// Copyright (c) 1991-1999 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 _gp_Parab2d_HeaderFile #define _gp_Parab2d_HeaderFile #include #include #include #include #include #include #include #include class Standard_ConstructionError; class gp_Ax2d; class gp_Ax22d; class gp_Pnt2d; class gp_Trsf2d; class gp_Vec2d; //! Describes a parabola in the plane (2D space). //! A parabola is defined by its focal length (that is, the //! distance between its focus and apex) and positioned in //! the plane with a coordinate system (a gp_Ax22d object) where: //! - the origin of the coordinate system is on the apex of //! the parabola, and //! - the "X Axis" of the coordinate system is 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. Its orientation (direct or indirect sense) //! gives an implicit orientation to the parabola. //! In this coordinate system, the equation for the parabola is: //! @code //! Y**2 = (2*P) * X. //! @endcode //! where P, referred to as the parameter of the parabola, is //! the distance between the focus and the directrix (P is //! twice the focal length). //! See Also //! GCE2d_MakeParab2d which provides functions for //! more complex parabola constructions //! Geom2d_Parabola which provides additional functions //! for constructing parabolas and works, in particular, with //! the parametric equations of parabolas class gp_Parab2d { public: DEFINE_STANDARD_ALLOC //! Creates an indefinite parabola. gp_Parab2d(); //! Creates a parabola with its vertex point, its axis of symmetry //! ("XAxis") and its focal length. //! The sense of parametrization is given by theSense. If theSense == TRUE //! (by default) then right-handed coordinate system is used, //! otherwise - left-handed. //! Warnings : It is possible to have FocalLength = 0. In this case, //! the parabola looks like a line, which is parallel to the symmetry-axis. //! Raises ConstructionError if FocalLength < 0.0 gp_Parab2d(const gp_Ax2d& theMirrorAxis, const Standard_Real theFocalLength, const Standard_Boolean theSense = Standard_True); //! Creates a parabola with its vertex point, its axis of symmetry //! ("XAxis"), correspond Y-axis and its focal length. //! Warnings : It is possible to have FocalLength = 0. In this case, //! the parabola looks like a line, which is parallel to the symmetry-axis. //! Raises ConstructionError if Focal < 0.0 gp_Parab2d(const gp_Ax22d& theAxes, const Standard_Real theFocalLength); //! Creates a parabola with the directrix and the focus point. //! Y-axis of the parabola (in User Coordinate System - UCS) is //! the direction of theDirectrix. X-axis always directs from theDirectrix //! to theFocus point and always comes through theFocus. //! Apex of the parabola is a middle point between the theFocus and the //! intersection point of theDirectrix and the X-axis. //! Warnings : It is possible to have FocalLength = 0 (when theFocus lies //! in theDirectrix). In this case, X-direction of the parabola is defined //! by theSense parameter. If theSense == TRUE (by default) then right-handed //! coordinate system is used, otherwise - left-handed. Result parabola will look //! like a line, which is perpendicular to the directrix. Standard_EXPORT gp_Parab2d(const gp_Ax2d& theDirectrix, const gp_Pnt2d& theFocus, const Standard_Boolean theSense = Standard_True); //! Changes the focal distance of the parabola //! Warnings : It is possible to have Focal = 0. //! Raises ConstructionError if Focal < 0.0 void SetFocal (const Standard_Real Focal); //! Changes the "Location" point of the parabola. It is the //! vertex of the parabola. void SetLocation (const gp_Pnt2d& P); //! Modifies this parabola, by redefining its local coordinate system so that //! its origin and "X Direction" become those of the axis //! MA. The "Y Direction" of the local coordinate system is //! then recomputed. The orientation of the local //! coordinate system is not modified. void SetMirrorAxis (const gp_Ax2d& A); //! Changes the local coordinate system of the parabola. //! The "Location" point of A becomes the vertex of the parabola. void SetAxis (const gp_Ax22d& A); //! Computes the coefficients of the implicit equation of the parabola //! (in WCS - World Coordinate System). //! @code //! A * (X**2) + B * (Y**2) + 2*C*(X*Y) + 2*D*X + 2*E*Y + F = 0. //! @endcode Standard_EXPORT void Coefficients (Standard_Real& A, Standard_Real& B, Standard_Real& C, Standard_Real& D, Standard_Real& E, Standard_Real& F) const; //! Computes the directrix of the parabola. //! The directrix is: //! - a line parallel to the "Y Direction" of the local //! coordinate system of this parabola, and //! - located on the negative side of the axis of symmetry, //! at a distance from the apex which is equal to the focal length of this parabola. //! The directrix is returned as an axis (a gp_Ax2d object), //! the origin of which is situated on the "X Axis" of this parabola. gp_Ax2d Directrix() const; //! Returns the distance between the vertex and the focus //! of the parabola. Standard_Real Focal() const; //! Returns the focus of the parabola. gp_Pnt2d Focus() const; //! Returns the vertex of the parabola. gp_Pnt2d Location() const; //! Returns the symmetry axis of the parabola. //! The "Location" point of this axis is the vertex of the parabola. gp_Ax2d MirrorAxis() const; //! Returns the local coordinate system of the parabola. //! The "Location" point of this axis is the vertex of the parabola. gp_Ax22d Axis() const; //! Returns the distance between the focus and the //! directrix of the parabola. Standard_Real Parameter() const; void Reverse(); //! Reverses the orientation of the local coordinate system //! of this parabola (the "Y Direction" is reversed). //! Therefore, the implicit orientation of this parabola is reversed. //! Note: //! - Reverse assigns the result to this parabola, while //! - Reversed creates a new one. Standard_NODISCARD gp_Parab2d Reversed() const; //! Returns true if the local coordinate system is direct //! and false in the other case. Standard_Boolean IsDirect() const; Standard_EXPORT void Mirror (const gp_Pnt2d& P); //! Performs the symmetrical transformation of a parabola with respect //! to the point P which is the center of the symmetry Standard_NODISCARD Standard_EXPORT gp_Parab2d Mirrored (const gp_Pnt2d& P) const; Standard_EXPORT void Mirror (const gp_Ax2d& A); //! Performs the symmetrical transformation of a parabola with respect //! to an axis placement which is the axis of the symmetry. Standard_NODISCARD Standard_EXPORT gp_Parab2d Mirrored (const gp_Ax2d& A) const; void Rotate (const gp_Pnt2d& P, const Standard_Real Ang); //! Rotates a parabola. P is the center of the rotation. //! Ang is the angular value of the rotation in radians. Standard_NODISCARD gp_Parab2d Rotated (const gp_Pnt2d& P, const Standard_Real Ang) const; void Scale (const gp_Pnt2d& P, const Standard_Real S); //! Scales a parabola. S is the scaling value. //! If S is negative the direction of the symmetry axis //! "XAxis" is reversed and the direction of the "YAxis" too. Standard_NODISCARD gp_Parab2d Scaled (const gp_Pnt2d& P, const Standard_Real S) const; void Transform (const gp_Trsf2d& T); //! Transforms an parabola with the transformation T from class Trsf2d. Standard_NODISCARD gp_Parab2d Transformed (const gp_Trsf2d& T) const; void Translate (const gp_Vec2d& V); //! Translates a parabola in the direction of the vector V. //! The magnitude of the translation is the vector's magnitude. Standard_NODISCARD gp_Parab2d Translated (const gp_Vec2d& V) const; void Translate (const gp_Pnt2d& P1, const gp_Pnt2d& P2); //! Translates a parabola from the point P1 to the point P2. Standard_NODISCARD gp_Parab2d Translated (const gp_Pnt2d& P1, const gp_Pnt2d& P2) const; protected: private: gp_Ax22d pos; Standard_Real focalLength; }; #include #endif // _gp_Parab2d_HeaderFile