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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_Ax2_HeaderFile
 #define _gp_Ax2_HeaderFile
 
 #include <gp_Ax1.hxx>
 #include <gp_Dir.hxx>
 #include <Precision.hxx>
 
 class gp_Trsf;
 class gp_Vec;
 
 //! Describes a right-handed coordinate system in 3D space.
 //! A coordinate system is defined by:
 //! -   its origin (also referred to as its "Location point"), and
 //! -   three orthogonal unit vectors, termed respectively the
 //! "X Direction", the "Y Direction" and the "Direction" (also
 //! referred to as the "main Direction").
 //! The "Direction" of the coordinate system is called its
 //! "main Direction" because whenever this unit vector is
 //! modified, the "X Direction" and the "Y Direction" are
 //! recomputed. However, when we modify either the "X
 //! Direction" or the "Y Direction", "Direction" is not modified.
 //! The "main Direction" is also the "Z Direction".
 //! Since an Ax2 coordinate system is right-handed, its
 //! "main Direction" is always equal to the cross product of
 //! its "X Direction" and "Y Direction". (To define a
 //! left-handed coordinate system, use gp_Ax3.)
 //! A coordinate system is used:
 //! -   to describe geometric entities, in particular to position
 //! them. The local coordinate system of a geometric
 //! entity serves the same purpose as the STEP function
 //! "axis placement two axes", or
 //! -   to define geometric transformations.
 //! Note: we refer to the "X Axis", "Y Axis" and "Z Axis",
 //! respectively, as to axes having:
 //! - the origin of the coordinate system as their origin, and
 //! -   the unit vectors "X Direction", "Y Direction" and "main
 //! Direction", respectively, as their unit vectors.
 //! The "Z Axis" is also the "main Axis".
 class gp_Ax2
 {
 public:
   DEFINE_STANDARD_ALLOC
 
   //! Creates an object corresponding to the reference
   //! coordinate system (OXYZ).
   constexpr gp_Ax2() noexcept
       : vydir(gp_Dir::D::Y),
         vxdir(gp_Dir::D::X)
   // axis uses default ctor which creates Z axis at origin
   {
   }
 
   //! Creates an axis placement with an origin P such that:
   //! -   N is the Direction, and
   //! -   the "X Direction" is normal to N, in the plane
   //! defined by the vectors (N, Vx): "X
   //! Direction" = (N ^ Vx) ^ N,
   //! Exception: raises ConstructionError if N and Vx are parallel (same or opposite orientation).
   gp_Ax2(const gp_Pnt& P, const gp_Dir& N, const gp_Dir& Vx)
       : axis(P, N),
         vydir(N),
         vxdir(N)
   {
     vxdir.CrossCross(Vx, N);
     vydir.Cross(vxdir);
   }
 
   //! Creates an axis placement with standard directions.
   constexpr gp_Ax2(const gp_Pnt& theP, const gp_Dir::D theN, const gp_Dir::D theVx) noexcept
       : axis(theP, theN),
         vydir(crossStandardDir(theN, theVx)), // Y = Z x X (right-handed)
         vxdir(theVx)
   {
     // Note: For standard directions, cross product is computed at compile time
     // This constructor assumes theN and theVx are orthogonal standard directions
   }
 
   //! Creates a coordinate system with an origin P, where V
   //! gives the "main Direction" (here, "X Direction" and "Y
   //! Direction" are defined automatically).
   Standard_EXPORT gp_Ax2(const gp_Pnt& P, const gp_Dir& V);
 
   //! Creates a coordinate system with an origin P and standard main direction.
   constexpr gp_Ax2(const gp_Pnt& theP, const gp_Dir::D theV) noexcept
       : axis(theP, theV),
         vydir(getPerpendicularYDir(theV)),
         vxdir(getPerpendicularXDir(theV))
   {
   }
 
   //! Creates a coordinate system at the origin with the given standard main direction.
   //! Replaces gp::XOY(), gp::YOZ(), gp::ZOX() static functions.
   constexpr explicit gp_Ax2(const gp_Dir::D theV) noexcept
       : axis(gp_Pnt(0., 0., 0.), theV),
         vydir(getPerpendicularYDir(theV)),
         vxdir(getPerpendicularXDir(theV))
   {
   }
 
