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 // Created on: 2015-06-18
 // Created by: Anton POLETAEV
 // Copyright (c) 2015 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 _Graphic3d_TransformPers_HeaderFile
 #define _Graphic3d_TransformPers_HeaderFile
 
 #include <Aspect_TypeOfTriedronPosition.hxx>
 #include <BVH_Box.hxx>
 #include <Graphic3d_Camera.hxx>
 #include <Graphic3d_TransformUtils.hxx>
 #include <Graphic3d_TransModeFlags.hxx>
 #include <Graphic3d_Vec.hxx>
 #include <NCollection_Mat4.hxx>
 
 DEFINE_STANDARD_HANDLE(Graphic3d_TransformPers, Standard_Transient)
 
 //! Transformation Persistence definition.
 //!
 //! Transformation Persistence defines a mutable Local Coordinate system which depends on camera position,
 //! so that visual appearance of the object becomes partially immutable while camera moves.
 //! Object visually preserves particular property such as size, placement, rotation or their combination.
 //!
 //! Graphic3d_TMF_ZoomPers, Graphic3d_TMF_RotatePers and Graphic3d_TMF_ZoomRotatePers define Local Coordinate system
 //! having origin in specified anchor point defined in World Coordinate system,
 //! while Graphic3d_TMF_TriedronPers and Graphic3d_TMF_2d define origin as 2D offset from screen corner in pixels.
 //!
 //! Graphic3d_TMF_2d, Graphic3d_TMF_TriedronPers and Graphic3d_TMF_ZoomPers defines Local Coordinate system where length units are pixels.
 //! Beware that Graphic3d_RenderingParams::ResolutionRatio() will be ignored!
 //! For other Persistence flags, normal (world) length units will apply.
 //!
 //! WARNING: Graphic3d_TMF_None is not permitted for defining instance of this class - NULL handle should be used for this purpose!
 class Graphic3d_TransformPers : public Standard_Transient
 {
   DEFINE_STANDARD_RTTIEXT(Graphic3d_TransformPers, Standard_Transient)
 public:
 
   //! Return true if specified mode is zoom/rotate transformation persistence.
   static Standard_Boolean IsZoomOrRotate (Graphic3d_TransModeFlags theMode)
   {
     return (theMode & (Graphic3d_TMF_ZoomPers | Graphic3d_TMF_RotatePers)) != 0;
   }
 
   //! Return true if specified mode is 2d/trihedron transformation persistence.
   static Standard_Boolean IsTrihedronOr2d (Graphic3d_TransModeFlags theMode)
   {
     return (theMode & (Graphic3d_TMF_TriedronPers | Graphic3d_TMF_2d)) != 0;
   }
 
 public:
 
   //! Set transformation persistence.
   Graphic3d_TransformPers (const Graphic3d_TransModeFlags theMode)
   : myMode (theMode)
   {
     if (IsZoomOrRotate (theMode))
     {
       SetPersistence (theMode, gp_Pnt(0.0, 0.0, 0.0));
     }
     else if (IsTrihedronOr2d (theMode))
     {
       SetPersistence (theMode, Aspect_TOTP_LEFT_LOWER, Graphic3d_Vec2i (0, 0));
     }
     else if (theMode == Graphic3d_TMF_CameraPers)
     {
       myMode = theMode;
     }
     else
     {
       throw Standard_ProgramError("Graphic3d_TransformPers::SetPersistence(), wrong persistence mode.");
     }
   }
 
   //! Set Zoom/Rotate transformation persistence with an anchor 3D point.
   //! Anchor point defines the origin of Local Coordinate system within World Coordinate system.
   //! Throws an exception if persistence mode is not Graphic3d_TMF_ZoomPers, Graphic3d_TMF_ZoomRotatePers or Graphic3d_TMF_RotatePers.
   Graphic3d_TransformPers (const Graphic3d_TransModeFlags theMode,
                            const gp_Pnt& thePnt)
   : myMode (Graphic3d_TMF_None)
   {
     SetPersistence (theMode, thePnt);
   }
 
