diff --git a/samples/tcl/snowflake.tcl b/samples/tcl/snowflake.tcl
index b9e4bafee4..2819d7ec0f 100644
--- a/samples/tcl/snowflake.tcl
+++ b/samples/tcl/snowflake.tcl
@@ -121,21 +121,21 @@ eval compound [explode mass w] mass
 compound sample occ name material sheets scale mass text
 
 compound snowflake lines text drawing
+bounding snowflake -save x1 y1 z1 x2 y2 z2
 
 # display in 3d view
 vinit Driver1/Viewer1/View1 w=1024 h=768
 vdisplay snowflake lines text
 vrenderparams -msaa 8
-vsetcolor snowflake 0 0 0 
-vsetcolor lines 0 0 0 
-vsetcolor text 0 0 0 
+vsetcolor snowflake BLACK
+vsetcolor lines BLACK
+vsetcolor text  BLACK
 vbackground -color WHITE
 vtop
 vfit
 
 # add dimension:
 # detect vertices extremal in X direction
-bounding snowflake -save x1 y1 z1 x2 y2 z2
 plane f1 x1 0 0 1 0 0
 plane f2 x2 0 0 1 0 0
 mkface f1 f1
@@ -159,7 +159,3 @@ for {set i 1} {$i <= 2} {incr i} {
   }
 }
 vdimension length -length -shapes $v1 $v2 -plane xoy -value 0.001 -dispunits mm -showunits -flyout 70 -label above -color black -text 5 3d sh
-
-if { [regexp HAVE_GL2PS [dversion]] } {
-    puts "You can use command vexport to generate PDF: vexport your_file_path.pdf"
-}
diff --git a/src/BRepTools/BRepTools.cxx b/src/BRepTools/BRepTools.cxx
index f626673fff..327fa12a60 100644
--- a/src/BRepTools/BRepTools.cxx
+++ b/src/BRepTools/BRepTools.cxx
@@ -903,25 +903,61 @@ void BRepTools::RemoveUnusedPCurves(const TopoDS_Shape& S)
 //purpose  : 
 //=======================================================================
 
-Standard_Boolean  BRepTools::Triangulation(const TopoDS_Shape&    S,
-                                           const Standard_Real    deflec)
+Standard_Boolean  BRepTools::Triangulation(const TopoDS_Shape& theShape,
+                                           const Standard_Real theLinDefl,
+                                           const Standard_Boolean theToCheckFreeEdges)
 {
-  TopExp_Explorer exf, exe;
-  TopLoc_Location l;
-  Handle(Poly_Triangulation) T;
-  Handle(Poly_PolygonOnTriangulation) Poly;
-
-  for (exf.Init(S, TopAbs_FACE); exf.More(); exf.Next()) {
-    const TopoDS_Face& F = TopoDS::Face(exf.Current());
-    T = BRep_Tool::Triangulation(F, l);
-    if (T.IsNull() || (T->Deflection() > deflec))
+  TopExp_Explorer anEdgeIter;
+  TopLoc_Location aDummyLoc;
+  for (TopExp_Explorer aFaceIter (theShape, TopAbs_FACE); aFaceIter.More(); aFaceIter.Next())
+  {
+    const TopoDS_Face& aFace = TopoDS::Face (aFaceIter.Current());
+    const Handle(Poly_Triangulation)& aTri = BRep_Tool::Triangulation (aFace, aDummyLoc);
+    if (aTri.IsNull()
+     || aTri->Deflection() > theLinDefl)
+    {
       return Standard_False;
-    for (exe.Init(F, TopAbs_EDGE); exe.More(); exe.Next()) {
-      const TopoDS_Edge& E = TopoDS::Edge(exe.Current());
-      Poly = BRep_Tool::PolygonOnTriangulation(E, T, l);
-      if (Poly.IsNull()) return Standard_False;
+    }
+
+    for (anEdgeIter.Init (aFace, TopAbs_EDGE); anEdgeIter.More(); anEdgeIter.Next())
+    {
+      const TopoDS_Edge& anEdge = TopoDS::Edge (anEdgeIter.Current());
+      const Handle(Poly_PolygonOnTriangulation)& aPoly = BRep_Tool::PolygonOnTriangulation (anEdge, aTri, aDummyLoc);
+      if (aPoly.IsNull())
+      {
+        return Standard_False;
+      }
     }
   }
+  if (!theToCheckFreeEdges)
+  {
+    return Standard_True;
+  }
+
+  Handle(Poly_Triangulation) anEdgeTri;
+  for (anEdgeIter.Init (theShape, TopAbs_EDGE, TopAbs_FACE); anEdgeIter.More(); anEdgeIter.Next())
+  {
+    const TopoDS_Edge& anEdge = TopoDS::Edge (anEdgeIter.Current());
+    const Handle(Poly_Polygon3D)& aPolygon = BRep_Tool::Polygon3D (anEdge, aDummyLoc);
+    if (!aPolygon.IsNull())
+    {
+      if (aPolygon->Deflection() > theLinDefl)
+      {
+        return Standard_False;
+      }
+    }
+    else
+    {
+      const Handle(Poly_PolygonOnTriangulation)& aPoly = BRep_Tool::PolygonOnTriangulation (anEdge, anEdgeTri, aDummyLoc);
+      if (aPoly.IsNull()
+       || anEdgeTri.IsNull()
+       || anEdgeTri->Deflection() > theLinDefl)
+      {
+        return Standard_False;
+      }
+    }
+  }
+
   return Standard_True;
 }
 