   //! Assigns the origin and "main Direction" of the axis A1 to
   //! this coordinate system, then recomputes its "X Direction" and "Y Direction".
   //! Note: The new "X Direction" is computed as follows:
   //! new "X Direction" = V1 ^(previous "X Direction" ^ V)
   //! where V is the "Direction" of A1.
   //! Exceptions
   //! Standard_ConstructionError if A1 is parallel to the "X
   //! Direction" of this coordinate system.
   void SetAxis(const gp_Ax1& A1);
 
   //! Changes the "main Direction" of this coordinate system,
   //! then recomputes its "X Direction" and "Y Direction".
   //! Note: the new "X Direction" is computed as follows:
   //! new "X Direction" = V ^ (previous "X Direction" ^ V)
   //! Exceptions
   //! Standard_ConstructionError if V is parallel to the "X
   //! Direction" of this coordinate system.
   void SetDirection(const gp_Dir& V);
 
   //! Changes the "Location" point (origin) of <me>.
   constexpr void SetLocation(const gp_Pnt& theP) noexcept { axis.SetLocation(theP); }
 
   //! Changes the "Xdirection" of <me>. The main direction
   //! "Direction" is not modified, the "Ydirection" is modified.
   //! If <Vx> is not normal to the main direction then <XDirection>
   //! is computed as follows XDirection = Direction ^ (Vx ^ Direction).
   //! Exceptions
   //! Standard_ConstructionError if Vx or Vy is parallel to
   //! the "main Direction" of this coordinate system.
   void SetXDirection(const gp_Dir& theVx)
   {
     vxdir = axis.Direction().CrossCrossed(theVx, axis.Direction());
     vydir = axis.Direction().Crossed(vxdir);
   }
 
   //! Changes the "Ydirection" of <me>. The main direction is not
   //! modified but the "Xdirection" is changed.
   //! If <Vy> is not normal to the main direction then "YDirection"
   //! is computed as follows
   //! YDirection = Direction ^ (<Vy> ^ Direction).
   //! Exceptions
   //! Standard_ConstructionError if Vx or Vy is parallel to
   //! the "main Direction" of this coordinate system.
   void SetYDirection(const gp_Dir& theVy)
   {
     vxdir = theVy.Crossed(axis.Direction());
     vydir = (axis.Direction()).Crossed(vxdir);
   }
 
   //! Computes the angular value, in radians, between the main direction of
   //! <me> and the main direction of <theOther>. Returns the angle
   //! between 0 and PI in radians.
   double Angle(const gp_Ax2& theOther) const { return axis.Angle(theOther.axis); }
 
   //! Returns the main axis of <me>. It is the "Location" point
   //! and the main "Direction".
   constexpr const gp_Ax1& Axis() const noexcept { return axis; }
 
   //! Returns the main direction of <me>.
   constexpr const gp_Dir& Direction() const noexcept { return axis.Direction(); }
 
   //! Returns the "Location" point (origin) of <me>.
   constexpr const gp_Pnt& Location() const noexcept { return axis.Location(); }
 
   //! Returns the "XDirection" of <me>.
   constexpr const gp_Dir& XDirection() const noexcept { return vxdir; }
 
   //! Returns the "YDirection" of <me>.
   constexpr const gp_Dir& YDirection() const noexcept { return vydir; }
 
   bool IsCoplanar(const gp_Ax2& Other,
                   const double  LinearTolerance,
                   const double  AngularTolerance) const;
 
   //! Returns True if:
   //! . the distance between <me> and the "Location" point of A1
   //! is lower of equal to LinearTolerance and
   //! . the main direction of <me> and the direction of A1 are normal.
   //! Note: the tolerance criterion for angular equality is given by AngularTolerance.
   bool IsCoplanar(const gp_Ax1& A1,
                   const double  LinearTolerance,
                   const double  AngularTolerance) const;
 
