diff --git a/CMakeLists.txt b/CMakeLists.txt
index 7bc0f6fa..bff76e87 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -8,7 +8,7 @@ if(NOT CMAKE_BUILD_TYPE)
 	set(CMAKE_BUILD_TYPE Release)
 endif()
 
-set(CMAKE_CXX_STANDARD 17)
+set(CMAKE_CXX_STANDARD 20)
 set(CMAKE_CXX_STANDARD_REQUIRED ON)
 
 add_compile_options(-Wall -Wextra -Wno-unused-result)
diff --git a/include/gproshan/geometry/convex_hull.h b/include/gproshan/geometry/convex_hull.h
index eb7291e4..a7e2abcb 100644
--- a/include/gproshan/geometry/convex_hull.h
+++ b/include/gproshan/geometry/convex_hull.h
@@ -20,13 +20,13 @@ class convex_hull
 		std::vector<index_t> CH;		///< convex hull points clockwise
 
 	public:
-		convex_hull(const std::vector<vertex> & points);
-		convex_hull(const vertex * points, const size_t & n_points);
-		operator const std::vector<index_t> & ();
+		convex_hull(const std::vector<vertex> & points, const real_t & precision = 1000);
+		convex_hull(const vertex * points, const size_t & n_points, const real_t & precision = 1000);
+		operator const std::vector<index_t> & () const;
 
 	private:
-		void andrew_algorithm(const vertex * points, const size_t & n_points);
-		bool ccw(const vertex & p, const vertex & q, const vertex & r);
+		void andrew_algorithm(const std::vector<ivec2> & points);
+		bool ccw(const ivec2 & p, const ivec2 & q, const ivec2 & r);
 };
 
 
diff --git a/include/gproshan/geometry/vec.h b/include/gproshan/geometry/vec.h
index 922f742c..acf42820 100644
--- a/include/gproshan/geometry/vec.h
+++ b/include/gproshan/geometry/vec.h
@@ -274,6 +274,14 @@ vec<T, N> operator / (const T & a, const vec<T, N> & v)
 	return res;
 }
 
+///< cross product
+template<class T>
+__host_device__
+T cross(const vec<T, 2> & u, const vec<T, 2> & v)
+{
+	return u.x() * v.y() - v.x() * u.y();
+}
+
 ///< cross product
 template<class T>
 __host_device__
diff --git a/include/gproshan/mdict/mdict.h b/include/gproshan/mdict/mdict.h
index 78f2d1de..cd4648d8 100644
--- a/include/gproshan/mdict/mdict.h
+++ b/include/gproshan/mdict/mdict.h
@@ -20,7 +20,6 @@ struct locval_t
 	real_t val;
 };
 
-bool operator < (const locval_t & a, const locval_t & b);
 
 void OMP(std::vector<locval_t> & alpha, const a_vec & x, const index_t & i, const a_mat & D, const size_t & L);
 
diff --git a/src/gproshan/features/key_points.cpp b/src/gproshan/features/key_points.cpp
index 38005fed..69c5de69 100644
--- a/src/gproshan/features/key_points.cpp
+++ b/src/gproshan/features/key_points.cpp
@@ -30,7 +30,7 @@ void key_points::compute_kps_areas(che * mesh, const real_t & percent)
 	for(index_t f = 0; f < mesh->n_trigs; ++f)
 		face_areas[f] = { mesh->area_trig(f), f };
 
-	std::sort(begin(face_areas), end(face_areas));
+	std::ranges::sort(face_areas);
 
 	is_kp.assign(mesh->n_vertices, false);
 	kps.reserve(mesh->n_vertices);
diff --git a/src/gproshan/geometry/convex_hull.cpp b/src/gproshan/geometry/convex_hull.cpp
index 37b9e9aa..d0dbbd4b 100644
--- a/src/gproshan/geometry/convex_hull.cpp
+++ b/src/gproshan/geometry/convex_hull.cpp
@@ -8,34 +8,41 @@
 namespace gproshan {
 
 
-convex_hull::convex_hull(const std::vector<vertex> & points): convex_hull(points.data(), size(points)) {}
+convex_hull::convex_hull(const std::vector<vertex> & points, const real_t & precision): convex_hull(points.data(), size(points), precision) {}
 
-convex_hull::convex_hull(const vertex * points, const size_t & n_points)
+convex_hull::convex_hull(const vertex * points, const size_t & n_points, const real_t & precision)
 {
-	andrew_algorithm(points, n_points);
+	std::vector<ivec2> points2d(n_points);
+
+	#pragma omp parallel for
+	for(index_t i = 0; i < n_points; ++i)
+	{
+		const vertex & p = points[i] * precision;
+		points2d[i] = {int(p.x()), int(p.y())};
+	}
+	andrew_algorithm(points2d);
 }
 
