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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_Dir_HeaderFile
 #define _gp_Dir_HeaderFile
 
 #include <gp_XYZ.hxx>
 #include <Standard_ConstructionError.hxx>
 #include <Standard_DomainError.hxx>
 #include <Standard_OutOfRange.hxx>
 
 class gp_Vec;
 class gp_Ax1;
 class gp_Ax2;
 class gp_Trsf;
 
 //! Describes a unit vector in 3D space. This unit vector is also called "Direction".
 //! See Also
 //! gce_MakeDir which provides functions for more complex
 //! unit vector constructions
 //! Geom_Direction which provides additional functions for
 //! constructing unit vectors and works, in particular, with the
 //! parametric equations of unit vectors.
 class gp_Dir 
 {
 public:
 
   DEFINE_STANDARD_ALLOC
 
   //! Creates a direction corresponding to X axis.
   gp_Dir()
   : coord (1., 0., 0.)
   {}
 
   //! Normalizes the vector theV and creates a direction. Raises ConstructionError if theV.Magnitude() <= Resolution.
   gp_Dir (const gp_Vec& theV);
 
   //! Creates a direction from a triplet of coordinates. Raises ConstructionError if theCoord.Modulus() <= Resolution from gp.
   gp_Dir (const gp_XYZ& theCoord);
 
   //! Creates a direction with its 3 cartesian coordinates. Raises ConstructionError if Sqrt(theXv*theXv + theYv*theYv + theZv*theZv) <= Resolution
   //! Modification of the direction's coordinates
   //! If Sqrt (theXv*theXv + theYv*theYv + theZv*theZv) <= Resolution from gp where
   //! theXv, theYv ,theZv are the new coordinates it is not possible to
   //! construct the direction and the method raises the
   //! exception ConstructionError.
   gp_Dir (const Standard_Real theXv, const Standard_Real theYv, const Standard_Real theZv);
 
   //! For this unit vector,  assigns the value Xi to:
   //! -   the X coordinate if theIndex is 1, or
   //! -   the Y coordinate if theIndex is 2, or
   //! -   the Z coordinate if theIndex is 3,
   //! and then normalizes it.
   //! Warning
   //! Remember that all the coordinates of a unit vector are
   //! implicitly modified when any single one is changed directly.
   //! Exceptions
   //! Standard_OutOfRange if theIndex is not 1, 2, or 3.
   //! Standard_ConstructionError if either of the following
   //! is less than or equal to gp::Resolution():
   //! -   Sqrt(Xv*Xv + Yv*Yv + Zv*Zv), or
   //! -   the modulus of the number triple formed by the new
   //! value theXi and the two other coordinates of this vector
   //! that were not directly modified.
   void SetCoord (const Standard_Integer theIndex, const Standard_Real theXi);
 
   //! For this unit vector,  assigns the values theXv, theYv and theZv to its three coordinates.
   //! Remember that all the coordinates of a unit vector are
   //! implicitly modified when any single one is changed directly.
   void SetCoord (const Standard_Real theXv, const Standard_Real theYv, const Standard_Real theZv);
 
   //! Assigns the given value to the X coordinate of this   unit vector.
   void SetX (const Standard_Real theX);
 
   //! Assigns the given value to the Y coordinate of this   unit vector.
   void SetY (const Standard_Real theY);
 
   //! Assigns the given value to the Z  coordinate of this   unit vector.
   void SetZ (const Standard_Real theZ);
 
   //! Assigns the three coordinates of theCoord to this unit vector.
   void SetXYZ (const gp_XYZ& theCoord);
 
   //! Returns the coordinate of range theIndex :
   //! theIndex = 1 => X is returned
   //! Ithendex = 2 => Y is returned
   //! theIndex = 3 => Z is returned
   //! Exceptions
   //! Standard_OutOfRange if theIndex is not 1, 2, or 3.
   Standard_Real Coord (const Standard_Integer theIndex) const  { return coord.Coord (theIndex); }
 
   //! Returns for the  unit vector  its three coordinates theXv, theYv, and theZv.
   void Coord (Standard_Real& theXv, Standard_Real& theYv, Standard_Real& theZv) const  { coord.Coord (theXv, theYv, theZv); }
 
