diff --git a/src/BRepTools/BRepTools_NurbsConvertModification.cxx b/src/BRepTools/BRepTools_NurbsConvertModification.cxx
index 67565185c9..f3941f0174 100644
--- a/src/BRepTools/BRepTools_NurbsConvertModification.cxx
+++ b/src/BRepTools/BRepTools_NurbsConvertModification.cxx
@@ -504,10 +504,9 @@ Standard_Boolean BRepTools_NurbsConvertModification::NewCurve2d
         }
         aMinDist *= aMinDist;
         //Old domain
-        Standard_Real t = 0.5 * (f2d + l2d);
-        gp_Pnt2d aPf = C2d->Value(t);
+        gp_Pnt2d aPf = C2d->Value(f2d);
         //New domain
-        gp_Pnt2d aNewPf = Curve2d->Value(t);
+        gp_Pnt2d aNewPf = Curve2d->Value(f2d);
         gp_Vec2d aT(aNewPf, aPf);
         if (aT.SquareMagnitude() > aMinDist)
         {
diff --git a/src/GeomConvert/GeomConvert_1.cxx b/src/GeomConvert/GeomConvert_1.cxx
index da4229b424..0f619b5534 100644
--- a/src/GeomConvert/GeomConvert_1.cxx
+++ b/src/GeomConvert/GeomConvert_1.cxx
@@ -383,6 +383,7 @@ Handle(Geom_BSplineSurface) GeomConvert::SurfaceToBSplineSurface
     //
     //For cylinders, cones, spheres, toruses
     const Standard_Boolean isUClosed = Abs((ULast - UFirst) - 2. * M_PI) <= Precision::PConfusion();
+    const Standard_Real eps = 100. * Epsilon(2. * M_PI);
     //
     if (Surf->IsKind(STANDARD_TYPE(Geom_Plane))) {
       TColgp_Array2OfPnt Poles (1, 2, 1, 2);
@@ -415,6 +416,11 @@ Handle(Geom_BSplineSurface) GeomConvert::SurfaceToBSplineSurface
       if (isUClosed) {
         Convert_CylinderToBSplineSurface Convert (Cyl, VFirst, VLast);
         TheSurface = BSplineSurfaceBuilder (Convert);
+        Standard_Integer aNbK = TheSurface->NbUKnots();
+        if (Abs(TheSurface->UKnot(1) - UFirst) > eps || Abs(TheSurface->UKnot(aNbK) - ULast) > eps)
+        {
+          TheSurface->CheckAndSegment(UFirst, ULast, VFirst, VLast);
+        }
       }
       else {
         Convert_CylinderToBSplineSurface 
@@ -431,6 +437,11 @@ Handle(Geom_BSplineSurface) GeomConvert::SurfaceToBSplineSurface
       if (isUClosed) {
         Convert_ConeToBSplineSurface Convert (Co, VFirst, VLast);
         TheSurface = BSplineSurfaceBuilder (Convert);
+        Standard_Integer aNbK = TheSurface->NbUKnots();
+        if (Abs(TheSurface->UKnot(1) - UFirst) > eps || Abs(TheSurface->UKnot(aNbK) - ULast) > eps)
+        {
+          TheSurface->CheckAndSegment(UFirst, ULast, VFirst, VLast);
+        }
       }
       else {
         Convert_ConeToBSplineSurface 
@@ -450,6 +461,11 @@ Handle(Geom_BSplineSurface) GeomConvert::SurfaceToBSplineSurface
         //Convert_SphereToBSplineSurface Convert (Sph, UFirst, ULast);
         Convert_SphereToBSplineSurface Convert (Sph, VFirst, VLast, Standard_False);
         TheSurface = BSplineSurfaceBuilder (Convert);
+        Standard_Integer aNbK = TheSurface->NbUKnots();
+        if (Abs(TheSurface->UKnot(1) - UFirst) > eps || Abs(TheSurface->UKnot(aNbK) - ULast) > eps)
+        {
+          TheSurface->CheckAndSegment(UFirst, ULast, VFirst, VLast);
+        }
       }
       else {
         Convert_SphereToBSplineSurface 
@@ -468,10 +484,20 @@ Handle(Geom_BSplineSurface) GeomConvert::SurfaceToBSplineSurface
         Convert_TorusToBSplineSurface Convert (Tr, VFirst, VLast, 
           Standard_False);
         TheSurface = BSplineSurfaceBuilder (Convert);
+        Standard_Integer aNbK = TheSurface->NbUKnots();
+        if (Abs(TheSurface->UKnot(1) - UFirst) > eps || Abs(TheSurface->UKnot(aNbK) - ULast) > eps)
+        {
+          TheSurface->CheckAndSegment(UFirst, ULast, VFirst, VLast);
+        }
       }
       else if (Strim->IsVClosed()) {
         Convert_TorusToBSplineSurface Convert (Tr, UFirst, ULast);
         TheSurface = BSplineSurfaceBuilder (Convert);
+        Standard_Integer aNbK = TheSurface->NbVKnots();
+        if (Abs(TheSurface->VKnot(1) - VFirst) > eps || Abs(TheSurface->VKnot(aNbK) - VLast) > eps)
+        {
+          TheSurface->CheckAndSegment(UFirst, ULast, VFirst, VLast);
+        }
       }
       else {
         Convert_TorusToBSplineSurface 
@@ -575,7 +601,6 @@ Handle(Geom_BSplineSurface) GeomConvert::SurfaceToBSplineSurface
         2 , C->Degree(),
         periodic, C->IsPeriodic());
 
-
     }
 
 
diff --git a/tests/bugs/moddata_3/bug32557 b/tests/bugs/moddata_3/bug32557
index 374a129033..721b4c0612 100644
--- a/tests/bugs/moddata_3/bug32557
+++ b/tests/bugs/moddata_3/bug32557
@@ -4,7 +4,13 @@ puts "==========================================================="
 puts ""
 
 restore [locate_data_file bug32557.brep] f
-
 nurbsconvert bf f
 checkmaxtol bf -ref 1.1e-7
 
+restore [locate_data_file bug32557_1.brep] f
+nurbsconvert bf f
+checkmaxtol bf -ref 1.1e-5
+
+restore [locate_data_file bug32557_2.brep] f
+nurbsconvert bf f
+checkmaxtol bf -ref 0.0002570
\ No newline at end of file