// 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_Hyperbola_HeaderFile #define _Geom2d_Hyperbola_HeaderFile #include #include #include #include #include #include class gp_Hypr2d; class gp_Ax2d; class gp_Ax22d; class gp_Pnt2d; class gp_Vec2d; class gp_Trsf2d; class Geom2d_Geometry; class Geom2d_Hyperbola; DEFINE_STANDARD_HANDLE(Geom2d_Hyperbola, Geom2d_Conic) //! Describes a branch of a hyperbola in the plane (2D space). //! A hyperbola 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 hyperbola, //! - 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 hyperbola. //! The branch of the hyperbola described is the one //! located on the positive side of the major axis. //! The orientation (direct or indirect) of the local //! coordinate system gives an explicit orientation to the //! hyperbola, determining the direction in which the //! parameter increases along the hyperbola. //! The Geom2d_Hyperbola hyperbola is parameterized as follows: //! P(U) = O + MajRad*Cosh(U)*XDir + MinRad*Sinh(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, //! - MajRad and MinRad are the major and minor radii of the hyperbola. //! The "X Axis" of the local coordinate system therefore //! defines the origin of the parameter of the hyperbola. //! The parameter range is ] -infinite,+infinite [. //! The following diagram illustrates the respective //! positions, in the plane of the hyperbola, of the three //! branches of hyperbolas constructed using the //! functions OtherBranch, ConjugateBranch1 and //! ConjugateBranch2: //! ^YAxis //! | //! FirstConjugateBranch //! | //! Other | Main //! --------------------- C //! --------------------->XAxis //! Branch | //! Branch //! | //! SecondConjugateBranch //! | //! Warning //! The value of the major radius (on the major axis) can //! be less than the value of the minor radius (on the minor axis). //! See Also //! GCE2d_MakeHyperbola which provides functions for //! more complex hyperbola constructions //! gp_Ax22d //! gp_Hypr2d for an equivalent, non-parameterized data structure class Geom2d_Hyperbola : public Geom2d_Conic { public: //! Creates an Hyperbola from a non persistent one from package gp Standard_EXPORT Geom2d_Hyperbola(const gp_Hypr2d& H); //! MajorAxis is the "XAxis" of the hyperbola. //! The YAxis is in the direct sense if "Sense" is True; //! The major radius of the hyperbola is on this "XAxis" and //! the minor radius is on the "YAxis" of the hyperbola. //! Raised if MajorRadius < 0.0 or if MinorRadius < 0.0 Standard_EXPORT Geom2d_Hyperbola(const gp_Ax2d& MajorAxis, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const Standard_Boolean Sense = Standard_True); //! The XDirection of "Axis" is the "XAxis" of the hyperbola and //! the YDirection of "Axis" is the "YAxis". //! The major radius of the hyperbola is on this "XAxis" and //! the minor radius is on the "YAxis" of the hyperbola. //! Raised if MajorRadius < 0.0 or if MinorRadius < 0.0 Standard_EXPORT Geom2d_Hyperbola(const gp_Ax22d& Axis, const Standard_Real MajorRadius, const Standard_Real MinorRadius); //! Converts the gp_Hypr2d hyperbola H into this hyperbola. Standard_EXPORT void SetHypr2d (const gp_Hypr2d& H); //! Assigns a value to the major or minor radius of this hyperbola. //! Exceptions //! Standard_ConstructionError if: //! - MajorRadius is less than 0.0, //! - MinorRadius is less than 0.0. Standard_EXPORT void SetMajorRadius (const Standard_Real MajorRadius); //! Assigns a value to the major or minor radius of this hyperbola. //! Exceptions //! Standard_ConstructionError if: //! - MajorRadius is less than 0.0, //! - MinorRadius is less than 0.0. Standard_EXPORT void SetMinorRadius (const Standard_Real MinorRadius); //! Converts this hyperbola into a gp_Hypr2d one. Standard_EXPORT gp_Hypr2d Hypr2d() const; //! Computes the parameter on the reversed hyperbola, //! for the point of parameter U on this hyperbola. //! For a hyperbola, the returned value is -U. Standard_EXPORT Standard_Real ReversedParameter (const Standard_Real U) const Standard_OVERRIDE; //! Returns RealFirst from Standard. Standard_EXPORT Standard_Real FirstParameter() const Standard_OVERRIDE; //! returns RealLast from Standard. Standard_EXPORT Standard_Real LastParameter() const Standard_OVERRIDE; //! Returns False. Standard_EXPORT Standard_Boolean IsClosed() const Standard_OVERRIDE; //! return False for an hyperbola. Standard_EXPORT Standard_Boolean IsPeriodic() const Standard_OVERRIDE; //! In the local coordinate system of the hyperbola the //! equation of the hyperbola is (X*X)/(A*A) - (Y*Y)/(B*B) = 1.0 //! and the equation of the first asymptote is Y = (B/A)*X //! where A is the major radius of the hyperbola and B is the //! minor radius