diff --git a/src/db/db/dbTriangles.cc b/src/db/db/dbTriangles.cc
index 92add3390..6f4e928f5 100644
--- a/src/db/db/dbTriangles.cc
+++ b/src/db/db/dbTriangles.cc
@@ -1414,6 +1414,23 @@ Triangles::clear ()
   m_id = 0;
 }
 
+template<class Poly, class Trans>
+void
+Triangles::make_contours (const Poly &poly, const Trans &trans, std::vector<std::vector<db::Vertex *> > &edge_contours)
+{
+  edge_contours.push_back (std::vector<db::Vertex *> ());
+  for (auto pt = poly.begin_hull (); pt != poly.end_hull (); ++pt) {
+    edge_contours.back ().push_back (insert_point (trans * *pt));
+  }
+
+  for (unsigned int h = 0; h < poly.holes (); ++h) {
+    edge_contours.push_back (std::vector<db::Vertex *> ());
+    for (auto pt = poly.begin_hole (h); pt != poly.end_hole (h); ++pt) {
+      edge_contours.back ().push_back (insert_point (trans * *pt));
+    }
+  }
+}
+
 void
 Triangles::create_constrained_delaunay (const db::Region &region, double dbu)
 {
@@ -1421,25 +1438,36 @@ Triangles::create_constrained_delaunay (const db::Region &region, double dbu)
 
   std::vector<std::vector<db::Vertex *> > edge_contours;
 
+  db::CplxTrans trans (dbu);
   for (auto p = region.begin_merged (); ! p.at_end (); ++p) {
-
-    edge_contours.push_back (std::vector<db::Vertex *> ());
-    for (auto pt = p->begin_hull (); pt != p->end_hull (); ++pt) {
-      edge_contours.back ().push_back (insert_point (db::DPoint (*pt) * dbu));
-    }
-
-    for (unsigned int h = 0; h < p->holes (); ++h) {
-      edge_contours.push_back (std::vector<db::Vertex *> ());
-      for (auto pt = p->begin_hole (h); pt != p->end_hole (h); ++pt) {
-        edge_contours.back ().push_back (insert_point (db::DPoint (*pt) * dbu));
-      }
-    }
-
+    make_contours (*p, trans, edge_contours);
   }
 
   constrain (edge_contours);
 }
 
+void
+Triangles::create_constrained_delaunay (const db::Polygon &p, double dbu)
+{
+  clear ();
+
+  std::vector<std::vector<db::Vertex *> > edge_contours;
+  make_contours (p, db::CplxTrans (dbu), edge_contours);
+
+  constrain (edge_contours);
+}
+
+void
+Triangles::create_constrained_delaunay (const db::DPolygon &p)
+{
+  clear ();
+
+  std::vector<std::vector<db::Vertex *> > edge_contours;
+  make_contours (p, db::DUnitTrans (), edge_contours);
+
+  constrain (edge_contours);
+}
+
 static bool is_skinny (const db::Triangle *tri, const Triangles::TriangulateParameters &param)
 {
   if (param.min_b < db::epsilon) {
@@ -1479,7 +1507,30 @@ Triangles::triangulate (const db::Region &region, const TriangulateParameters &p
   tl::SelfTimer timer (tl::verbosity () > parameters.base_verbosity, "Triangles::triangulate");
 
   create_constrained_delaunay (region, dbu);
+  refine (parameters);
+}
 
+void
+Triangles::triangulate (const db::Polygon &poly, const TriangulateParameters &parameters, double dbu)
+{
+  tl::SelfTimer timer (tl::verbosity () > parameters.base_verbosity, "Triangles::triangulate");
+
+  create_constrained_delaunay (poly, dbu);
+  refine (parameters);
+}
+
+void
+Triangles::triangulate (const db::DPolygon &poly, const TriangulateParameters &parameters)
+{
+  tl::SelfTimer timer (tl::verbosity () > parameters.base_verbosity, "Triangles::triangulate");
+
+  create_constrained_delaunay (poly);
+  refine (parameters);
+}
+
+void
+Triangles::refine (const TriangulateParameters &parameters)
+{
   if (parameters.min_b < db::epsilon && parameters.max_area < db::epsilon && parameters.max_area_border < db::epsilon) {
 
     //  no refinement requested - we're done.
diff --git a/src/db/db/dbTriangles.h b/src/db/db/dbTriangles.h
index 0e54508b8..26bb8d88c 100644
--- a/src/db/db/dbTriangles.h
+++ b/src/db/db/dbTriangles.h
@@ -154,6 +154,16 @@ public:
    */
   void triangulate (const db::Region &region, const TriangulateParameters &parameters, double dbu = 1.0);
 
+  /**
+   *  @brief Triangulates a polygon
+   */
+  void triangulate (const db::Polygon &poly, const TriangulateParameters &parameters, double dbu = 1.0);
+
+  /**
+   *  @brief Triangulates a floating-point polygon
+   */
+  void triangulate (const db::DPolygon &poly, const TriangulateParameters &parameters);
+
   /**
    *  @brief Statistics: number of flips (fixing)
    */
@@ -271,6 +281,16 @@ protected:
    */
   void create_constrained_delaunay (const db::Region &region, double dbu = 1.0);
 
+  /**
+   *  @brief Creates a constrained Delaunay triangulation from the given Polygon
+   */
+  void create_constrained_delaunay (const db::Polygon &poly, double dbu = 1.0);
+
+  /**
+   *  @brief Creates a constrained Delaunay triangulation from the given DPolygon
+   */
+  void create_constrained_delaunay (const db::DPolygon &poly);
+
   /**
    *  @brief Returns a value indicating whether the edge is "illegal" (violates the Delaunay criterion)
    */
@@ -312,6 +332,8 @@ private:
   void insert_new_vertex(db::Vertex *vertex, std::list<tl::weak_ptr<Triangle> > *new_triangles_out);
   std::vector<db::TriangleEdge *> ensure_edge_inner (db::Vertex *from, db::Vertex *to);
   void join_edges (std::vector<TriangleEdge *> &edges);
+  void refine (const TriangulateParameters &param);
+  template<class Poly, class Trans> void make_contours (const Poly &poly, const Trans &trans, std::vector<std::vector<db::Vertex *> > &contours);
 };
 
 }