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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_GTrsf_HeaderFile
 #define _gp_GTrsf_HeaderFile
 
 #include <gp_Ax1.hxx>
 #include <gp_Ax2.hxx>
 #include <gp_Mat.hxx>
 #include <gp_Trsf.hxx>
 #include <gp_TrsfForm.hxx>
 #include <gp_XYZ.hxx>
 #include <Standard_ConstructionError.hxx>
 #include <Standard_OutOfRange.hxx>
 
 
 // Avoid possible conflict with SetForm macro defined by windows.h
 #ifdef SetForm
 #undef SetForm
 #endif
 
 //! Defines a non-persistent transformation in 3D space.
 //! This transformation is a general transformation.
 //! It can be a gp_Trsf, an affinity, or you can define
 //! your own transformation giving the matrix of transformation.
 //!
 //! With a gp_GTrsf you can transform only a triplet of coordinates gp_XYZ.
 //! It is not possible to transform other geometric objects
 //! because these transformations can change the nature of non-elementary geometric objects.
 //! The transformation gp_GTrsf can be represented as follow:
 //! @code
 //!    V1   V2   V3    T       XYZ        XYZ
 //! | a11  a12  a13   a14 |   | x |      | x'|
 //! | a21  a22  a23   a24 |   | y |      | y'|
 //! | a31  a32  a33   a34 |   | z |   =  | z'|
 //! |  0    0    0     1  |   | 1 |      | 1 |
 //! @endcode
 //! where {V1, V2, V3} define the vectorial part of the
 //! transformation and T defines the translation part of the transformation.
 //! Warning
 //! A gp_GTrsf transformation is only applicable to coordinates.
 //! Be careful if you apply such a transformation to all points of a geometric object,
 //! as this can change the nature of the object and thus render it incoherent!
 //! Typically, a circle is transformed into an ellipse by an affinity transformation.
 //! To avoid modifying the nature of an object, use a gp_Trsf transformation instead,
 //! as objects of this class respect the nature of geometric objects.
 class gp_GTrsf 
 {
 public:
 
   DEFINE_STANDARD_ALLOC
 
   //! Returns the Identity transformation.
   gp_GTrsf()
   {
     shape = gp_Identity;
     matrix.SetScale (1.0);
     loc.SetCoord (0.0, 0.0, 0.0);
     scale = 1.0;
   }
 
   //! Converts the gp_Trsf transformation theT into a
   //! general transformation, i.e. Returns a GTrsf with
   //! the same matrix of coefficients as the Trsf theT.
   gp_GTrsf (const gp_Trsf& theT)
   {
     shape = theT.Form();
     matrix = theT.matrix;
     loc = theT.TranslationPart();
     scale = theT.ScaleFactor();
   }
 
   //! Creates a transformation based on the matrix theM and the
   //! vector theV where theM defines the vectorial part of
   //! the transformation, and V the translation part, or
   gp_GTrsf (const gp_Mat& theM, const gp_XYZ& theV)
   : matrix (theM),
     loc (theV)
   {
     shape = gp_Other;
     scale = 0.0;
   }
 
   //! Changes this transformation into an affinity of ratio theRatio
   //! with respect to the axis theA1.
   //! Note: an affinity is a point-by-point transformation that
   //! transforms any point P into a point P' such that if H is
   //! the orthogonal projection of P on the axis theA1 or the
   //! plane A2, the vectors HP and HP' satisfy:
   //! HP' = theRatio * HP.
   void SetAffinity (const gp_Ax1& theA1, const Standard_Real theRatio);
 
   //! Changes this transformation into an affinity of ratio theRatio
   //! with respect to  the plane defined by the origin, the "X Direction" and
   //! the "Y Direction" of coordinate system theA2.
   //! Note: an affinity is a point-by-point transformation that
   //! transforms any point P into a point P' such that if H is
   //! the orthogonal projection of P on the axis A1 or the
   //! plane theA2, the vectors HP and HP' satisfy:
   //! HP' = theRatio * HP.
   void SetAffinity (const gp_Ax2& theA2, const Standard_Real theRatio);
 
   //! Replaces  the coefficient (theRow, theCol) of the matrix representing
   //! this transformation by theValue.  Raises OutOfRange
   //! if  theRow < 1 or theRow > 3 or theCol < 1 or theCol > 4
   void SetValue (const Standard_Integer theRow, const Standard_Integer theCol, const Standard_Real theValue);
 