   //! Set 2d/trihedron transformation persistence with a corner and 2D offset.
   //! 2D offset defines the origin of Local Coordinate system as projection of 2D point on screen plane into World Coordinate system.
   //! Throws an exception if persistence mode is not Graphic3d_TMF_TriedronPers or Graphic3d_TMF_2d.
   //! The offset is a positive displacement from the view corner in pixels.
   Graphic3d_TransformPers (const Graphic3d_TransModeFlags theMode,
                            const Aspect_TypeOfTriedronPosition theCorner,
                            const Graphic3d_Vec2i& theOffset = Graphic3d_Vec2i (0, 0))
   : myMode (Graphic3d_TMF_None)
   {
     SetPersistence (theMode, theCorner, theOffset);
   }
 
   //! Return true for Graphic3d_TMF_ZoomPers, Graphic3d_TMF_ZoomRotatePers or Graphic3d_TMF_RotatePers modes.
   Standard_Boolean IsZoomOrRotate() const { return IsZoomOrRotate (myMode); }
 
   //! Return true for Graphic3d_TMF_TriedronPers and Graphic3d_TMF_2d modes.
   Standard_Boolean IsTrihedronOr2d() const { return IsTrihedronOr2d (myMode); }
 
   //! Transformation persistence mode flags.
   Graphic3d_TransModeFlags Mode() const { return myMode; }
 
   //! Transformation persistence mode flags.
   Graphic3d_TransModeFlags Flags() const { return myMode; }
 
   //! Set Zoom/Rotate transformation persistence with an anchor 3D point.
   //! Throws an exception if persistence mode is not Graphic3d_TMF_ZoomPers, Graphic3d_TMF_ZoomRotatePers or Graphic3d_TMF_RotatePers.
   void SetPersistence (const Graphic3d_TransModeFlags theMode,
                        const gp_Pnt& thePnt)
   {
     if (!IsZoomOrRotate (theMode))
     {
       throw Standard_ProgramError("Graphic3d_TransformPers::SetPersistence(), wrong persistence mode.");
     }
 
     myMode = theMode;
     myParams.Params3d.PntX = thePnt.X();
     myParams.Params3d.PntY = thePnt.Y();
     myParams.Params3d.PntZ = thePnt.Z();
   }
 
   //! Set 2d/trihedron transformation persistence with a corner and 2D offset.
   //! Throws an exception if persistence mode is not Graphic3d_TMF_TriedronPers or Graphic3d_TMF_2d.
   void SetPersistence (const Graphic3d_TransModeFlags theMode,
                        const Aspect_TypeOfTriedronPosition theCorner,
                        const Graphic3d_Vec2i& theOffset)
   {
     if (!IsTrihedronOr2d (theMode))
     {
       throw Standard_ProgramError("Graphic3d_TransformPers::SetPersistence(), wrong persistence mode.");
     }
 
     myMode = theMode;
     myParams.Params2d.Corner  = theCorner;
     myParams.Params2d.OffsetX = theOffset.x();
     myParams.Params2d.OffsetY = theOffset.y();
   }
 
 public:
 
   //! Return the anchor point for zoom/rotate transformation persistence.
   gp_Pnt AnchorPoint() const
   {
     if (!IsZoomOrRotate())
     {
       throw Standard_ProgramError("Graphic3d_TransformPers::AnchorPoint(), wrong persistence mode.");
     }
 
     return gp_Pnt (myParams.Params3d.PntX, myParams.Params3d.PntY, myParams.Params3d.PntZ);
   }
 
   //! Set the anchor point for zoom/rotate transformation persistence.
   void SetAnchorPoint (const gp_Pnt& thePnt)
   {
     if (!IsZoomOrRotate())
     {
       throw Standard_ProgramError("Graphic3d_TransformPers::SetAnchorPoint(), wrong persistence mode.");
     }
 
     myParams.Params3d.PntX = thePnt.X();
     myParams.Params3d.PntY = thePnt.Y();
     myParams.Params3d.PntZ = thePnt.Z();
   }
 
