From 5aa6d2a69e9474c99651ba0307394e8d0149c29a Mon Sep 17 00:00:00 2001
From: Menelaos Karavelas <menelaos.karavelas@gmail.com>
Date: Sat, 28 Nov 2015 09:10:50 +0200
Subject: [PATCH 1/2] [algorithms][centroid] the centroid algorithm should not
 be able to compute the centroid of a multipolygon (which is actually invalid)
 that contains one or more polygons that have empty exterior ring and
 non-empty interior rings; in such cases an exception should be thrown; this
 commit fixes the behavior of the centroid algorithm in the direction
 described above;

---
 include/boost/geometry/algorithms/centroid.hpp | 21 +++++++++++++++++++--
 1 file changed, 19 insertions(+), 2 deletions(-)

diff --git a/include/boost/geometry/algorithms/centroid.hpp b/include/boost/geometry/algorithms/centroid.hpp
index 8ef017a3f1..b0f46e3775 100644
--- a/include/boost/geometry/algorithms/centroid.hpp
+++ b/include/boost/geometry/algorithms/centroid.hpp
@@ -283,9 +283,26 @@ struct centroid_polygon_state
                              typename Strategy::state_type& state)
     {
         typedef typename ring_type<Polygon>::type ring_type;
-        typedef centroid_range_state<geometry::closure<ring_type>::value> per_ring;
+        typedef centroid_range_state
+            <
+                geometry::closure<ring_type>::value
+            > per_ring;
+
+        typename ring_return_type
+            <
+                Polygon const
+            >::type e_ring = exterior_ring(poly);
+
+        if (boost::empty(e_ring) && ! geometry::is_empty(poly))
+        {
+#if ! defined(BOOST_GEOMETRY_CENTROID_NO_THROW)
+            throw centroid_exception();
+#else
+            return;
+#endif
+        }
 
-        per_ring::apply(exterior_ring(poly), transformer, strategy, state);
+        per_ring::apply(e_ring, transformer, strategy, state);
 
         typename interior_return_type<Polygon const>::type
             rings = interior_rings(poly);

From 7e3edb242f80ebfb88986272b4c36da51f2a61a9 Mon Sep 17 00:00:00 2001
From: Menelaos Karavelas <menelaos.karavelas@gmail.com>
Date: Sat, 28 Nov 2015 09:13:24 +0200
Subject: [PATCH 2/2] [test][algorithms][centroid] add test case consisting of
 a multi-polygon that contains a polygon with empty exterior ring and
 non-empty interior ring; such a multi-polygon is expected to trigger an
 exception;

---
 test/algorithms/centroid_multi.cpp | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/test/algorithms/centroid_multi.cpp b/test/algorithms/centroid_multi.cpp
index 5f250116e2..93c5129ce8 100644
--- a/test/algorithms/centroid_multi.cpp
+++ b/test/algorithms/centroid_multi.cpp
@@ -133,6 +133,10 @@ void test_exceptions()
     test_centroid_exception<multi_linestring>("MULTILINESTRING()");
     test_centroid_exception<multi_linestring>("MULTILINESTRING(())");
     test_centroid_exception<multi_linestring>("MULTILINESTRING((), ())");
+
+    // Multi-polygon containing polygon with empty exterior ring
+    test_centroid_exception<multi_polygon>
+        ("MULTIPOLYGON(((4 1,4 3,8 3,8 1,4 1)),((),(0 0,1 0,1 1,0 1,0 0)))");
 }
 
 template <typename P>