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 // 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 <gp_Ax1.hxx>
 #include <gp_Ax3.hxx>
 #include <Standard_ConstructionError.hxx>
 #include <TColStd_Array1OfReal.hxx>
 
 //! 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()
   : majorRadius (RealLast()),
     minorRadius (RealSmall())
   {}
 
   //! a torus centered on the origin of coordinate system
   //! theA3, with major radius theMajorRadius and minor radius
   //! theMinorRadius, and with the reference plane defined
   //! by the origin, the "X Direction" and the "Y Direction" of theA3.
   //! Warnings :
   //! It is not forbidden to create a torus with
   //! theMajorRadius = theMinorRadius = 0.0
   //! Raises ConstructionError if theMinorRadius < 0.0 or if theMajorRadius < 0.0
   gp_Torus (const gp_Ax3& theA3, const Standard_Real theMajorRadius, const Standard_Real theMinorRadius)
   : pos (theA3),
     majorRadius (theMajorRadius),
     minorRadius (theMinorRadius)
   {
     Standard_ConstructionError_Raise_if (theMinorRadius < 0.0 || theMajorRadius < 0.0,
       "gp_Torus() - invalid construction parameters");
   }
 
   //! Modifies this torus, by redefining its local coordinate
   //! system so that:
   //! -   its origin and "main Direction" become those of the
   //! axis theA1 (the "X Direction" and "Y Direction" are then recomputed).
   //! Raises ConstructionError if the direction of theA1 is parallel to the "XDirection"
   //! of the coordinate system of the toroidal surface.
   void SetAxis (const gp_Ax1& theA1) { pos.SetAxis (theA1); }
 
   //! Changes the location of the torus.
   void SetLocation (const gp_Pnt& theLoc) { pos.SetLocation (theLoc); }
 
   //! Assigns value to the major radius  of this torus.
   //! Raises ConstructionError if theMajorRadius - MinorRadius <= Resolution()
   void SetMajorRadius (const Standard_Real theMajorRadius)
   {
     Standard_ConstructionError_Raise_if (theMajorRadius - minorRadius <= gp::Resolution(),
                                          "gp_Torus::SetMajorRadius() - invalid input parameters");
     majorRadius = theMajorRadius;
   }
 
   //! Assigns value to the  minor radius of this torus.
   //! Raises ConstructionError if theMinorRadius < 0.0 or if
   //! MajorRadius - theMinorRadius <= Resolution from gp.
   void SetMinorRadius (const Standard_Real theMinorRadius)
   {
     Standard_ConstructionError_Raise_if (theMinorRadius < 0.0 || majorRadius - theMinorRadius <= gp::Resolution(),
                                          "gp_Torus::SetMinorRadius() - invalid input parameters");
     minorRadius = theMinorRadius;
   }
 
   //! Changes the local coordinate system of the surface.
   void SetPosition (const gp_Ax3& theA3) { pos = theA3; }
 
   //! Computes the area of the torus.
   Standard_Real Area() const { return 4.0 * M_PI * M_PI * minorRadius * majorRadius; }
 
   //! Reverses the   U   parametrization of   the  torus
   //! reversing the YAxis.
   void UReverse() { pos.YReverse(); }
 
   //! Reverses the   V   parametrization of   the  torus
   //! reversing the ZAxis.
   void VReverse() { pos.ZReverse(); }
 
   //! returns true if the Ax3, the local coordinate system of this torus, is right handed.
   Standard_Boolean Direct() const { return pos.Direct(); }
 
   //! returns the symmetry axis of the torus.
   const gp_Ax1& Axis() const { return pos.Axis(); }
 
   //! Computes the coefficients of the implicit equation of the surface
   //! in the absolute Cartesian coordinate system:
   //! @code
   //!     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
   //! @endcode
   //! Raises DimensionError if the length of theCoef is lower than 35.
   Standard_EXPORT void Coefficients (TColStd_Array1OfReal& theCoef) const;
 
   //! Returns the Torus's location.
   const gp_Pnt& Location() const { return pos.Location(); }
 
   //! Returns the local coordinates system of the torus.
   const gp_Ax3& Position() const { return pos; }
 
   //! returns the major radius of the torus.
   Standard_Real MajorRadius() const { return majorRadius; }
 
   //! returns the minor radius of the torus.
   Standard_Real MinorRadius() const { return minorRadius; }
 
   //! Computes the volume of the torus.
   Standard_Real Volume() const
   {
     return (M_PI * minorRadius * minorRadius) * (2.0 * M_PI * majorRadius);
   }
 
   //! returns the axis X of the torus.
   gp_Ax1 XAxis() const
   {
     return gp_Ax1 (pos.Location(), pos.XDirection());
   }
 
