diff options
author | skachano <skachano@636b058d-ea47-450e-bf9e-a15bfbe3eedb> | 2015-12-07 09:39:53 +0000 |
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committer | skachano <skachano@636b058d-ea47-450e-bf9e-a15bfbe3eedb> | 2015-12-07 09:39:53 +0000 |
commit | 33c51358238382335caf892bbc24759c8aac59a0 (patch) | |
tree | 499e768570391c30af22eac4443667604fa717d6 /src/Witness_complex | |
parent | da39f7cd8a0db5d7fa13c9c87f8fc3e038c10d01 (diff) | |
parent | c8c2f91db880218bb7ab275fbadda53a23f88d35 (diff) |
Changes piled up for months
git-svn-id: svn+ssh://scm.gforge.inria.fr/svnroot/gudhi/branches/witness@932 636b058d-ea47-450e-bf9e-a15bfbe3eedb
Former-commit-id: 0447901e608890eb607456fd12f3ea53547b8f10
Diffstat (limited to 'src/Witness_complex')
11 files changed, 3851 insertions, 820 deletions
diff --git a/src/Witness_complex/example/CMakeLists.txt b/src/Witness_complex/example/CMakeLists.txt index 23919b4a..ff372d16 100644 --- a/src/Witness_complex/example/CMakeLists.txt +++ b/src/Witness_complex/example/CMakeLists.txt @@ -1,16 +1,7 @@ cmake_minimum_required(VERSION 2.6) project(GUDHIWitnessComplex) -#cmake -DCGAL_DIR=~/GitDrive/CGAL/ ../../.. -#if (CGAL_FOUND) - #message(STATUS "CGAL version: ${CGAL_VERSION}.") - #include( ${CGAL_USE_FILE} ) - - #find_package(Eigen3 3.1.0) - #include( ${EIGEN3_USE_FILE} ) - - #INCLUDE_DIRECTORIES(${EIGEN3_INCLUDE_DIR}) - #INCLUDE_DIRECTORIES(${CGAL_INCLUDE_DIRS}) +# A simple example add_executable ( simple_witness_complex simple_witness_complex.cpp ) add_test(simple_witness_complex ${CMAKE_CURRENT_BINARY_DIR}/simple_witness_complex) @@ -21,7 +12,7 @@ project(GUDHIWitnessComplex) add_executable( witness_complex_from_off witness_complex_from_off.cpp ) add_executable( witness_complex_from_wl_matrix witness_complex_from_wl_matrix.cpp ) -#endif() + # An example with Simplex-tree using CGAL alpha_shapes_3 @@ -51,6 +42,7 @@ if(CGAL_FOUND) if (EIGEN3_FOUND) message(STATUS "Eigen3 version: ${EIGEN3_VERSION}.") include( ${EIGEN3_USE_FILE} ) + message(STATUS "Eigen3 use file: ${EIGEN3_USE_FILE}.") include_directories (BEFORE "../../include") add_executable ( witness_complex_knn_landmarks witness_complex_knn_landmarks.cpp ) diff --git a/src/Witness_complex/example/protected_sets/output_tikz.h b/src/Witness_complex/example/protected_sets/output_tikz.h new file mode 100644 index 00000000..edfd9a5f --- /dev/null +++ b/src/Witness_complex/example/protected_sets/output_tikz.h @@ -0,0 +1,67 @@ +#ifndef OUTPUT_TIKZ_H +#define OUTPUT_TIKZ_H + +#include <vector> +#include <string> +#include <algorithm> +#include <fstream> +#include <cmath> + +void write_tikz_plot(std::vector<FT> data, std::string filename) +{ + int n = data.size(); + FT vmax = *(std::max_element(data.begin(), data.end())); + //std::cout << std::log10(vmax) << " " << std::floor(std::log10(vmax)); + + FT order10 = pow(10,std::floor(std::log10(vmax))); + int digit = std::floor( vmax / order10) + 1; + if (digit == 4 || digit == 6) digit = 5; + if (digit > 6) digit = 10; + FT plot_max = digit*order10; + std::cout << plot_max << " " << vmax; + FT hstep = 10.0/(n-1); + FT wstep = 10.0 / plot_max; + + std::cout << "(eps_max-eps_min)/(N-48) = " << (vmax-*data.begin())/(data.size()-48) << "\n"; + std::ofstream ofs(filename, std::ofstream::out); + + ofs << + "\\documentclass{standalone}\n" << + "\\usepackage[utf8]{inputenc}\n" << + "\\usepackage{amsmath}\n" << + "\\usepackage{tikz}\n\n" << + "\\begin{document}\n" << + "\\begin{tikzpicture}\n"; + + ofs << "\\draw[->] (0,0) -- (0,11);" << std::endl << + "\\draw[->] (0,0) -- (11,0);" << std::endl << + "\\foreach \\i in {1,...,10}" << std::endl << + "\\draw (0,\\i) -- (-0.05,\\i);" << std::endl << + "\\foreach \\i in {1,...,10}" << std::endl << + "\\draw (\\i,0) -- (\\i,-0.05);" << std::endl << std::endl << + + "\\foreach \\i in {1,...,10}" << std::endl << + "\\draw[dashed] (-0.05,\\i) -- (11,\\i);" << std::endl << std::endl << + + "\\node at (-0.5,11) {$*$}; " << std::endl << + "\\node at (11,-0.5) {$*$}; " << std::endl << + "\\node at (-0.5,-0.5) {0}; " << std::endl << + "\\node at (-0.5,10) {" << plot_max << "}; " << std::endl << + "%\\node at (10,-0.5) {2}; " << std::endl; + + ofs << "\\draw[red] (0," << wstep*data[0] << ")"; + for (int i = 1; i < n; ++i) + ofs << " -- (" << hstep*i << "," << wstep*data[i] << ")"; + ofs << ";\n"; + + ofs << + "\\end{tikzpicture}\n" << + "\\end{document}"; + + ofs.close(); + + + +} + +#endif diff --git a/src/Witness_complex/example/protected_sets/protected_sets.h b/src/Witness_complex/example/protected_sets/protected_sets.h new file mode 100644 index 00000000..ec627808 --- /dev/null +++ b/src/Witness_complex/example/protected_sets/protected_sets.h @@ -0,0 +1,597 @@ +#ifndef PROTECTED_SETS_H +#define PROTECTED_SETS_H + +#include <algorithm> +#include <CGAL/Cartesian_d.h> +#include <CGAL/Epick_d.h> +#include <CGAL/Euclidean_distance.h> +#include <CGAL/Kernel_d/Sphere_d.h> +#include <CGAL/Kernel_d/Hyperplane_d.h> +#include <CGAL/Kernel_d/Vector_d.h> + +#include <CGAL/point_generators_d.h> +#include <CGAL/constructions_d.h> + + +typedef CGAL::Epick_d<CGAL::Dynamic_dimension_tag> K; +typedef K::Point_d Point_d; +typedef K::Vector_d Vector_d; +typedef K::Oriented_side_d Oriented_side_d; +typedef K::Has_on_positive_side_d Has_on_positive_side_d; +typedef K::Sphere_d Sphere_d; +typedef K::Hyperplane_d Hyperplane_d; + +typedef CGAL::Delaunay_triangulation<K> Delaunay_triangulation; +typedef Delaunay_triangulation::Facet Facet; +typedef Delaunay_triangulation::Vertex_handle Delaunay_vertex; +typedef Delaunay_triangulation::Full_cell_handle Full_cell_handle; + +typedef std::vector<Point_d> Point_Vector; +typedef CGAL::Euclidean_distance<Traits_base> Euclidean_distance; + +FT _sfty = pow(10,-14); + +/////////////////////////////////////////////////////////////////////////////////////////////////////////// +// AUXILLARY FUNCTIONS +/////////////////////////////////////////////////////////////////////////////////////////////////////////// + +/** Insert a point in Delaunay triangulation. If you are working in a flat torus, the procedure adds all the 3^d copies in adjacent cubes as well + * + * W is the initial point vector + * chosen_landmark is the index of the chosen point in W + * landmarks_ind is the vector of indices of already chosen points in W + * delaunay is the Delaunay triangulation + * landmark_count is the current number of chosen vertices + * torus is true iff you are working on a flat torus [-1,1]^d + * OUT: Vertex handle to the newly inserted point + */ +Delaunay_vertex insert_delaunay_landmark_with_copies(Point_Vector& W, int chosen_landmark, std::vector<int>& landmarks_ind, Delaunay_triangulation& delaunay, int& landmark_count, bool torus) +{ + if (!torus) + { + Delaunay_vertex v =delaunay.insert(W[chosen_landmark]); + landmarks_ind.push_back(chosen_landmark); + landmark_count++; + return v; + } + else + { + int D = W[0].size(); + int nb_cells = pow(3, D); + Delaunay_vertex v; + for (int i = 0; i < nb_cells; ++i) + { + std::vector<FT> point; + int cell_i = i; + for (int l = 0; l < D; ++l) + { + point.push_back(W[chosen_landmark][l] + 2.0*(cell_i%3-1)); + cell_i /= 3; + } + v = delaunay.insert(point); + } + landmarks_ind.push_back(chosen_landmark); + landmark_count++; + return v; + } +} + +/** Small check if the vertex v is in the full cell fc + */ + +bool vertex_is_in_full_cell(Delaunay_triangulation::Vertex_handle v, Full_cell_handle fc) +{ + for (auto v_it = fc->vertices_begin(); v_it != fc->vertices_end(); ++v_it) + if (*v_it == v) + return true; + return false; +} + +/** Fill chosen point vector from indices with copies if you are working on a flat torus + * + * IN: W is the point vector + * OUT: landmarks is the output vector + * IN: landmarks_ind is the vector of indices + * IN: torus is true iff you are working on a flat torus [-1,1]^d + */ + +void