   //! Replaces the vectorial part of this transformation by theMatrix.
   void SetVectorialPart (const gp_Mat& theMatrix)
   {
     matrix = theMatrix;
     shape = gp_Other;
     scale = 0.0;
   }
 
   //! Replaces the translation part of
   //! this transformation by the coordinates of the number triple theCoord.
   Standard_EXPORT void SetTranslationPart (const gp_XYZ& theCoord);
 
   //! Assigns the vectorial and translation parts of theT to this transformation.
   void SetTrsf (const gp_Trsf& theT)
   {
     shape = theT.shape;
     matrix = theT.matrix;
     loc = theT.loc;
     scale = theT.scale;
   }
 
   //! Returns true if the determinant of the vectorial part of
   //! this transformation is negative.
   Standard_Boolean IsNegative() const { return matrix.Determinant() < 0.0; }
 
   //! Returns true if this transformation is singular (and
   //! therefore, cannot be inverted).
   //! Note: The Gauss LU decomposition is used to invert the
   //! transformation matrix. Consequently, the transformation
   //! is considered as singular if the largest pivot found is less
   //! than or equal to gp::Resolution().
   //! Warning
   //! If this transformation is singular, it cannot be inverted.
   Standard_Boolean IsSingular() const { return matrix.IsSingular(); }
 
   //! Returns the nature of the transformation.  It can be an
   //! identity transformation, a rotation, a translation, a mirror
   //! transformation (relative to a point, an axis or a plane), a
   //! scaling transformation, a compound transformation or
   //! some other type of transformation.
   gp_TrsfForm Form() const { return shape; }
 
   //! verify and set the shape of the GTrsf Other or CompoundTrsf
   //! Ex :
   //! @code
   //! myGTrsf.SetValue(row1,col1,val1);
   //! myGTrsf.SetValue(row2,col2,val2);
   //! ...
   //! myGTrsf.SetForm();
   //! @endcode
   Standard_EXPORT void SetForm();
 
   //! Returns the translation part of the GTrsf.
   const gp_XYZ& TranslationPart() const { return loc; }
 
   //! Computes the vectorial part of the GTrsf. The returned Matrix
   //! is a  3*3 matrix.
   const gp_Mat& VectorialPart() const { return matrix; }
 
   //! Returns the coefficients of the global matrix of transformation.
   //! Raises OutOfRange if theRow < 1 or theRow > 3 or theCol < 1 or theCol > 4
   Standard_Real Value (const Standard_Integer theRow, const Standard_Integer theCol) const;
 
   Standard_Real operator() (const Standard_Integer theRow, const Standard_Integer theCol) const { return Value (theRow, theCol); }
 
   Standard_EXPORT void Invert();
 
   //! Computes the reverse transformation.
   //! Raises an exception if the matrix of the transformation
   //! is not inversible.
   Standard_NODISCARD gp_GTrsf Inverted() const
   {
     gp_GTrsf aT = *this;
     aT.Invert();
     return aT;
   }
 
   //! Computes the transformation composed from theT and <me>.
   //! In a C++ implementation you can also write Tcomposed = <me> * theT.
   //! Example :
   //! @code
   //! gp_GTrsf T1, T2, Tcomp; ...............
   //! //composition :
   //! Tcomp = T2.Multiplied(T1);         // or   (Tcomp = T2 * T1)
   //! // transformation of a point
   //! gp_XYZ P(10.,3.,4.);
   //! gp_XYZ P1(P);
   //! Tcomp.Transforms(P1);               //using Tcomp
   //! gp_XYZ P2(P);
   //! T1.Transforms(P2);                  //using T1 then T2
   //! T2.Transforms(P2);                  // P1 = P2 !!!
   //! @endcode
   Standard_NODISCARD gp_GTrsf Multiplied (const gp_GTrsf& theT) const
    {
     gp_GTrsf aTres = *this;
     aTres.Multiply (theT);
     return aTres;
   }
 
   Standard_NODISCARD gp_GTrsf operator * (const gp_GTrsf& theT)  const { return Multiplied (theT); }
 
