diff --git a/libs/kimath/include/geometry/shape_poly_set.h b/libs/kimath/include/geometry/shape_poly_set.h
index bce4ac27ad..1e282cc8a5 100644
--- a/libs/kimath/include/geometry/shape_poly_set.h
+++ b/libs/kimath/include/geometry/shape_poly_set.h
@@ -1176,7 +1176,7 @@ class SHAPE_POLY_SET : public SHAPE
          * @return int -  The minimum distance between aPoint and all the segments of the aIndex-th
          *                polygon. If the point is contained in the polygon, the distance is zero.
          */
-        SEG::ecoord SquaredDistanceToPolygon( VECTOR2I aPoint, int aIndex );
+        SEG::ecoord SquaredDistanceToPolygon( VECTOR2I aPoint, int aIndex ) const;
 
         /**
          * Function DistanceToPolygon
@@ -1190,7 +1190,7 @@ class SHAPE_POLY_SET : public SHAPE
          *                  aIndex-th polygon. If the point is contained in the polygon, the
          *                  distance is zero.
          */
-        SEG::ecoord SquaredDistanceToPolygon( const SEG& aSegment, int aIndex );
+        SEG::ecoord SquaredDistanceToPolygon( const SEG& aSegment, int aIndex ) const;
 
         /**
          * Function SquaredDistance
@@ -1200,7 +1200,7 @@ class SHAPE_POLY_SET : public SHAPE
          * @return The minimum distance squared between aPoint and all the polygons in the set.
          *         If the point is contained in any of the polygons, the distance is zero.
          */
-        SEG::ecoord SquaredDistance( VECTOR2I aPoint );
+        SEG::ecoord SquaredDistance( VECTOR2I aPoint ) const;
 
         /**
          * Function SquaredDistance
@@ -1211,7 +1211,7 @@ class SHAPE_POLY_SET : public SHAPE
          * @return  The minimum distance squared between aSegment and all the polygons in the set.
          *          If the point is contained in the polygon, the distance is zero.
          */
-        SEG::ecoord SquaredDistance( const SEG& aSegment );
+        SEG::ecoord SquaredDistance( const SEG& aSegment ) const;
 
         /**
          * Function IsVertexInHole.
diff --git a/libs/kimath/include/geometry/shape_simple.h b/libs/kimath/include/geometry/shape_simple.h
index a9a9027cf2..2b8d6dcf24 100644
--- a/libs/kimath/include/geometry/shape_simple.h
+++ b/libs/kimath/include/geometry/shape_simple.h
@@ -52,6 +52,13 @@ public:
         m_points.SetClosed( true );
     }
 
+    SHAPE_SIMPLE( const SHAPE_LINE_CHAIN& aPoly ) :
+        SHAPE( SH_SIMPLE ),
+        m_points( aPoly )
+    {
+        m_points.SetClosed( true );
+    }
+
     SHAPE_SIMPLE( const SHAPE_SIMPLE& aOther ) :
        SHAPE( SH_SIMPLE ), m_points( aOther.m_points )
     {}
diff --git a/libs/kimath/src/geometry/shape_poly_set.cpp b/libs/kimath/src/geometry/shape_poly_set.cpp
index 21f9d19df5..1e59064ca9 100644
--- a/libs/kimath/src/geometry/shape_poly_set.cpp
+++ b/libs/kimath/src/geometry/shape_poly_set.cpp
@@ -1584,7 +1584,7 @@ SHAPE_POLY_SET::POLYGON SHAPE_POLY_SET::FilletPolygon( unsigned int aRadius, int
 }
 
 
-SEG::ecoord SHAPE_POLY_SET::SquaredDistanceToPolygon( VECTOR2I aPoint, int aPolygonIndex )
+SEG::ecoord SHAPE_POLY_SET::SquaredDistanceToPolygon( VECTOR2I aPoint, int aPolygonIndex ) const
 {
     // We calculate the min dist between the segment and each outline segment.  However, if the
     // segment to test is inside the outline, and does not cross any edge, it can be seen outside
@@ -1593,7 +1593,7 @@ SEG::ecoord SHAPE_POLY_SET::SquaredDistanceToPolygon( VECTOR2I aPoint, int aPoly
     if( containsSingle( aPoint, aPolygonIndex, 1 ) )
         return 0;
 
-    SEGMENT_ITERATOR iterator = IterateSegmentsWithHoles( aPolygonIndex );
+    CONST_SEGMENT_ITERATOR iterator = CIterateSegmentsWithHoles( aPolygonIndex );
 
     SEG polygonEdge = *iterator;
     SEG::ecoord minDistance = polygonEdge.SquaredDistance( aPoint );
@@ -1612,7 +1612,7 @@ SEG::ecoord SHAPE_POLY_SET::SquaredDistanceToPolygon( VECTOR2I aPoint, int aPoly
 }
 
 
-SEG::ecoord SHAPE_POLY_SET::SquaredDistanceToPolygon( const SEG& aSegment, int aPolygonIndex )
+SEG::ecoord SHAPE_POLY_SET::SquaredDistanceToPolygon( const SEG& aSegment, int aPolygonIndex ) const
 {
     // We calculate the min dist between the segment and each outline segment.  However, if the
     // segment to test is inside the outline, and does not cross any edge, it can be seen outside
@@ -1621,9 +1621,9 @@ SEG::ecoord SHAPE_POLY_SET::SquaredDistanceToPolygon( const SEG& aSegment, int a
     if( containsSingle( aSegment.A, aPolygonIndex, 1 ) )
         return 0;
 
-    SEGMENT_ITERATOR iterator = IterateSegmentsWithHoles( aPolygonIndex );
-    SEG              polygonEdge = *iterator;
-    SEG::ecoord      minDistance = polygonEdge.SquaredDistance( aSegment );
+    CONST_SEGMENT_ITERATOR iterator = CIterateSegmentsWithHoles( aPolygonIndex );
+    SEG                    polygonEdge = *iterator;
+    SEG::ecoord            minDistance = polygonEdge.SquaredDistance( aSegment );
 
     for( iterator++; iterator && minDistance > 0; iterator++ )
     {
@@ -1640,7 +1640,7 @@ SEG::ecoord SHAPE_POLY_SET::SquaredDistanceToPolygon( const SEG& aSegment, int a
 }
 
 
-SEG::ecoord SHAPE_POLY_SET::SquaredDistance( VECTOR2I aPoint )
+SEG::ecoord SHAPE_POLY_SET::SquaredDistance( VECTOR2I aPoint ) const
 {
     SEG::ecoord currentDistance;
     SEG::ecoord minDistance = SquaredDistanceToPolygon( aPoint, 0 );
@@ -1658,7 +1658,7 @@ SEG::ecoord SHAPE_POLY_SET::SquaredDistance( VECTOR2I aPoint )
 }
 
 
-SEG::ecoord SHAPE_POLY_SET::SquaredDistance( const SEG& aSegment )
+SEG::ecoord SHAPE_POLY_SET::SquaredDistance( const SEG& aSegment ) const
 {
     SEG::ecoord currentDistance;
     SEG::ecoord minDistance = SquaredDistanceToPolygon( aSegment, 0 );