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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).
   gp_Ax2() : vydir(0.,1.,0.)
   // vxdir(1.,0.,0.) use default ctor of gp_Dir, as it creates the same dir(1,0,0)
   {}
 
   //! 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 -   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);
 
   //! 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>.
   void SetLocation (const gp_Pnt& theP) { 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.
   Standard_Real 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".
   const gp_Ax1& Axis() const { return axis; }
 
   //! Returns the main direction of <me>.
   const gp_Dir& Direction() const { return axis.Direction(); }
 
   //! Returns the "Location" point (origin) of <me>.
   const gp_Pnt& Location() const { return axis.Location(); }
 
   //! Returns the "XDirection" of <me>.
   const gp_Dir& XDirection() const { return vxdir; }
 
   //! Returns the "YDirection" of <me>.
   const gp_Dir& YDirection() const { return vydir; }
 
   Standard_Boolean IsCoplanar (const gp_Ax2& Other, const Standard_Real LinearTolerance, const Standard_Real 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.
   Standard_Boolean IsCoplanar (const gp_Ax1& A1, const Standard_Real LinearTolerance, const Standard_Real 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);
 
   //! 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.
   Standard_NODISCARD Standard_EXPORT gp_Ax2 Mirrored (const gp_Pnt& P) const;
 
   //! Performs a symmetrical transformation of this coordinate
   //! system with respect to:
   //! -   the axis A1, and assigns the result to this coordinate systeme.
   //! 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.
   Standard_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 systeme.
   //! 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.
   Standard_NODISCARD Standard_EXPORT gp_Ax2 Mirrored (const gp_Ax2& A2) const;
 
   void Rotate (const gp_Ax1& theA1, const Standard_Real 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.
   Standard_NODISCARD gp_Ax2 Rotated (const gp_Ax1& theA1, const Standard_Real theAng) const
   {
     gp_Ax2 aTemp = *this;
     aTemp.Rotate (theA1, theAng);
     return aTemp;
   } 
 
   void Scale (const gp_Pnt& theP, const Standard_Real theS)
   {
     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.
   Standard_NODISCARD gp_Ax2 Scaled (const gp_Pnt& theP, const Standard_Real theS) const
   {
     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.
   Standard_NODISCARD gp_Ax2 Transformed (const gp_Trsf& theT) const
   {
     gp_Ax2 aTemp = *this;
     aTemp.Transform (theT);
     return aTemp;
   }
   
   void Translate (const gp_Vec& theV) { axis.Translate (theV); }
 
   //! Translates an axis plaxement in the direction of the vector <theV>.
   //! The magnitude of the translation is the vector's magnitude.
   Standard_NODISCARD gp_Ax2 Translated (const gp_Vec& theV) const
   {
     gp_Ax2 aTemp = *this;
     aTemp.Translate (theV);
     return aTemp;
   }
 
   void Translate (const gp_Pnt& theP1, const gp_Pnt& theP2) { axis.Translate (theP1, theP2); }
 
   //! Translates an axis placement from the point <theP1> to the point <theP2>.
   Standard_NODISCARD gp_Ax2 Translated (const gp_Pnt& theP1, const gp_Pnt& theP2) const
   {
     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, 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_Ax1 axis;
   gp_Dir vydir;
   gp_Dir vxdir;
 
 };
 
 // =======================================================================
 // function : SetAxis
 // purpose  :
 // =======================================================================
 inline void gp_Ax2::SetAxis (const gp_Ax1& theA1)
 {
   Standard_Real a =  theA1.Direction() * vxdir;
   if (Abs(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);
   }
 }
 
 // =======================================================================
 // function : SetDirection
 // purpose  :
 // =======================================================================
 inline void gp_Ax2::SetDirection (const gp_Dir& theV)
 { 
   Standard_Real a =  theV * vxdir;
   if (Abs(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);
   }
 }
 
 // =======================================================================
 // function : IsCoplanar
 // purpose  :
 // =======================================================================
 inline Standard_Boolean gp_Ax2::IsCoplanar (const gp_Ax2& theOther,
                                             const Standard_Real theLinearTolerance,
                                             const Standard_Real theAngularTolerance) const
 {
   const gp_Dir& DD =          axis.Direction();
   const gp_Pnt& PP =          axis.Location();
   const gp_Pnt& OP = theOther.axis.Location();
   Standard_Real 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);
 }
 
 // =======================================================================
 // function : IsCoplanar
 // purpose  :
 // =======================================================================
 inline Standard_Boolean gp_Ax2::IsCoplanar (const gp_Ax1& theA,
                                             const Standard_Real theLinearTolerance,
                                             const Standard_Real theAngularTolerance) const
 {
   const gp_Dir& DD = axis.Direction();
   const gp_Pnt& PP = axis.Location();
   const gp_Pnt& AP = theA.Location();
   Standard_Real 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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