   //! Computes the transformation composed with <me> and theT.
   //! <me> = <me> * theT
   Standard_EXPORT void Multiply (const gp_GTrsf& theT);
 
   void operator *= (const gp_GTrsf& theT) { Multiply (theT); }
 
   //! Computes the product of the transformation theT and this
   //! transformation and assigns the result to this transformation.
   //! this = theT * this
   Standard_EXPORT void PreMultiply (const gp_GTrsf& theT);
 
   Standard_EXPORT void Power (const Standard_Integer theN);
 
   //! Computes:
   //! -   the product of this transformation multiplied by itself
   //! theN times, if theN is positive, or
   //! -   the product of the inverse of this transformation
   //! multiplied by itself |theN| times, if theN is negative.
   //! If theN equals zero, the result is equal to the Identity
   //! transformation.
   //! I.e.:  <me> * <me> * .......* <me>, theN time.
   //! if theN =0 <me> = Identity
   //! if theN < 0 <me> = <me>.Inverse() *...........* <me>.Inverse().
   //!
   //! Raises an exception if N < 0 and if the matrix of the
   //! transformation not inversible.
   Standard_NODISCARD gp_GTrsf Powered (const Standard_Integer theN) const
   {
     gp_GTrsf aT = *this;
     aT.Power (theN);
     return aT;
   }
 
   void Transforms (gp_XYZ& theCoord) const;
 
   //! Transforms a triplet XYZ with a GTrsf.
   void Transforms (Standard_Real& theX, Standard_Real& theY, Standard_Real& theZ) const;
 
   gp_Trsf Trsf() const;
 
   //! Convert transformation to 4x4 matrix.
   template<class T>
   void GetMat4 (NCollection_Mat4<T>& theMat) const
   {
     if (shape == gp_Identity)
     {
       theMat.InitIdentity();
       return;
     }
 
     theMat.SetValue (0, 0, static_cast<T> (Value (1, 1)));
     theMat.SetValue (0, 1, static_cast<T> (Value (1, 2)));
     theMat.SetValue (0, 2, static_cast<T> (Value (1, 3)));
     theMat.SetValue (0, 3, static_cast<T> (Value (1, 4)));
     theMat.SetValue (1, 0, static_cast<T> (Value (2, 1)));
     theMat.SetValue (1, 1, static_cast<T> (Value (2, 2)));
     theMat.SetValue (1, 2, static_cast<T> (Value (2, 3)));
     theMat.SetValue (1, 3, static_cast<T> (Value (2, 4)));
     theMat.SetValue (2, 0, static_cast<T> (Value (3, 1)));
     theMat.SetValue (2, 1, static_cast<T> (Value (3, 2)));
     theMat.SetValue (2, 2, static_cast<T> (Value (3, 3)));
     theMat.SetValue (2, 3, static_cast<T> (Value (3, 4)));
     theMat.SetValue (3, 0, static_cast<T> (0));
     theMat.SetValue (3, 1, static_cast<T> (0));
     theMat.SetValue (3, 2, static_cast<T> (0));
     theMat.SetValue (3, 3, static_cast<T> (1));
   }
 
   //! Convert transformation from 4x4 matrix.
   template<class T>
   void SetMat4 (const NCollection_Mat4<T>& theMat)
   {
     shape = gp_Other;
     scale = 0.0;
     matrix.SetValue (1, 1, theMat.GetValue (0, 0));
     matrix.SetValue (1, 2, theMat.GetValue (0, 1));
     matrix.SetValue (1, 3, theMat.GetValue (0, 2));
     matrix.SetValue (2, 1, theMat.GetValue (1, 0));
     matrix.SetValue (2, 2, theMat.GetValue (1, 1));
     matrix.SetValue (2, 3, theMat.GetValue (1, 2));
     matrix.SetValue (3, 1, theMat.GetValue (2, 0));
     matrix.SetValue (3, 2, theMat.GetValue (2, 1));
     matrix.SetValue (3, 3, theMat.GetValue (2, 2));
     loc.SetCoord (theMat.GetValue (0, 3), theMat.GetValue (1, 3), theMat.GetValue (2, 3));
   }
 
   //! Dumps the content of me into the stream
   Standard_EXPORT void DumpJson (Standard_OStream& theOStream, Standard_Integer theDepth = -1) const;
 
 private:
 
   gp_Mat matrix;
   gp_XYZ loc;
   gp_TrsfForm shape;
   Standard_Real scale;
 
 };
 
