diff --git a/src/AppParCurves/AppParCurves_MultiPoint.cxx b/src/AppParCurves/AppParCurves_MultiPoint.cxx
index 12fef12342..c5f6e02ef1 100644
--- a/src/AppParCurves/AppParCurves_MultiPoint.cxx
+++ b/src/AppParCurves/AppParCurves_MultiPoint.cxx
@@ -173,21 +173,30 @@ const gp_Pnt2d& AppParCurves_MultiPoint::Point2d (const Standard_Integer Index)
 void AppParCurves_MultiPoint::Dump(Standard_OStream& o) const
 {
   o << "AppParCurves_MultiPoint dump:" << endl;
-  o << "It contains " << NbPoints() << " 3d points and " << NbPoints2d() <<" 2d points." << endl;
-  /*
-    if (Dimension(i) == 3) {
-      for (Standard_Integer j = 1; j <= tabPoint->Length(); j++) {
-	o << " Pole No. " << j << ": " << endl;
-	o << " Pole x = " << (tabPoint->Value(i)->Point(j)).X() << endl;
-	o << " Pole y = " << (tabPoint->Value(i)->Point(j)).Y() << endl;
-	o << " Pole z = " << (tabPoint->Value(i)->Point(j)).Z() << endl;
-      }
+  const Standard_Integer  aNbPnts3D = NbPoints(),
+                          aNbPnts2D = NbPoints2d();
+  o << "It contains " << aNbPnts3D << " 3d points and " << aNbPnts2D <<" 2d points." << endl;
+  
+  if(aNbPnts3D > 0)
+  {
+    for(Standard_Integer i = tabPoint->Lower(); i <= tabPoint->Upper(); i++)
+    {
+      o << "3D-Point #" << i << endl;
+
+      o << " Pole x = " << (tabPoint->Value(i)/*->Point(j)*/).X() << endl;
+      o << " Pole y = " << (tabPoint->Value(i)/*->Point(j)*/).Y() << endl;
+      o << " Pole z = " << (tabPoint->Value(i)/*->Point(j)*/).Z() << endl;
     }
-    else {
-      for (Standard_Integer j = 1; j <= tabPoint->Length(); j++) {
-	o << " Pole No. " << j << ": " << endl;
-	o << " Pole x = " << (tabPoint->Value(i)->Point2d(j)).X() << endl;
-	o << " Pole y = " << (tabPoint->Value(i)->Point2d(j)).Y() << endl;
-      }
-*/
+  }
+  
+  if(aNbPnts2D > 0)
+  {
+    for(Standard_Integer i = tabPoint2d->Lower(); i <= tabPoint2d->Upper(); i++)
+    {
+      o << "2D-Point #" << i << endl;
+
+      o << " Pole x = " << (tabPoint2d->Value(i)/*->Point2d(j)*/).X() << endl;
+      o << " Pole y = " << (tabPoint2d->Value(i)/*->Point2d(j)*/).Y() << endl;
+    }
+  }
 }
diff --git a/src/BRepFill/BRepFill_LocationLaw.cxx b/src/BRepFill/BRepFill_LocationLaw.cxx
index 77b38825bf..5a02d83b98 100644
--- a/src/BRepFill/BRepFill_LocationLaw.cxx
+++ b/src/BRepFill/BRepFill_LocationLaw.cxx
@@ -608,8 +608,7 @@ void BRepFill_LocationLaw::CurvilinearBounds(const Standard_Integer Index,
     gp_Trsf fila;
     fila.SetValues(M(1,1), M(1,2), M(1,3), V.X(),
 		   M(2,1), M(2,2), M(2,3), V.Y(),
-		   M(3,1), M(3,2), M(3,3), V.Z(),
-		   1.e-12, 1.e-14);
+		   M(3,1), M(3,2), M(3,3), V.Z());
     //TopLoc_Location Loc(fila);
     //W.Location(Loc.Multiplied(W.Location()));
     W = BRepBuilderAPI_Transform(W, fila, Standard_True); //copy
diff --git a/src/BRepFill/BRepFill_Pipe.cxx b/src/BRepFill/BRepFill_Pipe.cxx
index 04a2ec68de..8d8e5eef89 100644
--- a/src/BRepFill/BRepFill_Pipe.cxx
+++ b/src/BRepFill/BRepFill_Pipe.cxx
@@ -263,8 +263,7 @@ void BRepFill_Pipe::Perform(const TopoDS_Wire&  Spine,
   myLoc->Law(1)->D0(first, M, V);
     fila.SetValues(M(1,1), M(1,2), M(1,3), V.X(),
 		   M(2,1), M(2,2), M(2,3), V.Y(),
-		   M(3,1), M(3,2), M(3,3), V.Z(),
-		   1.e-12, 1.e-14);
+		   M(3,1), M(3,2), M(3,3), V.Z());
 
