diff --git a/testbed/data/polygon_test_01.dat b/testbed/data/polygon_test_01.dat
new file mode 100644
index 0000000..1f04160
--- /dev/null
+++ b/testbed/data/polygon_test_01.dat
@@ -0,0 +1,12 @@
+-0.388419120000000006598384061363 0.0368141516905975269002837535481
+-0.388419120000000006598384061363 0.0104235565411950892311665484158
+-0.611580879999999993401615938637 0.0104235565411950892311665484158
+-0.611580879999999993401615938637 0.1483950316905975341796875
+-0.578899596898762469621146919962 0.227294628589359948289683188705
+-0.500000000000000000000000000000 0.259975911690597527581303438637
++0.500000000000000000000000000000 0.259975911690597527581303438637
++0.578899596898762469621146919962 0.227294628589359948289683188705
++0.611580879999999993401615938637 0.1483950316905975341796875
++0.611580879999999993401615938637 0.0104235565411950614755909327869
++0.388419120000000006598384061363 0.0104235565411950892311665484158
++0.388419120000000006598384061363 0.0368141516905975130224959457337
diff --git a/testbed/data/polygon_test_02.dat b/testbed/data/polygon_test_02.dat
new file mode 100644
index 0000000..a8b9489
--- /dev/null
+++ b/testbed/data/polygon_test_02.dat
@@ -0,0 +1,13 @@
+0.9636984967276516 0.7676550649687783
+0.9636984967276516 -0.7676550649687641
+-0.3074475690811459 -0.7676550649687641
+0.09401654924378076 -0.2590574983578904
+0.10567230819363671 -0.09864698028880525
+-0.03901177977841874 -0.028405214140875046
+-0.428964921810446 -0.08483619470406722
+-0.5128305980156834 -0.12847817634298053
+-0.5512747518916774 -0.2148501697175078
+-0.5917836778064418 -0.7037530067555622
+-0.5520451065921502 -0.7676550649687641
+-0.9636984967276516 -0.7676550649687641
+-0.9636984967276516 0.767655064968778
diff --git a/testbed/data/polygon_test_03.dat b/testbed/data/polygon_test_03.dat
new file mode 100644
index 0000000..9554f2f
--- /dev/null
+++ b/testbed/data/polygon_test_03.dat
@@ -0,0 +1,7 @@
+0.9776422201600001 0.9776422201599928
+0.9776422201599999 -0.977642220160007
+-0.12788518519240472 -0.9776422201599928
+-0.3913394510746002 -0.33861494064331055
+-0.47812835166211676 -0.9776422201599928
+-0.9776422201600001 -0.9776422201599928
+-0.9776422201600001 0.977642220160007
diff --git a/unittest/main.cpp b/unittest/main.cpp
index dc86f4a..2a1f5b4 100644
--- a/unittest/main.cpp
+++ b/unittest/main.cpp
@@ -113,6 +113,81 @@ BOOST_AUTO_TEST_CASE(ConcaveBoundaryTest)
 }
 
 
+BOOST_AUTO_TEST_CASE(PolygonTest01)
+{
+  // Reported in issue #10
+  std::vector<p2t::Point*> polyline = {
+    new p2t::Point(-0.388419120000000006598384061363, 0.0368141516905975269002837535481),
+    new p2t::Point(-0.388419120000000006598384061363, 0.0104235565411950892311665484158),
+    new p2t::Point(-0.611580879999999993401615938637, 0.0104235565411950892311665484158),
+    new p2t::Point(-0.611580879999999993401615938637, 0.1483950316905975341796875),
+    new p2t::Point(-0.578899596898762469621146919962, 0.227294628589359948289683188705),
+    new p2t::Point(-0.500000000000000000000000000000, 0.259975911690597527581303438637),
+    new p2t::Point(+0.500000000000000000000000000000, 0.259975911690597527581303438637),
+    new p2t::Point(+0.578899596898762469621146919962, 0.227294628589359948289683188705),
+    new p2t::Point(+0.611580879999999993401615938637, 0.1483950316905975341796875),
+    new p2t::Point(+0.611580879999999993401615938637, 0.0104235565411950614755909327869),
+    new p2t::Point(+0.388419120000000006598384061363, 0.0104235565411950892311665484158),
+    new p2t::Point(+0.388419120000000006598384061363, 0.0368141516905975130224959457337)
+  };
+  p2t::CDT cdt{ polyline };
+  BOOST_CHECK_NO_THROW(cdt.Triangulate());
+  const auto result = cdt.GetTriangles();
+  BOOST_REQUIRE_EQUAL(result.size(), 10);
+  for (const auto p : polyline) {
+     delete p;
+  }
+}
+
+
+BOOST_AUTO_TEST_CASE(PolygonTest02)
+{
+  // Reported in issue #10
+  std::vector<p2t::Point*> polyline = {
+    new p2t::Point(0.9636984967276516, 0.7676550649687783),
+    new p2t::Point(0.9636984967276516, -0.7676550649687641),
+    new p2t::Point(-0.3074475690811459, -0.7676550649687641),
+    new p2t::Point(0.09401654924378076, -0.2590574983578904),
+    new p2t::Point(0.10567230819363671, -0.09864698028880525),
+    new p2t::Point(-0.03901177977841874, -0.028405214140875046),
+    new p2t::Point(-0.428964921810446, -0.08483619470406722),
+    new p2t::Point(-0.5128305980156834, -0.12847817634298053),
+    new p2t::Point(-0.5512747518916774, -0.2148501697175078),
+    new p2t::Point(-0.5917836778064418, -0.7037530067555622),
+    new p2t::Point(-0.5520451065921502, -0.7676550649687641),
+    new p2t::Point(-0.9636984967276516, -0.7676550649687641),
+    new p2t::Point(-0.9636984967276516, 0.767655064968778)
+  };
+  p2t::CDT cdt{ polyline };
+  BOOST_CHECK_NO_THROW(cdt.Triangulate());
+  const auto result = cdt.GetTriangles();
+  BOOST_REQUIRE_EQUAL(result.size(), 11);
+  for (const auto p : polyline) {
+    delete p;
+  }
+}
+
+BOOST_AUTO_TEST_CASE(PolygonTest03)
+{
+  // Reported in issue #10
+  std::vector<p2t::Point*> polyline = {
+    new p2t::Point(0.9776422201600001, 0.9776422201599928),
+    new p2t::Point(0.9776422201599999, -0.977642220160007),
+    new p2t::Point(-0.12788518519240472, -0.9776422201599928),
+    new p2t::Point(-0.3913394510746002, -0.33861494064331055),
+    new p2t::Point(-0.47812835166211676, -0.9776422201599928),
+    new p2t::Point(-0.9776422201600001, -0.9776422201599928),
+    new p2t::Point(-0.9776422201600001, 0.977642220160007)
+  };
+  p2t::CDT cdt{ polyline };
+  BOOST_CHECK_NO_THROW(cdt.Triangulate());
+  const auto result = cdt.GetTriangles();
+  BOOST_REQUIRE_EQUAL(result.size(), 5);
+  for (const auto p : polyline) {
+    delete p;
+  }
+}
+
 BOOST_AUTO_TEST_CASE(TestbedFilesTest)
 {
   for (const auto& filename : { "custom.dat", "diamond.dat", "star.dat", "test.dat" }) {