   //! Return the corner for 2d/trihedron transformation persistence.
   Aspect_TypeOfTriedronPosition Corner2d() const
   {
     if (!IsTrihedronOr2d())
     {
       throw Standard_ProgramError("Graphic3d_TransformPers::Corner2d(), wrong persistence mode.");
     }
 
     return myParams.Params2d.Corner;
   }
 
   //! Set the corner for 2d/trihedron transformation persistence.
   void SetCorner2d (const Aspect_TypeOfTriedronPosition thePos)
   {
     if (!IsTrihedronOr2d())
     {
       throw Standard_ProgramError("Graphic3d_TransformPers::SetCorner2d(), wrong persistence mode.");
     }
 
     myParams.Params2d.Corner = thePos;
   }
 
   //! Return the offset from the corner for 2d/trihedron transformation persistence.
   Graphic3d_Vec2i Offset2d() const
   {
     if (!IsTrihedronOr2d())
     {
       throw Standard_ProgramError("Graphic3d_TransformPers::Offset2d(), wrong persistence mode.");
     }
 
     return Graphic3d_Vec2i (myParams.Params2d.OffsetX, myParams.Params2d.OffsetY);
   }
 
   //! Set the offset from the corner for 2d/trihedron transformation persistence.
   void SetOffset2d (const Graphic3d_Vec2i& theOffset)
   {
     if (!IsTrihedronOr2d())
     {
       throw Standard_ProgramError("Graphic3d_TransformPers::SetOffset2d(), wrong persistence mode.");
     }
 
     myParams.Params2d.OffsetX = theOffset.x();
     myParams.Params2d.OffsetY = theOffset.y();
   }
 
 public:
 
   //! Find scale value based on the camera position and view dimensions
   //! @param theCamera [in] camera definition
   //! @param theViewportWidth [in] the width of viewport.
   //! @param theViewportHeight [in] the height of viewport.
   virtual Standard_Real persistentScale (const Handle(Graphic3d_Camera)& theCamera,
                                          const Standard_Integer theViewportWidth,
                                          const Standard_Integer theViewportHeight) const
   {
     (void )theViewportWidth;
     // use total size when tiling is active
     const Standard_Integer aVPSizeY = theCamera->Tile().IsValid() ? theCamera->Tile().TotalSize.y() : theViewportHeight;
 
     gp_Vec aVecToEye (theCamera->Direction());
     gp_Vec aVecToObj (theCamera->Eye(), gp_Pnt (myParams.Params3d.PntX, myParams.Params3d.PntY, myParams.Params3d.PntZ));
     const Standard_Real aFocus = aVecToObj.Dot (aVecToEye);
     const gp_XYZ aViewDim = theCamera->ViewDimensions (aFocus);
     return Abs(aViewDim.Y()) / Standard_Real(aVPSizeY);
   }
 
   //! Apply transformation to bounding box of presentation.
   //! @param theCamera [in] camera definition
   //! @param theProjection [in] the projection transformation matrix.
   //! @param theWorldView [in] the world view transformation matrix.
   //! @param theViewportWidth [in] the width of viewport (for 2d persistence).
   //! @param theViewportHeight [in] the height of viewport (for 2d persistence).
   //! @param theBoundingBox [in/out] the bounding box to transform.
   template<class T>
   void Apply (const Handle(Graphic3d_Camera)& theCamera,
               const NCollection_Mat4<T>& theProjection,
               const NCollection_Mat4<T>& theWorldView,
               const Standard_Integer theViewportWidth,
               const Standard_Integer theViewportHeight,
               Bnd_Box& theBoundingBox) const;
 
   //! Apply transformation to bounding box of presentation
   //! @param theCamera [in] camera definition
   //! @param theProjection [in] the projection transformation matrix.
   //! @param theWorldView [in] the world view transformation matrix.
   //! @param theViewportWidth [in] the width of viewport (for 2d persistence).
   //! @param theViewportHeight [in] the height of viewport (for 2d persistence).
   //! @param theBoundingBox [in/out] the bounding box to transform.
   template<class T>
   void Apply (const Handle(Graphic3d_Camera)& theCamera,
               const NCollection_Mat4<T>& theProjection,
               const NCollection_Mat4<T>& theWorldView,
               const Standard_Integer theViewportWidth,
               const Standard_Integer theViewportHeight,
               BVH_Box<T, 3>& theBoundingBox) const;
 
