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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:
   //! Standard directions in 3D space for optimized constexpr construction
   enum class D
   {
     X,  //!< Direction along positive X axis (1, 0, 0)
     Y,  //!< Direction along positive Y axis (0, 1, 0)
     Z,  //!< Direction along positive Z axis (0, 0, 1)
     NX, //!< Direction along negative X axis (-1, 0, 0)
     NY, //!< Direction along negative Y axis (0, -1, 0)
     NZ  //!< Direction along negative Z axis (0, 0, -1)
   };
 
   DEFINE_STANDARD_ALLOC
 
   //! Creates a direction corresponding to X axis.
   constexpr gp_Dir() noexcept
       : coord(1., 0., 0.)
   {
   }
 
   //! Creates a direction from a standard direction enumeration.
   constexpr explicit gp_Dir(const D theDir) noexcept
       : coord(theDir == D::X    ? 1.0
               : theDir == D::NX ? -1.0
                                 : 0.0,
               theDir == D::Y    ? 1.0
               : theDir == D::NY ? -1.0
                                 : 0.0,
               theDir == D::Z    ? 1.0
               : theDir == D::NZ ? -1.0
                                 : 0.0)
   {
   }
 
   //! Normalizes the vector theV and creates a direction. Raises ConstructionError if
   //! theV.Magnitude() <= Resolution.
   //! @note Constexpr-compatible when input is already normalized.
   constexpr gp_Dir(const gp_Vec& theV);
 
   //! Creates a direction from a triplet of coordinates. Raises ConstructionError if
   //! theCoord.Modulus() <= Resolution from gp.
   //! @note Constexpr-compatible when input is already normalized.
   constexpr gp_Dir(const gp_XYZ& theCoord);
 
   //! Creates a direction with its 3 cartesian coordinates. Raises ConstructionError if
   //! std::sqrt(theXv*theXv + theYv*theYv + theZv*theZv) <= Resolution Modification of the
   //! direction's coordinates If std::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.
   //! @note Constexpr-compatible when input is already normalized.
   constexpr gp_Dir(const double theXv, const double theYv, const double theZv);
 
   constexpr gp_Dir(const gp_Dir&) noexcept = default;
   constexpr gp_Dir(gp_Dir&&) noexcept      = default;
 
   constexpr gp_Dir& operator=(const gp_Dir&) noexcept = default;
   constexpr gp_Dir& operator=(gp_Dir&&) noexcept      = default;
 
   //! 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():
   //! -   std::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.
   //! @note Constexpr-compatible when result is already normalized.
   constexpr void SetCoord(const int theIndex, const double 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.
   //! @note Constexpr-compatible when input is already normalized.
   constexpr void SetCoord(const double theXv, const double theYv, const double theZv);
 
   //! Assigns the given value to the X coordinate of this unit vector.
   //! @note Constexpr-compatible when result is already normalized.
   constexpr void SetX(const double theX);
 
   //! Assigns the given value to the Y coordinate of this unit vector.
   //! @note Constexpr-compatible when result is already normalized.
   constexpr void SetY(const double theY);
 
   //! Assigns the given value to the Z coordinate of this unit vector.
   //! @note Constexpr-compatible when result is already normalized.
   constexpr void SetZ(const double theZ);
 
   //! Assigns the three coordinates of theCoord to this unit vector.
   //! @note Constexpr-compatible when input is already normalized.
   constexpr void SetXYZ(const gp_XYZ& theCoord);
 
   //! Returns the coordinate of range theIndex :
   //! theIndex = 1 => X is returned
   //! theIndex = 2 => Y is returned
   //! theIndex = 3 => Z is returned
   //! Exceptions
   //! Standard_OutOfRange if theIndex is not 1, 2, or 3.
   constexpr double Coord(const int theIndex) const { return coord.Coord(theIndex); }
 
   //! Returns for the unit vector its three coordinates theXv, theYv, and theZv.
   constexpr void Coord(double& theXv, double& theYv, double& theZv) const noexcept
   {
     coord.Coord(theXv, theYv, theZv);
   }
 
   //! Returns the X coordinate for a unit vector.
   constexpr double X() const noexcept { return coord.X(); }
 
   //! Returns the Y coordinate for a unit vector.
   constexpr double Y() const noexcept { return coord.Y(); }
 
   //! Returns the Z coordinate for a unit vector.
   constexpr double Z() const noexcept { return coord.Z(); }
 
   //! for this unit vector, returns its three coordinates as a number triple.
   constexpr const gp_XYZ& XYZ() const noexcept { return coord; }
 
