diff --git a/tests/mathutil/test_triangulator.py b/tests/mathutil/test_triangulator.py
new file mode 100644
index 0000000000..9e8e41c16e
--- /dev/null
+++ b/tests/mathutil/test_triangulator.py
@@ -0,0 +1,73 @@
+from panda3d.core import Triangulator
+
+
+def triangulate(vertices):
+    t = Triangulator()
+    for i, v in enumerate(vertices):
+        t.add_vertex(v)
+        t.add_polygon_vertex(i)
+
+    t.triangulate()
+
+    # Make sure that the result is consistent by starting each triangle with
+    # the lowest index value.  That makes it easier to use predetermined values
+    # in the test cases.
+    result = set()
+
+    for n in range(t.get_num_triangles()):
+        # Switch to lowest matching index value in case of duplicates.
+        v0 = vertices.index(vertices[t.get_triangle_v0(n)])
+        v1 = vertices.index(vertices[t.get_triangle_v1(n)])
+        v2 = vertices.index(vertices[t.get_triangle_v2(n)])
+        if v1 < v0:
+            v0, v1, v2 = v1, v2, v0
+        if v1 < v0:
+            v0, v1, v2 = v1, v2, v0
+        result.add((v0, v1, v2))
+
+    return result
+
+
+def test_triangulator_degenerate():
+    assert not triangulate([])
+    assert not triangulate([(0, 0)])
+    assert not triangulate([(0, 0), (0, 0)])
+    assert not triangulate([(0, 0), (1, 0)])
+    assert not triangulate([(0, 0), (0, 0), (0, 0)])
+    assert not triangulate([(0, 0), (1, 0), (1, 0)])
+    assert not triangulate([(1, 0), (1, 0), (1, 0)])
+    assert not triangulate([(1, 0), (0, 0), (1, 0)])
+    assert not triangulate([(0, 0), (0, 0), (0, 0), (0, 0)])
+
+
+def test_triangulator_triangle():
+    assert triangulate([(0, 0), (1, 0), (1, 1)]) == {(0, 1, 2)}
+
+
+def test_triangulator_tail():
+    # This triangle has a long "tail" where the polygon retraces its vertices.
+    assert triangulate([
+        (0, -1),
+        (0, 1),
+        (1, 0),
+        (2, 0),
+        (3, 1),
+        (4, 0),
+        (5, 0),
+        (4, 0),
+        (3, 1),
+        (2, 0),
+        (1, 0),
+    ]) == {(0, 2, 1)}
+
+
+def test_triangulator_hourglass():
+    # Two triangles with touching tips, effectively.
+    assert triangulate([
+        (-1, 1),
+        (-1, -1),
+        (0, 0),
+        (1, -1),
+        (1, 1),
+        (0, 0),
+    ]) == {(0, 1, 2), (2, 3, 4)}