   //! Performs a symmetrical transformation of this coordinate
   //! system with respect to:
   //! -   the point P, and assigns the result to this coordinate system.
   //! Warning
   //! This transformation is always performed on the origin.
   //! In case of a reflection with respect to a point:
   //! - the main direction of the coordinate system is not changed, and
   //! - the "X Direction" and the "Y Direction" are simply reversed
   //! In case of a reflection with respect to an axis or a plane:
   //! -   the transformation is applied to the "X Direction"
   //! and the "Y Direction", then
   //! -   the "main Direction" is recomputed as the cross
   //! product "X Direction" ^ "Y Direction".
   //! This maintains the right-handed property of the
   //! coordinate system.
   Standard_EXPORT void Mirror(const gp_Pnt& P) noexcept;
 
   //! Performs a symmetrical transformation of this coordinate
   //! system with respect to:
   //! -   the point P, and creates a new one.
   //! Warning
   //! This transformation is always performed on the origin.
   //! In case of a reflection with respect to a point:
   //! - the main direction of the coordinate system is not changed, and
   //! - the "X Direction" and the "Y Direction" are simply reversed
   //! In case of a reflection with respect to an axis or a plane:
   //! -   the transformation is applied to the "X Direction"
   //! and the "Y Direction", then
   //! -   the "main Direction" is recomputed as the cross
   //! product "X Direction" ^ "Y Direction".
   //! This maintains the right-handed property of the
   //! coordinate system.
   [[nodiscard]] Standard_EXPORT gp_Ax2 Mirrored(const gp_Pnt& P) const noexcept;
 
   //! Performs a symmetrical transformation of this coordinate
   //! system with respect to:
   //! -   the axis A1, and assigns the result to this coordinate system.
   //! Warning
   //! This transformation is always performed on the origin.
   //! In case of a reflection with respect to a point:
   //! - the main direction of the coordinate system is not changed, and
   //! - the "X Direction" and the "Y Direction" are simply reversed
   //! In case of a reflection with respect to an axis or a plane:
   //! -   the transformation is applied to the "X Direction"
   //! and the "Y Direction", then
   //! -   the "main Direction" is recomputed as the cross
   //! product "X Direction" ^ "Y Direction".
   //! This maintains the right-handed property of the
   //! coordinate system.
   Standard_EXPORT void Mirror(const gp_Ax1& A1);
 
   //! Performs a symmetrical transformation of this coordinate
   //! system with respect to:
   //! -   the axis A1, and creates a new one.
   //! Warning
   //! This transformation is always performed on the origin.
   //! In case of a reflection with respect to a point:
   //! - the main direction of the coordinate system is not changed, and
   //! - the "X Direction" and the "Y Direction" are simply reversed
   //! In case of a reflection with respect to an axis or a plane:
   //! -   the transformation is applied to the "X Direction"
   //! and the "Y Direction", then
   //! -   the "main Direction" is recomputed as the cross
   //! product "X Direction" ^ "Y Direction".
   //! This maintains the right-handed property of the
   //! coordinate system.
   [[nodiscard]] Standard_EXPORT gp_Ax2 Mirrored(const gp_Ax1& A1) const;
 
   //! Performs a symmetrical transformation of this coordinate
   //! system with respect to:
   //! -   the plane defined by the origin, "X Direction" and "Y
   //! Direction" of coordinate system A2 and assigns the result to this coordinate system.
   //! Warning
   //! This transformation is always performed on the origin.
   //! In case of a reflection with respect to a point:
   //! - the main direction of the coordinate system is not changed, and
   //! - the "X Direction" and the "Y Direction" are simply reversed
   //! In case of a reflection with respect to an axis or a plane:
   //! -   the transformation is applied to the "X Direction"
   //! and the "Y Direction", then
   //! -   the "main Direction" is recomputed as the cross
   //! product "X Direction" ^ "Y Direction".
   //! This maintains the right-handed property of the
   //! coordinate system.
   Standard_EXPORT void Mirror(const gp_Ax2& A2);
 
