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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_Trsf_HeaderFile
 #define _gp_Trsf_HeaderFile
 
 #include <gp_TrsfForm.hxx>
 #include <gp_Mat.hxx>
 #include <gp_XYZ.hxx>
 #include <NCollection_Mat4.hxx>
 #include <Standard_OStream.hxx>
 #include <Standard_OutOfRange.hxx>
 #include <Standard_SStream.hxx>
 
 class gp_Pnt;
 class gp_Trsf2d;
 class gp_Ax1;
 class gp_Ax2;
 class gp_Quaternion;
 class gp_Ax3;
 class gp_Vec;
 
 // Avoid possible conflict with SetForm macro defined by windows.h
 #ifdef SetForm
 #undef SetForm
 #endif
 
 //! Defines a non-persistent transformation in 3D space.
 //! The following transformations are implemented :
 //! . Translation, Rotation, Scale
 //! . Symmetry with respect to a point, a line, a plane.
 //! Complex transformations can be obtained by combining the
 //! previous elementary transformations using the method
 //! Multiply.
 //! The transformations 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} defines the vectorial part of the
 //! transformation and T defines the translation part of the
 //! transformation.
 //! This transformation never change the nature of the objects.
 class gp_Trsf 
 {
 public:
 
   DEFINE_STANDARD_ALLOC
 
   //! Returns the identity transformation.
   gp_Trsf();
 
   //! Creates  a 3D transformation from the 2D transformation theT.
   //! The resulting transformation has a homogeneous
   //! vectorial part, V3, and a translation part, T3, built from theT:
   //! a11    a12
   //! 0             a13
   //! V3 =    a21    a22    0       T3
   //! =   a23
   //! 0    0    1.
   //! 0
   //! It also has the same scale factor as theT. This
   //! guarantees (by projection) that the transformation
   //! which would be performed by theT in a plane (2D space)
   //! is performed by the resulting transformation in the xOy
   //! plane of the 3D space, (i.e. in the plane defined by the
   //! origin (0., 0., 0.) and the vectors DX (1., 0., 0.), and DY
   //! (0., 1., 0.)). The scale factor is applied to the entire space.
   Standard_EXPORT gp_Trsf (const gp_Trsf2d& theT);
 
   //! Makes the transformation into a symmetrical transformation.
   //! theP is the center of the symmetry.
   void SetMirror (const gp_Pnt& theP);
 
   //! Makes the transformation into a symmetrical transformation.
   //! theA1 is the center of the axial symmetry.
   Standard_EXPORT void SetMirror (const gp_Ax1& theA1);
 
   //! Makes the transformation into a symmetrical transformation.
   //! theA2 is the center of the planar symmetry
   //! and defines the plane of symmetry by its origin, "X
   //! Direction" and "Y Direction".
   Standard_EXPORT void SetMirror (const gp_Ax2& theA2);
 
   //! Changes the transformation into a rotation.
   //! theA1 is the rotation axis and theAng is the angular value of the
   //! rotation in radians.
   Standard_EXPORT void SetRotation (const gp_Ax1& theA1, const Standard_Real theAng);
 
   //! Changes the transformation into a rotation defined by quaternion.
   //! Note that rotation is performed around origin, i.e.
   //! no translation is involved.
   Standard_EXPORT void SetRotation (const gp_Quaternion& theR);
 
   //! Replaces the rotation part with specified quaternion.
   Standard_EXPORT void SetRotationPart (const gp_Quaternion& theR);
 
   //! Changes the transformation into a scale.
   //! theP is the center of the scale and theS is the scaling value.
   //! Raises ConstructionError  If <theS> is null.
   Standard_EXPORT void SetScale (const gp_Pnt& theP, const Standard_Real theS);
 
