diff --git a/Shape_detection/test/Shape_detection/test_region_growing_deprecated_constructors.cpp b/Shape_detection/test/Shape_detection/test_region_growing_deprecated_constructors.cpp
index ac00d003fdc..ae65c4f2ef9 100644
--- a/Shape_detection/test/Shape_detection/test_region_growing_deprecated_constructors.cpp
+++ b/Shape_detection/test/Shape_detection/test_region_growing_deprecated_constructors.cpp
@@ -48,14 +48,26 @@ using RT1 = SD::Point_set::Least_squares_line_fit_region<Kernel, Input_range_2,
 using RT2 = SD::Point_set::Least_squares_plane_fit_region<Kernel, Input_range_3, Point_map_3, Normal_map_3>;
 using RT3 = SD::Polygon_mesh::Least_squares_plane_fit_region<Kernel, Polygon_mesh>;
 
+using RT4 = SD::Point_set::Least_squares_circle_fit_region<Kernel, Input_range_2, Point_map_2, Normal_map_2>;
+using RT5 = SD::Point_set::Least_squares_sphere_fit_region<Kernel, Input_range_3, Point_map_3, Normal_map_3>;
+using RT6 = SD::Point_set::Least_squares_cylinder_fit_region<Kernel, Input_range_3, Point_map_3, Normal_map_3>;
+
 using S1 = SD::Point_set::Least_squares_line_fit_sorting<Kernel, Input_range_2, NQ1, Point_map_2>;
 using S2 = SD::Point_set::Least_squares_plane_fit_sorting<Kernel, Input_range_3, NQ2, Point_map_3>;
 using S3 = SD::Polygon_mesh::Least_squares_plane_fit_sorting<Kernel, Polygon_mesh, NQ3>;
 
+using S4 = SD::Point_set::Least_squares_circle_fit_sorting<Kernel, Input_range_2, NQ1, Point_map_2>;
+using S5 = SD::Point_set::Least_squares_sphere_fit_sorting<Kernel, Input_range_3, NQ2, Point_map_3>;
+using S6 = SD::Point_set::Least_squares_cylinder_fit_sorting<Kernel, Input_range_3, NQ2, Point_map_3, Normal_map_3>;
+
 using RG1 = SD::Region_growing<Input_range_2, NQ1, RT1, typename S1::Seed_map>;
 using RG2 = SD::Region_growing<Input_range_3, NQ2, RT2, typename S2::Seed_map>;
 using RG3 = SD::Region_growing<Face_range   , NQ3, RT3, typename S3::Seed_map>;
 
+using RG4 = SD::Region_growing<Input_range_2, NQ1, RT4, typename S4::Seed_map>;
+using RG5 = SD::Region_growing<Input_range_3, NQ2, RT5, typename S5::Seed_map>;
+using RG6 = SD::Region_growing<Input_range_3, NQ2, RT6, typename S6::Seed_map>;
+
 int main() {
 
   // Default parameter values.
@@ -64,6 +76,8 @@ int main() {
   const FT          angle_threshold    = FT(15);
   const std::size_t min_region_size    = 1;
   const FT          sphere_radius      = FT(2);
+  const FT          min_radius         = FT(0);
+  const FT          max_radius         = FT(1000000);
 
   const Kernel traits;
   const Input_range_2 input_range_2 = {
@@ -106,29 +120,64 @@ int main() {
     distance_threshold, angle_threshold, min_region_size,
     vertex_to_point_map, traits);
 
+  RT4 rt4(input_range_2,
+    distance_threshold, angle_threshold, min_region_size, min_radius, max_radius,
+    point_map_2, normal_map_2, traits);
+  RT5 rt5(input_range_3,
+    distance_threshold, angle_threshold, min_region_size, min_radius, max_radius,
+    point_map_3, normal_map_3, traits);
+  RT6 rt6(input_range_3,
+    distance_threshold, angle_threshold, min_region_size, min_radius, max_radius,
+    point_map_3, normal_map_3, traits);
+
   S1 s1(input_range_2, nq1, point_map_2);
   S2 s2(input_range_3, nq2, point_map_3);
   S3 s3(polygon_mesh , nq3, vertex_to_point_map);
 
