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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_Trsf2d_HeaderFile
 #define _gp_Trsf2d_HeaderFile
 
 #include <gp_TrsfForm.hxx>
 #include <gp_Mat2d.hxx>
 #include <gp_XY.hxx>
 #include <Standard_OutOfRange.hxx>
 
 class gp_Trsf;
 class gp_Pnt2d;
 class gp_Ax2d;
 class gp_Vec2d;
 
 //! Defines a non-persistent transformation in 2D space.
 //! The following transformations are implemented :
 //! - Translation, Rotation, Scale
 //! - Symmetry with respect to a point and a line.
 //! 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   T       XY        XY
 //! | a11  a12  a13 |   | x |     | x'|
 //! | a21  a22  a23 |   | y |     | y'|
 //! |  0    0    1  |   | 1 |     | 1 |
 //! @endcode
 //! where {V1, V2} 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_Trsf2d
 {
 public:
   DEFINE_STANDARD_ALLOC
 
   //! Returns identity transformation.
   constexpr gp_Trsf2d() noexcept;
 
   //! Creates a 2d transformation in the XY plane from a
   //! 3d transformation .
   gp_Trsf2d(const gp_Trsf& theT);
 
   //! Changes the transformation into a symmetrical transformation.
   //! theP is the center of the symmetry.
   void SetMirror(const gp_Pnt2d& theP) noexcept;
 
   //! Changes the transformation into a symmetrical transformation.
   //! theA is the center of the axial symmetry.
   Standard_EXPORT void SetMirror(const gp_Ax2d& theA) noexcept;
 
   //! Changes the transformation into a rotation.
   //! theP is the rotation's center and theAng is the angular value of the
   //! rotation in radian.
   void SetRotation(const gp_Pnt2d& theP, const double theAng);
 
   //! Changes the transformation into a scale.
   //! theP is the center of the scale and theS is the scaling value.
   void SetScale(const gp_Pnt2d& theP, const double theS);
 
   //! Changes a transformation allowing passage from the coordinate
   //! system "theFromSystem1" to the coordinate system "theToSystem2".
   Standard_EXPORT void SetTransformation(const gp_Ax2d& theFromSystem1,
                                          const gp_Ax2d& theToSystem2);
 
   //! Changes the transformation allowing passage from the basic
   //! coordinate system
   //! {P(0.,0.,0.), VX (1.,0.,0.), VY (0.,1.,0.)}
   //! to the local coordinate system defined with the Ax2d theToSystem.
   Standard_EXPORT void SetTransformation(const gp_Ax2d& theToSystem);
 
   //! Changes the transformation into a translation.
   //! theV is the vector of the translation.
   void SetTranslation(const gp_Vec2d& theV);
 
   //! Makes the transformation into a translation from
   //! the point theP1 to the point theP2.
   void SetTranslation(const gp_Pnt2d& theP1, const gp_Pnt2d& theP2);
 
   //! Replaces the translation vector with theV.
   Standard_EXPORT void SetTranslationPart(const gp_Vec2d& theV);
 
   //! Modifies the scale factor.
   Standard_EXPORT void SetScaleFactor(const double theS);
 
   //! Returns true if the determinant of the vectorial part of
   //! this transformation is negative..
   constexpr bool IsNegative() const noexcept { return (matrix.Determinant() < 0.0); }
 
   //! Returns the nature of the transformation. It can be an
   //! identity transformation, a rotation, a translation, a mirror
   //! (relative to a point or an axis), a scaling transformation,
   //! or a compound transformation.
   constexpr gp_TrsfForm Form() const noexcept { return shape; }
 
   //! Returns the scale factor.
   constexpr double ScaleFactor() const noexcept { return scale; }
 
   //! Returns the translation part of the transformation's matrix
   constexpr const gp_XY& TranslationPart() const noexcept { return loc; }
 
   //! Returns the vectorial part of the transformation. It is a
   //! 2*2 matrix which includes the scale factor.
   Standard_EXPORT gp_Mat2d VectorialPart() const;
 
   //! Returns the homogeneous vectorial part of the transformation.
   //! It is a 2*2 matrix which doesn't include the scale factor.
   //! The coefficients of this matrix must be multiplied by the
   //! scale factor to obtain the coefficients of the transformation.
   constexpr const gp_Mat2d& HVectorialPart() const noexcept { return matrix; }
 
   //! Returns the angle corresponding to the rotational component
   //! of the transformation matrix (operation opposite to SetRotation()).
   Standard_EXPORT double RotationPart() const;
 
   //! Returns the coefficients of the transformation's matrix.
   //! It is a 2 rows * 3 columns matrix.
   //! Raises OutOfRange if theRow < 1 or theRow > 2 or theCol < 1 or theCol > 3
   constexpr double Value(const int theRow, const int 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.
   [[nodiscard]] gp_Trsf2d Inverted() const
   {
     gp_Trsf2d aT = *this;
     aT.Invert();
     return aT;
   }
 
   [[nodiscard]] gp_Trsf2d Multiplied(const gp_Trsf2d& theT) const
   {
     gp_Trsf2d aTresult(*this);
     aTresult.Multiply(theT);
     return aTresult;
   }
 
   [[nodiscard]] gp_Trsf2d operator*(const gp_Trsf2d& theT) const { return Multiplied(theT); }
 