   fila.Multiply(myTrsf);
   TopLoc_Location LocFirst(fila);
@@ -293,8 +292,7 @@ void BRepFill_Pipe::Perform(const TopoDS_Wire&  Spine,
 //    try { // Not good, but there are no other means to test SetValues
   fila.SetValues(M(1,1), M(1,2), M(1,3), V.X(),
 		 M(2,1), M(2,2), M(2,3), V.Y(),
-		 M(3,1), M(3,2), M(3,3), V.Z(),
-		 1.e-12, 1.e-14);
+		 M(3,1), M(3,2), M(3,3), V.Z());
   fila.Multiply(myTrsf);
   TopLoc_Location LocLast(fila);
   if (! myLoc->IsClosed() || LocFirst != LocLast) {
diff --git a/src/BinTools/BinTools_LocationSet.cxx b/src/BinTools/BinTools_LocationSet.cxx
index fb4cbcf323..c76b17f9ca 100644
--- a/src/BinTools/BinTools_LocationSet.cxx
+++ b/src/BinTools/BinTools_LocationSet.cxx
@@ -46,9 +46,7 @@ static Standard_IStream& operator >>(Standard_IStream& IS, gp_Trsf& T)
 
   T.SetValues(V1[0],V1[1],V1[2],V[0],
 	      V2[0],V2[1],V2[2],V[1],
-	      V3[0],V3[1],V3[2],V[2],
-	      Precision::Angular(),
-	      Precision::Confusion());
+	      V3[0],V3[1],V3[2],V[2]);
   return IS;
 }
 
diff --git a/src/GeomFill/GeomFill_Sweep.cxx b/src/GeomFill/GeomFill_Sweep.cxx
index a65f63a3c1..b74a2ee3f4 100644
--- a/src/GeomFill/GeomFill_Sweep.cxx
+++ b/src/GeomFill/GeomFill_Sweep.cxx
@@ -527,8 +527,7 @@ static Standard_Boolean IsSweepParallelSpine (const Handle(GeomFill_LocationLaw)
 
   TfBegin.SetValues(GTfBegin(1,1), GTfBegin(1,2), GTfBegin(1,3), GTfBegin(1,4),
 		    GTfBegin(2,1), GTfBegin(2,2), GTfBegin(2,3), GTfBegin(2,4),
-		    GTfBegin(3,1), GTfBegin(3,2), GTfBegin(3,3), GTfBegin(3,4),
-		    1.e-12, 1.e-14);
+		    GTfBegin(3,1), GTfBegin(3,2), GTfBegin(3,3), GTfBegin(3,4));
 
 // Get the last transformation
   theLoc->D0(aLast, M, VEnd);
@@ -538,8 +537,7 @@ static Standard_Boolean IsSweepParallelSpine (const Handle(GeomFill_LocationLaw)
 
   TfEnd.SetValues(GTfEnd(1,1), GTfEnd(1,2), GTfEnd(1,3), GTfEnd(1,4),
 		  GTfEnd(2,1), GTfEnd(2,2), GTfEnd(2,3), GTfEnd(2,4),
-		  GTfEnd(3,1), GTfEnd(3,2), GTfEnd(3,3), GTfEnd(3,4),
-		  1.e-12, 1.e-14);
+		  GTfEnd(3,1), GTfEnd(3,2), GTfEnd(3,3), GTfEnd(3,4));
 