   //! Compute transformation.
   //! Computed matrix can be applied to model world transformation
   //! of an object to implement effect of transformation persistence.
   //! @param theCamera [in] camera definition
   //! @param theProjection [in] the projection transformation matrix.
   //! @param theWorldView [in] the world view transformation matrix.
   //! @param theViewportWidth [in] the width of viewport (for 2d persistence).
   //! @param theViewportHeight [in] the height of viewport (for 2d persistence).
   //! @return transformation matrix to be applied to model world transformation of an object.
   template<class T>
   NCollection_Mat4<T> Compute (const Handle(Graphic3d_Camera)& theCamera,
                                const NCollection_Mat4<T>& theProjection,
                                const NCollection_Mat4<T>& theWorldView,
                                const Standard_Integer theViewportWidth,
                                const Standard_Integer theViewportHeight) const;
 
   //! Apply transformation persistence on specified matrices.
   //! @param theCamera camera definition
   //! @param theProjection projection matrix to modify
   //! @param theWorldView  world-view matrix to modify
   //! @param theViewportWidth  viewport width
   //! @param theViewportHeight viewport height
   //! @param theAnchor if not NULL, overrides anchor point
   template<class T>
   void Apply (const Handle(Graphic3d_Camera)& theCamera,
               const NCollection_Mat4<T>& theProjection,
               NCollection_Mat4<T>& theWorldView,
               const Standard_Integer theViewportWidth,
               const Standard_Integer theViewportHeight,
               const gp_Pnt* theAnchor = NULL) const;
 
   //! Dumps the content of me into the stream
   Standard_EXPORT virtual void DumpJson (Standard_OStream& theOStream, Standard_Integer theDepth = -1) const;
 
 private:
 
   //! 3D anchor point for zoom/rotate transformation persistence.
   struct PersParams3d
   {
     Standard_Real PntX;
     Standard_Real PntY;
     Standard_Real PntZ;
 
     //! Dumps the content of me into the stream
     Standard_EXPORT void DumpJson (Standard_OStream& theOStream, Standard_Integer theDepth = -1) const;
   };
 
   //! 2d/trihedron transformation persistence parameters.
   struct PersParams2d
   {
     Standard_Integer OffsetX;
     Standard_Integer OffsetY;
     Aspect_TypeOfTriedronPosition Corner;
 
     //! Dumps the content of me into the stream
     Standard_EXPORT void DumpJson (Standard_OStream& theOStream, Standard_Integer theDepth = -1) const;
   };
 
 private:
 
   Graphic3d_TransModeFlags myMode;  //!< Transformation persistence mode flags
   union
   {
     PersParams3d Params3d;
     PersParams2d Params2d;
   } myParams;
 
 };
 
 // =======================================================================
 // function : Apply
 // purpose  : Apply transformation to world view and projection matrices.
 // =======================================================================
 template<class T>
 void Graphic3d_TransformPers::Apply (const Handle(Graphic3d_Camera)& theCamera,
                                      const NCollection_Mat4<T>& theProjection,
                                      NCollection_Mat4<T>& theWorldView,
                                      const Standard_Integer theViewportWidth,
                                      const Standard_Integer theViewportHeight,
                                      const gp_Pnt* theAnchor) const
 {
   (void )theViewportWidth;
   (void )theProjection;
   if (myMode == Graphic3d_TMF_None
    || theViewportHeight == 0)
   {
     return;
   }
 
   // use total size when tiling is active
   const Standard_Integer aVPSizeY = theCamera->Tile().IsValid() ? theCamera->Tile().TotalSize.y() : theViewportHeight;
 
