diff --git a/src/main/java/org/apache/commons/math4/geometry/euclidean/twod/PolygonsSet.java b/src/main/java/org/apache/commons/math4/geometry/euclidean/twod/PolygonsSet.java
index 9975a04b9..9b20b0c02 100644
--- a/src/main/java/org/apache/commons/math4/geometry/euclidean/twod/PolygonsSet.java
+++ b/src/main/java/org/apache/commons/math4/geometry/euclidean/twod/PolygonsSet.java
@@ -553,7 +553,7 @@ public class PolygonsSet extends AbstractRegion<Euclidean2D, Euclidean1D> {
                 setBarycenter((Point<Euclidean2D>) Cartesian2D.NaN);
             } else {
                 setSize(0);
-                setBarycenter((Point<Euclidean2D>) new Cartesian2D(0, 0));
+                setBarycenter((Point<Euclidean2D>) Cartesian2D.NaN);
             }
         } else if (v[0][0] == null) {
             // there is at least one open-loop: the polygon is infinite
diff --git a/src/test/java/org/apache/commons/math4/geometry/euclidean/twod/PolygonsSetTest.java b/src/test/java/org/apache/commons/math4/geometry/euclidean/twod/PolygonsSetTest.java
index 1ee2ccb14..4584d0312 100644
--- a/src/test/java/org/apache/commons/math4/geometry/euclidean/twod/PolygonsSetTest.java
+++ b/src/test/java/org/apache/commons/math4/geometry/euclidean/twod/PolygonsSetTest.java
@@ -221,15 +221,28 @@ public class PolygonsSetTest {
 
     @Test
     public void testEmpty() {
-        PolygonsSet empty = (PolygonsSet) new RegionFactory<Euclidean2D>().getComplement(new PolygonsSet(1.0e-10));
-        Assert.assertTrue(empty.isEmpty());
-        Assert.assertEquals(0, empty.getVertices().length);
-        Assert.assertEquals(0.0, empty.getBoundarySize(), 1.0e-10);
-        Assert.assertEquals(0.0, empty.getSize(), 1.0e-10);
+        // act
+        PolygonsSet poly = (PolygonsSet) new RegionFactory<Euclidean2D>().getComplement(new PolygonsSet(1e-10));
+
+        // assert
+        Assert.assertEquals(1e-10, poly.getTolerance(), Precision.EPSILON);
+        Assert.assertEquals(0.0, poly.getSize(), 1e-10);
+        Assert.assertEquals(0.0, poly.getBoundarySize(), 1e-10);
+        Assert.assertEquals(0, poly.getVertices().length);
+        Assert.assertEquals(true, poly.isEmpty());
+        Assert.assertEquals(false, poly.isFull());
+        GeometryTestUtils.assertVectorEquals(Cartesian2D.NaN, (Cartesian2D) poly.getBarycenter(), 1e-10);
+
+        checkPoints(Region.Location.OUTSIDE, poly, new Cartesian2D[] {
+                new Cartesian2D(Double.NEGATIVE_INFINITY, Double.NEGATIVE_INFINITY),
+                Cartesian2D.ZERO,
+                new Cartesian2D(Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY)});
+
+
         for (double y = -1; y < 1; y += 0.1) {
             for (double x = -1; x < 1; x += 0.1) {
                 Assert.assertEquals(Double.POSITIVE_INFINITY,
-                                    empty.projectToBoundary(new Cartesian2D(x, y)).getOffset(),
+                                    poly.projectToBoundary(new Cartesian2D(x, y)).getOffset(),
                                     1.0e-10);
             }
         }
@@ -237,16 +250,28 @@ public class PolygonsSetTest {
 
     @Test
     public void testFull() {
-        PolygonsSet empty = new PolygonsSet(1.0e-10);
-        Assert.assertFalse(empty.isEmpty());
-        Assert.assertEquals(0, empty.getVertices().length);
-        Assert.assertEquals(0.0, empty.getBoundarySize(), 1.0e-10);
-        Assert.assertEquals(Double.POSITIVE_INFINITY, empty.getSize(), 1.0e-10);
+        // act
+        PolygonsSet poly = new PolygonsSet(1e-10);
+
+        // assert
+        Assert.assertEquals(1e-10, poly.getTolerance(), Precision.EPSILON);
+        Assert.assertEquals(Double.POSITIVE_INFINITY, poly.getSize(), 1e-10);
+        Assert.assertEquals(0.0, poly.getBoundarySize(), 1e-10);
+        Assert.assertEquals(0, poly.getVertices().length);
+        Assert.assertEquals(false, poly.isEmpty());
+        Assert.assertEquals(true, poly.isFull());
+        GeometryTestUtils.assertVectorEquals(Cartesian2D.NaN, (Cartesian2D) poly.getBarycenter(), 1e-10);
+
+        checkPoints(Region.Location.INSIDE, poly, new Cartesian2D[] {
+                new Cartesian2D(Double.NEGATIVE_INFINITY, Double.NEGATIVE_INFINITY),
+                Cartesian2D.ZERO,
+                new Cartesian2D(Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY)});
+
         for (double y = -1; y < 1; y += 0.1) {
             for (double x = -1; x < 1; x += 0.1) {
                 Assert.assertEquals(Double.NEGATIVE_INFINITY,
-                                    empty.projectToBoundary(new Cartesian2D(x, y)).getOffset(),
-                                    1.0e-10);
+                                    poly.projectToBoundary(new Cartesian2D(x, y)).getOffset(),
+                                    1e-10);
             }
         }
     }