diff --git a/src/BRepTools/BRepTools.hxx b/src/BRepTools/BRepTools.hxx
index e1b180128b..5cfc5f7259 100644
--- a/src/BRepTools/BRepTools.hxx
+++ b/src/BRepTools/BRepTools.hxx
@@ -162,10 +162,18 @@ public:
   //! refer to surfaces not belonging to any face of <S>
   Standard_EXPORT static void RemoveUnusedPCurves (const TopoDS_Shape& S);
   
-  //! verifies that each face from the shape <S> has got
-  //! a triangulation  with a  deflection <= deflec  and
-  //! the edges a discretisation on  this triangulation.
-  Standard_EXPORT static Standard_Boolean Triangulation (const TopoDS_Shape& S, const Standard_Real deflec);
+  //! Verifies that each Face from the shape has got a triangulation with a deflection smaller or equal to specified one
+  //! and the Edges a discretization on this triangulation.
+  //! @param theShape   [in] shape to verify
+  //! @param theLinDefl [in] maximum allowed linear deflection
+  //! @param theToCheckFreeEdges [in] if TRUE, then free Edges are required to have 3D polygon
+  //! @return FALSE if input Shape contains Faces without triangulation,
+  //!               or that triangulation has worse (greater) deflection than specified one,
+  //!               or Edges in Shape lack polygons on triangulation
+  //!               or free Edges in Shape lack 3D polygons
+  Standard_EXPORT static Standard_Boolean Triangulation (const TopoDS_Shape& theShape,
+                                                         const Standard_Real theLinDefl,
+                                                         const Standard_Boolean theToCheckFreeEdges = Standard_False);
   
   //! Returns  True if  the    distance between the  two
   //! vertices is lower than their tolerance.
diff --git a/src/Select3D/Select3D_SensitiveSegment.cxx b/src/Select3D/Select3D_SensitiveSegment.cxx
index 8a0051ded0..520741138b 100644
--- a/src/Select3D/Select3D_SensitiveSegment.cxx
+++ b/src/Select3D/Select3D_SensitiveSegment.cxx
@@ -31,6 +31,7 @@ Select3D_SensitiveSegment::Select3D_SensitiveSegment (const Handle(SelectMgr_Ent
                                                       const gp_Pnt& theLastPnt)
 : Select3D_SensitiveEntity (theOwnerId)
 {
+  mySFactor = 3;
   myStart = theFirstPnt;
   myEnd = theLastPnt;
 }
diff --git a/src/StdPrs/StdPrs_ShadedShape.cxx b/src/StdPrs/StdPrs_ShadedShape.cxx
index 996c3840c8..69bf604cc3 100644
--- a/src/StdPrs/StdPrs_ShadedShape.cxx
+++ b/src/StdPrs/StdPrs_ShadedShape.cxx
@@ -542,9 +542,6 @@ void StdPrs_ShadedShape::Add (const Handle (Prs3d_Presentation)& thePrs,
     return;
   }
 
-  // add wireframe presentation for isolated edges and vertices
-  wireframeFromShape (thePrs, theShape, theDrawer);
-
   // Use automatic re-triangulation with deflection-check logic only if this feature is enable
   if (theDrawer->IsAutoTriangulation())
   {
@@ -552,6 +549,9 @@ void StdPrs_ShadedShape::Add (const Handle (Prs3d_Presentation)& thePrs,
     StdPrs_ToolTriangulatedShape::Tessellate (theShape, theDrawer);
   }
 