   // a small enough jitter compensation offset
   // to avoid image dragging within single pixel in corner cases
   const Standard_Real aJitterComp = 0.001;
   if (myMode == Graphic3d_TMF_TriedronPers)
   {
     // reset Z focus for trihedron persistence
     const Standard_Real aFocus = theCamera->IsOrthographic()
                                ? theCamera->Distance()
                                : (theCamera->ZFocusType() == Graphic3d_Camera::FocusType_Relative
                                 ? Standard_Real(theCamera->ZFocus() * theCamera->Distance())
                                 : Standard_Real(theCamera->ZFocus()));
 
     // scale factor to pixels
     const gp_XYZ aViewDim = theCamera->ViewDimensions (aFocus);
     const Standard_Real aScale = Abs(aViewDim.Y()) / Standard_Real(aVPSizeY);
     const gp_Dir aForward = theCamera->Direction();
     gp_XYZ aCenter = theCamera->Center().XYZ() + aForward.XYZ() * (aFocus - theCamera->Distance());
     if ((myParams.Params2d.Corner & (Aspect_TOTP_LEFT | Aspect_TOTP_RIGHT)) != 0)
     {
       const Standard_Real anOffsetX = (Standard_Real(myParams.Params2d.OffsetX) + aJitterComp) * aScale;
       const gp_Dir aSide   = aForward.Crossed (theCamera->Up());
       const gp_XYZ aDeltaX = aSide.XYZ() * (Abs(aViewDim.X()) * theCamera->NDC2dOffsetX() - anOffsetX);
       if ((myParams.Params2d.Corner & Aspect_TOTP_RIGHT) != 0)
       {
         aCenter += aDeltaX;
       }
       else
       {
         aCenter -= aDeltaX;
       }
     }
     if ((myParams.Params2d.Corner & (Aspect_TOTP_TOP | Aspect_TOTP_BOTTOM)) != 0)
     {
       const Standard_Real anOffsetY = (Standard_Real(myParams.Params2d.OffsetY) + aJitterComp) * aScale;
       const gp_XYZ aDeltaY = theCamera->Up().XYZ() * (Abs(aViewDim.Y()) * theCamera->NDC2dOffsetY() - anOffsetY);
       if ((myParams.Params2d.Corner & Aspect_TOTP_TOP) != 0)
       {
         aCenter += aDeltaY;
       }
       else
       {
         aCenter -= aDeltaY;
       }
     }
 
     NCollection_Mat4<Standard_Real> aWorldView = theCamera->OrientationMatrix();
     Graphic3d_TransformUtils::Translate (aWorldView, aCenter.X(), aCenter.Y(), aCenter.Z());
     Graphic3d_TransformUtils::Scale     (aWorldView, aScale,      aScale,      aScale);
     theWorldView.ConvertFrom (aWorldView);
     return;
   }
   else if (myMode == Graphic3d_TMF_2d)
   {
     const Standard_Real aFocus = theCamera->IsOrthographic()
                                ? theCamera->Distance()
                                : (theCamera->ZFocusType() == Graphic3d_Camera::FocusType_Relative
                                 ? Standard_Real(theCamera->ZFocus() * theCamera->Distance())
                                 : Standard_Real(theCamera->ZFocus()));
 
     // scale factor to pixels
     const gp_XYZ        aViewDim = theCamera->ViewDimensions (aFocus);
     const Standard_Real aScale   = Abs(aViewDim.Y()) / Standard_Real(aVPSizeY);
     gp_XYZ aCenter (0.0, 0.0, -aFocus);
     if ((myParams.Params2d.Corner & (Aspect_TOTP_LEFT | Aspect_TOTP_RIGHT)) != 0)
     {
       aCenter.SetX (-aViewDim.X() * theCamera->NDC2dOffsetX() + (Standard_Real(myParams.Params2d.OffsetX) + aJitterComp) * aScale);
       if ((myParams.Params2d.Corner & Aspect_TOTP_RIGHT) != 0)
       {
         aCenter.SetX (-aCenter.X());
       }
     }
     if ((myParams.Params2d.Corner & (Aspect_TOTP_TOP | Aspect_TOTP_BOTTOM)) != 0)
     {
       aCenter.SetY (-aViewDim.Y() * theCamera->NDC2dOffsetY() + (Standard_Real(myParams.Params2d.OffsetY) + aJitterComp) * aScale);
       if ((myParams.Params2d.Corner & Aspect_TOTP_TOP) != 0)
       {
         aCenter.SetY (-aCenter.Y());
       }
     }
 