   //! Returns True if the angle between the two directions is
   //! lower or equal to theAngularTolerance.
   bool IsEqual(const gp_Dir& theOther, const double 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).
   bool IsNormal(const gp_Dir& theOther, const double theAngularTolerance) const
   {
     double 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).
   bool IsOpposite(const gp_Dir& theOther, const double 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.
   bool IsParallel(const gp_Dir& theOther, const double theAngularTolerance) const
   {
     double 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 double 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 double 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.
   //! @note Constexpr-compatible when result is already normalized.
   constexpr void Cross(const gp_Dir& theRight);
 
   constexpr 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.
   //! @note Constexpr-compatible when result is already normalized.
   [[nodiscard]] constexpr gp_Dir Crossed(const gp_Dir& theRight) const;
 
   [[nodiscard]] constexpr gp_Dir operator^(const gp_Dir& theRight) const
   {
     return Crossed(theRight);
   }
 
   //! @note Constexpr-compatible when result is already normalized.
   constexpr 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.
   //! @note Constexpr-compatible when result is already normalized.
   [[nodiscard]] constexpr gp_Dir CrossCrossed(const gp_Dir& theV1, const gp_Dir& theV2) const;
 
   //! Computes the scalar product
   constexpr double Dot(const gp_Dir& theOther) const noexcept { return coord.Dot(theOther.coord); }
 
   constexpr double operator*(const gp_Dir& theOther) const noexcept { 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.
   constexpr double DotCross(const gp_Dir& theV1, const gp_Dir& theV2) const noexcept
   {
     return coord.Dot(theV1.coord.Crossed(theV2.coord));
   }
 
   constexpr void Reverse() noexcept { 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.
   [[nodiscard]] constexpr gp_Dir Reversed() const noexcept
   {
     gp_Dir aV = *this;
     aV.coord.Reverse();
     return aV;
   }
 
   [[nodiscard]] constexpr gp_Dir operator-() const noexcept { return Reversed(); }
 
   Standard_EXPORT void Mirror(const gp_Dir& theV) noexcept;
 
   //! Performs the symmetrical transformation of a direction
   //! with respect to the direction theV which is the center
   //! of the symmetry.
   [[nodiscard]] Standard_EXPORT gp_Dir Mirrored(const gp_Dir& theV) const noexcept;
 
   Standard_EXPORT void Mirror(const gp_Ax1& theA1) noexcept;
 
   //! Performs the symmetrical transformation of a direction
   //! with respect to an axis placement which is the axis
   //! of the symmetry.
   [[nodiscard]] Standard_EXPORT gp_Dir Mirrored(const gp_Ax1& theA1) const noexcept;
 
   Standard_EXPORT void Mirror(const gp_Ax2& theA2) noexcept;
 
   //! 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).
   [[nodiscard]] Standard_EXPORT gp_Dir Mirrored(const gp_Ax2& theA2) const noexcept;
 
   void Rotate(const gp_Ax1& theA1, const double theAng);
 
   //! Rotates a direction. theA1 is the axis of the rotation.
   //! theAng is the angular value of the rotation in radians.
   [[nodiscard]] gp_Dir Rotated(const gp_Ax1& theA1, const double 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.
   [[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, int theDepth = -1) const;
 
   //! Inits the content of me from the stream
   Standard_EXPORT bool InitFromJson(const Standard_SStream& theSStream, int& theStreamPos);
 
 private:
   gp_XYZ coord;
 };
 
 #include <gp_Trsf.hxx>
 
 //=================================================================================================
 
 inline constexpr gp_Dir::gp_Dir(const gp_Vec& theV)
     : gp_Dir(theV.XYZ())
 {
 }
 
 //=================================================================================================
 
 inline constexpr gp_Dir::gp_Dir(const gp_XYZ& theXYZ)
     : gp_Dir(theXYZ.X(), theXYZ.Y(), theXYZ.Z())
 {
 }
 
 //=================================================================================================
 
 inline constexpr gp_Dir::gp_Dir(const double theXv, const double theYv, const double theZv)
 {
   const double aSqMod = theXv * theXv + theYv * theYv + theZv * theZv;
 
   // Fast path: already normalized - fully constexpr
   if (aSqMod >= (1.0 - gp::Resolution()) && aSqMod <= (1.0 + gp::Resolution()))
   {
     coord.SetCoord(theXv, theYv, theZv);
     return;
   }
 
   // Slow path: runtime only (sqrt not constexpr - compile error if reached in constexpr context)
   Standard_ConstructionError_Raise_if(aSqMod <= gp::Resolution() * gp::Resolution(),
                                       "gp_Dir() - input vector has zero norm");
   const double aD = sqrt(aSqMod);
   coord.SetCoord(theXv / aD, theYv / aD, theZv / aD);
 }
 
