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 // Created on: 1993-03-24
 // 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 _Geom2d_Ellipse_HeaderFile
 #define _Geom2d_Ellipse_HeaderFile
 
 #include <Standard.hxx>
 #include <Standard_Type.hxx>
 
 #include <Geom2d_Conic.hxx>
 #include <Standard_Integer.hxx>
 class gp_Elips2d;
 class gp_Ax2d;
 class gp_Ax22d;
 class gp_Pnt2d;
 class gp_Vec2d;
 class gp_Trsf2d;
 class Geom2d_Geometry;
 
 class Geom2d_Ellipse;
 DEFINE_STANDARD_HANDLE(Geom2d_Ellipse, Geom2d_Conic)
 
 //! Describes an ellipse in the plane (2D space).
 //! An ellipse is defined by its major and minor radii and,
 //! as with any conic curve, is positioned in the plane
 //! with a coordinate system (gp_Ax22d object) where:
 //! - the origin is the center of the ellipse,
 //! - the "X Direction" defines the major axis, and
 //! - the "Y Direction" defines the minor axis.
 //! This coordinate system is the local coordinate system of the ellipse.
 //! The orientation (direct or indirect) of the local
 //! coordinate system gives an explicit orientation to the
 //! ellipse, determining the direction in which the
 //! parameter increases along the ellipse.
 //! The Geom2d_Ellipse ellipse is parameterized by an angle:
 //! P(U) = O + MajorRad*Cos(U)*XDir + MinorRad*Sin(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,
 //! - MajorRad and MinorRad are the major and
 //! minor radii of the ellipse.
 //! The "X Axis" of the local coordinate system therefore
 //! defines the origin of the parameter of the ellipse.
 //! An ellipse is a closed and periodic curve. The period
 //! is 2.*Pi and the parameter range is [ 0,2.*Pi [.
 //! See Also
 //! GCE2d_MakeEllipse which provides functions for
 //! more complex ellipse constructions
 //! gp_Ax22d
 //! gp_Elips2d for an equivalent, non-parameterized data structure
 class Geom2d_Ellipse : public Geom2d_Conic
 {
 
 public:
   //! Creates an ellipse by conversion of the gp_Elips2d ellipse E.
   Standard_EXPORT Geom2d_Ellipse(const gp_Elips2d& E);
 
   //! Creates an ellipse defined by its major and minor radii,
   //! MajorRadius and MinorRadius, and positioned
   //! in the plane by its major axis MajorAxis; the
   //! center of the ellipse is the origin of MajorAxis
   //! and the unit vector of MajorAxis is the "X
   //! Direction" of the local coordinate system of the
   //! ellipse; this coordinate system is direct if Sense
   //! is true (default value) or indirect if Sense is false.
   //! Warnings :
   //! It is not forbidden to create an ellipse with MajorRadius =
   //! MinorRadius.
   //! Exceptions
   //! Standard_ConstructionError if:
   //! - MajorRadius is less than MinorRadius, or
   //! - MinorRadius is less than 0.
   Standard_EXPORT Geom2d_Ellipse(const gp_Ax2d&         MajorAxis,
                                  const Standard_Real    MajorRadius,
                                  const Standard_Real    MinorRadius,
                                  const Standard_Boolean Sense = Standard_True);
 
   //! Creates an ellipse defined by its major and minor radii,
   //! MajorRadius and MinorRadius, where the
   //! coordinate system Axis locates the ellipse and
   //! defines its orientation in the plane such that:
   //! - the center of the ellipse is the origin of Axis,
   //! - the "X Direction" of Axis defines the major
   //! axis of the ellipse,
   //! - the "Y Direction" of Axis defines the minor
   //! axis of the ellipse,
   //! - the orientation of Axis (direct or indirect)
   //! gives the orientation of the ellipse.
   //! Warnings :
   //! It is not forbidden to create an ellipse with MajorRadius =
   //! MinorRadius.
   //! Exceptions
   //! Standard_ConstructionError if:
   //! - MajorRadius is less than MinorRadius, or
   //! - MinorRadius is less than 0.
   Standard_EXPORT Geom2d_Ellipse(const gp_Ax22d&     Axis,
                                  const Standard_Real MajorRadius,
                                  const Standard_Real MinorRadius);
 
   //! Converts the gp_Elips2d ellipse E into this ellipse.
   Standard_EXPORT void SetElips2d(const gp_Elips2d& E);
 
   //! Assigns a value to the major radius of this ellipse.
   //! Exceptions
   //! Standard_ConstructionError if:
   //! - the major radius of this ellipse becomes less than
   //! the minor radius, or
   //! - MinorRadius is less than 0.
   Standard_EXPORT void SetMajorRadius(const Standard_Real MajorRadius);
 
