// 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_Elips2d_HeaderFile #define _gp_Elips2d_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 an ellipse in the plane (2D space). //! An ellipse is defined by its major and minor radii and //! positioned in the plane with a coordinate system (a //! gp_Ax22d object) as follows: //! - the origin of the coordinate system is the center of the ellipse, //! - its "X Direction" defines the major axis of the ellipse, and //! - its "Y Direction" defines the minor axis of the ellipse. //! This coordinate system is the "local coordinate system" //! of the ellipse. Its orientation (direct or indirect) gives an //! implicit orientation to the ellipse. In this coordinate //! system, the equation of the ellipse is: //! X*X / (MajorRadius**2) + Y*Y / (MinorRadius**2) = 1.0 //! See Also //! gce_MakeElips2d which provides functions for more //! complex ellipse constructions //! Geom2d_Ellipse which provides additional functions for //! constructing ellipses and works, in particular, with the //! parametric equations of ellipses class gp_Elips2d { public: DEFINE_STANDARD_ALLOC //! Creates an indefinite ellipse. gp_Elips2d(); //! Creates an ellipse with the major axis, the major and the //! minor radius. The location of the MajorAxis is the center //! of the ellipse. //! The sense of parametrization is given by Sense. //! Warnings : //! It is possible to create an ellipse with //! MajorRadius = MinorRadius. //! Raises ConstructionError if MajorRadius < MinorRadius or MinorRadius < 0.0 gp_Elips2d(const gp_Ax2d& MajorAxis, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const Standard_Boolean Sense = Standard_True); //! Creates an ellipse with radii MajorRadius and //! MinorRadius, positioned in the plane by coordinate system A where: //! - the origin of A is the center of the ellipse, //! - the "X Direction" of A defines the major axis of //! the ellipse, that is, the major radius MajorRadius //! is measured along this axis, and //! - the "Y Direction" of A defines the minor axis of //! the ellipse, that is, the minor radius MinorRadius //! is measured along this axis, and //! - the orientation (direct or indirect sense) of A //! gives the orientation of the ellipse. //! Warnings : //! It is possible to create an ellipse with //! MajorRadius = MinorRadius. //! Raises ConstructionError if MajorRadius < MinorRadius or MinorRadius < 0.0 gp_Elips2d(const gp_Ax22d& A, const Standard_Real MajorRadius, const Standard_Real MinorRadius); //! Modifies this ellipse, by redefining its local coordinate system so that //! - its origin becomes P. void SetLocation (const gp_Pnt2d& P); //! Changes the value of the major radius. //! Raises ConstructionError if MajorRadius < MinorRadius. void SetMajorRadius (const Standard_Real MajorRadius); //! Changes the value of the minor radius. //! Raises ConstructionError if MajorRadius < MinorRadius or MinorRadius < 0.0 void SetMinorRadius (const Standard_Real MinorRadius); //! Modifies this ellipse, by redefining its local coordinate system so that //! it becomes A. void SetAxis (const gp_Ax22d& A); //! Modifies this ellipse, by redefining its local coordinate system so that //! its origin and its "X Direction" become those //! of the axis A. The "Y Direction" is then //! recomputed. The orientation of the local coordinate //! system is not modified. void SetXAxis (const gp_Ax2d& A); //! Modifies this ellipse, by redefining its local coordinate system so that //! its origin and its "Y Direction" become those //! of the axis A. The "X Direction" is then //! recomputed. The orientation of the local coordinate //! system is not modified. void SetYAxis (const gp_Ax2d& A); //! Computes the area of the ellipse. Standard_Real Area() const; //! Returns the coefficients of the implicit equation of the ellipse. //! A * (X**2) + B * (Y**2) + 2*C*(X*Y) + 2*D*X + 2*E*Y + F = 0. Standard_EXPORT void Coefficients (Standard_Real& A, Standard_Real& B, Standard_Real& C, Standard_Real& D, Standard_Real& E, Standard_Real& F) const; //! 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) gp_Ax2d Directrix1() const; //! This line is obtained by the symmetrical transformation //! of "Directrix1" with respect to the minor axis of the ellipse. //! //! Raised if Eccentricity = 0.0. (The ellipse degenerates into a //! circle). gp_Ax2d 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_Real Eccentricity() const; //! Returns the distance between the center of the ellipse //! and focus1 or focus2. Standard_Real Focal() const; //! Returns the first focus of the ellipse. This focus is on the //! positive side of the major axis of the ellipse. gp_Pnt2d Focus1() const; //! Returns the second focus of the ellipse. This focus is on the //! negative side of the major axis of the ellipse. gp_Pnt2d Focus2() const; //! Returns the center of the ellipse. const gp_Pnt2d& Location() const; //! Returns the major radius of the Ellipse. Standard_Real MajorRadius() const; //! Returns the minor radius of the Ellipse. Standard_Real MinorRadius() const; //! Returns p = (1 - e * e) * MajorRadius where e is the eccentricity //! of the ellipse. //! Returns 0 if MajorRadius = 0 Standard_Real Parameter() const; //! Returns the major axis of the ellipse. const gp_Ax22d& Axis() const; //! Returns the major axis of the ellipse. gp_Ax2d XAxis() const; //! Returns the minor axis of the ellipse. //! Reverses the direction of the circle. gp_Ax2d YAxis() const; void Reverse(); Standard_NODISCARD gp_Elips2d 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 ellipse with respect //! to the point P which is the center of the symmetry Standard_NODISCARD Standard_EXPORT gp_Elips2d Mirrored (const gp_Pnt2d& P) const; Standard_EXPORT void Mirror (const gp_Ax2d& A); //! Performs the symmetrical transformation of a ellipse with respect //! to an axis placement which is the axis of the symmetry. Standard_NODISCARD Standard_EXPORT gp_Elips2d Mirrored (const gp_Ax2d& A) const; void Rotate (const gp_Pnt2d& P, const Standard_Real Ang); Standard_NODISCARD gp_Elips2d Rotated (const gp_Pnt2d& P, const Standard_Real Ang) const; void Scale (const gp_Pnt2d& P, const Standard_Real S); //! Scales a ellipse. S is the scaling value. Standard_NODISCARD gp_Elips2d Scaled (const gp_Pnt2d& P, const Standard_Real S) const; void Transform (const gp_Trsf2d& T); //! Transforms an ellipse with the transformation T from class Trsf2d. Standard_NODISCARD gp_Elips2d Transformed (const gp_Trsf2d& T) const; void Translate (const gp_Vec2d& V); //! Translates a ellipse in the direction of the vector V. //! The magnitude of the translation is the vector's magnitude. Standard_NODISCARD gp_Elips2d Translated (const gp_Vec2d& V) const; void Translate (const gp_Pnt2d& P1, const gp_Pnt2d& P2); //! Translates a ellipse from the point P1 to the point P2. Standard_NODISCARD gp_Elips2d Translated (const gp_Pnt2d& P1, const gp_Pnt2d& P2) const; protected: private: gp_Ax22d pos; Standard_Real majorRadius; Standard_Real minorRadius; }; #include #endif // _gp_Elips2d_HeaderFile