   //! Returns the X coordinate for a  unit vector.
   Standard_Real X() const { return coord.X(); }
 
   //! Returns the Y coordinate for a  unit vector.
   Standard_Real Y() const { return coord.Y(); }
 
   //! Returns the Z coordinate for a  unit vector.
   Standard_Real Z() const { return coord.Z(); }
 
   //! for this unit vector, returns  its three coordinates as a number triplea.
   const gp_XYZ& XYZ() const { return coord; }
 
   //! Returns True if the angle between the two directions is
   //! lower or equal to theAngularTolerance.
   Standard_Boolean IsEqual (const gp_Dir& theOther, const Standard_Real theAngularTolerance) const
   {
     return Angle (theOther) <= theAngularTolerance;
   }
 
   //! Returns True if  the angle between this unit vector and the unit vector theOther is equal to Pi/2 (normal).
   Standard_Boolean IsNormal (const gp_Dir& theOther, const Standard_Real theAngularTolerance) const
   {
     Standard_Real anAng = M_PI / 2.0 - Angle (theOther);
     if (anAng < 0)
     {
       anAng = -anAng;
     }
     return anAng <= theAngularTolerance;
   }
 
   //! Returns True if  the angle between this unit vector and the unit vector theOther is equal to  Pi (opposite).
   Standard_Boolean IsOpposite (const gp_Dir& theOther, const Standard_Real theAngularTolerance) const
   {
     return M_PI - Angle (theOther) <= theAngularTolerance;
   }
 
   //! Returns true if the angle between this unit vector and the
   //! unit vector theOther is equal to 0 or to Pi.
   //! Note: the tolerance criterion is given by theAngularTolerance.
   Standard_Boolean IsParallel (const gp_Dir& theOther, const Standard_Real theAngularTolerance) const
   {
     Standard_Real anAng = Angle (theOther);
     return anAng <= theAngularTolerance || M_PI - anAng <= theAngularTolerance;
   }
 
   //! Computes the angular value in radians between <me> and
   //! <theOther>. This value is always positive in 3D space.
   //! Returns the angle in the range [0, PI]
   Standard_EXPORT Standard_Real Angle (const gp_Dir& theOther) const;
 
   //! Computes the angular value between <me> and <theOther>.
   //! <theVRef> is the direction of reference normal to <me> and <theOther>
   //! and its orientation gives the positive sense of rotation.
   //! If the cross product <me> ^ <theOther> has the same orientation
   //! as <theVRef> the angular value is positive else negative.
   //! Returns the angular value in the range -PI and PI (in radians). Raises  DomainError if <me> and <theOther> are not parallel this exception is raised
   //! when <theVRef> is in the same plane as <me> and <theOther>
   //! The tolerance criterion is Resolution from package gp.
   Standard_EXPORT Standard_Real AngleWithRef (const gp_Dir& theOther, const gp_Dir& theVRef) const;
 
   //! Computes the cross product between two directions
   //! Raises the exception ConstructionError if the two directions
   //! are parallel because the computed vector cannot be normalized
   //! to create a direction.
   void Cross (const gp_Dir& theRight);
 
   void operator ^= (const gp_Dir& theRight) { Cross (theRight); }
 
   //! Computes the triple vector product.
   //! <me> ^ (V1 ^ V2)
   //! Raises the exception ConstructionError if V1 and V2 are parallel
   //! or <me> and (V1^V2) are parallel because the computed vector
   //! can't be normalized to create a direction.
   Standard_NODISCARD gp_Dir Crossed (const gp_Dir& theRight) const;
 
   Standard_NODISCARD gp_Dir operator ^ (const gp_Dir& theRight) const { return Crossed (theRight); }
 
   void CrossCross (const gp_Dir& theV1, const gp_Dir& theV2);
 
   //! Computes the double vector product this ^ (theV1 ^ theV2).
   //! -   CrossCrossed creates a new unit vector.
   //! Exceptions
   //! Standard_ConstructionError if:
   //! -   theV1 and theV2 are parallel, or
   //! -   this unit vector and (theV1 ^ theV2) are parallel.
   //! This is because, in these conditions, the computed vector
   //! is null and cannot be normalized.
   Standard_NODISCARD gp_Dir CrossCrossed (const gp_Dir& theV1, const gp_Dir& theV2) const;
 
