// 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 #include #include #include #include #include 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