   Handle(Geom_Surface) aSurf = theSec->BSplineSurface();
   Standard_Real Umin;
@@ -611,8 +609,7 @@ static Standard_Boolean IsSweepParallelSpine (const Handle(GeomFill_LocationLaw)
       OCC_CATCH_SIGNALS
       Tf2.SetValues(Tf(1,1), Tf(1,2), Tf(1,3), Tf(1,4),
 		    Tf(2,1), Tf(2,2), Tf(2,3), Tf(2,4),
-		    Tf(3,1), Tf(3,2), Tf(3,3), Tf(3,4),
-		    1.e-12, 1.e-14);
+		    Tf(3,1), Tf(3,2), Tf(3,3), Tf(3,4));
     }
     catch (Standard_ConstructionError) {
       IsTrsf = Standard_False;
@@ -799,8 +796,7 @@ static Standard_Boolean IsSweepParallelSpine (const Handle(GeomFill_LocationLaw)
 //        OCC_CATCH_SIGNALS
 	Tf2.SetValues(Tf(1,1), Tf(1,2), Tf(1,3), Tf(1,4),
 		      Tf(2,1), Tf(2,2), Tf(2,3), Tf(2,4),
-		      Tf(3,1), Tf(3,2), Tf(3,3), Tf(3,4),
-		      1.e-14, 1.e-15);
+		      Tf(3,1), Tf(3,2), Tf(3,3), Tf(3,4));
 //      }
 //      catch (Standard_ConstructionError) {
 //	IsTrsf = Standard_False;
diff --git a/src/ProjLib/ProjLib_ComputeApproxOnPolarSurface.cxx b/src/ProjLib/ProjLib_ComputeApproxOnPolarSurface.cxx
index 39b53eb01b..8e0ab0cc99 100644
--- a/src/ProjLib/ProjLib_ComputeApproxOnPolarSurface.cxx
+++ b/src/ProjLib/ProjLib_ComputeApproxOnPolarSurface.cxx
@@ -1106,6 +1106,38 @@ Handle(Adaptor2d_HCurve2d)
                   V1 = V0 + vsens*vperiod;
                   Pts2d(i).SetCoord(U1,V1);
                   myProjIsDone = Standard_True;
+
+                  if((i == 2) && (!IsEqual(uperiod, 0.0) || !IsEqual(vperiod, 0.0)))
+                  {//Make 1st point more precise for periodic surfaces
+                    const Standard_Integer aSize = 3;
+                    const gp_Pnt2d aP(Pts2d(2)); 
+                    Standard_Real aUpar[aSize], aVpar[aSize];
+                    Pts2d(1).Coord(aUpar[1], aVpar[1]);
+                    aUpar[0] = aUpar[1] - uperiod;
+                    aUpar[2] = aUpar[1] + uperiod;
+                    aVpar[0] = aVpar[1] - vperiod;
+                    aVpar[2] = aVpar[1] + vperiod;
+
+                    Standard_Real aSQdistMin = RealLast();
+                    Standard_Integer aBestUInd = 1, aBestVInd = 1;
+                    const Standard_Integer  aSizeU = IsEqual(uperiod, 0.0) ? 1 : aSize,
+                                            aSizeV = IsEqual(vperiod, 0.0) ? 1 : aSize;
+                    for(Standard_Integer uInd = 0; uInd < aSizeU; uInd++)
+                    {
+                      for(Standard_Integer vInd = 0; vInd < aSizeV; vInd++)
+                      {
+                        Standard_Real aSQdist = aP.SquareDistance(gp_Pnt2d(aUpar[uInd], aVpar[vInd]));
+                        if(aSQdist < aSQdistMin)
+                        {
+                          aSQdistMin = aSQdist;
+                          aBestUInd = uInd;
+                          aBestVInd = vInd;
+                        }
+                      }
+                    }
+
+                    Pts2d(1).SetCoord(aUpar[aBestUInd], aVpar[aBestVInd]);
+                  }//if(i == 2) condition
                 }
               }
             }
diff --git a/src/Prs3d/Prs3d_Presentation.cxx b/src/Prs3d/Prs3d_Presentation.cxx
index a205f09122..57bcb11348 100644
--- a/src/Prs3d/Prs3d_Presentation.cxx
+++ b/src/Prs3d/Prs3d_Presentation.cxx
@@ -195,8 +195,7 @@ TColStd_Array2OfReal matrix(1,4,1,4);
   trsf.SetValues(
         matrix.Value(1,1),matrix.Value(1,2),matrix.Value(1,3),matrix.Value(1,4),
         matrix.Value(2,1),matrix.Value(2,2),matrix.Value(2,3),matrix.Value(2,4),
-        matrix.Value(3,1),matrix.Value(3,2),matrix.Value(3,3),matrix.Value(3,4),
-        0.001,0.0001);  
+        matrix.Value(3,1),matrix.Value(3,2),matrix.Value(3,3),matrix.Value(3,4));  
   Handle(Geom_Transformation) gtrsf = new Geom_Transformation(trsf); 
 
   return gtrsf;
diff --git a/src/PrsMgr/PrsMgr_Prs.cxx b/src/PrsMgr/PrsMgr_Prs.cxx
index 60b214d9c0..5909869b0b 100644
--- a/src/PrsMgr/PrsMgr_Prs.cxx
+++ b/src/PrsMgr/PrsMgr_Prs.cxx
@@ -58,8 +58,7 @@ Handle(Graphic3d_Structure) PrsMgr_Prs::Compute(const Handle(Graphic3d_DataStruc
   Standard_Integer LC(AMatrix.LowerCol()),LR(AMatrix.LowerRow());
   TheTrsf.SetValues(AMatrix(LR,LC),AMatrix(LR,LC+1),AMatrix(LR,LC+2),AMatrix(LR,LC+3),
 		    AMatrix(LR+1,LC),AMatrix(LR+1,LC+1),AMatrix(LR+1,LC+2),AMatrix(LR+1,LC+3),
-		    AMatrix(LR+2,LC),AMatrix(LR+2,LC+1),AMatrix(LR+2,LC+2),AMatrix(LR+2,LC+3),
-		    Precision::Angular(),Precision::Confusion());
+		    AMatrix(LR+2,LC),AMatrix(LR+2,LC+1),AMatrix(LR+2,LC+2),AMatrix(LR+2,LC+3));
    Handle(Geom_Transformation) G = new Geom_Transformation(TheTrsf);
   
   return myPresentation3d->Compute(aProjector,G);
@@ -90,8 +89,7 @@ void PrsMgr_Prs::Compute(const Handle(Graphic3d_DataStructureManager)& aProjecto
   Standard_Integer LC(AMatrix.LowerCol()),LR(AMatrix.LowerRow());
   TheTrsf.SetValues(AMatrix(LR,LC),AMatrix(LR,LC+1),AMatrix(LR,LC+2),AMatrix(LR,LC+3),
 		    AMatrix(LR+1,LC),AMatrix(LR+1,LC+1),AMatrix(LR+1,LC+2),AMatrix(LR+1,LC+3),
-		    AMatrix(LR+2,LC),AMatrix(LR+2,LC+1),AMatrix(LR+2,LC+2),AMatrix(LR+2,LC+3),
-		    Precision::Angular(),Precision::Confusion());
+		    AMatrix(LR+2,LC),AMatrix(LR+2,LC+1),AMatrix(LR+2,LC+2),AMatrix(LR+2,LC+3));
   Handle(Geom_Transformation) G = new Geom_Transformation(TheTrsf);
 
 
diff --git a/src/TopTools/TopTools_LocationSet.cxx b/src/TopTools/TopTools_LocationSet.cxx
index 1c015a8e2d..225624313f 100644
--- a/src/TopTools/TopTools_LocationSet.cxx
+++ b/src/TopTools/TopTools_LocationSet.cxx
@@ -237,9 +237,7 @@ static void ReadTrsf(gp_Trsf& T,
   
