diff --git a/Polygon_mesh_processing/test/Polygon_mesh_processing/data/tri1-hole.off b/Polygon_mesh_processing/test/Polygon_mesh_processing/data/tri1-hole.off
new file mode 100644
index 00000000000..7ba3bb6021b
--- /dev/null
+++ b/Polygon_mesh_processing/test/Polygon_mesh_processing/data/tri1-hole.off
@@ -0,0 +1,37 @@
+OFF
+16 17 0
+
+0 0 0
+0.333333 0 0
+0.666667 0 0
+1 0 0
+0 0.333333 0.333333
+0.333333 0.333333 0.333333
+0.666667 0.333333 0.333333
+1 0.333333 0.333333
+0 0.666667 0.666667
+0.333333 0.666667 0.666667
+0.666667 0.666667 0.666667
+1 0.666667 0.666667
+0 1 1
+0.333333 1 1
+0.666667 1 1
+1 1 1
+
+3  0 1 4
+3  1 5 4
+3  4 5 8
+3  5 9 8
+3  8 9 12
+3  9 13 12
+3  2 6 5
+3  5 6 9
+3  6 10 9
+3  9 10 13
+3  10 14 13
+3  2 3 6
+3  3 7 6
+3  6 7 10
+3  7 11 10
+3  10 11 14
+3  11 15 14
diff --git a/Polygon_mesh_processing/test/Polygon_mesh_processing/data/tri2-out.off b/Polygon_mesh_processing/test/Polygon_mesh_processing/data/tri2-out.off
new file mode 100644
index 00000000000..1127abddf90
--- /dev/null
+++ b/Polygon_mesh_processing/test/Polygon_mesh_processing/data/tri2-out.off
@@ -0,0 +1,38 @@
+OFF
+16 18 0
+
+0 0 0
+0.33333299999999999 0 0
+0.66666700000000001 0 0
+1 0 0
+0 0.33333299999999999 0.33333299999999999
+0.33333299999999999 0.33333299999999999 0.33333299999999999
+0.67039400000000005 0.27928500000000001 0.33333299999999999
+1 0.33333299999999999 0.33333299999999999
+0 0.66666700000000001 0.66666700000000001
+0.33333299999999999 0.66666700000000001 0.66666700000000001
+0.66666700000000001 0.66666700000000001 0.66666700000000001
+1 0.66666700000000001 0.66666700000000001
+0 1 1
+0.37796099999999999 1.08385 1
+0.73563699999999999 1.01488 0.94896599999999998
+0.96348599999999995 1.0906100000000001 1
+
+3  4 1 0
+3  4 5 1
+3  8 5 4
+3  8 9 5
+3  12 9 8
+3  12 13 9
+3  5 2 1
+3  5 6 2
+3  9 6 5
+3  9 10 6
+3  13 10 9
+3  13 14 10
+3  6 3 2
+3  6 7 3
+3  10 7 6
+3  10 11 7
+3  14 11 10
+3  14 15 11
diff --git a/Polygon_mesh_processing/test/Polygon_mesh_processing/measures_test.cpp b/Polygon_mesh_processing/test/Polygon_mesh_processing/measures_test.cpp
index b0609f34987..ed8d1b30019 100644
--- a/Polygon_mesh_processing/test/Polygon_mesh_processing/measures_test.cpp
+++ b/Polygon_mesh_processing/test/Polygon_mesh_processing/measures_test.cpp
@@ -284,6 +284,63 @@ void test_compare()
   assert(fim2[m2_only[0]] == 0);
   assert(fim2[m2_only[1]] == 3);
   assert(fim2[m2_only[2]] == 4);
+  /*************************
+   **** tri and hole****
+   * **********************/
+  CGAL::clear(mesh1);
+  CGAL::clear(mesh2);
+  common.clear();
+  m1_only.clear();
+  m2_only.clear();
+  input.open("data/tri1.off");
+  if(! (input >> mesh1))
+  {
+    std::cerr << "Invalid input." << std::endl;
+    assert (false);
+    return;
+  }
+  input.close();
+  input.open("data/tri1-hole.off");
+  if(! (input >> mesh2))
+  {
+    std::cerr << "Invalid input." << std::endl;
+    assert (false);
+    return;
+  }
+  input.close();
+  PMP::compare_meshes(mesh1, mesh2, std::back_inserter(common), std::back_inserter(m1_only), std::back_inserter(m2_only), CGAL::parameters::all_default(), CGAL::parameters::all_default());
+  assert(common.size() == 17);
+  assert(m1_only.size() == 1);
+  assert(m2_only.size() == 0);
+
+  /*************************
+   **** tri and orient****
+   * **********************/
+  CGAL::clear(mesh1);
+  CGAL::clear(mesh2);
+  common.clear();
+  m1_only.clear();
+  m2_only.clear();
+  input.open("data/tri2.off");
+  if(! (input >> mesh1))
+  {
+    std::cerr << "Invalid input." << std::endl;
+    assert (false);
+    return;
+  }
+  input.close();
+  input.open("data/tri2-out.off");
+  if(! (input >> mesh2))
+  {
+    std::cerr << "Invalid input." << std::endl;
+    assert (false);
+    return;
+  }
+  input.close();
+  PMP::compare_meshes(mesh1, mesh2, std::back_inserter(common), std::back_inserter(m1_only), std::back_inserter(m2_only), CGAL::parameters::require_same_orientation(true), CGAL::parameters::all_default());
+  assert(common.size() == 0);
+  assert(m1_only.size() == 18);
+  assert(m2_only.size() == 18);
 
 }