// 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_Elips_HeaderFile #define _gp_Elips_HeaderFile #include #include #include #include #include #include #include class Standard_ConstructionError; class gp_Ax2; class gp_Ax1; class gp_Pnt; class gp_Trsf; class gp_Vec; //! Describes an ellipse in 3D space. //! An ellipse is defined by its major and minor radii and //! positioned in space with a coordinate system (a gp_Ax2 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. //! Together, the origin, "X Direction" and "Y Direction" of //! this coordinate system define the plane of the ellipse. //! This coordinate system is the "local coordinate system" //! of the ellipse. In this coordinate system, the equation of //! the ellipse is: //! X*X / (MajorRadius**2) + Y*Y / (MinorRadius**2) = 1.0 //! The "main Direction" of the local coordinate system gives //! the normal vector to the plane of the ellipse. This vector //! gives an implicit orientation to the ellipse (definition of the //! trigonometric sense). We refer to the "main Axis" of the //! local coordinate system as the "Axis" of the ellipse. //! See Also //! gce_MakeElips which provides functions for more //! complex ellipse constructions //! Geom_Ellipse which provides additional functions for //! constructing ellipses and works, in particular, with the //! parametric equations of ellipses class gp_Elips { public: DEFINE_STANDARD_ALLOC //! Creates an indefinite ellipse. gp_Elips(); //! The major radius of the ellipse is on the "XAxis" and the //! minor radius is on the "YAxis" of the ellipse. The "XAxis" //! is defined with the "XDirection" of A2 and the "YAxis" is //! defined with the "YDirection" of A2. //! Warnings : //! It is not forbidden to create an ellipse with MajorRadius = //! MinorRadius. //! Raises ConstructionError if MajorRadius < MinorRadius or MinorRadius < 0. gp_Elips(const gp_Ax2& A2, const Standard_Real MajorRadius, const Standard_Real MinorRadius); //! Changes the axis normal to the plane of the ellipse. //! It modifies the definition of this plane. //! The "XAxis" and the "YAxis" are recomputed. //! The local coordinate system is redefined so that: //! - its origin and "main Direction" become those of the //! axis A1 (the "X Direction" and "Y Direction" are then //! recomputed in the same way as for any gp_Ax2), or //! Raises ConstructionError if the direction of A1 //! is parallel to the direction of the "XAxis" of the ellipse. void SetAxis (const gp_Ax1& A1); //! Modifies this ellipse, by redefining its local coordinate //! so that its origin becomes P. void SetLocation (const gp_Pnt& P); //! The major radius of the ellipse is on the "XAxis" (major axis) //! of the ellipse. //! Raises ConstructionError if MajorRadius < MinorRadius. void SetMajorRadius (const Standard_Real MajorRadius); //! The minor radius of the ellipse is on the "YAxis" (minor axis) //! of the ellipse. //! Raises ConstructionError if MinorRadius > MajorRadius or MinorRadius < 0. void SetMinorRadius (const Standard_Real MinorRadius); //! Modifies this ellipse, by redefining its local coordinate //! so that it becomes A2e. void SetPosition (const gp_Ax2& A2); //! Computes the area of the Ellipse. Standard_Real Area() const; //! Computes the axis normal to the plane of the ellipse. const gp_Ax1& Axis() const; //! Computes the first or second directrix of this ellipse. //! These are the lines, in the plane of the ellipse, normal to //! the major axis, at a distance equal to //! MajorRadius/e from the center of the ellipse, where //! e is the eccentricity of the ellipse. //! The first directrix (Directrix1) is on the positive side of //! the major axis. The second directrix (Directrix2) is on //! the negative side. //! The directrix is returned as an axis (gp_Ax1 object), the //! origin of which is situated on the "X Axis" of the local //! coordinate system of this ellipse. //! Exceptions //! Standard_ConstructionError if the eccentricity is null //! (the ellipse has degenerated into a circle). gp_Ax1 Directrix1() const; //! This line is obtained by the symmetrical transformation //! of "Directrix1" with respect to the "YAxis" of the ellipse. //! Exceptions //! Standard_ConstructionError if the eccentricity is null //! (the ellipse has degenerated into a circle). gp_Ax1 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. //! Raises ConstructionError if MajorRadius = 0.0 Standard_Real Eccentricity() const; //! Computes the focal distance. It is the distance between the //! two focus focus1 and focus2 of the ellipse. Standard_Real Focal() const; //! Returns the first focus of the ellipse. This focus is on the //! positive side of the "XAxis" of the ellipse. gp_Pnt Focus1() const; //! Returns the second focus of the ellipse. This focus is on the //! negative side of the "XAxis" of the ellipse. gp_Pnt Focus2() const; //! Returns the center of the ellipse. It is the "Location" //! point of the coordinate system of the ellipse. const gp_Pnt& 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 coordinate system of the ellipse. const gp_Ax2& Position() const; //! Returns the "XAxis" of the ellipse whose origin //! is the center of this ellipse. It is the major axis of the //! ellipse. gp_Ax1 XAxis() const; //! Returns the "YAxis" of the ellipse whose unit vector is the "X Direction" or the "Y Direction" //! of the local coordinate system of this ellipse. //! This is the minor axis of the ellipse. gp_Ax1 YAxis() const; Standard_EXPORT void Mirror (const gp_Pnt& P); //! Performs the symmetrical transformation of an ellipse with //! respect to the point P which is the center of the symmetry. Standard_NODISCARD Standard_EXPORT gp_Elips Mirrored (const gp_Pnt& P) const; Standard_EXPORT void Mirror (const gp_Ax1& A1); //! Performs the symmetrical transformation of an ellipse with //! respect to an axis placement which is the axis of the symmetry. Standard_NODISCARD Standard_EXPORT gp_Elips Mirrored (const gp_Ax1& A1) const; Standard_EXPORT void Mirror (const gp_Ax2& A2); //! Performs the symmetrical transformation of an ellipse with //! respect to a plane. The axis placement A2 locates the plane //! of the symmetry (Location, XDirection, YDirection). Standard_NODISCARD Standard_EXPORT gp_Elips Mirrored (const gp_Ax2& A2) const; void Rotate (const gp_Ax1& A1, const Standard_Real Ang); //! Rotates an ellipse. A1 is the axis of the rotation. //! Ang is the angular value of the rotation in radians. Standard_NODISCARD gp_Elips Rotated (const gp_Ax1& A1, const Standard_Real Ang) const; void Scale (const gp_Pnt& P, const Standard_Real S); //! Scales an ellipse. S is the scaling value. Standard_NODISCARD gp_Elips Scaled (const gp_Pnt& P, const Standard_Real S) const; void Transform (const gp_Trsf& T); //! Transforms an ellipse with the transformation T from class Trsf. Standard_NODISCARD gp_Elips Transformed (const gp_Trsf& T) const; void Translate (const gp_Vec& V); //! Translates an ellipse in the direction of the vector V. //! The magnitude of the translation is the vector's magnitude. Standard_NODISCARD gp_Elips Translated (const gp_Vec& V) const; void Translate (const gp_Pnt& P1, const gp_Pnt& P2); //! Translates an ellipse from the point P1 to the point P2. Standard_NODISCARD gp_Elips Translated (const gp_Pnt& P1, const gp_Pnt& P2) const; protected: private: gp_Ax2 pos; Standard_Real majorRadius; Standard_Real minorRadius; }; #include #endif // _gp_Elips_HeaderFile