-convex_hull::operator const std::vector<index_t> & ()
+convex_hull::operator const std::vector<index_t> & () const
 {
 	return CH;
 }
 
 ///< Andrew's Convex Hull Algorithm: Competitive Programming 4
-void convex_hull::andrew_algorithm(const vertex * points, const size_t & n_points)
+void convex_hull::andrew_algorithm(const std::vector<ivec2> & points)
 {
-	std::vector<index_t> idx(n_points);
+	std::vector<index_t> idx(size(points));
 	std::iota(begin(idx), end(idx), 0);
 
-	std::sort(begin(idx), end(idx),
-		[&points](const index_t & i, const index_t & j)
-		{
-			return points[i] < points[j];
-		});
+	std::ranges::sort(idx, [&points](const index_t & i, const index_t & j)
+					{
+						return points[i] < points[j];
+					});
 
-	CH.resize(2 * n_points);
+	CH.resize(2 * size(points));
 
 	index_t k = 0;
-	for(index_t p = 0; p < n_points; ++p)
+	for(index_t p = 0; p < size(points); ++p)
 	{
 		const index_t & i = idx[p];
 		while(k > 1 && !ccw(points[CH[k - 2]], points[CH[k - 1]], points[i])) --k;
@@ -43,7 +50,7 @@ void convex_hull::andrew_algorithm(const vertex * points, const size_t & n_point
 	}
 
 	index_t t = k;
-	for(index_t p = n_points - 2; p > 0; --p)
+	for(index_t p = size(points) - 2; p > 0; --p)
 	{
 		const index_t & i = idx[p];
 		while(k > t && !ccw(points[CH[k - 2]], points[CH[k - 1]], points[i])) --k;
@@ -55,10 +62,9 @@ void convex_hull::andrew_algorithm(const vertex * points, const size_t & n_point
 	CH.resize(k);
 }
 
-bool convex_hull::ccw(const vertex & p, const vertex & q, const vertex & r)
+bool convex_hull::ccw(const ivec2 & p, const ivec2 & q, const ivec2 & r)
 {
-	// TODO vec2
-	return cross(q - p, r - p).z() > 0;
+	return cross(q - p, r - p) > 0;
 }
 
 
diff --git a/src/gproshan/mdict/mdict.cpp b/src/gproshan/mdict/mdict.cpp
index 39ff79a6..d377b25d 100644
--- a/src/gproshan/mdict/mdict.cpp
+++ b/src/gproshan/mdict/mdict.cpp
@@ -17,11 +17,6 @@ const real_t sigma = 0.01;
 
 // SPARSE
 
-bool operator < (const locval_t & a, const locval_t & b)
-{
-	return (a.i == b.i) ? a.j < b.j : a.i < b.i;
-}
-
 std::ostream & operator << (std::ostream & os, const locval_t & lc)
 {
 	return os << '(' << lc.i << ',' << lc.j << ") = " << lc.val;
@@ -77,7 +72,10 @@ void sp_KSVD(a_mat & D, const a_mat & X, const size_t & L, size_t k)
 	{
 		a_sp_mat alpha = OMP_all(locval, X, D, L);
 
-		std::sort(locval.begin(), locval.end());
+		std::ranges::sort(locval, [](const locval_t & a, const locval_t & b)
+								{
+									return a.i == b.i ? a.j < b.j : a.i < b.i;
+								});
 
 		rows.push_back(0);
 		for(index_t k = 1; k < size(locval); ++k)
@@ -360,7 +358,10 @@ void sp_KSVD(a_mat & A, const std::vector<patch> & patches, const size_t & L, si
 	{
 		a_sp_mat alpha = OMP_all(locval, patches, A, L);
 
-		std::sort(locval.begin(), locval.end());
+		std::ranges::sort(locval, [](const locval_t & a, const locval_t & b)
+								{
+									return a.i == b.i ? a.j < b.j : a.i < b.i;
+								});
 
 		rows.push_back(0);
 		for(index_t k = 1; k < size(locval); ++k)
diff --git a/src/gproshan/mdict/msparse_coding.cpp b/src/gproshan/mdict/msparse_coding.cpp
index fc3b85f6..09ca3209 100644
--- a/src/gproshan/mdict/msparse_coding.cpp
+++ b/src/gproshan/mdict/msparse_coding.cpp
@@ -891,7 +891,7 @@ real_t msparse_coding::mesh_reconstruction(const fmask_t & mask)
 		rp.xyz.row(2) = x.t();
 	}
 