   T.SetValues(V1[0],V1[1],V1[2],V[0],
 	      V2[0],V2[1],V2[2],V[1],
-	      V3[0],V3[1],V3[2],V[2],
-	      Precision::Angular(),
-	      Precision::Confusion());
+	      V3[0],V3[1],V3[2],V[2]);
   return;
 }
 //=======================================================================
diff --git a/src/Vrml/Vrml_MatrixTransform.cxx b/src/Vrml/Vrml_MatrixTransform.cxx
index 0a78a08de4..44060649f6 100644
--- a/src/Vrml/Vrml_MatrixTransform.cxx
+++ b/src/Vrml/Vrml_MatrixTransform.cxx
@@ -28,8 +28,7 @@ Vrml_MatrixTransform::Vrml_MatrixTransform()
   gp_Trsf T;
   T.SetValues ( 1, 0, 0, 0,
 	        0, 1, 0, 0,
-	        0, 0, 1, 0,
-	        Precision::Angular(), Precision::Confusion());
+	        0, 0, 1, 0);
   T.SetScaleFactor(1); 
 
   myMatrix = T;
diff --git a/src/gp/gp_Trsf.cdl b/src/gp/gp_Trsf.cdl
index 2ebff2d577..763090a626 100644
--- a/src/gp/gp_Trsf.cdl
+++ b/src/gp/gp_Trsf.cdl
@@ -204,8 +204,7 @@ is
   SetValues(me : in out;
             a11, a12, a13, a14,
             a21, a22, a23, a24,
-            a31, a32, a33, a34 : Real;
-            Tolang, TolDist : Real)
+            a31, a32, a33, a34 : Real)
 
         ---Purpose: Sets the coefficients  of the transformation.  The
         --          transformation  of the  point  x,y,z is  the point
@@ -213,16 +212,11 @@ is
         --          
         --          x' = a11 x + a12 y + a13 z + a14
         --          y' = a21 x + a22 y + a23 z + a24
-        --          z' = a31 x + a32 y + a43 z + a34
-        --          
-        --          Tolang and  TolDist are  used  to  test  for  null
-        --          angles and null distances to determine the form of
-        --          the transformation (identity, translation, etc..).
+        --          z' = a31 x + a32 y + a33 z + a34
         --          
         --          The method Value(i,j) will return aij.
-        --          Raises ConstructionError if the determinant of  the aij is null. Or  if
-        --          the matrix as not a uniform scale.
-
+        --          Raises ConstructionError if the determinant of  the aij is null.
+        --          The matrix is orthogonalyzed before future using.
     raises
         ConstructionError from Standard
 
@@ -371,7 +365,9 @@ is
         ---C++: inline
         --- Purpose : Transformation of a triplet XYZ with a Trsf
 
-
+  Orthogonalize(me: in out)
+    is protected;
+        --- Purpose : Makes orthogonalization of "matrix"
 
 fields
 
diff --git a/src/gp/gp_Trsf.cxx b/src/gp/gp_Trsf.cxx
index 8d7fae2d17..e19b2e4e64 100644
--- a/src/gp/gp_Trsf.cxx
+++ b/src/gp/gp_Trsf.cxx
@@ -322,14 +322,7 @@ void gp_Trsf::SetValues(const Standard_Real a11,
                         const Standard_Real a31, 
                         const Standard_Real a32,
                         const Standard_Real a33, 
-                        const Standard_Real a34, 
-//                      const Standard_Real Tolang, 
-                        const Standard_Real , 
-                        const Standard_Real
-#ifndef No_Exception
-                                            TolDist
-#endif
-                       )
+                        const Standard_Real a34)
 {
   gp_XYZ col1(a11,a21,a31);
   gp_XYZ col2(a12,a22,a32);
@@ -341,63 +334,19 @@ void gp_Trsf::SetValues(const Standard_Real a11,
   Standard_Real As = s;
   if (As < 0) As = - As;
   Standard_ConstructionError_Raise_if
-    (As < gp::Resolution(),"gp_Trsf::SeValues, null determinant");
+    (As < gp::Resolution(),"gp_Trsf::SetValues, null determinant");
   if (s > 0)
     s = Pow(s,1./3.);
   else
     s = -Pow(-s,1./3.);
   M.Divide(s);
   