+  // add wireframe presentation for isolated edges and vertices
+  wireframeFromShape (thePrs, theShape, theDrawer);
+
   // add special wireframe presentation for faces without triangulation
   wireframeNoTriangFacesFromShape (thePrs, theShape, theDrawer);
 
diff --git a/src/StdPrs/StdPrs_ToolTriangulatedShape.cxx b/src/StdPrs/StdPrs_ToolTriangulatedShape.cxx
index 743bc9774f..07db4abeaf 100644
--- a/src/StdPrs/StdPrs_ToolTriangulatedShape.cxx
+++ b/src/StdPrs/StdPrs_ToolTriangulatedShape.cxx
@@ -240,7 +240,7 @@ void StdPrs_ToolTriangulatedShape::Normal (const TopoDS_Face&  theFace,
 Standard_Boolean StdPrs_ToolTriangulatedShape::IsTessellated (const TopoDS_Shape&         theShape,
                                                               const Handle(Prs3d_Drawer)& theDrawer)
 {
-  return BRepTools::Triangulation (theShape, Prs3d::GetDeflection (theShape, theDrawer));
+  return BRepTools::Triangulation (theShape, Prs3d::GetDeflection (theShape, theDrawer), true);
 }
 
 // =======================================================================
diff --git a/src/StdPrs/StdPrs_WFShape.cxx b/src/StdPrs/StdPrs_WFShape.cxx
index f9d5ea929b..c6aeea6c7f 100644
--- a/src/StdPrs/StdPrs_WFShape.cxx
+++ b/src/StdPrs/StdPrs_WFShape.cxx
@@ -100,6 +100,11 @@ void StdPrs_WFShape::Add (const Handle(Prs3d_Presentation)& thePresentation,
     return;
   }
 
+  if (theDrawer->IsAutoTriangulation())
+  {
+    StdPrs_ToolTriangulatedShape::Tessellate (theShape, theDrawer);
+  }
+
   // draw triangulation-only edges
   if (Handle(Graphic3d_ArrayOfPrimitives) aTriFreeEdges = AddEdgesOnTriangulation (theShape, Standard_True))
   {
diff --git a/src/StdSelect/StdSelect_BRepSelectionTool.cxx b/src/StdSelect/StdSelect_BRepSelectionTool.cxx
index 6c74978253..284e2c0f0a 100644
--- a/src/StdSelect/StdSelect_BRepSelectionTool.cxx
+++ b/src/StdSelect/StdSelect_BRepSelectionTool.cxx
@@ -113,8 +113,8 @@ void StdSelect_BRepSelectionTool::Load (const Handle(SelectMgr_Selection)& theSe
                                         const Standard_Real theMaxParam)
 {
   Standard_Integer aPriority = (thePriority == -1) ? GetStandardPriority (theShape, theType) : thePriority;
-
-  if( isAutoTriangulation && !BRepTools::Triangulation (theShape, Precision::Infinite()) )
+  if (isAutoTriangulation
+  && !BRepTools::Triangulation (theShape, Precision::Infinite(), true))
   {
     BRepMesh_IncrementalMesh aMesher(theShape, theDeflection, Standard_False, theDeviationAngle);
   }
@@ -448,7 +448,15 @@ void StdSelect_BRepSelectionTool::GetEdgeSensitive (const TopoDS_Shape& theShape
   if (!aPoints.IsNull()
    && !aPoints->IsEmpty())
   {
-    theSensitive = new Select3D_SensitiveCurve (theOwner, aPoints);
+    if (aPoints->Length() == 2)
+    {
+      // don't waste memory, create a segment
+      theSensitive = new Select3D_SensitiveSegment (theOwner, aPoints->First(), aPoints->Last());
+    }
+    else
+    {
+      theSensitive = new Select3D_SensitiveCurve (theOwner, aPoints);
+    }
     return;
   }
 
diff --git a/tests/bugs/vis/bug25098 b/tests/bugs/vis/bug25098
index dec8510ac4..c434bc741d 100644
--- a/tests/bugs/vis/bug25098
+++ b/tests/bugs/vis/bug25098
@@ -1,10 +1,7 @@
 puts "============"
-puts "OCC25098"
+puts "0025098: Visualization - Calculation of depth on selection of a wire is not accurate"
 puts "============"
 puts ""
-####################################################################################
-# Visualization - Calculation of depth on selection of a wire is not accurate
-####################################################################################
 
 proc ParseEntityInfo {theInfoString} {
   set aStringArr [split $theInfoString " "]
@@ -34,7 +31,7 @@ proc ParseEntityInfo {theInfoString} {
 }
 
