// 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_Parabola_HeaderFile #define _Geom_Parabola_HeaderFile #include #include #include #include #include #include class gp_Parab; class gp_Ax2; class gp_Ax1; class gp_Pnt; class gp_Vec; class gp_Trsf; class Geom_Geometry; class Geom_Parabola; DEFINE_STANDARD_HANDLE(Geom_Parabola, Geom_Conic) //! Describes a parabola in 3D space. //! A parabola is defined by its focal length (i.e. the //! distance between its focus and its apex) and is //! positioned in space with a coordinate system //! (gp_Ax2 object) where: //! - the origin is the apex of the parabola, //! - the "X Axis" defines the axis of symmetry; the //! parabola is on the positive side of this axis, //! - the origin, "X Direction" and "Y Direction" define the //! plane of the parabola. //! This coordinate system is the local coordinate //! system of the parabola. //! The "main Direction" of this coordinate system is a //! vector normal to the plane of the parabola. 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 parabola. //! The "main Direction" 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 Geom_Parabola : public Geom_Conic { public: //! Creates a parabola from a non transient one. Standard_EXPORT Geom_Parabola(const gp_Parab& Prb); //! Creates a parabola with its local coordinate system "A2" //! and it's focal length "Focal". //! The XDirection of A2 defines the axis of symmetry of the //! parabola. The YDirection of A2 is parallel to the directrix //! of the parabola. The Location point of A2 is the vertex of //! the parabola //! Raised if Focal < 0.0 Standard_EXPORT Geom_Parabola(const gp_Ax2& A2, const Standard_Real 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. The normal to the plane //! of the parabola is the cross product between the XAxis and the //! YAxis. Standard_EXPORT Geom_Parabola(const gp_Ax1& D, const gp_Pnt& F); //! Assigns the value Focal to the focal distance of this parabola. //! Exceptions Standard_ConstructionError if Focal is negative. Standard_EXPORT void SetFocal (const Standard_Real Focal); //! Converts the gp_Parab parabola Prb into this parabola. Standard_EXPORT void SetParab (const gp_Parab& Prb); //! Returns the non transient parabola from gp with the same //! geometric properties as . Standard_EXPORT gp_Parab Parab() 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 Standard_Real ReversedParameter (const Standard_Real U) const Standard_OVERRIDE; //! Returns the value of the first or last parameter of this //! parabola. This is, respectively: //! - Standard_Real::RealFirst(), or //! - Standard_Real::RealLast(). Standard_EXPORT Standard_Real FirstParameter() const Standard_OVERRIDE; //! Returns the value of the first or last parameter of this //! parabola. This is, respectively: //! - Standard_Real::RealFirst(), or //! - Standard_Real::RealLast(). Standard_EXPORT Standard_Real LastParameter() const Standard_OVERRIDE; //! Returns False Standard_EXPORT Standard_Boolean IsClosed() const Standard_OVERRIDE; //! Returns False Standard_EXPORT Standard_Boolean IsPeriodic() const Standard_OVERRIDE; //! Computes the directrix of this parabola. //! This is a line normal to the axis of symmetry, in the //! plane of this parabola, located on the negative side //! of its axis of symmetry, at a distance from the apex //! equal to the focal length. //! The directrix is returned as an axis (gp_Ax1 object), //! where the origin is located on the "X Axis" of this parabola. Standard_EXPORT gp_Ax1 Directrix() const; //! Returns 1. (which is the eccentricity of any parabola). Standard_EXPORT Standard_Real Eccentricity() const Standard_OVERRIDE; //! 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_Pnt Focus() const; //! Computes the focal distance of this parabola //! The focal distance is the distance between the apex //! and the focus of the parabola. Standard_EXPORT Standard_Real 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 Standard_Real 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 void D0 (const Standard_Real U, gp_Pnt& 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_Pnt& P, gp_Vec& 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_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 parabola, //! 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 parabola. Standard_EXPORT void Transform (const gp_Trsf& T) Standard_OVERRIDE; //! Returns the parameter on the transformed curve for //! the transform of the point of parameter U on . //! //! me->Transformed(T)->Value(me->TransformedParameter(U,T)) //! //! is the same point as //! //! me->Value(U).Transformed(T) //! //! This methods returns * T.ScaleFactor() Standard_EXPORT Standard_Real TransformedParameter (const Standard_Real U, const gp_Trsf& T) const Standard_OVERRIDE; //! 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 Standard_Real ParametricTransformation (const gp_Trsf& T) const Standard_OVERRIDE; //! Creates a new object which is a copy of this parabola. 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_Parabola,Geom_Conic) protected: private: Standard_Real focalLength; }; #endif // _Geom_Parabola_HeaderFile