-	std::sort(patches_error.begin(), patches_error.end());
+	std::ranges::sort(patches_error);
 
 	fprintf(stderr, "error %16s%16s\n", "best", "worst");
 	for(index_t i = 0; i < 10; ++i)
diff --git a/src/gproshan/mdict/patch.cpp b/src/gproshan/mdict/patch.cpp
index cf6864a8..189a31f1 100644
--- a/src/gproshan/mdict/patch.cpp
+++ b/src/gproshan/mdict/patch.cpp
@@ -414,7 +414,7 @@ void patch::add_extra_xyz_disjoint(che * mesh, std::vector<vpatches_t> & vpatche
 			vpatches_t & ma = vpatches[mesh->halfedge(he_next(he))];
 			vpatches_t & mb = vpatches[mesh->halfedge(he_prev(he))];
 
-			if(ma.find(p) != ma.end() && mb.find(p) != mb.end())
+			if(ma.contains(p) && mb.contains(p))
 			{
 				arma::uvec xi = { vpatches[min_v][p], ma[p], mb[p] };
 				abc = xyz.cols(xi);
@@ -600,7 +600,7 @@ void patch::jet_fit_directions(che * mesh, const index_t & v)
 
 	My_Monge_form monge_form;
 	My_Monge_via_jet_fitting monge_fit;
-	monge_form = monge_fit(in_points.begin(), in_points.end(), d_fitting, d_monge);
+	monge_form = monge_fit(begin(in_points), end(in_points), d_fitting, d_monge);
 
 	vertex normal = mesh->normal(v);
 	monge_form.comply_wrt_given_normal(DVector(normal.x(), normal.y(), normal.z()));
@@ -736,9 +736,9 @@ void patch::compute_avg_distance(che * mesh, std::vector<vpatches_t> & vpatches,
 			distances.push_back(norm(a - b));
 		}
 	*/
-	std::sort(distances.begin(), distances.end());
+	std::ranges::sort(distances);
 	size_t n_elem = size(distances);
-	if(size(distances)%2 ==0)
+	if(size(distances) % 2 ==0)
 	{
 		avg_dist = (distances[n_elem/2] + distances[(n_elem/2 -1)])/2;
 	}
diff --git a/src/gproshan/mesh/che_fill_hole.cpp b/src/gproshan/mesh/che_fill_hole.cpp
index 4d99018c..1fc5497d 100644
--- a/src/gproshan/mesh/che_fill_hole.cpp
+++ b/src/gproshan/mesh/che_fill_hole.cpp
@@ -118,7 +118,7 @@ che * mesh_fill_hole(che * mesh, const std::vector<index_t> & border_vertices, c
 		}
 		else // fill rest partial holes
 		{
-			reverse(merge_vertices[!c].begin(), merge_vertices[!c].end());
+			reverse(begin(merge_vertices[!c]), end(merge_vertices[!c]));
 			for(index_t v: merge_vertices[!c])
 				vertices[c].push_back(hole->point(v));
 
@@ -172,7 +172,7 @@ che * mesh_fill_hole(che * mesh, const std::vector<index_t> & border_vertices, c
 	}
 	else
 	{
-		reverse(merge_vertices[!c].begin(), merge_vertices[!c].end());
+		reverse(begin(merge_vertices[!c]), end(merge_vertices[!c]));
 
 		for(index_t v: merge_vertices[!c])
 			vertices[c].push_back(hole->point(v));
diff --git a/src/gproshan/pointcloud/knn.cpp b/src/gproshan/pointcloud/knn.cpp
index 9c7986d9..6a35d8d9 100644
--- a/src/gproshan/pointcloud/knn.cpp
+++ b/src/gproshan/pointcloud/knn.cpp
@@ -49,7 +49,7 @@ std::vector<index_t> grid::operator () (const point & p, int k) const
 			continue;
 
 		const auto & iter = voxels.find(pos);
-		if(iter == voxels.end())
+		if(iter == end(voxels))
 			continue;
 