     theWorldView.InitIdentity();
     Graphic3d_TransformUtils::Translate (theWorldView, T(aCenter.X()), T(aCenter.Y()), T(aCenter.Z()));
     Graphic3d_TransformUtils::Scale     (theWorldView, T(aScale),      T(aScale),      T(aScale));
     return;
   }
   else if ((myMode & Graphic3d_TMF_CameraPers) != 0)
   {
     theWorldView.InitIdentity();
   }
   else
   {
     // Compute reference point for transformation in untransformed projection space.
     NCollection_Mat4<Standard_Real> aWorldView = theCamera->OrientationMatrix();
     if (theAnchor != NULL)
     {
       Graphic3d_TransformUtils::Translate (aWorldView, theAnchor->X(), theAnchor->Y(), theAnchor->Z());
     }
     else
     {
       Graphic3d_TransformUtils::Translate (aWorldView, myParams.Params3d.PntX, myParams.Params3d.PntY, myParams.Params3d.PntZ);
     }
 
     if ((myMode & Graphic3d_TMF_RotatePers) != 0)
     {
       // lock rotation by nullifying rotation component
       aWorldView.SetValue (0, 0, 1.0);
       aWorldView.SetValue (1, 0, 0.0);
       aWorldView.SetValue (2, 0, 0.0);
 
       aWorldView.SetValue (0, 1, 0.0);
       aWorldView.SetValue (1, 1, 1.0);
       aWorldView.SetValue (2, 1, 0.0);
 
       aWorldView.SetValue (0, 2, 0.0);
       aWorldView.SetValue (1, 2, 0.0);
       aWorldView.SetValue (2, 2, 1.0);
     }
 
     if ((myMode & Graphic3d_TMF_ZoomPers) != 0)
     {
       // lock zooming
       Standard_Real aScale = persistentScale (theCamera, theViewportWidth, theViewportHeight);
       Graphic3d_TransformUtils::Scale (aWorldView, aScale, aScale, aScale);
     }
     theWorldView.ConvertFrom (aWorldView);
     return;
   }
 }
 
 // =======================================================================
 // function : Apply
 // purpose  : Apply transformation to bounding box of presentation.
 // =======================================================================
 template<class T>
 void Graphic3d_TransformPers::Apply (const Handle(Graphic3d_Camera)& theCamera,
                                      const NCollection_Mat4<T>& theProjection,
                                      const NCollection_Mat4<T>& theWorldView,
                                      const Standard_Integer theViewportWidth,
                                      const Standard_Integer theViewportHeight,
                                      Bnd_Box& theBoundingBox) const
 {
   if (theBoundingBox.IsVoid())
   {
     return;
   }
 
   T aXmin, aYmin, aZmin, aXmax, aYmax, aZmax;
 
   theBoundingBox.Get (aXmin, aYmin, aZmin, aXmax, aYmax, aZmax);
 
   typename BVH_Box<T, 3>::BVH_VecNt aMin (aXmin, aYmin, aZmin);
   typename BVH_Box<T, 3>::BVH_VecNt aMax (aXmax, aYmax, aZmax);
   BVH_Box<T, 3> aBBox (aMin, aMax);
 
   Apply (theCamera, theProjection, theWorldView, theViewportWidth, theViewportHeight, aBBox);
 
   theBoundingBox = Bnd_Box();
   theBoundingBox.Update (aBBox.CornerMin().x(), aBBox.CornerMin().y(), aBBox.CornerMin().z(),
                          aBBox.CornerMax().x(), aBBox.CornerMax().y(), aBBox.CornerMax().z());
 }
 