   //! Assigns a value to the minor radius of this ellipse.
   //! Exceptions
   //! Standard_ConstructionError if:
   //! - the major radius of this ellipse becomes less than
   //! the minor radius, or
   //! - MinorRadius is less than 0.
   Standard_EXPORT void SetMinorRadius(const Standard_Real MinorRadius);
 
   //! Converts this ellipse into a gp_Elips2d ellipse.
   Standard_EXPORT gp_Elips2d Elips2d() const;
 
   //! Computes the parameter on the reversed ellipse for
   //! the point of parameter U on this ellipse.
   //! For an ellipse, the returned value is: 2.*Pi - U.
   Standard_EXPORT Standard_Real ReversedParameter(const Standard_Real U) const Standard_OVERRIDE;
 
   //! Computes the directrices of this ellipse.
   //! 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".
   //! Raises ConstructionError if Eccentricity = 0.0. (The ellipse degenerates
   //! into a circle)
   Standard_EXPORT gp_Ax2d Directrix1() const;
 
   //! This line is obtained by the symmetrical transformation
   //! of "Directrix1" with respect to the "YAxis" of the ellipse.
   //! Raises ConstructionError if Eccentricity = 0.0. (The ellipse degenerates into a
   //! circle).
   Standard_EXPORT 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_EXPORT Standard_Real Eccentricity() const Standard_OVERRIDE;
 
   //! Computes the focal distance. The focal distance is the distance between the center
   //! and a focus of the ellipse.
   Standard_EXPORT Standard_Real Focal() const;
 
   //! Returns the first focus of the ellipse. This focus is on the
   //! positive side of the "XAxis" of the ellipse.
   Standard_EXPORT gp_Pnt2d Focus1() const;
 
   //! Returns the second focus of the ellipse. This focus is on
   //! the negative side of the "XAxis" of the ellipse.
   Standard_EXPORT gp_Pnt2d Focus2() const;
 
   //! Returns the major radius of this ellipse.
   Standard_EXPORT Standard_Real MajorRadius() const;
 
   //! Returns the minor radius of this ellipse.
   Standard_EXPORT Standard_Real MinorRadius() const;
 
   //! Computes the parameter of this ellipse. This value is
   //! given by the formula p = (1 - e * e) * MajorRadius where e is the eccentricity
   //! of the ellipse.
   //! Returns 0 if MajorRadius = 0
   Standard_EXPORT Standard_Real Parameter() const;
 
   //! Returns the value of the first parameter of this
   //! ellipse. This is  0.0, which gives the start point of this ellipse.
   //! The start point and end point of an ellipse are coincident.
   Standard_EXPORT Standard_Real FirstParameter() const Standard_OVERRIDE;
 
   //! Returns the value of the  last parameter of this
   //! ellipse. This is  2.*Pi, which gives the end point of this ellipse.
   //! The start point and end point of an ellipse are coincident.
   Standard_EXPORT Standard_Real LastParameter() const Standard_OVERRIDE;
 
   //! return True.
   Standard_EXPORT Standard_Boolean IsClosed() const Standard_OVERRIDE;
 
   //! return True.
   Standard_EXPORT Standard_Boolean IsPeriodic() const Standard_OVERRIDE;
 
   //! Returns in P the point of parameter U.
   //! P = C + MajorRadius * Cos (U) * XDir + MinorRadius * Sin (U) * YDir
   //! where C is the center of the ellipse , XDir the direction of
   //! the "XAxis" and "YDir" the "YAxis" of the ellipse.
   Standard_EXPORT void D0(const Standard_Real U, gp_Pnt2d& P) const Standard_OVERRIDE;
 
   Standard_EXPORT void D1(const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1) const Standard_OVERRIDE;
 
   //! Returns the point P of parameter U. The vectors V1 and V2
   //! are the first and second derivatives at this point.
   Standard_EXPORT void D2(const Standard_Real U,
                           gp_Pnt2d&           P,
                           gp_Vec2d&           V1,
                           gp_Vec2d&           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_Pnt2d&           P,
                           gp_Vec2d&           V1,
                           gp_Vec2d&           V2,
                           gp_Vec2d&           V3) const Standard_OVERRIDE;
 
   //! For the point of parameter U of this ellipse,
   //! computes the vector corresponding to the Nth derivative.
   //! Exceptions Standard_RangeError if N is less than 1.
   Standard_EXPORT gp_Vec2d DN(const Standard_Real    U,
                               const Standard_Integer N) const Standard_OVERRIDE;
 
   //! Applies the transformation T to this ellipse.
   Standard_EXPORT void Transform(const gp_Trsf2d& T) Standard_OVERRIDE;
 
   //! Creates a new object which is a copy of this ellipse.
   Standard_EXPORT Handle(Geom2d_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(Geom2d_Ellipse, Geom2d_Conic)
 
 protected:
 private:
   Standard_Real majorRadius;
   Standard_Real minorRadius;
 };
 
 #endif // _Geom2d_Ellipse_HeaderFile

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