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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.
   constexpr gp_Elips() noexcept
       : 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.
   constexpr gp_Elips(const gp_Ax2& theA2, const double theMajorRadius, const double 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.
   constexpr void SetLocation(const gp_Pnt& theP) noexcept { 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 double 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 double 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.
   constexpr void SetPosition(const gp_Ax2& theA2) noexcept { pos = theA2; }
 
   //! Computes the area of the Ellipse.
   constexpr double Area() const noexcept { return M_PI * majorRadius * minorRadius; }
 
   //! Computes the axis normal to the plane of the ellipse.
   constexpr const gp_Ax1& Axis() const noexcept { 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
   double Eccentricity() const;
 
   //! Computes the focal distance. It is the distance between the
   //! two focus focus1 and focus2 of the ellipse.
   double 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.
   constexpr const gp_Pnt& Location() const noexcept { return pos.Location(); }
 
   //! Returns the major radius of the ellipse.
   constexpr double MajorRadius() const noexcept { return majorRadius; }
 
   //! Returns the minor radius of the ellipse.
   constexpr double MinorRadius() const noexcept { return minorRadius; }
 
   //! Returns p = (1 - e * e) * MajorRadius where e is the eccentricity
   //! of the ellipse.
   //! Returns 0 if MajorRadius = 0
   double Parameter() const;
 
   //! Returns the coordinate system of the ellipse.
   constexpr const gp_Ax2& Position() const noexcept { return pos; }
 
   //! Returns the "XAxis" of the ellipse whose origin
   //! is the center of this ellipse. It is the major axis of the
   //! ellipse.
   constexpr gp_Ax1 XAxis() const noexcept { 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.
   constexpr gp_Ax1 YAxis() const noexcept { return gp_Ax1(pos.Location(), pos.YDirection()); }
 
   Standard_EXPORT void Mirror(const gp_Pnt& theP) noexcept;
 
   //! Performs the symmetrical transformation of an ellipse with
   //! respect to the point theP which is the center of the symmetry.
   [[nodiscard]] Standard_EXPORT gp_Elips Mirrored(const gp_Pnt& theP) const noexcept;
 
   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.
   [[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).
   [[nodiscard]] Standard_EXPORT gp_Elips Mirrored(const gp_Ax2& theA2) const;
 
   void Rotate(const gp_Ax1& theA1, const double 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.
   [[nodiscard]] gp_Elips Rotated(const gp_Ax1& theA1, const double theAng) const
   {
     gp_Elips anE = *this;
     anE.pos.Rotate(theA1, theAng);
     return anE;
   }
 
   void Scale(const gp_Pnt& theP, const double theS);
 
   //! Scales an ellipse. theS is the scaling value.
   [[nodiscard]] gp_Elips Scaled(const gp_Pnt& theP, const double theS) const;
 
   void Transform(const gp_Trsf& theT);
 
   //! Transforms an ellipse with the transformation theT from class Trsf.
   [[nodiscard]] gp_Elips Transformed(const gp_Trsf& theT) const;
 
   constexpr void Translate(const gp_Vec& theV) noexcept { pos.Translate(theV); }
 
   //! Translates an ellipse in the direction of the vector theV.
   //! The magnitude of the translation is the vector's magnitude.
   [[nodiscard]] constexpr gp_Elips Translated(const gp_Vec& theV) const noexcept
   {
     gp_Elips anE = *this;
     anE.pos.Translate(theV);
     return anE;
   }
 
   constexpr void Translate(const gp_Pnt& theP1, const gp_Pnt& theP2) noexcept
   {
     pos.Translate(theP1, theP2);
   }
 
   //! Translates an ellipse from the point theP1 to the point theP2.
   [[nodiscard]] constexpr gp_Elips Translated(const gp_Pnt& theP1,
                                               const gp_Pnt& theP2) const noexcept
   {
     gp_Elips anE = *this;
     anE.pos.Translate(theP1, theP2);
     return anE;
   }
 
 private:
   gp_Ax2 pos;
   double majorRadius;
   double minorRadius;
 };
 
 //=================================================================================================
 
 inline gp_Ax1 gp_Elips::Directrix1() const
 {
   double 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());
 }
 
 //=================================================================================================
 
 inline gp_Ax1 gp_Elips::Directrix2() const
 {
   double 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());
 }
 
 //=================================================================================================
 
 inline double gp_Elips::Eccentricity() const
 {
   if (majorRadius == 0.0)
   {
     return 0.0;
   }
   else
   {
     return sqrt(majorRadius * majorRadius - minorRadius * minorRadius) / majorRadius;
   }
 }
 
 //=================================================================================================
 
 inline gp_Pnt gp_Elips::Focus1() const
 {
   double        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());
 }
 
 //=================================================================================================
 
 inline gp_Pnt gp_Elips::Focus2() const
 {
   double        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());
 }
 
 //=================================================================================================
 
 inline double gp_Elips::Parameter() const
 {
   if (majorRadius == 0.0)
   {
     return 0.0;
   }
   else
   {
     return (minorRadius * minorRadius) / majorRadius;
   }
 }
 
 //=================================================================================================
 
 inline void gp_Elips::Scale(const gp_Pnt& theP, const double 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
 
 //=================================================================================================
 
 inline gp_Elips gp_Elips::Scaled(const gp_Pnt& theP, const double 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;
 }
 
 //=================================================================================================
 
 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);
 }
 
 //=================================================================================================
 
 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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