diff --git a/masque/utils/vertices.py b/masque/utils/vertices.py
index 5fddd52..36d2e59 100644
--- a/masque/utils/vertices.py
+++ b/masque/utils/vertices.py
@@ -51,6 +51,10 @@ def remove_colinear_vertices(vertices: ArrayLike, closed_path: bool = True) -> N
     if not closed_path:
         slopes_equal[[0, -1]] = False
 
+    if slopes_equal.all() and vertices.shape[0] > 0:
+        # All colinear, keep the first and last
+        return vertices[[0, vertices.shape[0] - 1]]
+
     return vertices[~slopes_equal]