+  S4 s4(input_range_2, nq1, point_map_2);
+  S5 s5(input_range_3, nq2, point_map_3);
+  S6 s6(input_range_3, nq2, point_map_3);
+
   s1.sort();
   s2.sort();
   s3.sort();
 
+  s4.sort();
+  s5.sort();
+  s6.sort();
+
   RG1 rg1(input_range_2, nq1, rt1, s1.seed_map());
   RG2 rg2(input_range_3, nq2, rt2, s2.seed_map());
   RG3 rg3(face_range   , nq3, rt3, s3.seed_map());
 
+  RG4 rg4(input_range_2, nq1, rt4, s4.seed_map());
+  RG5 rg5(input_range_3, nq2, rt5, s5.seed_map());
+  RG6 rg6(input_range_3, nq2, rt6, s6.seed_map());
+
   std::vector< std::vector<std::size_t> > regions1;
   std::vector< std::vector<std::size_t> > regions2;
   std::vector< std::vector<std::size_t> > regions3;
+
+  std::vector< std::vector<std::size_t> > regions4;
+  std::vector< std::vector<std::size_t> > regions5;
+  std::vector< std::vector<std::size_t> > regions6;
+
   rg1.detect(std::back_inserter(regions1));
   rg2.detect(std::back_inserter(regions2));
   rg3.detect(std::back_inserter(regions3));
 
+  rg4.detect(std::back_inserter(regions4));
+  rg5.detect(std::back_inserter(regions5));
+  rg6.detect(std::back_inserter(regions6));
+
   assert(regions1.size() == 1);
   assert(regions2.size() == 1);
   assert(regions3.size() == 4);
 
+  assert(regions4.size() > 0);
+  assert(regions5.size() > 0);
+  assert(regions6.size() > 0);
+
   std::cout << "rg_deprecated, sc_test_success: " << true << std::endl;
   return EXIT_SUCCESS;
 }
diff --git a/Shape_detection/test/Shape_detection/test_region_growing_on_point_set_2_with_sorting.cpp b/Shape_detection/test/Shape_detection/test_region_growing_on_point_set_2_with_sorting.cpp
index fd140f316a1..e36707686fd 100644
--- a/Shape_detection/test/Shape_detection/test_region_growing_on_point_set_2_with_sorting.cpp
+++ b/Shape_detection/test/Shape_detection/test_region_growing_on_point_set_2_with_sorting.cpp
@@ -35,16 +35,15 @@ using Line_sorting   = SD::Point_set::Least_squares_line_fit_sorting<Kernel, Inp
 using Circle_region  = SD::Point_set::Least_squares_circle_fit_region<Kernel, Input_range, Point_map, Normal_map>;
 using Circle_sorting = SD::Point_set::Least_squares_circle_fit_sorting<Kernel, Input_range, Neighbor_query, Point_map>;
 
-template <typename Region_type, typename Sorting>
-bool test (int argc, char** argv, const std::size_t minr, const std::size_t maxr)
-{
+template<typename Region_type, typename Sorting>
+bool test(int argc, char** argv, const std::string name, const std::size_t minr, const std::size_t maxr) {
   using Region_growing = SD::Region_growing<Input_range, Neighbor_query, Region_type, typename Sorting::Seed_map>;
 
   // Default parameter values.
-  const std::size_t k                  = 12;
-  const FT          distance_threshold = FT(45) / FT(10);
-  const FT          angle_threshold    = FT(45);
-  const std::size_t min_region_size    = 5;
+  const std::size_t k               = 12;
+  const FT          max_distance    = FT(45) / FT(10);
+  const FT          max_angle       = FT(45);
+  const std::size_t min_region_size = 5;
 
   // Load data.
   std::ifstream in(argc > 1 ? argv[1] : "data/point_set_2.xyz");
@@ -66,8 +65,8 @@ bool test (int argc, char** argv, const std::size_t minr, const std::size_t maxr
   Region_type region_type(
     input_range,
     CGAL::parameters::
-    maximum_distance(distance_threshold).
-    maximum_angle(angle_threshold).
+    maximum_distance(max_distance).
+    maximum_angle(max_angle).
     minimum_region_size(min_region_size));
 
