diff --git a/CDT/include/CDT.hpp b/CDT/include/CDT.hpp
index 563296cf..7ccadf7a 100644
--- a/CDT/include/CDT.hpp
+++ b/CDT/include/CDT.hpp
@@ -184,10 +184,7 @@ void Triangulation<T, TNearPointLocator>::eraseTrianglesAtIndices(
 template <typename T, typename TNearPointLocator>
 void Triangulation<T, TNearPointLocator>::initializedWithCustomSuperGeometry()
 {
-    for(std::size_t i = 0; i < vertices.size(); ++i)
-    {
-        m_nearPtLocator.addPoint(VertInd(i), vertices);
-    }
+    m_nearPtLocator.initialize(vertices);
     m_nTargetVerts = vertices.size();
     m_superGeomType = SuperGeometryType::Custom;
 }
@@ -416,10 +413,7 @@ void Triangulation<T, TNearPointLocator>::addSuperTriangle(const Box2d<T>& box)
         {VertInd(0), VertInd(1), VertInd(2)},
         {noNeighbor, noNeighbor, noNeighbor}};
     addTriangle(superTri);
-
-    m_nearPtLocator.addPoint(VertInd(0), vertices);
-    m_nearPtLocator.addPoint(VertInd(1), vertices);
-    m_nearPtLocator.addPoint(VertInd(2), vertices);
+    m_nearPtLocator.initialize(vertices);
 }
 
 template <typename T, typename TNearPointLocator>
diff --git a/CDT/include/KDTree.h b/CDT/include/KDTree.h
index f84cf677..b39e982e 100644
--- a/CDT/include/KDTree.h
+++ b/CDT/include/KDTree.h
@@ -91,6 +91,17 @@ class KDTree
         m_root = addNewNode();
     }
 
+    /// Constructor with bounding box known in advance
+    KDTree(const point_type& min, const point_type& max)
+        : m_rootDir(NodeSplitDirection::X)
+        , m_min(min)
+        , m_max(max)
+        , m_isRootBoxInitialized(true)
+        , m_tasksStack(InitialStackDepth, NearestTask())
+    {
+        m_root = addNewNode();
+    }
+
     /// Insert a point into kd-tree
     /// @note external point-buffer is used to reduce kd-tree's memory footprint
     /// @param iPoint index of point in external point-buffer
@@ -333,6 +344,19 @@ class KDTree
             m_max = point_type::make(
                 std::max(m_max.x, p.x), std::max(m_max.y, p.y));
         }
+        // Make sure bounding box does not have a zero size by adding padding:
+        // zero-size bounding box cannot be extended properly
+        const TCoordType padding(1);
+        if(m_min.x == m_max.x)
+        {
+            m_min.x -= padding;
+            m_max.x += padding;
+        }
+        if(m_min.y == m_max.y)
+        {
+            m_min.y -= padding;
+            m_max.y += padding;
+        }
         m_isRootBoxInitialized = true;
     }
 
@@ -372,4 +396,4 @@ class KDTree
 
 } // namespace KDTree
 
-#endif // header guard
\ No newline at end of file
+#endif // header guard
diff --git a/CDT/include/LocatorKDTree.h b/CDT/include/LocatorKDTree.h
index f128b54e..5227ec05 100644
--- a/CDT/include/LocatorKDTree.h
+++ b/CDT/include/LocatorKDTree.h
@@ -25,7 +25,25 @@ template <
 class LocatorKDTree
 {
 public:
-    /// Add point to R-tree
+    /// Initialize KD-tree with points
+    void initialize(const std::vector<V2d<TCoordType> >& points)
+    {
+        typedef V2d<TCoordType> V2d_t;
+        V2d_t min = points.front();
+        V2d_t max = min;
+        typedef typename std::vector<V2d_t>::const_iterator Cit;
+        for(Cit it = points.begin(); it != points.end(); ++it)
+        {
+            min = V2d_t::make(std::min(min.x, it->x), std::min(min.y, it->y));
+            max = V2d_t::make(std::max(max.x, it->x), std::max(max.y, it->y));
+        }
+        m_kdTree = KDTree_t(min, max);
+        for(VertInd i = 0; i < points.size(); ++i)
+        {
+            m_kdTree.insert(i, points);
+        }
+    }
+    /// Add point to KD-tree
     void addPoint(const VertInd i, const std::vector<V2d<TCoordType> >& points)
     {
         m_kdTree.insert(i, points);
@@ -39,12 +57,13 @@ class LocatorKDTree
     }
 
 private:
-    KDTree::KDTree<
+    typedef KDTree::KDTree<
         TCoordType,
         NumVerticesInLeaf,
         InitialStackDepth,
         StackDepthIncrement>
-        m_kdTree;
+        KDTree_t;
+    KDTree_t m_kdTree;
 };
 
 } // namespace CDT