diff --git a/masque/shapes/arc.py b/masque/shapes/arc.py
index f3c9f79..f95c4f6 100644
--- a/masque/shapes/arc.py
+++ b/masque/shapes/arc.py
@@ -362,17 +362,20 @@ class Arc(PositionableImpl, Shape):
             yn, yp = sorted(rx * sin_r * cos_a + ry * cos_r * sin_a)
 
             # If our arc subtends a coordinate axis, use the extremum along that axis
-            if a0 < xpt < a1 or a0 < xpt + 2 * pi < a1:
-                xp = xr
+            if abs(a1 - a0) >= 2 * pi:
+                xn, xp, yn, yp = -xr, xr, -yr, yr
+            else:
+                if a0 <= xpt <= a1 or a0 <= xpt + 2 * pi <= a1:
+                    xp = xr
 
-            if a0 < xnt < a1 or a0 < xnt + 2 * pi < a1:
-                xn = -xr
+                if a0 <= xnt <= a1 or a0 <= xnt + 2 * pi <= a1:
+                    xn = -xr
 
-            if a0 < ypt < a1 or a0 < ypt + 2 * pi < a1:
-                yp = yr
+                if a0 <= ypt <= a1 or a0 <= ypt + 2 * pi <= a1:
+                    yp = yr
 
-            if a0 < ynt < a1 or a0 < ynt + 2 * pi < a1:
-                yn = -yr
+                if a0 <= ynt <= a1 or a0 <= ynt + 2 * pi <= a1:
+                    yn = -yr
 
             mins.append([xn, yn])
             maxs.append([xp, yp])