   // Sort indices.
@@ -82,7 +81,9 @@ bool test (int argc, char** argv, const std::size_t minr, const std::size_t maxr
   std::vector< std::vector<std::size_t> > regions;
   region_growing.detect(std::back_inserter(regions));
   region_growing.clear();
-  assert(regions.size() == 62);
+
+  std::cout << "- num regions " + name + ": " << regions.size() << std::endl;
+  assert(regions.size() >= minr && regions.size() <= maxr);
 
   // Test free functions and stability.
   for (std::size_t k = 0; k < 3; ++k) {
@@ -90,25 +91,21 @@ bool test (int argc, char** argv, const std::size_t minr, const std::size_t maxr
     SD::internal::region_growing_lines(
       input_range, std::back_inserter(regions),
       CGAL::parameters::
-      maximum_distance(distance_threshold).
-      maximum_angle(angle_threshold).
+      maximum_distance(max_distance).
+      maximum_angle(max_angle).
       minimum_region_size(min_region_size));
     assert(regions.size() == 62);
   }
-  assert(regions.size() >= minr && regions.size() <= maxr);
 
-  const bool cartesian_double_test_success = (regions.size() >= minr && regions.size() <= maxr);
-  std::cout << "cartesian_double_test_success: " << cartesian_double_test_success << std::endl;
-
-  const bool success = cartesian_double_test_success;
+  const bool success = true;
+  std::cout << "rg_" + name + "_sortpoints2, sc_test_success: " << success << std::endl;
   return success;
 }
 
 int main(int argc, char *argv[]) {
 
   return ((
-    test<Line_region, Line_sorting>(argc, argv, 62, 66) &&
-    test<Circle_region, Circle_sorting>(argc, argv, 196, 200)
+    test<Line_region, Line_sorting>(argc, argv, "lines", 62, 66) && // test lines
+    test<Circle_region, Circle_sorting>(argc, argv, "circles", 62, 66) // test circles
   ) ? EXIT_SUCCESS : EXIT_FAILURE );
-
 }
diff --git a/Shape_detection/test/Shape_detection/test_region_growing_on_point_set_3_with_sorting.cpp b/Shape_detection/test/Shape_detection/test_region_growing_on_point_set_3_with_sorting.cpp
index 9baede56975..754a1599470 100644
--- a/Shape_detection/test/Shape_detection/test_region_growing_on_point_set_3_with_sorting.cpp
+++ b/Shape_detection/test/Shape_detection/test_region_growing_on_point_set_3_with_sorting.cpp
@@ -37,17 +37,20 @@ using Sphere_sorting = SD::Point_set::Least_squares_sphere_fit_sorting<Kernel, I
 using Cylinder_region = SD::Point_set::Least_squares_cylinder_fit_region<Kernel, Input_range, Point_map, Normal_map>;
 using Cylinder_sorting = SD::Point_set::Least_squares_cylinder_fit_sorting<Kernel, Input_range, Neighbor_query, Point_map, Normal_map>;
 
-template <typename Region_type, typename Sorting, typename SortingCode,
-          typename RegionCode, typename AssertionCode>
-bool test (int argc, char** argv, const SortingCode& /*sc*/, const RegionCode& /*reg*/, const AssertionCode& assertion)
-{
+template<
+typename Region_type,
+typename Sorting,
+typename Lambda_region,
+typename Lambda_assertion>
+bool test(
+  int argc, char** argv, const std::string name,
+  const Lambda_region& lambda_region,
+  const Lambda_assertion& lambda_assertion) {
+
   using Region_growing = SD::Region_growing<Input_range, Neighbor_query, Region_type, typename Sorting::Seed_map>;
 
   // Default parameter values.
-  const std::size_t k                  = 12;
-  const FT          distance_threshold = FT(2);
-  const FT          angle_threshold    = FT(20);
-  const std::size_t min_region_size    = 50;
+  const std::size_t k = 12;
 