 
 //=======================================================================
 //function : SetAffinity
 // purpose :
 //=======================================================================
 inline void gp_GTrsf::SetAffinity (const gp_Ax1& theA1, const Standard_Real theRatio)
 {
   shape = gp_Other;
   scale = 0.0;
   matrix.SetDot (theA1.Direction().XYZ());
   matrix.Multiply (1.0 - theRatio);
   matrix.SetDiagonal (matrix.Value (1,1) + theRatio,
                       matrix.Value (2,2) + theRatio,
                       matrix.Value (3,3) + theRatio);
   loc = theA1.Location().XYZ();
   loc.Reverse ();
   loc.Multiply (matrix);
   loc.Add (theA1.Location().XYZ());
 }
 
 //=======================================================================
 //function : SetAffinity
 // purpose :
 //=======================================================================
 inline void gp_GTrsf::SetAffinity (const gp_Ax2& theA2, const Standard_Real theRatio)
 {
   shape = gp_Other;
   scale = 0.0;
   matrix.SetDot (theA2.Direction().XYZ());
   matrix.Multiply (theRatio - 1.);
   loc = theA2.Location().XYZ();
   loc.Reverse ();
   loc.Multiply (matrix);
   matrix.SetDiagonal (matrix.Value (1,1) + 1.,
                       matrix.Value (2,2) + 1.,
                       matrix.Value (3,3) + 1.);
 }
 
 //=======================================================================
 //function : SetValue
 // purpose :
 //=======================================================================
 inline void gp_GTrsf::SetValue (const Standard_Integer theRow,
                                 const Standard_Integer theCol,
                                 const Standard_Real theValue)
 {
   Standard_OutOfRange_Raise_if
     (theRow < 1 || theRow > 3 || theCol < 1 || theCol > 4, " ");
   if (theCol == 4)
   {
     loc.SetCoord (theRow, theValue);
     if (shape == gp_Identity)
     {
       shape = gp_Translation;
     }
     return;
   }
   else
   {
     if (!(shape == gp_Other) && !(scale == 1.0))
     {
       matrix.Multiply (scale);
     }
     matrix.SetValue (theRow, theCol, theValue);
     shape = gp_Other;
     scale = 0.0;
     return;
   }
 }
 
 //=======================================================================
 //function : Value
 // purpose :
 //=======================================================================
 inline Standard_Real gp_GTrsf::Value (const Standard_Integer theRow,
                                       const Standard_Integer theCol) const
 {
   Standard_OutOfRange_Raise_if
     (theRow < 1 || theRow > 3 || theCol < 1 || theCol > 4, " ");
   if (theCol == 4)
   {
     return loc.Coord (theRow);
   }
   if (shape == gp_Other)
   {
     return matrix.Value (theRow, theCol);
   }
   return scale * matrix.Value (theRow, theCol);
 }
 
 //=======================================================================
 //function : Transforms
 // purpose :
 //=======================================================================
 inline void gp_GTrsf::Transforms (gp_XYZ& theCoord) const
 {
   theCoord.Multiply (matrix);
   if (!(shape == gp_Other) && !(scale == 1.0))
   {
     theCoord.Multiply (scale);
   }
   theCoord.Add (loc);
 }
 
 //=======================================================================
 //function : Transforms
 // purpose :
 //=======================================================================
 inline void gp_GTrsf::Transforms (Standard_Real& theX, Standard_Real& theY, Standard_Real& theZ) const
 {
   gp_XYZ aTriplet (theX, theY, theZ);
   aTriplet.Multiply (matrix);
   if (!(shape == gp_Other) && !(scale == 1.0))
   {
     aTriplet.Multiply (scale);
   }
   aTriplet.Add (loc);
   aTriplet.Coord (theX, theY, theZ);
 }
 
 //=======================================================================
 //function : Trsf
 // purpose :
 //=======================================================================
 inline gp_Trsf gp_GTrsf::Trsf() const
 {
   if (Form() == gp_Other)
   {
     throw Standard_ConstructionError("gp_GTrsf::Trsf() - non-orthogonal GTrsf");
   }
   gp_Trsf aT;
   aT.shape = shape;
   aT.scale = scale;
   aT.matrix = matrix;
   aT.loc = loc;
   return aT;
 }
 
 #endif // _gp_GTrsf_HeaderFile

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