// 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_Parabola_HeaderFile #define _Geom2d_Parabola_HeaderFile #include "Standard.hxx" #include "Standard_Type.hxx" #include "Geom2d_Conic.hxx" class gp_Parab2d; class gp_Ax2d; class gp_Ax22d; class gp_Trsf2d; class Geom2d_Geometry; //! Describes a parabola in the plane (2D space). //! A parabola is defined by its focal length (i.e. the //! distance between its focus and its apex) and is //! positioned in the plane with a coordinate system //! (gp_Ax22d object) where: //! - the origin is the apex of the parabola, and //! - the "X Axis" defines the axis of symmetry; the //! parabola is on the positive side of this axis. //! This coordinate system is the local coordinate //! system of the parabola. //! The orientation (direct or indirect) of the local //! coordinate system gives an explicit orientation to the //! parabola, determining the direction in which the //! parameter increases along the parabola. //! The Geom_Parabola parabola is parameterized as follows: //! P(U) = O + U*U/(4.*F)*XDir + 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, //! - F is the focal length of the parabola. //! The parameter of the parabola is therefore its Y //! coordinate in the local coordinate system, with the "X //! Axis" of the local coordinate system defining the //! origin of the parameter. //! The parameter range is ] -infinite,+infinite [. class Geom2d_Parabola : public Geom2d_Conic { public: //! Creates a parabola from a non persistent one. Standard_EXPORT Geom2d_Parabola(const gp_Parab2d& Prb); //! Creates a parabola with its "MirrorAxis" and it's focal //! length "Focal". //! MirrorAxis is the axis of symmetry of the curve, it is the //! "XAxis". The "YAxis" is parallel to the directrix of the //! parabola and is in the direct sense if Sense is True. //! The "Location" point of "MirrorAxis" is the vertex of the parabola //! Raised if Focal < 0.0 Standard_EXPORT Geom2d_Parabola(const gp_Ax2d& MirrorAxis, const double Focal, const bool Sense = true); //! Creates a parabola with its Axis and it's focal //! length "Focal". //! The XDirection of Axis is the axis of symmetry of the curve, //! it is the "XAxis". The "YAxis" is parallel to the directrix of the //! parabola. The "Location" point of "Axis" is the vertex //! of the parabola. //! Raised if Focal < 0.0 Standard_EXPORT Geom2d_Parabola(const gp_Ax22d& Axis, const double Focal); //! D is the directrix of the parabola and F the focus point. //! The symmetry axis "XAxis" of the parabola is normal to the //! directrix and pass through the focus point F, but its //! "Location" point is the vertex of the parabola. //! The "YAxis" of the parabola is parallel to D and its "Location" //! point is the vertex of the parabola. Standard_EXPORT Geom2d_Parabola(const gp_Ax2d& D, const gp_Pnt2d& F); //! Assigns the value Focal to the focal length of this parabola. //! Exceptions Standard_ConstructionError if Focal is negative. Standard_EXPORT void SetFocal(const double Focal); //! Converts the gp_Parab2d parabola Prb into this parabola. Standard_EXPORT void SetParab2d(const gp_Parab2d& Prb); //! Returns the non persistent parabola from gp with the same //! geometric properties as . Standard_EXPORT gp_Parab2d Parab2d() const; //! Computes the parameter on the reversed parabola //! for the point of parameter U on this parabola. //! For a parabola, the returned value is -U. Standard_EXPORT double ReversedParameter(const double U) const final; //! Returns RealFirst from Standard. Standard_EXPORT double FirstParameter() const final; //! Returns RealLast from Standard. Standard_EXPORT double LastParameter() const final; //! Returns False Standard_EXPORT bool IsClosed() const final; //! Returns False Standard_EXPORT bool IsPeriodic() const final; //! The directrix is parallel to the "YAxis" of the parabola. //! The "Location" point of the directrix is the intersection //! point between the directrix and the symmetry axis ("XAxis") of the parabola. Standard_EXPORT gp_Ax2d Directrix() const; //! Returns the eccentricity e = 1.0 Standard_EXPORT double Eccentricity() const final; //! Computes the focus of this parabola The focus is on the //! positive side of the "X Axis" of the local coordinate system of the parabola. Standard_EXPORT gp_Pnt2d Focus() const; //! Computes the focal length of this parabola. //! The focal length is the distance between the apex and the focus of the parabola. Standard_EXPORT double Focal() const; //! Computes the parameter of this parabola, which is //! the distance between its focus and its directrix. This //! distance is twice the focal length. //! If P is the parameter of the parabola, the equation of //! the parabola in its local coordinate system is: Y**2 = 2.*P*X. Standard_EXPORT double Parameter() const; //! Returns in P the point of parameter U. //! If U = 0 the returned point is the origin of the XAxis and //! the YAxis of the parabola and it is the vertex of the parabola. //! P = S + F * (U * U * XDir + * U * YDir) //! where S is the vertex of the parabola, XDir the XDirection and //! YDir the YDirection of the parabola's local coordinate system. Standard_EXPORT gp_Pnt2d EvalD0(const double U) const final; //! Returns the point P of parameter U and the first derivative V1. Standard_EXPORT Geom2d_Curve::ResD1 EvalD1(const double U) const final; //! Returns the point P of parameter U, the first and second //! derivatives V1 and V2. Standard_EXPORT Geom2d_Curve::ResD2 EvalD2(const double U) const final; //! Returns the point P of parameter U, the first second and third //! derivatives V1 V2 and V3. Standard_EXPORT Geom2d_Curve::ResD3 EvalD3(const double U) const final; //! For the point of parameter U of this parabola, //! computes the vector corresponding to the Nth derivative. //! Exceptions Standard_RangeError if N is less than 1. Standard_EXPORT gp_Vec2d EvalDN(const double U, const int N) const final; //! Applies the transformation T to this parabola. Standard_EXPORT void Transform(const gp_Trsf2d& T) final; //! Computes the parameter on the transformed //! parabola, for the point of parameter U on this parabola. //! For a parabola, the returned value is equal to U //! multiplied by the scale factor of transformation T. Standard_EXPORT double TransformedParameter(const double U, const gp_Trsf2d& T) const final; //! Returns a coefficient to compute the parameter on //! the transformed curve for the transform of the //! point on . //! //! Transformed(T)->Value(U * ParametricTransformation(T)) //! //! is the same point as //! //! Value(U).Transformed(T) //! //! This methods returns T.ScaleFactor() Standard_EXPORT double ParametricTransformation(const gp_Trsf2d& T) const final; //! Creates a new object, which is a copy of this parabola. Standard_EXPORT occ::handle Copy() const final; //! Dumps the content of me into the stream Standard_EXPORT void DumpJson(Standard_OStream& theOStream, int theDepth = -1) const final; DEFINE_STANDARD_RTTIEXT(Geom2d_Parabola, Geom2d_Conic) private: double focalLength; }; #endif // _Geom2d_Parabola_HeaderFile