// 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_Torus_HeaderFile #define _gp_Torus_HeaderFile #include #include #include #include #include #include #include #include class Standard_ConstructionError; class Standard_DimensionError; class gp_Ax3; class gp_Ax1; class gp_Pnt; class gp_Ax2; class gp_Trsf; class gp_Vec; //! Describes a torus. //! A torus is defined by its major and minor radii and //! positioned in space with a coordinate system (a gp_Ax3 //! object) as follows: //! - The origin of the coordinate system is the center of the torus; //! - The surface is obtained by rotating a circle of radius //! equal to the minor radius of the torus about the "main //! Direction" of the coordinate system. This circle is //! located in the plane defined by the origin, the "X //! Direction" and the "main Direction" of the coordinate //! system. It is centered on the "X Axis" of this coordinate //! system, and located at a distance, from the origin of //! this coordinate system, equal to the major radius of the torus; //! - The "X Direction" and "Y Direction" define the //! reference plane of the torus. //! The coordinate system described above is the "local //! coordinate system" of the torus. //! Note: when a gp_Torus torus is converted into a //! Geom_ToroidalSurface torus, some implicit properties //! of its local coordinate system are used explicitly: //! - its origin, "X Direction", "Y Direction" and "main //! Direction" are used directly to define the parametric //! directions on the torus and the origin of the parameters, //! - its implicit orientation (right-handed or left-handed) //! gives the orientation (direct, indirect) to the //! Geom_ToroidalSurface torus. //! See Also //! gce_MakeTorus which provides functions for more //! complex torus constructions //! Geom_ToroidalSurface which provides additional //! functions for constructing tori and works, in particular, //! with the parametric equations of tori. class gp_Torus { public: DEFINE_STANDARD_ALLOC //! creates an indefinite Torus. gp_Torus(); //! a torus centered on the origin of coordinate system //! A3, with major radius MajorRadius and minor radius //! MinorRadius, and with the reference plane defined //! by the origin, the "X Direction" and the "Y Direction" of A3. //! Warnings : //! It is not forbidden to create a torus with //! MajorRadius = MinorRadius = 0.0 //! Raises ConstructionError if MinorRadius < 0.0 or if MajorRadius < 0.0 gp_Torus(const gp_Ax3& A3, const Standard_Real MajorRadius, const Standard_Real MinorRadius); //! Modifies this torus, by redefining its local coordinate //! system so that: //! - its origin and "main Direction" become those of the //! axis A1 (the "X Direction" and "Y Direction" are then recomputed). //! Raises ConstructionError if the direction of A1 is parallel to the "XDirection" //! of the coordinate system of the toroidal surface. void SetAxis (const gp_Ax1& A1); //! Changes the location of the torus. void SetLocation (const gp_Pnt& Loc); //! Assigns value to the major radius of this torus. //! Raises ConstructionError if MajorRadius - MinorRadius <= Resolution() void SetMajorRadius (const Standard_Real MajorRadius); //! Assigns value to the minor radius of this torus. //! Raises ConstructionError if MinorRadius < 0.0 or if //! MajorRadius - MinorRadius <= Resolution from gp. void SetMinorRadius (const Standard_Real MinorRadius); //! Changes the local coordinate system of the surface. void SetPosition (const gp_Ax3& A3); //! Computes the area of the torus. Standard_Real Area() const; //! Reverses the U parametrization of the torus //! reversing the YAxis. void UReverse(); //! Reverses the V parametrization of the torus //! reversing the ZAxis. void