   //! Modifies this transformation so that it transforms the
   //! coordinate system defined by theFromSystem1 into the
   //! one defined by theToSystem2. After this modification, this
   //! transformation transforms:
   //! -   the origin of theFromSystem1 into the origin of theToSystem2,
   //! -   the "X Direction" of theFromSystem1 into the "X
   //! Direction" of theToSystem2,
   //! -   the "Y Direction" of theFromSystem1 into the "Y
   //! Direction" of theToSystem2, and
   //! -   the "main Direction" of theFromSystem1 into the "main
   //! Direction" of theToSystem2.
   //! Warning
   //! When you know the coordinates of a point in one
   //! coordinate system and you want to express these
   //! coordinates in another one, do not use the
   //! transformation resulting from this function. Use the
   //! transformation that results from SetTransformation instead.
   //! SetDisplacement and SetTransformation create
   //! related transformations: the vectorial part of one is the
   //! inverse of the vectorial part of the other.
   Standard_EXPORT void SetDisplacement (const gp_Ax3& theFromSystem1, const gp_Ax3& theToSystem2);
 
   //! Modifies this transformation so that it transforms the
   //! coordinates of any point, (x, y, z), relative to a source
   //! coordinate system into the coordinates (x', y', z') which
   //! are relative to a target coordinate system, but which
   //! represent the same point
   //! The transformation is from the coordinate
   //! system "theFromSystem1" to the coordinate system "theToSystem2".
   //! Example :
   //! @code
   //! gp_Ax3 theFromSystem1, theToSystem2;
   //! double x1, y1, z1;  // are the coordinates of a point in the local system theFromSystem1
   //! double x2, y2, z2;  // are the coordinates of a point in the local system theToSystem2
   //! gp_Pnt P1 (x1, y1, z1)
   //! gp_Trsf T;
   //! T.SetTransformation (theFromSystem1, theToSystem2);
   //! gp_Pnt P2 = P1.Transformed (T);
   //! P2.Coord (x2, y2, z2);
   //! @endcode
   Standard_EXPORT void SetTransformation (const gp_Ax3& theFromSystem1, const gp_Ax3& theToSystem2);
 
   //! Modifies this transformation so that it transforms the
   //! coordinates of any point, (x, y, z), relative to a source
   //! coordinate system into the coordinates (x', y', z') which
   //! are relative to a target coordinate system, but which
   //! represent the same point
   //! The transformation is from the default coordinate system
   //! @code
   //! {P(0.,0.,0.), VX (1.,0.,0.), VY (0.,1.,0.), VZ (0., 0. ,1.) }
   //! @endcode
   //! to the local coordinate system defined with the Ax3 theToSystem.
   //! Use in the same way  as the previous method. FromSystem1 is
   //! defaulted to the absolute coordinate system.
   Standard_EXPORT void SetTransformation (const gp_Ax3& theToSystem);
 
   //! Sets transformation by directly specified rotation and translation.
   Standard_EXPORT void SetTransformation (const gp_Quaternion& R, const gp_Vec& theT);
 
   //! Changes the transformation into a translation.
   //! theV is the vector of the translation.
   void SetTranslation (const gp_Vec& theV);
 
   //! Makes the transformation into a translation where the translation vector
   //! is the vector (theP1, theP2) defined from point theP1 to point theP2.
   void SetTranslation (const gp_Pnt& theP1, const gp_Pnt& theP2);
 
   //! Replaces the translation vector with the vector theV.
   Standard_EXPORT void SetTranslationPart (const gp_Vec& theV);
 
   //! Modifies the scale factor.
   //! Raises ConstructionError  If theS is null.
   Standard_EXPORT void SetScaleFactor (const Standard_Real theS);
 
   void SetForm (const gp_TrsfForm theP) { shape = theP; }
 
   //! Sets the coefficients  of the transformation.  The
   //! transformation  of the  point  x,y,z is  the point
   //! x',y',z' with :
   //! @code
   //! x' = a11 x + a12 y + a13 z + a14
   //! y' = a21 x + a22 y + a23 z + a24
   //! z' = a31 x + a32 y + a33 z + a34
   //! @endcode
   //! The method Value(i,j) will return aij.
   //! Raises ConstructionError if the determinant of  the aij is null.
   //! The matrix is orthogonalized before future using.
   Standard_EXPORT void SetValues (const Standard_Real a11, const Standard_Real a12, const Standard_Real a13, const Standard_Real a14, const Standard_Real a21, const Standard_Real a22, const Standard_Real a23, const Standard_Real a24, const Standard_Real a31, const Standard_Real a32, const Standard_Real a33, const Standard_Real a34);
 
