// Created on: 1993-03-10 // 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 _Geom_Ellipse_HeaderFile #define _Geom_Ellipse_HeaderFile #include #include #include #include #include #include class gp_Elips; class gp_Ax2; class gp_Ax1; class gp_Pnt; class gp_Vec; class gp_Trsf; class Geom_Geometry; class Geom_Ellipse; DEFINE_STANDARD_HANDLE(Geom_Ellipse, Geom_Conic) //! Describes an ellipse in 3D space. //! An ellipse is defined by its major and minor radii and, //! as with any conic curve, is positioned in space with a //! right-handed coordinate system (gp_Ax2 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. //! The origin, "X Direction" and "Y Direction" of this //! coordinate system define the plane of the ellipse. The //! coordinate system is the local coordinate system of the ellipse. //! The "main Direction" of this coordinate system is the //! vector normal to the plane of the ellipse. The axis, of //! which the origin and unit vector are respectively the //! origin and "main Direction" of the local coordinate //! system, is termed the "Axis" or "main Axis" of the ellipse. //! The "main Direction" of the local coordinate system //! gives an explicit orientation to the ellipse (definition of //! the trigonometric sense), determining the direction in //! which the parameter increases along the ellipse. //! The Geom_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 [. class Geom_Ellipse : public Geom_Conic { public: //! Constructs an ellipse by conversion of the gp_Elips ellipse E. Standard_EXPORT Geom_Ellipse(const gp_Elips& E); //! Constructs an ellipse //! defined by its major and minor radii, MajorRadius //! and MinorRadius, where A2 locates the ellipse //! and defines its orientation in 3D space such that: //! - the center of the ellipse is the origin of A2, //! - the "X Direction" of A2 defines the major axis //! of the ellipse, i.e. the major radius //! MajorRadius is measured along this axis, //! - the "Y Direction" of A2 defines the minor axis //! of the ellipse, i.e. the minor radius //! MinorRadius is measured along this axis, //! - A2 is the local coordinate system of the ellipse. //! Exceptions //! Standard_ConstructionError if: //! - MajorRadius is less than MinorRadius, or //! - MinorRadius is less than 0. //! Warning The Geom package does not prevent the //! construction of an ellipse where MajorRadius and //! MinorRadius are equal. Standard_EXPORT Geom_Ellipse(const gp_Ax2& A2, const Standard_Real MajorRadius, const Standard_Real MinorRadius); //! Converts the gp_Elips ellipse E into this ellipse. Standard_EXPORT void SetElips (const gp_Elips& E); //! Assigns a value to the major radius of this ellipse. //! ConstructionError raised if MajorRadius < MinorRadius. Standard_EXPORT void SetMajorRadius (const Standard_Real MajorRadius); //! Assigns a value to the minor radius of this ellipse. //! ConstructionError raised if MajorRadius < MinorRadius or if MinorRadius < 0. Standard_EXPORT void SetMinorRadius (const Standard_Real MinorRadius); //! returns the non transient ellipse from gp with the same Standard_EXPORT gp_Elips Elips() 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; //! 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". //! Raised if Eccentricity = 0.0. (The ellipse degenerates //! into a circle) Standard_EXPORT gp_Ax1 Directrix1() const; //! This line is obtained by the symmetrical transformation //! of "Directrix1" with respect to the "YAxis" of the ellipse. //! //! Raised if Eccentricity = 0.0. (The ellipse degenerates into a //! circle). Standard_EXPORT 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. //! Returns 0 if MajorRadius = 0 Standard_EXPORT Standard_Real Eccentricity() const Standard_OVERRIDE; //! Computes the focal distance. It is the distance between the //! the two 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_Pnt 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_Pnt 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; //! Returns 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 respectively: //! - 0.0, which gives the start point of this ellipse, or //! 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 respectively: //! - 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_Pnt& P) const Standard_OVERRIDE; Standard_EXPORT void D1 (const Standard_Real U, gp_Pnt& P, gp_Vec& 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_Pnt& P, gp_Vec& V1, gp_Vec& 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_Pnt& P, gp_Vec& V1, gp_Vec& V2, gp_Vec& 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_Vec 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_Trsf& T) Standard_OVERRIDE; //! Creates a new object which is a copy of this ellipse. Standard_EXPORT Handle(Geom_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(Geom_Ellipse,Geom_Conic) protected: private: Standard_Real majorRadius; Standard_Real minorRadius; }; #endif // _Geom_Ellipse_HeaderFile