   //! Performs a symmetrical transformation of this coordinate
   //! system with respect to:
   //! -   the plane defined by the origin, "X Direction" and "Y
   //! Direction" of coordinate system A2 and creates a new one.
   //! Warning
   //! This transformation is always performed on the origin.
   //! In case of a reflection with respect to a point:
   //! - the main direction of the coordinate system is not changed, and
   //! - the "X Direction" and the "Y Direction" are simply reversed
   //! In case of a reflection with respect to an axis or a plane:
   //! -   the transformation is applied to the "X Direction"
   //! and the "Y Direction", then
   //! -   the "main Direction" is recomputed as the cross
   //! product "X Direction" ^ "Y Direction".
   //! This maintains the right-handed property of the
   //! coordinate system.
   [[nodiscard]] Standard_EXPORT gp_Ax2 Mirrored(const gp_Ax2& A2) const;
 
   void Rotate(const gp_Ax1& theA1, const double theAng)
   {
     gp_Pnt aTemp = axis.Location();
     aTemp.Rotate(theA1, theAng);
     axis.SetLocation(aTemp);
     vxdir.Rotate(theA1, theAng);
     vydir.Rotate(theA1, theAng);
     axis.SetDirection(vxdir.Crossed(vydir));
   }
 
   //! Rotates an axis placement. <theA1> is the axis of the rotation.
   //! theAng is the angular value of the rotation in radians.
   [[nodiscard]] gp_Ax2 Rotated(const gp_Ax1& theA1, const double theAng) const
   {
     gp_Ax2 aTemp = *this;
     aTemp.Rotate(theA1, theAng);
     return aTemp;
   }
 
   constexpr void Scale(const gp_Pnt& theP, const double theS) noexcept
   {
     gp_Pnt aTemp = axis.Location();
     aTemp.Scale(theP, theS);
     axis.SetLocation(aTemp);
     if (theS < 0.0)
     {
       vxdir.Reverse();
       vydir.Reverse();
     }
   }
 
   //! Applies a scaling transformation on the axis placement.
   //! The "Location" point of the axisplacement is modified.
   //! Warnings:
   //! If the scale <S> is negative:
   //! . the main direction of the axis placement is not changed.
   //! . The "XDirection" and the "YDirection" are reversed.
   //! So the axis placement stay right handed.
   [[nodiscard]] constexpr gp_Ax2 Scaled(const gp_Pnt& theP, const double theS) const noexcept
   {
     gp_Ax2 aTemp = *this;
     aTemp.Scale(theP, theS);
     return aTemp;
   }
 
   void Transform(const gp_Trsf& theT)
   {
     gp_Pnt aTemp = axis.Location();
     aTemp.Transform(theT);
     axis.SetLocation(aTemp);
     vxdir.Transform(theT);
     vydir.Transform(theT);
     axis.SetDirection(vxdir.Crossed(vydir));
   }
 
   //! Transforms an axis placement with a Trsf.
   //! The "Location" point, the "XDirection" and the "YDirection" are transformed with theT.
   //! The resulting main "Direction" of <me> is the cross product between
   //! the "XDirection" and the "YDirection" after transformation.
   [[nodiscard]] gp_Ax2 Transformed(const gp_Trsf& theT) const
   {
     gp_Ax2 aTemp = *this;
     aTemp.Transform(theT);
     return aTemp;
   }
 
   constexpr void Translate(const gp_Vec& theV) noexcept { axis.Translate(theV); }
 
   //! Translates an axis plaxement in the direction of the vector <theV>.
   //! The magnitude of the translation is the vector's magnitude.
   [[nodiscard]] constexpr gp_Ax2 Translated(const gp_Vec& theV) const noexcept
   {
     gp_Ax2 aTemp = *this;
     aTemp.Translate(theV);
     return aTemp;
   }
 
   constexpr void Translate(const gp_Pnt& theP1, const gp_Pnt& theP2) noexcept
   {
     axis.Translate(theP1, theP2);
   }
 
   //! Translates an axis placement from the point <theP1> to the point <theP2>.
   [[nodiscard]] constexpr gp_Ax2 Translated(const gp_Pnt& theP1, const gp_Pnt& theP2) const noexcept
   {
     gp_Ax2 aTemp = *this;
     aTemp.Translate(theP1, theP2);
     return aTemp;
   }
 