   //! Returns true if the determinant of the vectorial part of
   //! this transformation is negative.
   Standard_Boolean IsNegative() const { return (scale < 0.0); }
 
   //! 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, or a compound transformation.
   gp_TrsfForm Form() const { return shape; }
 
   //! Returns the scale factor.
   Standard_Real ScaleFactor() const { return scale; }
 
   //! Returns the translation part of the transformation's matrix
   const gp_XYZ& TranslationPart() const { return loc; }
 
   //! Returns the boolean True if there is non-zero rotation.
   //! In the presence of rotation, the output parameters store the axis
   //! and the angle of rotation. The method always returns positive
   //! value "theAngle", i.e., 0. < theAngle <= PI.
   //! Note that this rotation is defined only by the vectorial part of
   //! the transformation; generally you would need to check also the
   //! translational part to obtain the axis (gp_Ax1) of rotation.
   Standard_EXPORT Standard_Boolean GetRotation (gp_XYZ& theAxis, Standard_Real& theAngle) const;
 
   //! Returns quaternion representing rotational part of the transformation.
   Standard_EXPORT gp_Quaternion GetRotation() const;
 
   //! Returns the vectorial part of the transformation. It is
   //! a 3*3 matrix which includes the scale factor.
   Standard_EXPORT gp_Mat VectorialPart() const;
 
   //! Computes the homogeneous vectorial part of the transformation.
   //! It is a 3*3 matrix which doesn't include the scale factor.
   //! In other words, the vectorial part of this transformation is equal
   //! to its homogeneous vectorial part, multiplied by the scale factor.
   //! The coefficients of this matrix must be multiplied by the
   //! scale factor to obtain the coefficients of the transformation.
   const gp_Mat& HVectorialPart() const { return matrix; }
 
   //! Returns the coefficients of the transformation's matrix.
   //! It is a 3 rows * 4 columns matrix.
   //! This coefficient includes the scale factor.
   //! Raises OutOfRanged 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_EXPORT void Invert();
 
   //! Computes the reverse transformation
   //! Raises an exception if the matrix of the transformation
   //! is not inversible, it means that the scale factor is lower
   //! or equal to Resolution from package gp.
   //! Computes the transformation composed with T and  <me>.
   //! In a C++ implementation you can also write Tcomposed = <me> * T.
   //! Example :
   //! @code
   //! gp_Trsf T1, T2, Tcomp; ...............
   //! Tcomp = T2.Multiplied(T1);         // or   (Tcomp = T2 * T1)
   //! gp_Pnt P1(10.,3.,4.);
   //! gp_Pnt P2 = P1.Transformed(Tcomp); // using Tcomp
   //! gp_Pnt P3 = P1.Transformed(T1);    // using T1 then T2
   //! P3.Transform(T2);                  // P3 = P2 !!!
   //! @endcode
   Standard_NODISCARD gp_Trsf Inverted() const
   {
     gp_Trsf aT = *this;
     aT.Invert();
     return aT;
   }
   
   Standard_NODISCARD gp_Trsf Multiplied (const gp_Trsf& theT) const
   {
     gp_Trsf aTresult (*this);
     aTresult.Multiply (theT);
     return aTresult;
   }
 
   Standard_NODISCARD gp_Trsf operator * (const gp_Trsf& theT) const { return Multiplied (theT); }
 
   //! Computes the transformation composed with <me> and theT.
   //! <me> = <me> * theT
   Standard_EXPORT void Multiply (const gp_Trsf& theT);
 
   void operator *= (const gp_Trsf& theT) { Multiply (theT); }
 
   //! Computes the transformation composed with <me> and T.
   //! <me> = theT * <me>
   Standard_EXPORT void PreMultiply (const gp_Trsf& theT);
 