 pload VISUALIZATION MODELING
-vinit
+vinit View1
 
 box b 10 10 10
 vdisplay b
@@ -130,9 +127,9 @@ if {[string equal $aWireType "Detected Shape: TopoDS_TWire"] == 0} {
 }
 
 set aWireChildSensitiveType [string trim [lindex $aOut [expr $aWireTypeStringNb + 1]]]
-if {[string equal $aWireChildSensitiveType "Detected Child: Select3D_SensitiveCurve"] == 0} {
+if {[string equal $aWireChildSensitiveType "Detected Child: Select3D_SensitiveSegment"] == 0} {
   puts "Wrong type of wire's inner sensitive! Value is: "
   puts $aWireChildSensitiveType
-  puts "Must be: Detected Child: Select3D_SensitiveCurve"
+  puts "Must be: Detected Child: Select3D_SensitiveSegment"
   puts "ERROR"
 }
diff --git a/tests/bugs/vis/bug31425 b/tests/bugs/vis/bug31425
new file mode 100644
index 0000000000..341d9b3c6b
--- /dev/null
+++ b/tests/bugs/vis/bug31425
@@ -0,0 +1,17 @@
+puts "============="
+puts "0031425: Visualization - free Edge has selection sensitivity inconsistent to presentation"
+puts "============="
+
+pload MODELING VISUALIZATION
+circle circ 150 0 200 1 0 0 100
+mkedge e circ
+wire w e
+vclear
+vinit View1
+vdisplay e
+vaspects e -setLineWidth 2
+vfit
+vviewparams -scale 25.38 -proj 0.5 -0.5 0.5 -up -0.4 0.4 0.8 -at 125.128 46.4744 271.346
+checkpoint pick [vmoveto 275 175] {150 31 294} 1.0
+
+vdump $::imagedir/${::casename}.png
diff --git a/tests/hlr/begin b/tests/hlr/begin
index c06d28ab84..5eb81b45c2 100644
--- a/tests/hlr/begin
+++ b/tests/hlr/begin
@@ -11,7 +11,7 @@ set depsilon 1.e-7
 proc COMPUTE_HLR {viewname algotype} {
      uplevel #0 top
      uplevel #0 clear
-     uplevel #0 vinit
+     uplevel #0 vinit View1
      uplevel #0 vdisplay a
      uplevel #0 $viewname
      uplevel #0 vcomputehlr a result -algoType $algotype
diff --git a/tests/hlr/poly_hlr/bug23625_1 b/tests/hlr/poly_hlr/bug23625_1
index 79d0e80de2..27ea8b6e14 100644
--- a/tests/hlr/poly_hlr/bug23625_1
+++ b/tests/hlr/poly_hlr/bug23625_1
@@ -3,8 +3,16 @@ puts "OCC23625"
 puts "============"
 puts ""
 
+puts "REQUIRED All: Meshing statuses: SelfIntersectingWire Failure"
+
 set viewname "vfront"
-set length 28096.2
+set length 28388
 
 restore [locate_data_file bug23625_a1.brep] a
+
+# workaround bug 0031426 until fix
+vinit View1
+vdefaults -autoTriang 0
+incmesh a 7.6 12
+
 COMPUTE_HLR $viewname $algotype
diff --git a/tests/hlr/poly_hlr/bug23625_2 b/tests/hlr/poly_hlr/bug23625_2
index bf6139d390..568c972e7a 100644
--- a/tests/hlr/poly_hlr/bug23625_2
+++ b/tests/hlr/poly_hlr/bug23625_2
@@ -4,7 +4,7 @@ puts "============"
 puts ""
 
 set viewname "vfront"
-set length 28990.3
+set length 28991.6
 
 restore [locate_data_file bug23625_a2.brep] a
 COMPUTE_HLR $viewname $algotype
diff --git a/tests/hlr/poly_hlr/bug25813_3 b/tests/hlr/poly_hlr/bug25813_3
index 9f874b1c1c..9cddd23203 100644
--- a/tests/hlr/poly_hlr/bug25813_3
+++ b/tests/hlr/poly_hlr/bug25813_3
@@ -1,4 +1,4 @@
-puts "TODO OCC30286 Linux: Error : The length of result shape is 302.441, expected 301.998"
+puts "TODO OCC30286 Linux: Error : The length of result shape is 302.443, expected 301.999"
 
 puts "==========================================="
 puts "OCC25813: regression in Hidden Line Removal"
@@ -6,7 +6,7 @@ puts "==========================================="
 puts ""
 
 set viewname ""
-set length 301.998
+set length 301.999
 
 ptorus a 30 10