   //! 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);
 
 protected:
   //! Helper to compute perpendicular X direction for standard main directions
   static constexpr gp_Dir::D getPerpendicularXDir(const gp_Dir::D theMainDir) noexcept;
 
   //! Helper to compute Y direction (main x X) for standard directions
   static constexpr gp_Dir::D getPerpendicularYDir(const gp_Dir::D theMainDir) noexcept;
 
   //! Helper to compute cross product of two standard directions (right-handed: A x B)
   static constexpr gp_Dir::D crossStandardDir(const gp_Dir::D theA, const gp_Dir::D theB) noexcept;
 
 private:
   gp_Ax1 axis;
   gp_Dir vydir;
   gp_Dir vxdir;
 };
 
 //=================================================================================================
 
 inline constexpr gp_Dir::D gp_Ax2::getPerpendicularXDir(const gp_Dir::D theMainDir) noexcept
 {
   return (theMainDir == gp_Dir::D::X || theMainDir == gp_Dir::D::NX)   ? gp_Dir::D::Y
          : (theMainDir == gp_Dir::D::Y || theMainDir == gp_Dir::D::NY) ? gp_Dir::D::Z
                                                                        : gp_Dir::D::X;
 }
 
 //=================================================================================================
 
 inline constexpr gp_Dir::D gp_Ax2::getPerpendicularYDir(const gp_Dir::D theMainDir) noexcept
 {
   return (theMainDir == gp_Dir::D::Z)    ? gp_Dir::D::Y
          : (theMainDir == gp_Dir::D::NZ) ? gp_Dir::D::NY
          : (theMainDir == gp_Dir::D::X)  ? gp_Dir::D::Z
          : (theMainDir == gp_Dir::D::NX) ? gp_Dir::D::NZ
          : (theMainDir == gp_Dir::D::Y)  ? gp_Dir::D::X
                                          : gp_Dir::D::NX; // NY case
 }
 
 //=================================================================================================
 
 inline constexpr gp_Dir::D gp_Ax2::crossStandardDir(const gp_Dir::D theA,
                                                     const gp_Dir::D theB) noexcept
 {
   // Handle positive directions first
   if (theA == gp_Dir::D::X)
   {
     if (theB == gp_Dir::D::Y)
       return gp_Dir::D::Z;
     if (theB == gp_Dir::D::Z)
       return gp_Dir::D::NY;
     if (theB == gp_Dir::D::NY)
       return gp_Dir::D::NZ;
     if (theB == gp_Dir::D::NZ)
       return gp_Dir::D::Y;
     // X x X = 0, X x NX = 0 (parallel, should not happen)
     return gp_Dir::D::Z; // fallback
   }
   if (theA == gp_Dir::D::Y)
   {
     if (theB == gp_Dir::D::Z)
       return gp_Dir::D::X;
     if (theB == gp_Dir::D::X)
       return gp_Dir::D::NZ;
     if (theB == gp_Dir::D::NX)
       return gp_Dir::D::Z;
     if (theB == gp_Dir::D::NZ)
       return gp_Dir::D::NX;
     // Y x Y = 0, Y x NY = 0 (parallel, should not happen)
     return gp_Dir::D::X; // fallback
   }
   if (theA == gp_Dir::D::Z)
   {
     if (theB == gp_Dir::D::X)
       return gp_Dir::D::Y;
     if (theB == gp_Dir::D::Y)
       return gp_Dir::D::NX;
     if (theB == gp_Dir::D::NX)
       return gp_Dir::D::NY;
     if (theB == gp_Dir::D::NY)
       return gp_Dir::D::X;
     // Z x Z = 0, Z x NZ = 0 (parallel, should not happen)
     return gp_Dir::D::Y; // fallback
   }
   // Handle negative directions: -A x B = -(A x B)
   if (theA == gp_Dir::D::NX)
   {
     if (theB == gp_Dir::D::Y)
       return gp_Dir::D::NZ;
     if (theB == gp_Dir::D::Z)
       return gp_Dir::D::Y;
     if (theB == gp_Dir::D::NY)
       return gp_Dir::D::Z;
     if (theB == gp_Dir::D::NZ)
       return gp_Dir::D::NY;
     return gp_Dir::D::NZ; // fallback
   }
   if (theA == gp_Dir::D::NY)
   {
     if (theB == gp_Dir::D::Z)
       return gp_Dir::D::NX;
     if (theB == gp_Dir::D::X)
       return gp_Dir::D::Z;
     if (theB == gp_Dir::D::NX)
       return gp_Dir::D::NZ;
     if (theB == gp_Dir::D::NZ)
       return gp_Dir::D::X;
     return gp_Dir::D::NX; // fallback
   }
   if (theA == gp_Dir::D::NZ)
   {
     if (theB == gp_Dir::D::X)
       return gp_Dir::D::NY;
     if (theB == gp_Dir::D::Y)
       return gp_Dir::D::X;
     if (theB == gp_Dir::D::NX)
       return gp_Dir::D::Y;
     if (theB == gp_Dir::D::NY)
       return gp_Dir::D::NX;
     return gp_Dir::D::NY; // fallback
   }
   return gp_Dir::D::Z; // fallback
 }
 