-  // check if the matrix is a rotation matrix
-  // the transposition should be the invert.
-  gp_Mat TM(M);
-  TM.Transpose();
-  TM.Multiply(M);
-  //
-  // don t trust the initial values !
-  //
-  gp_Mat anIdentity ;
-  anIdentity.SetIdentity() ;
-  TM.Subtract(anIdentity);
-  As = TM.Value(1,1);
-  if (As < 0) As = - As;
-  Standard_ConstructionError_Raise_if
-    (As > TolDist,"gp_Trsf::SeValues, non uniform");
-  As = TM.Value(1,2);
-  if (As < 0) As = - As;
-  Standard_ConstructionError_Raise_if
-    (As > TolDist,"gp_Trsf::SeValues, non uniform");
-  As = TM.Value(1,3);
-  if (As < 0) As = - As;
-  Standard_ConstructionError_Raise_if
-    (As > TolDist,"gp_Trsf::SeValues, non uniform");
-  As = TM.Value(2,1);
-  if (As < 0) As = - As;
-  Standard_ConstructionError_Raise_if
-    (As > TolDist,"gp_Trsf::SeValues, non uniform");
-  As = TM.Value(2,2);
-  if (As < 0) As = - As;
-  Standard_ConstructionError_Raise_if
-    (As > TolDist,"gp_Trsf::SeValues, non uniform");
-  As = TM.Value(2,3);
-  if (As < 0) As = - As;
-  Standard_ConstructionError_Raise_if
-    (As > TolDist,"gp_Trsf::SeValues, non uniform");
-  As = TM.Value(3,1);
-  if (As < 0) As = - As;
-  Standard_ConstructionError_Raise_if
-    (As > TolDist,"gp_Trsf::SeValues, non uniform");
-  As = TM.Value(3,2);
-  if (As < 0) As = - As;
-  Standard_ConstructionError_Raise_if
-    (As > TolDist,"gp_Trsf::SeValues, non uniform");
-  As = TM.Value(3,3);
-  if (As < 0) As = - As;
-  Standard_ConstructionError_Raise_if
-    (As > TolDist,"gp_Trsf::SeValues, non uniform");
   scale = s;
   shape = gp_CompoundTrsf;
+
   matrix = M;
+  Orthogonalize();
+  
   loc = col4;
 }
 
@@ -811,3 +760,42 @@ Standard_Boolean gp_Trsf::GetRotation (gp_XYZ&        theAxis,
   theAxis = aVec.XYZ();
   return Standard_True;
 }
+
+//=======================================================================
+//function : Orthogonalize
+//purpose  : 
+//=======================================================================
+void gp_Trsf::Orthogonalize()
+{
+  gp_Mat aTM(matrix);
+
+  gp_XYZ aV1 = aTM.Column(1);
+  gp_XYZ aV2 = aTM.Column(2);
+  gp_XYZ aV3 = aTM.Column(3);
+
+  aV1.Normalize();
+
+  aV2 -= aV1*(aV2.Dot(aV1));
+  aV2.Normalize();
+
+  aV3 -= aV1*(aV3.Dot(aV1)) + aV2*(aV3.Dot(aV2));
+  aV3.Normalize();
+
+  aTM.SetCols(aV1, aV2, aV3);
+
+  aV1 = aTM.Row(1);
+  aV2 = aTM.Row(2);
+  aV3 = aTM.Row(3);
+
+  aV1.Normalize();
+
+  aV2 -= aV1*(aV2.Dot(aV1));
+  aV2.Normalize();
+
+  aV3 -= aV1*(aV3.Dot(aV1)) + aV2*(aV3.Dot(aV2));
+  aV3.Normalize();
+
+  aTM.SetRows(aV1, aV2, aV3);
+
+  matrix = aTM;
+}
diff --git a/src/gp/gp_Trsf2d.cdl b/src/gp/gp_Trsf2d.cdl
index 474f82e538..8ca5e235bd 100644
--- a/src/gp/gp_Trsf2d.cdl
+++ b/src/gp/gp_Trsf2d.cdl
@@ -242,6 +242,31 @@ is
   Transforms (me; Coord : out XY)   is static;
         ---C++: inline    
         --- Purpose : Transforms  a doublet XY with a Trsf2d
+
+  SetValues(me : in out;
+            a11, a12, a13, a21, a22, a23 : Real)
+
+        ---Purpose: Sets the coefficients  of the transformation. The 
+         --         transformation  of the  point  x,y is  the point
+         --         x',y' with :
+         --
+         --         x' = a11 x + a12 y + a13
+         --         y' = a21 x + a22 y + a23
+         --
+         --         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 orthogonalyzed before future using.
+
+    raises
+        ConstructionError from Standard
+
+    is static;
+        
+  Orthogonalize(me: in out)
+    is protected;
+        --- Purpose : Makes orthogonalization of "matrix"
+  
+
 fields
 
   scale  : Real;
diff --git a/src/gp/gp_Trsf2d.cxx b/src/gp/gp_Trsf2d.cxx
index cfaf435a8e..7fae973f69 100644
--- a/src/gp/gp_Trsf2d.cxx
+++ b/src/gp/gp_Trsf2d.cxx
@@ -23,31 +23,32 @@
 void gp_Trsf2d::SetMirror (const gp_Ax2d& A)
 {
   shape = gp_Ax1Mirror;
-  scale = - 1.0;
   const gp_Dir2d& V = A.Direction ();
   const gp_Pnt2d& P = A.Location ();
   Standard_Real VX = V.X();
   Standard_Real VY = V.Y();
   Standard_Real X0 = P.X();
   Standard_Real Y0 = P.Y();
-  matrix.SetCol (1, gp_XY (1.0 - 2.0 * VX * VX, -2.0 * VX * VY));
-  matrix.SetCol (2, gp_XY (-2.0 * VX * VY, 1.0 - 2.0 * VY * VY));
 