   //! Computes the scalar product
   Standard_Real Dot (const gp_Dir& theOther) const { return coord.Dot (theOther.coord); }
 
   Standard_Real operator * (const gp_Dir& theOther) const { return Dot (theOther); }
 
   //! Computes the triple scalar product <me> * (theV1 ^ theV2).
   //! Warnings :
   //! The computed vector theV1' = theV1 ^ theV2 is not normalized
   //! to create a unitary vector. So this method never
   //! raises an exception even if theV1 and theV2 are parallel.
   Standard_Real DotCross (const gp_Dir& theV1, const gp_Dir& theV2) const
   {
     return coord.Dot (theV1.coord.Crossed (theV2.coord));
   }
 
   void Reverse() { coord.Reverse(); }
 
   //! Reverses the orientation of a direction
   //! geometric transformations
   //! Performs the symmetrical transformation of a direction
   //! with respect to the direction V which is the center of
   //! the  symmetry.]
   Standard_NODISCARD gp_Dir Reversed() const
   {
     gp_Dir aV = *this;
     aV.coord.Reverse();
     return aV;
   }
 
   Standard_NODISCARD gp_Dir operator -() const { return Reversed(); }
 
   Standard_EXPORT void Mirror (const gp_Dir& theV);
 
   //! Performs the symmetrical transformation of a direction
   //! with respect to the direction theV which is the center of
   //! the  symmetry.
   Standard_NODISCARD Standard_EXPORT gp_Dir Mirrored (const gp_Dir& theV) const;
 
   Standard_EXPORT void Mirror (const gp_Ax1& theA1);
 
   //! Performs the symmetrical transformation of a direction
   //! with respect to an axis placement which is the axis
   //! of the symmetry.
   Standard_NODISCARD Standard_EXPORT gp_Dir Mirrored (const gp_Ax1& theA1) const;
 
   Standard_EXPORT void Mirror (const gp_Ax2& theA2);
 
   //! Performs the symmetrical transformation of a direction
   //! with respect to a plane. The axis placement theA2 locates
   //! the plane of the symmetry : (Location, XDirection, YDirection).
   Standard_NODISCARD Standard_EXPORT gp_Dir Mirrored (const gp_Ax2& theA2) const;
 
   void Rotate(const gp_Ax1& theA1, const Standard_Real theAng);
 
   //! Rotates a direction. theA1 is the axis of the rotation.
   //! theAng is the angular value of the rotation in radians.
   Standard_NODISCARD gp_Dir Rotated (const gp_Ax1& theA1, const Standard_Real theAng) const
   {
     gp_Dir aV = *this;
     aV.Rotate (theA1, theAng);
     return aV;
   }
 
   Standard_EXPORT void Transform (const gp_Trsf& theT);
 
   //! Transforms a direction with a "Trsf" from gp.
   //! Warnings :
   //! If the scale factor of the "Trsf" theT is negative then the
   //! direction <me> is reversed.
   Standard_NODISCARD gp_Dir Transformed (const gp_Trsf& theT) const
   {
     gp_Dir aV = *this;
     aV.Transform (theT);
     return aV;
   }
 
   //! Dumps the content of me into the stream
   Standard_EXPORT void DumpJson (Standard_OStream& theOStream, Standard_Integer theDepth = -1) const;
 
   //! Inits the content of me from the stream
   Standard_EXPORT Standard_Boolean InitFromJson (const Standard_SStream& theSStream, Standard_Integer& theStreamPos);
 
 private:
 
   gp_XYZ coord;
 
 };
 
 #include <gp_Trsf.hxx>
 
 // =======================================================================
 // function : gp_Dir
 // purpose  :
 // =======================================================================
 inline gp_Dir::gp_Dir (const gp_Vec& theV)
 {
   const gp_XYZ& aXYZ = theV.XYZ();
   Standard_Real aX = aXYZ.X();
   Standard_Real aY = aXYZ.Y();
   Standard_Real aZ = aXYZ.Z();
   Standard_Real aD = sqrt (aX * aX + aY * aY + aZ * aZ);
   Standard_ConstructionError_Raise_if (aD <= gp::Resolution(), "gp_Dir() - input vector has zero norm");
   coord.SetX (aX / aD);
   coord.SetY (aY / aD);
   coord.SetZ (aZ / aD);
 }
 
