diff --git a/masque/shapes/arc.py b/masque/shapes/arc.py
index 7b1cedc..25a9b2e 100644
--- a/masque/shapes/arc.py
+++ b/masque/shapes/arc.py
@@ -212,8 +212,9 @@ class Arc(Shape):
             n += [poly_num_points]
         if poly_max_arclen is not None:
             n += [perimeter / poly_max_arclen]
-        thetas_inner = numpy.linspace(a_ranges[0][1], a_ranges[0][0], max(n), endpoint=True)
-        thetas_outer = numpy.linspace(a_ranges[1][0], a_ranges[1][1], max(n), endpoint=True)
+        num_points = int(round(max(n)))
+        thetas_inner = numpy.linspace(a_ranges[0][1], a_ranges[0][0], num_points, endpoint=True)
+        thetas_outer = numpy.linspace(a_ranges[1][0], a_ranges[1][1], num_points, endpoint=True)
 
         sin_th_i, cos_th_i = (numpy.sin(thetas_inner), numpy.cos(thetas_inner))
         sin_th_o, cos_th_o = (numpy.sin(thetas_outer), numpy.cos(thetas_outer))
diff --git a/masque/shapes/circle.py b/masque/shapes/circle.py
index f7221d5..404aeae 100644
--- a/masque/shapes/circle.py
+++ b/masque/shapes/circle.py
@@ -81,7 +81,8 @@ class Circle(Shape):
             n += [poly_num_points]
         if poly_max_arclen is not None:
             n += [2 * pi * self.radius / poly_max_arclen]
-        thetas = numpy.linspace(2 * pi, 0, max(n), endpoint=False)
+        num_points = int(round(max(n)))
+        thetas = numpy.linspace(2 * pi, 0, num_points, endpoint=False)
         xs = numpy.cos(thetas) * self.radius
         ys = numpy.sin(thetas) * self.radius
         xys = numpy.vstack((xs, ys)).T
diff --git a/masque/shapes/ellipse.py b/masque/shapes/ellipse.py
index 9779e69..3288614 100644
--- a/masque/shapes/ellipse.py
+++ b/masque/shapes/ellipse.py
@@ -139,7 +139,8 @@ class Ellipse(Shape):
             n += [poly_num_points]
         if poly_max_arclen is not None:
             n += [perimeter / poly_max_arclen]
-        thetas = numpy.linspace(2 * pi, 0, max(n), endpoint=False)
+        num_points = int(round(max(n)))
+        thetas = numpy.linspace(2 * pi, 0, num_points, endpoint=False)
 
         sin_th, cos_th = (numpy.sin(thetas), numpy.cos(thetas))
         xs = r0 * cos_th