-  loc.SetCoord  (-2.0 * ((VX * VX - 1.0) * X0 + (VX * VY * Y0)),
-                 -2.0 * ((VX * VY * X0) + (VY * VY - 1.0) * Y0));
+  SetValues(1.0-2.0*VX*VX, -2.0*VX*VY, -2.0*((VX * VX - 1.0)*X0 + (VX*VY*Y0)), 
+            -2.0*VX*VY, 1.0-2.0*VY*VY, -2.0*((VX*VY*X0)+(VY*VY-1.0)*Y0));
+
+  scale = - 1.0;
 }
 
 void gp_Trsf2d::SetTransformation (const gp_Ax2d& FromA1,
 				   const gp_Ax2d& ToA2)
 {
   shape = gp_CompoundTrsf;
-  scale = 1.0;
   //matrix from XOY to A2 :
   const gp_XY& V1 = ToA2.Direction().XY();
   gp_XY V2 (-V1.Y(), V1.X());
-  matrix.SetCol (1, V1);
-  matrix.SetCol (2, V2);
-  loc = ToA2.Location().XY();
+
+  SetValues(V1.X(), V2.X(), ToA2.Location().X(),
+            V1.Y(), V2.Y(), ToA2.Location().Y());
+
+  scale = 1.0;
+
   matrix.Transpose();
   loc.Multiply (matrix);
   loc.Reverse();
@@ -65,12 +66,14 @@ void gp_Trsf2d::SetTransformation (const gp_Ax2d& FromA1,
 void gp_Trsf2d::SetTransformation (const gp_Ax2d& A)
 {
   shape = gp_CompoundTrsf;
-  scale = 1.0;
   const gp_XY& V1 = A.Direction().XY();
   gp_XY V2 (-V1.Y(), V1.X());
-  matrix.SetCol (1, V1);
-  matrix.SetCol (2, V2);
-  loc = A.Location().XY();
+
+  SetValues(V1.X(), V2.X(), A.Location().X(),
+            V1.Y(), V2.Y(), A.Location().Y());
+
+  scale = 1.0;
+
   matrix.Transpose();
   loc.Multiply (matrix);
   loc.Reverse();
@@ -497,3 +500,73 @@ void gp_Trsf2d::PreMultiply (const gp_Trsf2d& T)
   }
 }
 