   //! returns the axis Y of the torus.
   gp_Ax1 YAxis() const
   {
     return gp_Ax1 (pos.Location(), pos.YDirection());
   }
 
   Standard_EXPORT void Mirror (const gp_Pnt& theP);
 
   //! Performs the symmetrical transformation of a torus
   //! with respect to the point theP which is the center of the
   //! symmetry.
   Standard_NODISCARD Standard_EXPORT gp_Torus Mirrored (const gp_Pnt& theP) const;
 
   Standard_EXPORT void Mirror (const gp_Ax1& theA1);
 
   //! 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& theA1) const;
 
   Standard_EXPORT void Mirror (const gp_Ax2& theA2);
 
   //! Performs the symmetrical transformation of a torus with respect
   //! to a plane. The axis placement theA2 locates the plane of the
   //! of the symmetry : (Location, XDirection, YDirection).
   Standard_NODISCARD Standard_EXPORT gp_Torus Mirrored (const gp_Ax2& theA2) const;
 
   void Rotate (const gp_Ax1& theA1, const Standard_Real theAng) { pos.Rotate (theA1, theAng); }
 
   //! Rotates a torus. theA1 is the axis of the rotation.
   //! theAng is the angular value of the rotation in radians.
   Standard_NODISCARD gp_Torus Rotated (const gp_Ax1& theA1, const Standard_Real theAng) const
   {
     gp_Torus aC = *this;
     aC.pos.Rotate (theA1, theAng);
     return aC;
   }
 
   void Scale (const gp_Pnt& theP, const Standard_Real theS);
 
   //! 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& theP, const Standard_Real theS) const;
 
   void Transform (const gp_Trsf& theT);
 
   //! Transforms a torus with the transformation theT from class Trsf.
   Standard_NODISCARD gp_Torus Transformed (const gp_Trsf& theT) const;
 
   void Translate (const gp_Vec& theV) { pos.Translate (theV); }
 
   //! Translates a torus in the direction of the vector theV.
   //! The magnitude of the translation is the vector's magnitude.
   Standard_NODISCARD gp_Torus Translated (const gp_Vec& theV) const
   {
     gp_Torus aC = *this;
     aC.pos.Translate (theV);
     return aC;
   }
 
   void Translate (const gp_Pnt& theP1, const gp_Pnt& theP2) { pos.Translate (theP1, theP2); }
 
   //! Translates a torus from the point theP1 to the point theP2.
   Standard_NODISCARD gp_Torus Translated (const gp_Pnt& theP1, const gp_Pnt& theP2) const
   {
     gp_Torus aC = *this;
     aC.pos.Translate (theP1, theP2);
     return aC;
   }
 
 private:
 
   gp_Ax3 pos;
   Standard_Real majorRadius;
   Standard_Real minorRadius;
 
 };
 
 //=======================================================================
 //function : Scale
 // purpose :
 //=======================================================================
 inline void gp_Torus::Scale (const gp_Pnt& theP,
                              const Standard_Real theS)
 {
   pos.Scale (theP, theS);
   Standard_Real s = theS;
   if (s < 0)
   {
     s = -s;
   }
   majorRadius *= s;
   minorRadius *= s;
 }
 
 //=======================================================================
 //function : Scaled
 // purpose :
 //=======================================================================
 inline gp_Torus gp_Torus::Scaled (const gp_Pnt& theP,
                                   const Standard_Real theS) const
 {
   gp_Torus aC = *this;
   aC.pos.Scale (theP, theS);
   aC.majorRadius *= theS;
   if (aC.majorRadius < 0)
   {
     aC.majorRadius = -aC.majorRadius;
   }
   aC.minorRadius *= theS;
   if (aC.minorRadius < 0)
   {
     aC.minorRadius = -aC.minorRadius;
   }
   return aC;
 }
 
 //=======================================================================
 //function : Transform
 // purpose :
 //=======================================================================
 inline void gp_Torus::Transform (const gp_Trsf& theT)
 {
   pos.Transform (theT);
   Standard_Real aT = theT.ScaleFactor();
   if (aT < 0)
   {
     aT = -aT;
   }
   minorRadius *= aT;
   majorRadius *= aT;
 }
 
 //=======================================================================
 //function : Transformed
 // purpose :
 //=======================================================================
 inline gp_Torus gp_Torus::Transformed (const gp_Trsf& theT) const
 {
   gp_Torus aC = *this;
   aC.pos.Transform (theT);
   aC.majorRadius *= theT.ScaleFactor();
   if (aC.majorRadius < 0)
   {
     aC.majorRadius = -aC.majorRadius;
   }
   aC.minorRadius *= theT.ScaleFactor();
   if (aC.minorRadius < 0)
   {
     aC.minorRadius = -aC.minorRadius;
   }
   return aC;
 }
 
 #endif // _gp_Torus_HeaderFile

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