diff --git a/test/algorithms/relational_operations/equals_on_spheroid.cpp b/test/algorithms/relational_operations/equals_on_spheroid.cpp
index 80c8593e8..5e24fdfab 100644
--- a/test/algorithms/relational_operations/equals_on_spheroid.cpp
+++ b/test/algorithms/relational_operations/equals_on_spheroid.cpp
@@ -40,17 +40,25 @@ struct test_point_point
         test_geometry<P1, P2>(str + "pp_05", "POINT(10 0)", "POINT(-350 0)", true);
         test_geometry<P1, P2>(str + "pp_06", "POINT(180 10)", "POINT(-180 10)", true);
         test_geometry<P1, P2>(str + "pp_06a", "POINT(540 10)", "POINT(-540 10)", true);
+
+#ifdef BOOST_GEOMETRY_NORMALIZE_LATITUDE
         test_geometry<P1, P2>(str + "pp_06b", "POINT(540 370)", "POINT(-540 -350)", true);
         test_geometry<P1, P2>(str + "pp_06c", "POINT(1260 370)", "POINT(-1260 -350)", true);
         test_geometry<P1, P2>(str + "pp_06d", "POINT(2340 370)", "POINT(-2340 -350)", true);
+#endif
+
         test_geometry<P1, P2>(str + "pp_06e", "POINT(-180 10)", "POINT(-540 10)", true);
         test_geometry<P1, P2>(str + "pp_06f", "POINT(180 10)", "POINT(-540 10)", true);
 
         // north & south pole
         test_geometry<P1, P2>(str + "pp_07", "POINT(0 90)", "POINT(0 90)", true);
+
+#ifdef BOOST_GEOMETRY_NORMALIZE_LATITUDE
         test_geometry<P1, P2>(str + "pp_07a", "POINT(0 450)", "POINT(10 -270)", true);
         test_geometry<P1, P2>(str + "pp_07b", "POINT(0 270)", "POINT(10 90)", false);
         test_geometry<P1, P2>(str + "pp_07c", "POINT(0 -450)", "POINT(10 90)", false);
+#endif
+
         test_geometry<P1, P2>(str + "pp_08", "POINT(0 90)", "POINT(10 90)", true);
         test_geometry<P1, P2>(str + "pp_09", "POINT(0 90)", "POINT(0 -90)", false);
         test_geometry<P1, P2>(str + "pp_10", "POINT(0 -90)", "POINT(0 -90)", true);
@@ -68,12 +76,52 @@ struct test_point_point
         test_geometry<P1, P2>(str + "pp_17", "POINT(-10 45)", "POINT(10 -45)", false);
         test_geometry<P1, P2>(str + "pp_18", "POINT(-10 -45)", "POINT(10 45)", false);
         test_geometry<P1, P2>(str + "pp_19", "POINT(10 -135)", "POINT(10 45)", false);
+
+#ifdef BOOST_GEOMETRY_NORMALIZE_LATITUDE
         test_geometry<P1, P2>(str + "pp_20", "POINT(190 135)", "POINT(10 45)", true);
         test_geometry<P1, P2>(str + "pp_21", "POINT(190 150)", "POINT(10 30)", true);
         test_geometry<P1, P2>(str + "pp_21a", "POINT(-170 150)", "POINT(10 30)", true);
         test_geometry<P1, P2>(str + "pp_22", "POINT(190 -135)", "POINT(10 -45)", true);
         test_geometry<P1, P2>(str + "pp_23", "POINT(190 -150)", "POINT(10 -30)", true);
         test_geometry<P1, P2>(str + "pp_23a", "POINT(-170 -150)", "POINT(10 -30)", true);
+#endif
+    }
+};
+
+
+template <typename P1, typename P2 = P1>
+struct test_point_point_with_height
+{
+    static inline void apply(std::string const& header)
+    {
+        std::string const str = header + "-";
+
+        test_geometry<P1, P2>(str + "pp_01",
+                              "POINT(0 0 10)",
+                              "POINT(0 0 20)",
+                              true);
+
+        test_geometry<P1, P2>(str + "pp_02",
+                              "POINT(0 0 10)",
+                              "POINT(10 0 10)",
+                              false);
+
+        // points whose longitudes differ by 360 degrees
+        test_geometry<P1, P2>(str + "pp_03",
+                              "POINT(0 0 10)",
+                              "POINT(360 0 10)",
+                              true);
+
+        // points whose longitudes differ by 360 degrees
+        test_geometry<P1, P2>(str + "pp_04",
+                              "POINT(10 0 10)",
+                              "POINT(370 0 10)",
+                              true);
+
+        test_geometry<P1, P2>(str + "pp_05",
+                              "POINT(10 0 10)",
+                              "POINT(10 0 370)",
+                              false);
     }
 };
 
@@ -132,6 +180,30 @@ BOOST_AUTO_TEST_CASE( equals_point_point_se )
 #endif
 }
 
+BOOST_AUTO_TEST_CASE( equals_point_point_with_height_se )
+{
+    typedef bg::cs::spherical_equatorial<bg::degree> cs_type;
+
+    test_point_point<bgm::point<int, 3, cs_type> >::apply("seh");
+    test_point_point<bgm::point<double, 3, cs_type> >::apply("seh");
+    test_point_point<bgm::point<long double, 3, cs_type> >::apply("seh");
+
+    // mixed point types
+    test_point_point
+        <
+            bgm::point<double, 3, cs_type>, bgm::point<int, 3, cs_type>
+        >::apply("seh");
+
+    test_point_point
+        <
+            bgm::point<double, 3, cs_type>, bgm::point<long double, 3, cs_type>
+        >::apply("seh");
+
+#if defined(HAVE_TTMATH)
+    test_point_point<bgm::point<ttmath_big, 3, cs_type> >::apply("seh");
+#endif
+}
+
 BOOST_AUTO_TEST_CASE( equals_point_point_geo )
 {
     typedef bg::cs::geographic<bg::degree> cs_type;