+//=======================================================================
+//function : SetValues
+//purpose  : 
+//=======================================================================
+void gp_Trsf2d::SetValues(const Standard_Real a11,
+                          const Standard_Real a12,
+                          const Standard_Real a13,
+                          const Standard_Real a21,
+                          const Standard_Real a22,
+                          const Standard_Real a23)
+{
+  gp_XY col1(a11,a21);
+  gp_XY col2(a12,a22);
+  gp_XY col3(a13,a23);
+  // compute the determinant
+  gp_Mat2d M(col1,col2);
+  Standard_Real s = M.Determinant();
+  Standard_Real As = s;
+  if (As < 0)
+    As = - As;
+  Standard_ConstructionError_Raise_if
+    (As < gp::Resolution(),"gp_Trsf2d::SetValues, null determinant");
+
+  if (s > 0)
+    s = sqrt(s);
+  else
+    s = sqrt(-s);
+  
+  M.Divide(s);
+
+  scale = s;
+  shape = gp_CompoundTrsf;
+
+  matrix = M;
+  Orthogonalize();
+  
+  loc = col3;
+}
+
+
+//=======================================================================
+//function : Orthogonalize
+//purpose  : 
+//=======================================================================
+void gp_Trsf2d::Orthogonalize()
+{
+  gp_Mat2d aTM(matrix);
+
+  gp_XY aV1 = aTM.Column(1);
+  gp_XY aV2 = aTM.Column(2);
+
+  aV1.Normalize();
+
+  aV2 -= aV1*(aV2.Dot(aV1));
+  aV2.Normalize();
+
+  aTM.SetCols(aV1, aV2);
+
+  aV1 = aTM.Row(1);
+  aV2 = aTM.Row(2);
+
+  aV1.Normalize();
+
+  aV2 -= aV1*(aV2.Dot(aV1));
+  aV2.Normalize();
+
+  aTM.SetRows(aV1, aV2);
+
+  matrix = aTM;
+}
diff --git a/tests/bugs/modalg_5/bug22831 b/tests/bugs/modalg_5/bug22831
index 9929eb05aa..ed76b72127 100644
--- a/tests/bugs/modalg_5/bug22831
+++ b/tests/bugs/modalg_5/bug22831
@@ -1,7 +1,3 @@
-puts "TODO DEBUG_OCC24121 Debian60-64 Windows: \\*\\* Exception \\*\\*.*"
-puts "TODO DEBUG_OCC24121 Debian60-64 Windows: An exception was caught"
-puts "TODO DEBUG_OCC24121 Debian60-64 Windows: TEST INCOMPLETE"
-
 puts "============"
 puts "OCC22831"
 puts "============"
diff --git a/tests/de/iges_1/J9 b/tests/de/iges_1/J9
index 33c68b37f5..3ff8684b74 100644
--- a/tests/de/iges_1/J9
+++ b/tests/de/iges_1/J9
@@ -8,8 +8,8 @@ set ref_data {
 DATA        : Faulties = 0  ( 0 )  Warnings = 0  ( 1 )  Summary  = 0  ( 1 )
 TPSTAT      : Faulties = 0  ( 28 )  Warnings = 115  ( 7 )  Summary  = 115  ( 35 )
 CHECKSHAPE  : Wires    = 0  ( 0 )  Faces    = 0  ( 0 )  Shells   = 0  ( 1 )   Solids   = 0 ( 1 )
-NBSHAPES    : Solid    = 0  ( 18 )  Shell    = 0  ( 18 )  Face     = 1190  ( 1190 )   Summary  = 15075  ( 7693 )
-STATSHAPE   : Solid    = 0  ( 18 )  Shell    = 0  ( 18 )  Face     = 1190  ( 1190 )   FreeWire = 0  ( 0 )   FreeEdge  = 0 ( 0 )   SharedEdge = 6284  ( 3134 )
+NBSHAPES    : Solid    = 0  ( 18 )  Shell    = 0  ( 18 )  Face     = 1190  ( 1190 )   Summary  = 15073  ( 7693 )
+STATSHAPE   : Solid    = 0  ( 18 )  Shell    = 0  ( 18 )  Face     = 1190  ( 1190 )   FreeWire = 0  ( 0 )   FreeEdge  = 0 ( 0 )   SharedEdge = 6283  ( 3134 )
 TOLERANCE   : MaxTol   =   0.2496383637  (   0.2496258832 )  AvgTol   =  0.002193043247  (  0.004111699336 )
 LABELS      : N0Labels = 27  ( 27 )  N1Labels = 0  ( 0 )  N2Labels = 0  ( 0 )   TotalLabels = 27  ( 27 )   NameLabels = 27  ( 27 )   ColorLabels = 0  ( 0 )   LayerLabels = 0  ( 0 )
 PROPS       : Centroid = 0  ( 0 )  Volume   = 0  ( 0 )  Area     = 0  ( 0 )
diff --git a/tests/de/iges_1/K3 b/tests/de/iges_1/K3
index a68c905db2..ea16d18962 100644
--- a/tests/de/iges_1/K3
+++ b/tests/de/iges_1/K3
@@ -12,7 +12,7 @@ CHECKSHAPE  : Wires    = 12  ( 18 )  Faces    = 16  ( 16 )  Shells   = 0  ( 0 )
 NBSHAPES    : Solid    = 0  ( 0 )  Shell    = 0  ( 0 )  Face     = 5163  ( 5163 )   Summary  = 68418  ( 68418 )
 STATSHAPE   : Solid    = 0  ( 0 )  Shell    = 0  ( 0 )  Face     = 5163  ( 5163 )   FreeWire = 10  ( 10 )   FreeEdge  = 283 ( 283 )   SharedEdge = 29071  ( 29075 )
 TOLERANCE   : MaxTol   =   0.9874083984  (   0.9875071265 )  AvgTol   =    0.0111430941  (   0.01115568387 )
-LABELS      : N0Labels = 5392  ( 5458 )  N1Labels = 18  ( 4437 )  N2Labels = 0  ( 0 )   TotalLabels = 5410  ( 9895 )   NameLabels = 5392  ( 5458 )   ColorLabels = 5391  ( 9829 )   LayerLabels = 5391  ( 9829 )
+LABELS      : N0Labels = 5392  ( 5458 )  N1Labels = 18  ( 4443 )  N2Labels = 0  ( 0 )   TotalLabels = 5410  ( 9901 )   NameLabels = 5392  ( 5458 )   ColorLabels = 5391  ( 9835 )   LayerLabels = 5391  ( 9835 )
 PROPS       : Centroid = 0  ( 0 )  Volume   = 0  ( 0 )  Area     = 0  ( 0 )
 NCOLORS     : NColors  = 4  ( 4 )
 COLORS      : Colors   = BLACK BLUE1 CYAN1 GREEN  ( BLACK BLUE1 CYAN1 GREEN )
diff --git a/tests/de/iges_2/B8 b/tests/de/iges_2/B8
index 222077ef71..fdda334316 100644
--- a/tests/de/iges_2/B8
+++ b/tests/de/iges_2/B8
@@ -16,7 +16,7 @@ CHECKSHAPE  : Wires    = 12  ( 17 )  Faces    = 12  ( 11 )  Shells   = 0  ( 0 )
 NBSHAPES    : Solid    = 0  ( 0 )  Shell    = 0  ( 0 )  Face     = 4729  ( 4729 )   Summary  = 63154  ( 63144 )
 STATSHAPE   : Solid    = 0  ( 0 )  Shell    = 0  ( 0 )  Face     = 4729  ( 4729 )   FreeWire = 18  ( 18 )   FreeEdge  = 452 ( 452 )   SharedEdge = 26794  ( 26793 )
 TOLERANCE   : MaxTol   =   0.9804479161  (   0.9805459497 )  AvgTol   =   0.01153089029  (   0.01154870945 )
-LABELS      : N0Labels = 5089  ( 5165 )  N1Labels = 26  ( 3844 )  N2Labels = 0  ( 0 )   TotalLabels = 5115  ( 9009 )   NameLabels = 5089  ( 5165 )   ColorLabels = 5086  ( 8933 )   LayerLabels = 5086  ( 8933 )
+LABELS      : N0Labels = 5089  ( 5165 )  N1Labels = 26  ( 3846 )  N2Labels = 0  ( 0 )   TotalLabels = 5115  ( 9011 )   NameLabels = 5089  ( 5165 )   ColorLabels = 5086  ( 8935 )   LayerLabels = 5086  ( 8935 )
 PROPS       : Centroid = 0  ( 0 )  Volume   = 0  ( 0 )  Area     = 0  ( 0 )
 NCOLORS     : NColors  = 3  ( 3 )
 COLORS      : Colors   = BLUE1 CYAN1 GREEN  ( BLUE1 CYAN1 GREEN )
diff --git a/tests/de/iges_2/E6 b/tests/de/iges_2/E6
index 1ad5fe8d17..fc944857b5 100644
--- a/tests/de/iges_2/E6
+++ b/tests/de/iges_2/E6
@@ -15,7 +15,7 @@ CHECKSHAPE  : Wires    = 0  ( 0 )  Faces    = 0  ( 0 )  Shells   = 0  ( 0 )   So
 NBSHAPES    : Solid    = 0  ( 0 )  Shell    = 0  ( 0 )  Face     = 1177  ( 1177 )   Summary  = 18232  ( 18230 )
 STATSHAPE   : Solid    = 0  ( 0 )  Shell    = 0  ( 0 )  Face     = 1177  ( 1177 )   FreeWire = 5  ( 5 )   FreeEdge  = 714 ( 714 )   SharedEdge = 7614  ( 7614 )
 TOLERANCE   : MaxTol   =   0.9436610236  (   0.8261873283 )  AvgTol   =   0.01104814109  (    0.0107628002 )
-LABELS      : N0Labels = 1884  ( 1885 )  N1Labels = 0  ( 1020 )  N2Labels = 0  ( 0 )   TotalLabels = 1884  ( 2905 )   NameLabels = 1884  ( 1885 )   ColorLabels = 1873  ( 2904 )   LayerLabels = 1873  ( 2904 )
+LABELS      : N0Labels = 1884  ( 1885 )  N1Labels = 0  ( 1019 )  N2Labels = 0  ( 0 )   TotalLabels = 1884  ( 2904 )   NameLabels = 1884  ( 1885 )   ColorLabels = 1873  ( 2903 )   LayerLabels = 1873  ( 2903 )
 PROPS       : Centroid = 0  ( 0 )  Volume   = 0  ( 0 )  Area     = 0  ( 0 )
 NCOLORS     : NColors  = 7  ( 7 )
 COLORS      : Colors   = BLACK BLUE1 CYAN1 GREEN RED WHITE YELLOW  ( BLACK BLUE1 CYAN1 GREEN RED WHITE YELLOW )
diff --git a/tests/de/iges_2/G1 b/tests/de/iges_2/G1
index 8e96c58bcf..1704c39fa7 100755
--- a/tests/de/iges_2/G1
+++ b/tests/de/iges_2/G1
@@ -1,6 +1,5 @@
 # !!!! This file is generated automatically, do not edit manually! See end script
 puts "TODO CR23096 ALL: TPSTAT : Faulty" 
-puts "TODO CR23096 ALL: CHECKSHAPE : Faulty" 
 puts "TODO CR23096 ALL: LABELS : Faulty" 
 
