diff --git a/masque/shapes/polygon.py b/masque/shapes/polygon.py
index 9f52af8..a0b214b 100644
--- a/masque/shapes/polygon.py
+++ b/masque/shapes/polygon.py
@@ -6,6 +6,7 @@ from numpy import pi
 from . import Shape, normalized_shape_tuple
 from .. import PatternError
 from ..utils import is_scalar, rotation_matrix_2d, vector2
+from ..utils import remove_colinear_vertices, remove_duplicate_vertices
 
 __author__ = 'Jan Petykiewicz'
 
@@ -267,8 +268,7 @@ class Polygon(Shape):
 
         :returns: self
         '''
-        duplicates = (self.vertices == numpy.roll(self.vertices, 1, axis=0)).all(axis=1)
-        self.vertices = self.vertices[~duplicates]
+        self.vertices = remove_duplicate_vertices(self.vertices, closed_path=True)
         return self
 
     def remove_colinear_vertices(self) -> 'Polygon':
@@ -277,19 +277,5 @@ class Polygon(Shape):
 
         :returns: self
         '''
-        dv0 = numpy.roll(self.vertices, 1, axis=0) - self.vertices
-        dv1 = numpy.roll(dv0, -1, axis=0)
-
-        # find cases where at least one coordinate is 0 in successive dv's
-        eq = dv1 == dv0
-        aa_colinear = numpy.logical_and(eq, dv0 == 0).any(axis=1)
-
-        # find cases where slope is equal
-        with numpy.errstate(divide='ignore', invalid='ignore'):   # don't care about zeroes
-            slope_quotient = (dv0[:, 0] * dv1[:, 1]) / (dv1[:, 0] * dv0[:, 1])
-        slopes_equal = numpy.abs(slope_quotient - 1) < 1e-14
-
-        colinear = numpy.logical_or(aa_colinear, slopes_equal)
-        self.vertices = self.vertices[~colinear]
+        self.vertices = remove_colinear_vertices(self.vertices, closed_path=True)
         return self
-
diff --git a/masque/utils.py b/masque/utils.py
index 5d99835..b1faa5f 100644
--- a/masque/utils.py
+++ b/masque/utils.py
@@ -55,3 +55,35 @@ def rotation_matrix_2d(theta: float) -> numpy.ndarray:
     """
     return numpy.array([[numpy.cos(theta), -numpy.sin(theta)],
                         [numpy.sin(theta), +numpy.cos(theta)]])
+
+
+def remove_duplicate_vertices(vertices: numpy.ndarray, closed_path: bool = True) -> numpy.ndarray:
+        duplicates = (vertices == numpy.roll(vertices, 1, axis=0)).all(axis=1)
+        if not closed_path:
+            duplicates[0] = False
+        return vertices[~duplicates]
+
+
+def remove_colinear_vertices(vertices: numpy.ndarray, closed_path: bool = True) -> numpy.ndarray:
+        '''
+        Given a list of vertices, remove any superflous vertices (i.e.
+            those which lie along the line formed by their neighbors)
+
+        :param vertices: Nx2 ndarray of vertices
+        :param closed_path: If True, the vertices are assumed to represent an implicitly
+            closed path. If False, the path is assumed to be open. Default True.
+        :return:
+        '''
+        # Check for dx0/dy0 == dx1/dy1
+
+        dv = numpy.roll(vertices, 1, axis=0) - vertices #[y0 - yn1, y1-y0, ...]
+        dxdy = dv * numpy.roll(dv, 1, axis=0)[:, ::-1] # [[dx1*dy0, dx1*dy0], ...]
+
+        dxdy_diff = numpy.abs(numpy.diff(dxdy, axis=1))[:, 0]
+        err_mult = 2 * numpy.abs(dxdy).sum(axis=1) + 1e-40
+
+        slopes_equal = (dxdy_diff / err_mult) < 1e-15
+        if not closed_path:
+            slopes_equal[[0, -1]] = False
+
+        return vertices[~slopes_equal]