 // =======================================================================
 // function : gp_Dir
 // purpose  :
 // =======================================================================
 inline gp_Dir::gp_Dir (const gp_XYZ& theXYZ)
 {
   Standard_Real aX = theXYZ.X();
   Standard_Real aY = theXYZ.Y();
   Standard_Real aZ = theXYZ.Z();
   Standard_Real aD = sqrt (aX * aX + aY * aY + aZ * aZ);
   Standard_ConstructionError_Raise_if (aD <= gp::Resolution(), "gp_Dir() - input vector has zero norm");
   coord.SetX (aX / aD);
   coord.SetY (aY / aD);
   coord.SetZ (aZ / aD);
 }
 
 // =======================================================================
 // function : gp_Dir
 // purpose  :
 // =======================================================================
 inline gp_Dir::gp_Dir (const Standard_Real theXv,
                        const Standard_Real theYv,
                        const Standard_Real theZv)
 {
   Standard_Real aD = sqrt (theXv * theXv + theYv * theYv + theZv * theZv);
   Standard_ConstructionError_Raise_if (aD <= gp::Resolution(), "gp_Dir() - input vector has zero norm");
   coord.SetX (theXv / aD);
   coord.SetY (theYv / aD);
   coord.SetZ (theZv / aD);
 }
 
 // =======================================================================
 // function : SetCoord
 // purpose  :
 // =======================================================================
 inline void gp_Dir::SetCoord (const Standard_Integer theIndex,
                               const Standard_Real theXi)
 {
   Standard_Real aX = coord.X();
   Standard_Real aY = coord.Y();
   Standard_Real aZ = coord.Z();
   Standard_OutOfRange_Raise_if (theIndex < 1 || theIndex > 3, "gp_Dir::SetCoord() - index is out of range [1, 3]");
   if (theIndex == 1)
   {
     aX = theXi;
   }
   else if (theIndex == 2)
   {
     aY = theXi;
   }
   else
   {
     aZ = theXi;
   }
   Standard_Real aD = sqrt (aX * aX + aY * aY + aZ * aZ);
   Standard_ConstructionError_Raise_if (aD <= gp::Resolution(), "gp_Dir::SetCoord() - result vector has zero norm");
   coord.SetX (aX / aD);
   coord.SetY (aY / aD);
   coord.SetZ (aZ / aD);
 }
 
 // =======================================================================
 // function : SetCoord
 // purpose  :
 // =======================================================================
 inline void gp_Dir::SetCoord (const Standard_Real theXv,
                               const Standard_Real theYv,
                               const Standard_Real theZv) {
   Standard_Real aD = sqrt (theXv * theXv + theYv * theYv + theZv * theZv);
   Standard_ConstructionError_Raise_if (aD <= gp::Resolution(), "gp_Dir::SetCoord() - input vector has zero norm");
   coord.SetX (theXv / aD);
   coord.SetY (theYv / aD);
   coord.SetZ (theZv / aD);
 }
 
 // =======================================================================
 // function : SetX
 // purpose  :
 // =======================================================================
 inline void gp_Dir::SetX (const Standard_Real theX)
 {
   Standard_Real anY = coord.Y();
   Standard_Real aZ = coord.Z();
   Standard_Real aD = sqrt (theX * theX + anY * anY + aZ * aZ);
   Standard_ConstructionError_Raise_if (aD <= gp::Resolution(), "gp_Dir::SetX() - result vector has zero norm");
   coord.SetX (theX / aD);
   coord.SetY (anY / aD);
   coord.SetZ (aZ / aD);
 }
 
