-- 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.

class Ellipse from Geom2d inherits Conic from Geom2d

    	--- Purpose :  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
      
uses Ax2d     from gp,
     Ax22d    from gp,
     Elips2d  from gp,
     Pnt2d    from gp,
     Trsf2d   from gp,
     Vec2d    from gp,
     Geometry from Geom2d


raises ConstructionError from Standard,
       RangeError        from Standard


is


  Create (E : Elips2d)  returns Ellipse;
        --- Purpose :
        --  Creates an ellipse by conversion of the gp_Elips2d ellipse E.


  Create (MajorAxis : Ax2d; MajorRadius, MinorRadius : Real;
          Sense: Boolean from Standard = Standard_True)
     returns Ellipse
    	--- Purpose :  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.
     raises ConstructionError;


  Create (Axis : Ax22d; MajorRadius, MinorRadius : Real)
     returns Ellipse
    	--- Purpose : 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.
     raises ConstructionError;
	

  SetElips2d (me : mutable; E : Elips2d);
        --- Purpose: Converts the gp_Elips2d ellipse E into this ellipse.
     


  SetMajorRadius (me : mutable; MajorRadius : Real)
     raises ConstructionError;
	--- Purpose : 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.


  SetMinorRadius (me : mutable; MinorRadius : Real)
     raises ConstructionError;
	--- Purpose : 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.


  Elips2d (me)  returns Elips2d;
        --- Purpose : Converts this ellipse into a gp_Elips2d ellipse.


  ReversedParameter(me; U : Real) returns Real is redefined static;
  	---Purpose: 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.


  Directrix1 (me)   returns Ax2d
        --- Purpose : 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)
     raises ConstructionError;
	


  Directrix2 (me)   returns Ax2d
        --- Purpose :
        --  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).
    raises ConstructionError;
	
  Eccentricity (me)   returns Real is redefined static;
	--- Purpose :
	--  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


  Focal (me)   returns Real;
	--- Purpose :
	--  Computes the focal distance. The focal distance is the distance between the center
    	-- and a focus of the ellipse. 

  Focus1 (me)   returns Pnt2d;
	--- Purpose :
	--  Returns the first focus of the ellipse. This focus is on the
        --  positive side of the "XAxis" of the ellipse.


  Focus2 (me)   returns Pnt2d;
        --- Purpose :
	--  Returns the second focus of the ellipse. This focus is on
	--  the negative side of the "XAxis" of the ellipse.


  MajorRadius (me)  returns Real;
    	---Purpose: Returns the major radius of this ellipse.

  MinorRadius (me)  returns Real;
    	---Purpose: Returns the minor radius of this ellipse.

  Parameter (me)   returns Real;
        --- Purpose :
    	--   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


  FirstParameter (me)   returns Real is redefined static;
        --- Purpose : 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.


  LastParameter (me)  returns Real is redefined static;
        --- Purpose : 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.



  IsClosed (me)  returns Boolean is redefined static;
        --- Purpose : return True.


  IsPeriodic (me)  returns Boolean is redefined static;
        --- Purpose : return True.


  D0(me; U : Real; P : out Pnt2d) is redefined static;
	---Purpose: 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.



  D1 (me; U : Real; P : out Pnt2d; V1 : out Vec2d) is redefined static;
        -- Purpose :
        -- Returns the point P of parameter U and the first derivative 
        -- at this point.


  D2 (me; U : Real; P : out Pnt2d; V1, V2 : out Vec2d) is redefined static;
        --- Purpose :
        --  Returns the point P of parameter U. The vectors V1 and V2 
        --  are the first and second derivatives at this point.


  D3 (me; U : Real; P : out Pnt2d; V1, V2, V3 : out Vec2d) is redefined static;
        --- Purpose :
        --  Returns the point P of parameter U, the first second and
        --  third derivatives V1 V2 and V3.


  DN (me; U : Real; N : Integer)  returns Vec2d
        --- Purpose : 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.
          raises RangeError
     is redefined static;




  Transform (me : mutable; T : Trsf2d) is redefined static;

    	---Purpose: Applies the transformation T to this ellipse.

  Copy (me)  returns like me
     is redefined static;
    	---Purpose: Creates a new object which is a copy of this ellipse.     
fields

     majorRadius : Real;
     minorRadius : Real;

end;