 // =======================================================================
 // function : Apply
 // purpose  : Apply transformation to bounding box of presentation.
 // =======================================================================
 template<class T>
 void Graphic3d_TransformPers::Apply (const Handle(Graphic3d_Camera)& theCamera,
                                      const NCollection_Mat4<T>& theProjection,
                                      const NCollection_Mat4<T>& theWorldView,
                                      const Standard_Integer theViewportWidth,
                                      const Standard_Integer theViewportHeight,
                                      BVH_Box<T, 3>& theBoundingBox) const
 {
   NCollection_Mat4<T> aTPers = Compute (theCamera, theProjection, theWorldView, theViewportWidth, theViewportHeight);
   if (aTPers.IsIdentity()
   || !theBoundingBox.IsValid())
   {
     return;
   }
 
   const typename BVH_Box<T, 3>::BVH_VecNt& aMin = theBoundingBox.CornerMin();
   const typename BVH_Box<T, 3>::BVH_VecNt& aMax = theBoundingBox.CornerMax();
 
   typename BVH_Box<T, 4>::BVH_VecNt anArrayOfCorners[8];
   anArrayOfCorners[0] = typename BVH_Box<T, 4>::BVH_VecNt (aMin.x(), aMin.y(), aMin.z(), static_cast<T> (1.0));
   anArrayOfCorners[1] = typename BVH_Box<T, 4>::BVH_VecNt (aMin.x(), aMin.y(), aMax.z(), static_cast<T> (1.0));
   anArrayOfCorners[2] = typename BVH_Box<T, 4>::BVH_VecNt (aMin.x(), aMax.y(), aMin.z(), static_cast<T> (1.0));
   anArrayOfCorners[3] = typename BVH_Box<T, 4>::BVH_VecNt (aMin.x(), aMax.y(), aMax.z(), static_cast<T> (1.0));
   anArrayOfCorners[4] = typename BVH_Box<T, 4>::BVH_VecNt (aMax.x(), aMin.y(), aMin.z(), static_cast<T> (1.0));
   anArrayOfCorners[5] = typename BVH_Box<T, 4>::BVH_VecNt (aMax.x(), aMin.y(), aMax.z(), static_cast<T> (1.0));
   anArrayOfCorners[6] = typename BVH_Box<T, 4>::BVH_VecNt (aMax.x(), aMax.y(), aMin.z(), static_cast<T> (1.0));
   anArrayOfCorners[7] = typename BVH_Box<T, 4>::BVH_VecNt (aMax.x(), aMax.y(), aMax.z(), static_cast<T> (1.0));
 
   theBoundingBox.Clear();
   for (Standard_Integer anIt = 0; anIt < 8; ++anIt)
   {
     typename BVH_Box<T, 4>::BVH_VecNt& aCorner = anArrayOfCorners[anIt];
     aCorner  = aTPers * aCorner;
     aCorner = aCorner / aCorner.w();
     theBoundingBox.Add (typename BVH_Box<T, 3>::BVH_VecNt (aCorner.x(), aCorner.y(), aCorner.z()));
   }
 }
 
 // =======================================================================
 // function : Compute
 // purpose  : Compute transformation.
 // =======================================================================
 template<class T>
 NCollection_Mat4<T> Graphic3d_TransformPers::Compute (const Handle(Graphic3d_Camera)& theCamera,
                                                       const NCollection_Mat4<T>& theProjection,
                                                       const NCollection_Mat4<T>& theWorldView,
                                                       const Standard_Integer theViewportWidth,
                                                       const Standard_Integer theViewportHeight) const
 {
   if (myMode == Graphic3d_TMF_None)
   {
     return NCollection_Mat4<T>();
   }
 
   NCollection_Mat4<T> aWorldView (theWorldView);
   NCollection_Mat4<T> anUnviewMat;
   if (!theWorldView.Inverted (anUnviewMat))
   {
     return NCollection_Mat4<T>();
   }
 
   // compute only world-view matrix difference to avoid floating point instability
   // caused by projection matrix modifications outside of this algorithm (e.g. by Z-fit)
   Apply (theCamera, theProjection, aWorldView, theViewportWidth, theViewportHeight);
   return anUnviewMat * aWorldView;
 }
 
 #endif // _Graphic3d_TransformPers_HeaderFile

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