 
diff --git a/tests/mesh/data/standard/J1 b/tests/mesh/data/standard/J1
index b39110db37..69a06e7d79 100755
--- a/tests/mesh/data/standard/J1
+++ b/tests/mesh/data/standard/J1
@@ -1,3 +1,3 @@
 set TheFileName shading_082.brep
 set bug_cross "OCC22687"
-set nbcross(All) 16
+set nbcross(All) 0
diff --git a/tests/offset/wire_closed_inside_0_075/C7 b/tests/offset/wire_closed_inside_0_075/C7
index 066233d4ec..497da0a356 100644
--- a/tests/offset/wire_closed_inside_0_075/C7
+++ b/tests/offset/wire_closed_inside_0_075/C7
@@ -1,16 +1,6 @@
-set os "ALL"
-if {[array get env os_type] != ""} {
-  set os $env(os_type)
-}
-
-if {
-        [string compare $os "Debian40"] == 0
-    ||  [string compare $os "Mandriva2008"] == 0
-   } {
-  puts "TODO OCC23068 $os: Faulty shapes in variables faulty_1 to faulty_4"
-  puts "TODO OCC23068 $os: Error : The length of result shape is"
-  puts "TODO OCC23068 $os: Error : Result shape is WRONG"
-}
+puts "TODO OCC23068 ALL: Faulty shapes in variables faulty_1 to faulty_4"
+puts "TODO OCC23068 ALL: Error : The length of the resulting shape is"
+puts "TODO OCC23068 ALL: Error : The resulting shape is WRONG because it must contain"
 
 restore [locate_data_file offset_wire_038.brep] s