 //=================================================================================================
 
 inline constexpr void gp_Dir::SetCoord(const int theIndex, const double theXi)
 {
   Standard_OutOfRange_Raise_if(theIndex < 1 || theIndex > 3,
                                "gp_Dir::SetCoord() - index is out of range [1, 3]");
   if (theIndex == 1)
   {
     SetX(theXi);
   }
   else if (theIndex == 2)
   {
     SetY(theXi);
   }
   else
   {
     SetZ(theXi);
   }
 }
 
 //=================================================================================================
 
 inline constexpr void gp_Dir::SetCoord(const double theXv, const double theYv, const double theZv)
 {
   const double aSqMod = theXv * theXv + theYv * theYv + theZv * theZv;
 
   // Fast path: already normalized - fully constexpr
   if (aSqMod >= (1.0 - gp::Resolution()) && aSqMod <= (1.0 + gp::Resolution()))
   {
     coord.SetCoord(theXv, theYv, theZv);
     return;
   }
 
   // Slow path: runtime only (sqrt not constexpr - compile error if reached in constexpr context)
   Standard_ConstructionError_Raise_if(aSqMod <= gp::Resolution() * gp::Resolution(),
                                       "gp_Dir::SetCoord() - input vector has zero norm");
   const double aD = sqrt(aSqMod);
   coord.SetCoord(theXv / aD, theYv / aD, theZv / aD);
 }
 
 //=================================================================================================
 
 inline constexpr void gp_Dir::SetX(const double theX)
 {
   SetCoord(theX, coord.Y(), coord.Z());
 }
 
 //=================================================================================================
 
 inline constexpr void gp_Dir::SetY(const double theY)
 {
   SetCoord(coord.X(), theY, coord.Z());
 }
 
 //=================================================================================================
 
 inline constexpr void gp_Dir::SetZ(const double theZ)
 {
   SetCoord(coord.X(), coord.Y(), theZ);
 }
 
 //=================================================================================================
 
 inline constexpr void gp_Dir::SetXYZ(const gp_XYZ& theXYZ)
 {
   SetCoord(theXYZ.X(), theXYZ.Y(), theXYZ.Z());
 }
 
 //=================================================================================================
 
 inline constexpr void gp_Dir::Cross(const gp_Dir& theRight)
 {
   coord.Cross(theRight.coord);
   const double aSqMod = coord.SquareModulus();
 
   // Fast path: already normalized - fully constexpr
   if (aSqMod >= (1.0 - gp::Resolution()) && aSqMod <= (1.0 + gp::Resolution()))
   {
     return;
   }
 
   // Slow path: runtime only (sqrt not constexpr - compile error if reached in constexpr context)
   Standard_ConstructionError_Raise_if(aSqMod <= gp::Resolution() * gp::Resolution(),
                                       "gp_Dir::Cross() - result vector has zero norm");
   coord.Divide(sqrt(aSqMod));
 }
 
 //=================================================================================================
 
 inline constexpr gp_Dir gp_Dir::Crossed(const gp_Dir& theRight) const
 {
   gp_Dir aV = *this;
   aV.Cross(theRight);
   return aV;
 }
 
 //=================================================================================================
 
 inline constexpr void gp_Dir::CrossCross(const gp_Dir& theV1, const gp_Dir& theV2)
 {
   coord.CrossCross(theV1.coord, theV2.coord);
   const double aSqMod = coord.SquareModulus();
 
   // Fast path: already normalized - fully constexpr
   if (aSqMod >= (1.0 - gp::Resolution()) && aSqMod <= (1.0 + gp::Resolution()))
   {
     return;
   }
 
   // Slow path: runtime only (sqrt not constexpr - compile error if reached in constexpr context)
   Standard_ConstructionError_Raise_if(aSqMod <= gp::Resolution() * gp::Resolution(),
                                       "gp_Dir::CrossCross() - result vector has zero norm");
   coord.Divide(sqrt(aSqMod));
 }
 
 //=================================================================================================
 
 inline constexpr gp_Dir gp_Dir::CrossCrossed(const gp_Dir& theV1, const gp_Dir& theV2) const
 {
   gp_Dir aV = *this;
   aV.CrossCross(theV1, theV2);
   return aV;
 }
 
 //=================================================================================================
 
 inline void gp_Dir::Rotate(const gp_Ax1& theA1, const double theAng)
 {
   gp_Trsf aT;
   aT.SetRotation(theA1, theAng);
   coord.Multiply(aT.HVectorialPart());
 }
 
 #endif // _gp_Dir_HeaderFile

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