 		for(const index_t & v: iter->second)
diff --git a/src/gproshan/scenes/scene.cpp b/src/gproshan/scenes/scene.cpp
index 31d5d54e..f64806a9 100644
--- a/src/gproshan/scenes/scene.cpp
+++ b/src/gproshan/scenes/scene.cpp
@@ -165,7 +165,7 @@ bool scene::load_mtl(const std::string & file)
 						: materials.back().map_bump;
 				sscanf(line, "%*s %s", str);
 				if(str[0] == '-') continue;		// ignoring map textures with options
-				if(texture_id.find(str) == texture_id.end())
+				if(!texture_id.contains(str))
 				{
 					texture_id[str] = size(texture_name);
 					texture_name.push_back(str);
diff --git a/src/gproshan/viewer/viewer.cpp b/src/gproshan/viewer/viewer.cpp
index a6a66d5a..3d2f9211 100644
--- a/src/gproshan/viewer/viewer.cpp
+++ b/src/gproshan/viewer/viewer.cpp
@@ -452,7 +452,6 @@ void viewer::init_menus()
 	add_menu("Viewer",
 	{
 		add_process("Help", m_help, GLFW_KEY_F1),
-		add_process("Close", m_close, GLFW_KEY_ESCAPE),
 		add_process("Maximize", m_maximize, GLFW_KEY_F11),
 		add_process("Hide/Show ImGui", m_hide_show_imgui, GLFW_KEY_I),
 		add_process("Save/Load view", m_save_load_view, GLFW_KEY_PERIOD),
@@ -461,29 +460,30 @@ void viewer::init_menus()
 		add_process("Background color inc", m_bgc_inc, GLFW_KEY_RIGHT),
 		add_process("Background color dec", m_bgc_dec, GLFW_KEY_LEFT),
 		add_process("Background color white", m_bgc_white, GLFW_KEY_1),
-		add_process("Background color black", m_bgc_black, GLFW_KEY_0)
+		add_process("Background color black", m_bgc_black, GLFW_KEY_0),
+		add_process("Close", m_close, GLFW_KEY_ESCAPE)
 	});
 
 	add_menu("Render",
 	{
+		add_process("Render Flat", m_render_flat, GLFW_KEY_TAB),
 		add_process("Render Point Cloud", m_render_pointcloud, GLFW_KEY_F5),
 		add_process("Render Wireframe", m_render_wireframe, GLFW_KEY_F6),
 		add_process("Render Triangles", m_render_triangles, GLFW_KEY_F7),
 		add_process("Render GL", m_render_gl, GLFW_KEY_F8),
-		add_process("Level Curves", m_render_lines, GLFW_KEY_SPACE),
-		add_process("Render Flat", m_render_flat, GLFW_KEY_TAB),
-		add_process("Setup Raytracing", m_setup_raytracing, GLFW_KEY_R),
 		add_process("Render Embree", m_render_embree, GLFW_KEY_F9),
 	#ifdef GPROSHAN_OPTIX
 		add_process("Render OptiX", m_render_optix, GLFW_KEY_F10),
 	#endif // GPROSHAN_OPTIX
-		add_process("Raycasting", m_raycasting, GLFW_KEY_ENTER)
+		add_process("Setup Raytracing", m_setup_raytracing, GLFW_KEY_R),
+		add_process("Raycasting", m_raycasting, GLFW_KEY_ENTER),
+		add_process("Level Curves", m_render_lines, GLFW_KEY_SPACE)
 	});
 
 	add_menu("Mesh",
 	{
-		add_process("Reload/Reset", m_reset_mesh, GLFW_KEY_INSERT),
 		add_process("Save Mesh", m_save_mesh, GLFW_KEY_W),
+		add_process("Reload/Reset", m_reset_mesh, GLFW_KEY_INSERT),
 		add_process("Remove Selected Mesh", m_remove_mesh, GLFW_KEY_DELETE),
 		add_process("Pop Mesh", m_pop_mesh, GLFW_KEY_BACKSPACE),
 		add_process("Normalize Mesh", m_normalize_mesh),
@@ -534,7 +534,7 @@ int viewer::add_process(const char * name, const function_t & f, const int & key
 	static int nk = 1000;
 
 	const int & fkey = key == -1 ? ++nk : key;
-	if(processes.find(fkey) != processes.end())
+	if(processes.contains(fkey))
 	{
 		fprintf(stderr, "repeated key: [%d] %s (%s)\n", key, glfw_key_name.at(key), name);
 		return -1;
@@ -674,7 +674,7 @@ void viewer::keyboard_callback(GLFWwindow * window, int key, int, int action, in
 	if(action == GLFW_RELEASE) return;
 
 	viewer * view = (viewer *) glfwGetWindowUserPointer(window);
-	if(view->processes.find(key) == view->processes.end())
+	if(!view->processes.contains(key))
 		return;
 
 	process_t & pro = view->processes[key];