   Standard_EXPORT void Power (const Standard_Integer theN);
 
   //! Computes the following composition of transformations
   //! <me> * <me> * .......* <me>, theN time.
   //! if theN = 0 <me> = Identity
   //! if theN < 0 <me> = <me>.Inverse() *...........* <me>.Inverse().
   //!
   //! Raises if theN < 0 and if the matrix of the transformation not
   //! inversible.
   Standard_NODISCARD gp_Trsf Powered (const Standard_Integer theN) const
   {
     gp_Trsf aT = *this;
     aT.Power (theN);
     return aT;
   }
 
   void Transforms (Standard_Real& theX, Standard_Real& theY, Standard_Real& theZ) const;
 
   //! Transformation of a triplet XYZ with a Trsf
   void Transforms (gp_XYZ& theCoord) 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));
   }
 
   //! 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);
 
 friend class gp_GTrsf;
 
 protected:
 
   //! Makes orthogonalization of "matrix"
   Standard_EXPORT void Orthogonalize();
 
 private:
 
   Standard_Real scale;
   gp_TrsfForm shape;
   gp_Mat matrix;
   gp_XYZ loc;
 
 };
 
 #include <gp_Trsf2d.hxx>
 #include <gp_Vec.hxx>
 #include <gp_Pnt.hxx>
 
 //=======================================================================
 //function : gp_Trsf
 // purpose :
 //=======================================================================
 inline gp_Trsf::gp_Trsf ()
 : scale (1.0),
   shape (gp_Identity),
   matrix (1, 0, 0, 0, 1, 0, 0, 0, 1),
   loc (0.0, 0.0, 0.0)
 {}
 
 //=======================================================================
 //function : SetMirror
 // purpose :
 //=======================================================================
 inline void gp_Trsf::SetMirror (const gp_Pnt& theP)
 {
   shape = gp_PntMirror;
   scale = -1.0;
   loc = theP.XYZ();
   matrix.SetIdentity();
   loc.Multiply (2.0);
 }
 
 //=======================================================================
 //function : SetTranslation
 // purpose :
 //=======================================================================
 inline void gp_Trsf::SetTranslation (const gp_Vec& theV) 
 {
   shape = gp_Translation;
   scale = 1.;
   matrix.SetIdentity();
   loc = theV.XYZ();
 }
 
 //=======================================================================
 //function : SetTranslation
 // purpose :
 //=======================================================================
 inline void gp_Trsf::SetTranslation (const gp_Pnt& theP1,
                                      const gp_Pnt& theP2) 
 {
   shape = gp_Translation;
   scale = 1.0;
   matrix.SetIdentity();
   loc = (theP2.XYZ()).Subtracted (theP1.XYZ());
 }
 
 //=======================================================================
 //function : Value
 // purpose :
 //=======================================================================
 inline Standard_Real gp_Trsf::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 scale * matrix.Value (theRow, theCol);
   }
   else
   {
     return loc.Coord (theRow);
   }
 }
 
 //=======================================================================
 //function : Transforms
 // purpose :
 //=======================================================================
 inline void gp_Trsf::Transforms (Standard_Real& theX,
                                  Standard_Real& theY,
                                  Standard_Real& theZ) const 
 {
   gp_XYZ aTriplet (theX, theY, theZ);
   aTriplet.Multiply (matrix);
   if (scale != 1.0)
   {
     aTriplet.Multiply (scale);
   }
   aTriplet.Add (loc);
   theX = aTriplet.X();
   theY = aTriplet.Y();
   theZ = aTriplet.Z();
 }
 
 //=======================================================================
 //function : Transforms
 // purpose :
 //=======================================================================
 inline void gp_Trsf::Transforms (gp_XYZ& theCoord) const
 {
   theCoord.Multiply (matrix);
   if (scale != 1.0)
   {
     theCoord.Multiply (scale);
   }
   theCoord.Add (loc);
 }
 
 #endif // _gp_Trsf_HeaderFile

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