 //=================================================================================================
 
 inline void gp_Ax2::SetAxis(const gp_Ax1& theA1)
 {
   double a = theA1.Direction() * vxdir;
   if (std::abs(std::abs(a) - 1.) <= Precision::Angular())
   {
     if (a > 0.)
     {
       vxdir = vydir;
       vydir = axis.Direction();
       axis  = theA1;
     }
     else
     {
       vxdir = axis.Direction();
       axis  = theA1;
     }
   }
   else
   {
     axis  = theA1;
     vxdir = axis.Direction().CrossCrossed(vxdir, axis.Direction());
     vydir = axis.Direction().Crossed(vxdir);
   }
 }
 
 //=================================================================================================
 
 inline void gp_Ax2::SetDirection(const gp_Dir& theV)
 {
   double a = theV * vxdir;
   if (std::abs(std::abs(a) - 1.) <= Precision::Angular())
   {
     if (a > 0.)
     {
       vxdir = vydir;
       vydir = axis.Direction();
       axis.SetDirection(theV);
     }
     else
     {
       vxdir = axis.Direction();
       axis.SetDirection(theV);
     }
   }
   else
   {
     axis.SetDirection(theV);
     vxdir = theV.CrossCrossed(vxdir, theV);
     vydir = theV.Crossed(vxdir);
   }
 }
 
 //=================================================================================================
 
 inline bool gp_Ax2::IsCoplanar(const gp_Ax2& theOther,
                                const double  theLinearTolerance,
                                const double  theAngularTolerance) const
 {
   const gp_Dir& DD = axis.Direction();
   const gp_Pnt& PP = axis.Location();
   const gp_Pnt& OP = theOther.axis.Location();
   double        D1 =
     (DD.X() * (OP.X() - PP.X()) + DD.Y() * (OP.Y() - PP.Y()) + DD.Z() * (OP.Z() - PP.Z()));
   if (D1 < 0)
   {
     D1 = -D1;
   }
   return D1 <= theLinearTolerance && axis.IsParallel(theOther.axis, theAngularTolerance);
 }
 
 //=================================================================================================
 
 inline bool gp_Ax2::IsCoplanar(const gp_Ax1& theA,
                                const double  theLinearTolerance,
                                const double  theAngularTolerance) const
 {
   const gp_Dir& DD = axis.Direction();
   const gp_Pnt& PP = axis.Location();
   const gp_Pnt& AP = theA.Location();
   double        D1 =
     (DD.X() * (AP.X() - PP.X()) + DD.Y() * (AP.Y() - PP.Y()) + DD.Z() * (AP.Z() - PP.Z()));
   if (D1 < 0)
   {
     D1 = -D1;
   }
   return D1 <= theLinearTolerance && axis.IsNormal(theA, theAngularTolerance);
 }
 
 #endif // _gp_Ax2_HeaderFile

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