VReverse(); //! returns true if the Ax3, the local coordinate system of this torus, is right handed. Standard_Boolean Direct() const; //! returns the symmetry axis of the torus. const gp_Ax1& Axis() const; //! Computes the coefficients of the implicit equation of the surface //! in the absolute Cartesian coordinate system: //! Coef(1) * X^4 + Coef(2) * Y^4 + Coef(3) * Z^4 + //! Coef(4) * X^3 * Y + Coef(5) * X^3 * Z + Coef(6) * Y^3 * X + //! Coef(7) * Y^3 * Z + Coef(8) * Z^3 * X + Coef(9) * Z^3 * Y + //! Coef(10) * X^2 * Y^2 + Coef(11) * X^2 * Z^2 + //! Coef(12) * Y^2 * Z^2 + Coef(13) * X^2 * Y * Z + //! Coef(14) * X * Y^2 * Z + Coef(15) * X * Y * Z^2 + //! Coef(16) * X^3 + Coef(17) * Y^3 + Coef(18) * Z^3 + //! Coef(19) * X^2 * Y + Coef(20) * X^2 * Z + Coef(21) * Y^2 * X + //! Coef(22) * Y^2 * Z + Coef(23) * Z^2 * X + Coef(24) * Z^2 * Y + //! Coef(25) * X * Y * Z + //! Coef(26) * X^2 + Coef(27) * Y^2 + Coef(28) * Z^2 + //! Coef(29) * X * Y + Coef(30) * X * Z + Coef(31) * Y * Z + //! Coef(32) * X + Coef(33) * Y + Coef(34) * Z + //! Coef(35) = 0.0 //! Raises DimensionError if the length of Coef is lower than 35. Standard_EXPORT void Coefficients (TColStd_Array1OfReal& Coef) const; //! Returns the Torus's location. const gp_Pnt& Location() const; //! Returns the local coordinates system of the torus. const gp_Ax3& Position() const; //! returns the major radius of the torus. Standard_Real MajorRadius() const; //! returns the minor radius of the torus. Standard_Real MinorRadius() const; //! Computes the volume of the torus. Standard_Real Volume() const; //! returns the axis X of the torus. gp_Ax1 XAxis() const; //! returns the axis Y of the torus. gp_Ax1 YAxis() const; Standard_EXPORT void Mirror (const gp_Pnt& P); //! Performs the symmetrical transformation of a torus //! with respect to the point P which is the center of the //! symmetry. Standard_NODISCARD Standard_EXPORT gp_Torus Mirrored (const gp_Pnt& P) const; Standard_EXPORT void Mirror (const gp_Ax1& A1); //! Performs the symmetrical transformation of a torus with //! respect to an axis placement which is the axis of the //! symmetry. Standard_NODISCARD Standard_EXPORT gp_Torus Mirrored (const gp_Ax1& A1) const; Standard_EXPORT void Mirror (const gp_Ax2& A2); //! Performs the symmetrical transformation of a torus with respect //! to a plane. The axis placement A2 locates the plane of the //! of the symmetry : (Location, XDirection, YDirection). Standard_NODISCARD Standard_EXPORT gp_Torus Mirrored (const gp_Ax2& A2) const; void Rotate (const gp_Ax1& A1, const Standard_Real Ang); //! Rotates a torus. A1 is the axis of the rotation. //! Ang is the angular value of the rotation in radians. Standard_NODISCARD gp_Torus Rotated (const gp_Ax1& A1, const Standard_Real Ang) const; void Scale (const gp_Pnt& P, const Standard_Real S); //! Scales a torus. S is the scaling value. //! The absolute value of S is used to scale the torus Standard_NODISCARD gp_Torus Scaled (const gp_Pnt& P, const Standard_Real S) const; void Transform (const gp_Trsf& T); //! Transforms a torus with the transformation T from class Trsf. Standard_NODISCARD gp_Torus Transformed (const gp_Trsf& T) const; void Translate (const gp_Vec& V); //! Translates a torus in the direction of the vector V. //! The magnitude of the translation is the vector's magnitude. Standard_NODISCARD gp_Torus Translated (const gp_Vec& V) const; void Translate (const gp_Pnt& P1, const gp_Pnt& P2); //! Translates a torus from the point P1 to the point P2. Standard_NODISCARD gp_Torus Translated (const gp_Pnt& P1, const gp_Pnt& P2) const; protected: private: gp_Ax3 pos; Standard_Real majorRadius; Standard_Real minorRadius; }; #include #endif // _gp_Torus_HeaderFile