of the hyperbola. //! Raised if MajorRadius = 0.0 Standard_EXPORT gp_Ax2d Asymptote1() const; //! In the local coordinate system of the hyperbola the //! equation of the hyperbola is (X*X)/(A*A) - (Y*Y)/(B*B) = 1.0 //! and the equation of the first asymptote is Y = -(B/A)*X. //! where A is the major radius of the hyperbola and B is the //! minor radius of the hyperbola. //! raised if MajorRadius = 0.0 Standard_EXPORT gp_Ax2d Asymptote2() const; //! Computes the first conjugate branch relative to this hyperbola. //! Note: The diagram given under the class purpose //! indicates where these two branches of hyperbola are //! positioned in relation to this branch of hyperbola. Standard_EXPORT gp_Hypr2d ConjugateBranch1() const; //! Computes the second conjugate branch relative to this hyperbola. //! Note: The diagram given under the class purpose //! indicates where these two branches of hyperbola are //! positioned in relation to this branch of hyperbola. Standard_EXPORT gp_Hypr2d ConjugateBranch2() const; //! This directrix is the line normal to the XAxis of the hyperbola //! in the local plane (Z = 0) at a distance d = MajorRadius / e //! from the center of the hyperbola, where e is the eccentricity of //! the hyperbola. //! 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". Standard_EXPORT gp_Ax2d Directrix1() const; //! This line is obtained by the symmetrical transformation //! of "Directrix1" with respect to the "YAxis" of the hyperbola. Standard_EXPORT gp_Ax2d Directrix2() const; //! Returns the eccentricity of the hyperbola (e > 1). //! If f is the distance between the location of the hyperbola //! and the Focus1 then the eccentricity e = f / MajorRadius. //! raised if MajorRadius = 0.0 Standard_EXPORT Standard_Real Eccentricity() const Standard_OVERRIDE; //! Computes the focal distance. It is the distance between the //! two focus of the hyperbola. Standard_EXPORT Standard_Real Focal() const; //! Returns the first focus of the hyperbola. This focus is on the //! positive side of the "XAxis" of the hyperbola. Standard_EXPORT gp_Pnt2d Focus1() const; //! Returns the second focus of the hyperbola. This focus is on the //! negative side of the "XAxis" of the hyperbola. Standard_EXPORT gp_Pnt2d Focus2() const; //! Returns the major or minor radius of this hyperbola. //! The major radius is also the distance between the //! center of the hyperbola and the apex of the main //! branch (located on the "X Axis" of the hyperbola). Standard_EXPORT Standard_Real MajorRadius() const; //! Returns the major or minor radius of this hyperbola. //! The minor radius is also the distance between the //! center of the hyperbola and the apex of a conjugate //! branch (located on the "Y Axis" of the hyperbola). Standard_EXPORT Standard_Real MinorRadius() const; //! Computes the "other" branch of this hyperbola. This //! is a symmetrical branch with respect to the center of this hyperbola. //! Note: The diagram given under the class purpose //! indicates where the "other" branch is positioned in //! relation to this branch of the hyperbola. //! ^ YAxis //! | //! FirstConjugateBranch //! | //! Other | Main //! ---------------------------- C //! ------------------------------------------>XAxis //! Branch | Branch //! | //! | //! SecondConjugateBranch //! | //! Warning //! The major radius can be less than the minor radius. Standard_EXPORT gp_Hypr2d OtherBranch() const; //! Computes the parameter of this hyperbola. //! The parameter is: //! p = (e*e - 1) * MajorRadius //! where e is the eccentricity of this hyperbola and //! MajorRadius its major radius. //! Exceptions //! Standard_DomainError if the major radius of this //! hyperbola is null. Standard_EXPORT Standard_Real Parameter() const; //! Returns in P the point of parameter U. //! P = C + MajorRadius * Cosh (U) * XDir + //! MinorRadius * Sinh (U) * YDir //! where C is the center of the hyperbola , XDir the XDirection and //! YDir the YDirection of the hyperbola's local coordinate system. Standard_EXPORT void D0 (const Standard_Real U, gp_Pnt2d& P) const Standard_OVERRIDE; //! Returns the point P of parameter U and the first derivative V1. 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 first and second //! derivatives V1 and V2. 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 hyperbola, //! 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 hyperbola. Standard_EXPORT void Transform (const gp_Trsf2d& T) Standard_OVERRIDE; //! Creates a new object which is a copy of this hyperbola. 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_Hyperbola,Geom2d_Conic) protected: private: Standard_Real majorRadius; Standard_Real minorRadius; }; #endif // _Geom2d_Hyperbola_HeaderFile