diff --git a/masque/test/test_utils.py b/masque/test/test_utils.py
index d142896..941e54c 100644
--- a/masque/test/test_utils.py
+++ b/masque/test/test_utils.py
@@ -5,7 +5,15 @@ from numpy.testing import assert_equal, assert_allclose
 from numpy import pi
 import pytest
 
-from ..utils import remove_duplicate_vertices, remove_colinear_vertices, poly_contains_points, rotation_matrix_2d, apply_transforms, normalize_mirror, DeferredDict
+from ..utils import (
+    DeferredDict,
+    apply_transforms,
+    normalize_mirror,
+    poly_contains_points,
+    remove_colinear_vertices,
+    remove_duplicate_vertices,
+    rotation_matrix_2d,
+)
 from ..file.utils import tmpfile
 from ..utils.curves import bezier
 from ..error import PatternError
@@ -23,6 +31,23 @@ def test_remove_duplicate_vertices() -> None:
     assert_equal(v_clean_open, [[0, 0], [1, 1], [2, 2], [0, 0]])
 
 
+def test_remove_duplicate_vertices_tolerance_defaults_to_exact_match() -> None:
+    v = [[0, 0], [1, 1], [1 + 1e-13, 1], [2, 2], [1e-13, 0]]
+
+    assert_allclose(remove_duplicate_vertices(v, closed_path=True), v, atol=0, rtol=0)
+    assert_allclose(
+        remove_duplicate_vertices(v, closed_path=True, tolerance=1e-12),
+        [[0, 0], [1 + 1e-13, 1], [2, 2]],
+        atol=0,
+        rtol=0,
+        )
+
+
+def test_remove_duplicate_vertices_rejects_negative_tolerance() -> None:
+    with pytest.raises(ValueError, match='non-negative'):
+        remove_duplicate_vertices([[0, 0]], tolerance=-1)
+
+
 def test_remove_colinear_vertices() -> None:
     v = [[0, 0], [1, 0], [2, 0], [2, 1], [2, 2], [1, 1], [0, 0]]
     v_clean = remove_colinear_vertices(v, closed_path=True)
diff --git a/masque/utils/vertices.py b/masque/utils/vertices.py
index 5a5df9f..0eaf13e 100644
--- a/masque/utils/vertices.py
+++ b/masque/utils/vertices.py
@@ -5,7 +5,11 @@ import numpy
 from numpy.typing import NDArray, ArrayLike
 
 
-def remove_duplicate_vertices(vertices: ArrayLike, closed_path: bool = True) -> NDArray[numpy.float64]:
+def remove_duplicate_vertices(
+        vertices: ArrayLike,
+        closed_path: bool = True,
+        tolerance: float = 0.0,
+        ) -> NDArray[numpy.float64]:
     """
     Given a list of vertices, remove any consecutive duplicates.
 
@@ -13,14 +17,22 @@ def remove_duplicate_vertices(vertices: ArrayLike, closed_path: bool = True) ->
         vertices: `[[x0, y0], [x1, y1], ...]`
         closed_path: If True, `vertices` is interpreted as an implicity-closed path
             (i.e. the last vertex will be removed if it is the same as the first)
+        tolerance: Maximum coordinate-wise absolute difference for two vertices to
+            be considered duplicates. Default `0` requires exact equality.
 
     Returns:
         `vertices` with no consecutive duplicates. This may be a view into the original array.
     """
+    if tolerance < 0:
+        raise ValueError(f'tolerance must be non-negative, got {tolerance}')
+
     vertices = numpy.asarray(vertices)
     if vertices.shape[0] <= 1:
         return vertices
-    duplicates = (vertices == numpy.roll(vertices, -1, axis=0)).all(axis=1)
+    if tolerance == 0:
+        duplicates = (vertices == numpy.roll(vertices, -1, axis=0)).all(axis=1)
+    else:
+        duplicates = (numpy.abs(vertices - numpy.roll(vertices, -1, axis=0)) <= tolerance).all(axis=1)
     if not closed_path:
         duplicates[-1] = False