diff --git a/masque/shapes/arc.py b/masque/shapes/arc.py
index 9ae06ce..f3c9f79 100644
--- a/masque/shapes/arc.py
+++ b/masque/shapes/arc.py
@@ -463,13 +463,18 @@ class Arc(PositionableImpl, Shape):
                    `[[a_min_inner, a_max_inner], [a_min_outer, a_max_outer]]`
         """
         aa = []
+        d_angle = self.angles[1] - self.angles[0]
+        if abs(d_angle) >= 2 * pi:
+            # Full ring
+            return numpy.tile([0, 2 * pi], (2, 1)).astype(float)
+
         for sgn in (-1, +1):
             wh = sgn * self.width / 2.0
             rx = self.radius_x + wh
             ry = self.radius_y + wh
 
             a0, a1 = (numpy.arctan2(rx * numpy.sin(ai), ry * numpy.cos(ai)) for ai in self.angles)
-            sign = numpy.sign(self.angles[1] - self.angles[0])
+            sign = numpy.sign(d_angle)
             if sign != numpy.sign(a1 - a0):
                 a1 += sign * 2 * pi