   // Load data.
   std::ifstream in(argc > 1 ? argv[1] : "data/point_set_3.xyz");
@@ -66,29 +69,29 @@ bool test (int argc, char** argv, const SortingCode& /*sc*/, const RegionCode& /
     k_neighbors(k).
     point_map(input_range.point_map()));
 
-  Region_type region_type(
-    input_range,
-    CGAL::parameters::
-    maximum_distance(distance_threshold).
-    maximum_angle(angle_threshold).
-    minimum_region_size(min_region_size).
-    point_map(input_range.point_map()).
-    normal_map(input_range.normal_map()));
-
   // Sort indices.
   Sorting sorting(
     input_range, neighbor_query,
-    CGAL::parameters::point_map(input_range.point_map()));
+    CGAL::parameters::
+    point_map(input_range.point_map()).
+    normal_map(input_range.normal_map()));
   sorting.sort();
 
   // Run region growing.
+  Region_type region_type = lambda_region(input_range);
   Region_growing region_growing(
     input_range, neighbor_query, region_type, sorting.seed_map());
 
   std::vector< std::vector<std::size_t> > regions;
   region_growing.detect(std::back_inserter(regions));
   region_growing.clear();
-  assert(regions.size() == 7);
+  const bool result = lambda_assertion(regions);
+  assert(result);
+
+  // Default parameter values.
+  const FT          max_distance    = FT(2);
+  const FT          max_angle       = FT(20);
+  const std::size_t min_region_size = 50;
 
   // Test free functions and stability.
   for (std::size_t k = 0; k < 3; ++k) {
@@ -96,103 +99,92 @@ bool test (int argc, char** argv, const SortingCode& /*sc*/, const RegionCode& /
     SD::internal::region_growing_planes(
       input_range, std::back_inserter(regions),
       CGAL::parameters::
-      maximum_distance(distance_threshold).
-      maximum_angle(angle_threshold).
+      maximum_distance(max_distance).
+      maximum_angle(max_angle).
       minimum_region_size(min_region_size).
       point_map(input_range.point_map()).
       normal_map(input_range.normal_map()));
     assert(regions.size() == 7);
   }
 
-  bool result = assertion(regions);
-  assert (result);
-  std::cout << "exact_inexact_test_success: " << result << std::endl;
-  return result;
+  const bool success = true;
+  std::cout << "rg_" + name + "_sortpoints3, epick_test_success: " << success << std::endl;
+  return success;
 }
 
 int main(int argc, char *argv[]) {
+  bool success = true;
 
-  bool success =
-    test<Plane_region, Plane_sorting>
-    (argc, argv,
-     [](const auto& input_range, auto& neighbor_query) -> Plane_sorting
-     {
-       return Plane_sorting (input_range, neighbor_query,
-                             input_range.point_map());
-     },
-     [](const auto& input_range) -> Plane_region
-     {
-       // Default parameter values for the data file point_set_3.xyz.
-       const FT          distance_threshold = FT(2);
-       const FT          angle_threshold    = FT(20);
-       const std::size_t min_region_size    = 50;
-       return Plane_region
-         (input_range,
-          distance_threshold, angle_threshold, min_region_size,
-          input_range.point_map(), input_range.normal_map());
-     },
-     [](const auto& r) -> bool {
-       std::cout << "- num regions planes: " << r.size() << std::endl;
-       return (r.size() >= 6 && r.size() <= 8);
-      });
-  if (!success)
-    return EXIT_FAILURE;
+  // Test planes.
+  success = test<Plane_region, Plane_sorting>(argc, argv, "planes",
+    [](const auto& input_range) -> Plane_region {
 
