 pos;
   Standard_Real majorRadius;
   Standard_Real minorRadius;
 
 };
 
 // =======================================================================
 // function : Directrix1
 // purpose  :
 // =======================================================================
 inline gp_Ax1 gp_Elips::Directrix1() const
 {
   Standard_Real anE = Eccentricity();
   Standard_ConstructionError_Raise_if (anE <= gp::Resolution(), "gp_Elips::Directrix1() - zero eccentricity");
   gp_XYZ anOrig = pos.XDirection().XYZ();
   anOrig.Multiply (majorRadius / anE);
   anOrig.Add (pos.Location().XYZ());
   return gp_Ax1 (gp_Pnt (anOrig), pos.YDirection());
 }
 
 // =======================================================================
 // function : Directrix2
 // purpose  :
 // =======================================================================
 inline gp_Ax1 gp_Elips::Directrix2() const
 {
   Standard_Real anE = Eccentricity();
   Standard_ConstructionError_Raise_if (anE <= gp::Resolution(), "gp_Elips::Directrix2() - zero eccentricity");
   gp_XYZ anOrig = pos.XDirection().XYZ();
   anOrig.Multiply (-majorRadius / anE);
   anOrig.Add (pos.Location().XYZ());
   return gp_Ax1 (gp_Pnt (anOrig), pos.YDirection());
 }
 
 // =======================================================================
 // function : Eccentricity
 // purpose  :
 // =======================================================================
 inline Standard_Real gp_Elips::Eccentricity() const
 {
   if (majorRadius == 0.0)
   {
     return 0.0;
   }
   else
   {
     return sqrt (majorRadius * majorRadius - minorRadius * minorRadius) / majorRadius;
   }
 }
 
 // =======================================================================
 // function : Focus1
 // purpose  :
 // =======================================================================
 inline gp_Pnt gp_Elips::Focus1() const
 {
   Standard_Real aC = sqrt (majorRadius * majorRadius - minorRadius * minorRadius);
   const gp_Pnt& aPP = pos.Location();
   const gp_Dir& aDD = pos.XDirection();
   return gp_Pnt (aPP.X() + aC * aDD.X(),
                  aPP.Y() + aC * aDD.Y(),
                  aPP.Z() + aC * aDD.Z());
 }
 
 // =======================================================================
 // function : Focus2
 // purpose  :
 // =======================================================================
 inline gp_Pnt gp_Elips::Focus2() const
 {
   Standard_Real aC = sqrt (majorRadius * majorRadius - minorRadius * minorRadius);
   const gp_Pnt& aPP = pos.Location();
   const gp_Dir& aDD = pos.XDirection();
   return gp_Pnt (aPP.X() - aC * aDD.X(),
                  aPP.Y() - aC * aDD.Y(),
                  aPP.Z() - aC * aDD.Z());
 }
 
 // =======================================================================
 // function : Parameter
 // purpose  :
 // =======================================================================
 inline Standard_Real gp_Elips::Parameter() const
 {
   if (majorRadius == 0.0)
   {
     return 0.0;
   }
   else
   {
     return (minorRadius * minorRadius) / majorRadius;
   }
 }
 
 // =======================================================================
 // function : Scale
 // purpose  :
 // =======================================================================
 inline void gp_Elips::Scale (const gp_Pnt& theP,
                              const Standard_Real theS)
   //  Modified by skv - Fri Apr  8 10:28:10 2005 OCC8559 Begin
   // { pos.Scale(P, S); }
 {
   majorRadius *= theS;
   if (majorRadius < 0)
   {
     majorRadius = -majorRadius;
   }
   minorRadius *= theS;
   if (minorRadius < 0)
   {
     minorRadius = -minorRadius;
   }
   pos.Scale (theP, theS);
 }
 //  Modified by skv - Fri Apr  8 10:28:10 2005 OCC8559 End
 
 // =======================================================================
 // function : Scaled
 // purpose  :
 // =======================================================================
 inline gp_Elips gp_Elips::Scaled (const gp_Pnt& theP,
                                   const Standard_Real theS) const
 {
   gp_Elips 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 : Transform
 // purpose  :
 // =======================================================================
 inline void gp_Elips::Transform (const gp_Trsf& theT)
 {
   majorRadius *= theT.ScaleFactor();
   if (majorRadius < 0)
   {
     majorRadius = -majorRadius;
   }
   minorRadius *= theT.ScaleFactor();
   if (minorRadius < 0)
   {
     minorRadius = -minorRadius;
   }
   pos.Transform (theT);
 }
 
 // =======================================================================
 // function : Transformed
 // purpose  :
 // =======================================================================
 inline gp_Elips gp_Elips::Transformed (const gp_Trsf& theT) const
 {
   gp_Elips 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_Elips_HeaderFile

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