   //! Computes the transformation composed from <me> and theT.
   //! <me> = <me> * theT
   Standard_EXPORT void Multiply(const gp_Trsf2d& theT);
 
   void operator*=(const gp_Trsf2d& theT) { Multiply(theT); }
 
   //! Computes the transformation composed from <me> and theT.
   //! <me> = theT * <me>
   Standard_EXPORT void PreMultiply(const gp_Trsf2d& theT);
 
   Standard_EXPORT void Power(const int 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.
   gp_Trsf2d Powered(const int theN)
   {
     gp_Trsf2d aT = *this;
     aT.Power(theN);
     return aT;
   }
 
   constexpr void Transforms(double& theX, double& theY) const noexcept;
 
   //! Transforms a doublet XY with a Trsf2d
   constexpr void Transforms(gp_XY& theCoord) const noexcept;
 
   //! Sets the coefficients of the transformation. The
   //! transformation of the point x,y is the point
   //! x',y' with :
   //! @code
   //! x' = a11 x + a12 y + a13
   //! y' = a21 x + a22 y + a23
   //! @endcode
   //! The method Value(i,j) will return aij.
   //! Raises ConstructionError if the determinant of the aij is null.
   //! If the matrix as not a uniform scale it will be orthogonalized before future using.
   Standard_EXPORT void SetValues(const double a11,
                                  const double a12,
                                  const double a13,
                                  const double a21,
                                  const double a22,
                                  const double a23);
 
   friend class gp_GTrsf2d;
 
 protected:
   //! Makes orthogonalization of "matrix"
   Standard_EXPORT void Orthogonalize();
 
 private:
   double      scale;
   gp_TrsfForm shape;
   gp_Mat2d    matrix;
   gp_XY       loc;
 };
 
 #include <gp_Trsf.hxx>
 #include <gp_Pnt2d.hxx>
 
 //=================================================================================================
 
 inline constexpr gp_Trsf2d::gp_Trsf2d() noexcept
     : scale(1.0),
       shape(gp_Identity),
 
       loc(0.0, 0.0)
 {
   matrix.SetIdentity();
 }
 
 //=================================================================================================
 
 inline gp_Trsf2d::gp_Trsf2d(const gp_Trsf& theT)
     : scale(theT.ScaleFactor()),
       shape(theT.Form()),
       loc(theT.TranslationPart().X(), theT.TranslationPart().Y())
 {
   const gp_Mat& M = theT.HVectorialPart();
   matrix(1, 1)    = M(1, 1);
   matrix(1, 2)    = M(1, 2);
   matrix(2, 1)    = M(2, 1);
   matrix(2, 2)    = M(2, 2);
 }
 
 //=================================================================================================
 
 inline void gp_Trsf2d::SetRotation(const gp_Pnt2d& theP, const double theAng)
 {
   shape = gp_Rotation;
   scale = 1.0;
   loc   = theP.XY();
   loc.Reverse();
   matrix.SetRotation(theAng);
   loc.Multiply(matrix);
   loc.Add(theP.XY());
 }
 
 //=================================================================================================
 
 inline void gp_Trsf2d::SetMirror(const gp_Pnt2d& theP) noexcept
 {
   shape = gp_PntMirror;
   scale = -1.0;
   matrix.SetIdentity();
   loc = theP.XY();
   loc.Multiply(2.0);
 }
 
 //=================================================================================================
 
 inline void gp_Trsf2d::SetScale(const gp_Pnt2d& theP, const double theS)
 {
   shape = gp_Scale;
   scale = theS;
   matrix.SetIdentity();
   loc = theP.XY();
   loc.Multiply(1.0 - theS);
 }
 
 //=================================================================================================
 
 inline void gp_Trsf2d::SetTranslation(const gp_Vec2d& theV)
 {
   shape = gp_Translation;
   scale = 1.0;
   matrix.SetIdentity();
   loc = theV.XY();
 }
 
 //=================================================================================================
 
 inline void gp_Trsf2d::SetTranslation(const gp_Pnt2d& theP1, const gp_Pnt2d& theP2)
 {
   shape = gp_Translation;
   scale = 1.0;
   matrix.SetIdentity();
   loc = (theP2.XY()).Subtracted(theP1.XY());
 }
 
 //=================================================================================================
 
 inline constexpr double gp_Trsf2d::Value(const int theRow, const int theCol) const
 {
   Standard_OutOfRange_Raise_if(theRow < 1 || theRow > 2 || theCol < 1 || theCol > 3, " ");
   if (theCol < 3)
   {
     return scale * matrix.myMat[theRow - 1][theCol - 1];
   }
   else
   {
     return loc.Coord(theRow);
   }
 }
 
 //=================================================================================================
 
 inline constexpr void gp_Trsf2d::Transforms(double& theX, double& theY) const noexcept
 {
   gp_XY aDoublet(theX, theY);
   aDoublet.Multiply(matrix);
   if (scale != 1.0)
   {
     aDoublet.Multiply(scale);
   }
   aDoublet.Add(loc);
   aDoublet.Coord(theX, theY);
 }
 
 //=================================================================================================
 
 inline constexpr void gp_Trsf2d::Transforms(gp_XY& theCoord) const noexcept
 {
   theCoord.Multiply(matrix);
   if (scale != 1.0)
   {
     theCoord.Multiply(scale);
   }
   theCoord.Add(loc);
 }
 
 #endif // _gp_Trsf2d_HeaderFile

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