-  success =
-    test<Sphere_region, Sphere_sorting>
-    (argc, argv,
-     [](const auto& input_range, auto& neighbor_query) -> Sphere_sorting
-     {
-       return Sphere_sorting (input_range, neighbor_query,
-                              input_range.point_map());
-     },
-     [](const auto& input_range) -> Sphere_region
-     {
-       const double tolerance = 0.01;
-       const double max_angle = 10.;
+       const FT          max_distance    = FT(2);
+       const FT          max_angle       = FT(20);
        const std::size_t min_region_size = 50;
-       // No constraint on radius
-       const double min_radius = 0.;
-       const double max_radius = std::numeric_limits<double>::max();
-       return Sphere_region
-         (input_range, tolerance, max_angle, min_region_size,
-          min_radius, max_radius,
-          input_range.point_map(), input_range.normal_map());
-     },
-     [](const auto& r) -> bool {
-        std::cout << "- num regions spheres: " << r.size() << std::endl;
-        return (r.size() > 10 && r.size() < 90);
-      });
-  if (!success)
-    return EXIT_FAILURE;
+       return Plane_region(input_range, CGAL::parameters::
+          maximum_distance(max_distance).
+          maximum_angle(max_angle).
+          minimum_region_size(min_region_size).
+          point_map(input_range.point_map()).
+          normal_map(input_range.normal_map()));
+    },
+    [](const auto& region) -> bool {
+      std::cout << "- num regions planes: " << region.size() << std::endl;
+      return (region.size() >= 6 && region.size() <= 8);
+    }
+  );
 
-  success =
-    test<Cylinder_region, Cylinder_sorting>
-    (argc, argv,
-     [](const auto& input_range, auto& neighbor_query) -> Cylinder_sorting
-     {
-       return Cylinder_sorting (input_range, neighbor_query,
-                                input_range.point_map(), input_range.normal_map());
-     },
-     [](const auto& input_range) -> Cylinder_region
-     {
-       const double tolerance = 0.05;
-       const double max_angle = 5.;
+  if (!success) {
+    return EXIT_FAILURE;
+  }
+
+  // Test spheres.
+  success = test<Sphere_region, Sphere_sorting>(argc, argv, "spheres",
+    [](const auto& input_range) -> Sphere_region {
+
+       const FT          max_distance    = FT(1) / FT(100);
+       const FT          max_angle       = FT(10);
+       const std::size_t min_region_size = 50;
+       return Sphere_region(input_range, CGAL::parameters::
+          maximum_distance(max_distance).
+          maximum_angle(max_angle).
+          minimum_region_size(min_region_size).
+          point_map(input_range.point_map()).
+          normal_map(input_range.normal_map()));
+    },
+    [](const auto& region) -> bool {
+      std::cout << "- num regions spheres: " << region.size() << std::endl;
+      return (region.size() > 36 && region.size() < 40);
+    }
+  );
+
+  if (!success) {
+    return EXIT_FAILURE;
+  }
+
+  // Test cylinders.
+  success = test<Cylinder_region, Cylinder_sorting>(argc, argv, "cylinders",
+    [](const auto& input_range) -> Cylinder_region {
+
+       const FT          max_distance    = FT(1) / FT(20);
+       const FT          max_angle       = FT(5);
        const std::size_t min_region_size = 200;
-       // No constraint on radius
-       const double min_radius = 0.;
-       const double max_radius = std::numeric_limits<double>::max();
-       return Cylinder_region
-         (input_range, tolerance, max_angle, min_region_size,
-          min_radius, max_radius,
-          input_range.point_map(), input_range.normal_map());
-     },
-     [](const auto& r) -> bool {
-        std::cout << "- num regions cylinders: " << r.size() << std::endl;
-        return (r.size() > 2 && r.size() < 30);
-      });
-  if (!success)
-    return EXIT_FAILURE;
+       return Cylinder_region(input_range, CGAL::parameters::
+          maximum_distance(max_distance).
+          maximum_angle(max_angle).
+          minimum_region_size(min_region_size).
+          point_map(input_range.point_map()).
+          normal_map(input_range.normal_map()));
+    },
+    [](const auto& region) -> bool {
+      std::cout << "- num regions cylinders: " << region.size() << std::endl;
+      return (region.size() > 6 && region.size() < 10);
+    }
+  );
 
+  if (!success) {
+    return EXIT_FAILURE;
+  }
   return EXIT_SUCCESS;
 }