 // =======================================================================
 // function : SetY
 // purpose  :
 // =======================================================================
 inline void gp_Dir::SetY (const Standard_Real theY)
 {
   Standard_Real aZ = coord.Z();
   Standard_Real aX = coord.X();
   Standard_Real aD = sqrt (aX * aX + theY * theY + aZ * aZ);
   Standard_ConstructionError_Raise_if (aD <= gp::Resolution(), "gp_Dir::SetY() - result vector has zero norm");
   coord.SetX (aX / aD);
   coord.SetY (theY / aD);
   coord.SetZ (aZ / aD);
 }
 
 // =======================================================================
 // function : SetZ
 // purpose  :
 // =======================================================================
 inline void gp_Dir::SetZ (const Standard_Real theZ)
 {
   Standard_Real aX = coord.X();
   Standard_Real anY = coord.Y();
   Standard_Real aD = sqrt (aX * aX + anY * anY + theZ * theZ);
   Standard_ConstructionError_Raise_if (aD <= gp::Resolution(), "gp_Dir::SetZ() - result vector has zero norm");
   coord.SetX (aX / aD);
   coord.SetY (anY / aD);
   coord.SetZ (theZ / aD);
 }
 
 // =======================================================================
 // function : SetXYZ
 // purpose  :
 // =======================================================================
 inline void gp_Dir::SetXYZ (const gp_XYZ& theXYZ)
 {
   Standard_Real aX = theXYZ.X();
   Standard_Real anY = theXYZ.Y();
   Standard_Real aZ = theXYZ.Z();
   Standard_Real aD = sqrt(aX * aX + anY * anY + aZ * aZ);
   Standard_ConstructionError_Raise_if (aD <= gp::Resolution(), "gp_Dir::SetX() - input vector has zero norm");
   coord.SetX (aX / aD);
   coord.SetY (anY / aD);
   coord.SetZ (aZ / aD);
 }
 
 // =======================================================================
 // function : Cross
 // purpose  :
 // =======================================================================
 inline void gp_Dir::Cross(const gp_Dir& theRight)
 {
   coord.Cross (theRight.coord);
   Standard_Real aD = coord.Modulus();
   Standard_ConstructionError_Raise_if (aD <= gp::Resolution(), "gp_Dir::Cross() - result vector has zero norm");
   coord.Divide (aD);
 }
 
 // =======================================================================
 // function : Crossed
 // purpose  :
 // =======================================================================
 inline gp_Dir gp_Dir::Crossed (const gp_Dir& theRight) const
 {
   gp_Dir aV = *this;
   aV.coord.Cross (theRight.coord);
   Standard_Real aD = aV.coord.Modulus();
   Standard_ConstructionError_Raise_if (aD <= gp::Resolution(), "gp_Dir::Crossed() - result vector has zero norm");
   aV.coord.Divide (aD);
   return aV;
 }
 
 // =======================================================================
 // function : CrossCross
 // purpose  :
 // =======================================================================
 inline void gp_Dir::CrossCross (const gp_Dir& theV1, const gp_Dir& theV2)
 {
   coord.CrossCross (theV1.coord, theV2.coord);
   Standard_Real aD = coord.Modulus();
   Standard_ConstructionError_Raise_if (aD <= gp::Resolution(), "gp_Dir::CrossCross() - result vector has zero norm");
   coord.Divide (aD);
 }
 
 // =======================================================================
 // function : CrossCrossed
 // purpose  :
 // =======================================================================
 inline gp_Dir gp_Dir::CrossCrossed (const gp_Dir& theV1, const gp_Dir& theV2) const
 {
   gp_Dir aV = *this;
   (aV.coord).CrossCross (theV1.coord, theV2.coord);
   Standard_Real aD = aV.coord.Modulus();
   Standard_ConstructionError_Raise_if (aD <= gp::Resolution(), "gp_Dir::CrossCrossed() - result vector has zero norm");
   aV.coord.Divide (aD);
   return aV;
 }
 
 // =======================================================================
 // function : Rotate
 // purpose  :
 // =======================================================================
 inline void gp_Dir::Rotate(const gp_Ax1& theA1, const Standard_Real theAng)
 {
   gp_Trsf aT;
   aT.SetRotation (theA1, theAng);
   coord.Multiply (aT.HVectorialPart());
 }
 
 #endif // _gp_Dir_HeaderFile

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