fill_landmarks(Point_Vector& W, Point_Vector& landmarks, std::vector<int>& landmarks_ind, bool torus) +{ + if (!torus) + for (unsigned j = 0; j < landmarks_ind.size(); ++j) + landmarks.push_back(W[landmarks_ind[j]]); + else + { + int D = W[0].size(); + int nb_cells = pow(3, D); + int nbL = landmarks_ind.size(); + // Fill landmarks + for (int i = 0; i < nb_cells-1; ++i) + for (int j = 0; j < nbL; ++j) + { + int cell_i = i; + Point_d point; + for (int l = 0; l < D; ++l) + { + point.push_back(W[landmarks_ind[j]][l] + 2.0*(cell_i-1)); + cell_i /= 3; + } + landmarks.push_back(point); + } + } +} + +/** Fill a vector of all simplices in the Delaunay triangulation giving integer indices to vertices + * + * IN: t is the Delaunay triangulation + * OUT: full_cells is the output vector + */ + +void fill_full_cell_vector(Delaunay_triangulation& t, std::vector<std::vector<int>>& full_cells) +{ + // Store vertex indices in a map + int ind = 0; //index of a vertex + std::map<Delaunay_triangulation::Vertex_handle, int> index_of_vertex; + for (auto v_it = t.vertices_begin(); v_it != t.vertices_end(); ++v_it) + if (t.is_infinite(v_it)) + continue; + else + index_of_vertex[v_it] = ind++; + // Write full cells as vectors in full_cells + for (auto fc_it = t.full_cells_begin(); fc_it != t.full_cells_end(); ++fc_it) + { + if (t.is_infinite(fc_it)) + continue; + Point_Vector vertices; + for (auto fc_v_it = fc_it->vertices_begin(); fc_v_it != fc_it->vertices_end(); ++fc_v_it) + vertices.push_back((*fc_v_it)->point()); + Sphere_d cs( vertices.begin(), vertices.end()); + Point_d csc = cs.center(); + bool in_cube = true; + for (auto xi = csc.cartesian_begin(); xi != csc.cartesian_end(); ++xi) + if (*xi > 1.0 || *xi < -1.0) + { + in_cube = false; break; + } + if (!in_cube) + continue; + std::vector<int> cell; + for (auto v_it = fc_it->vertices_begin(); v_it != fc_it->vertices_end(); ++v_it) + cell.push_back(index_of_vertex[*v_it]); + full_cells.push_back(cell); + } +} + +//////////////////////////////////////////////////////////////////////////////////////////////////////////// +// IS VIOLATED TEST +//////////////////////////////////////////////////////////////////////////////////////////////////////////// + +/** Check if a newly created cell is protected from old vertices + * + * t is the Delaunay triangulation + * vertices is the vector containing the point to insert and a facet f in t + * v1 is the vertex of t, such that f and v1 form a simplex + * v2 is the vertex of t, such that f and v2 form another simplex + * delta is the protection constant + * power_protection is true iff the delta-power protection is used + */ + +bool new_cell_is_violated(Delaunay_triangulation& t, std::vector<Point_d>& vertices, const Delaunay_vertex& v1, const Delaunay_vertex v2, FT delta, bool power_protection, FT theta0) +{ + assert(vertices.size() == vertices[0].size() || + vertices.size() == vertices[0].size() + 1); //simplex size = d | d+1 + assert(v1 != v2); + if (vertices.size() == vertices[0].size() + 1) + // FINITE CASE + { + Sphere_d cs(vertices.begin(), vertices.end()); + Point_d center_cs = cs.center(); + FT r = sqrt(Euclidean_distance().transformed_distance(center_cs, vertices[0])); + /* + for (auto v_it = t.vertices_begin(); v_it != t.vertices_end(); ++v_it) + if (!t.is_infinite(v_it)) + { + //CGAL::Oriented_side side = Oriented_side_d()(cs, (v_it)->point()); + if (std::find(vertices.begin(), vertices.end(), v_it->point()) == vertices.end()) + { + FT dist2 = Euclidean_distance().transformed_distance(center_cs, (v_it)->point()); + if (!power_protection) + if (dist2 >= r*r-_sfty && dist2 <= (r+delta)*(r+delta)) + return true; + if (power_protection) + if (dist2 >= r*r-_sfty && dist2 <= r*r+delta*delta) + return true; + } + } + */ + // Check if the simplex is thick enough + Hyperplane_d tau_h(vertices.begin()+1, vertices.end()); + Vector_d orth_tau = tau_h.orthogonal_vector(); + /* + p_s1 = Vector_d(*(vertices.begin()), *(vertices.begin()+1)); + */ + //std::cout << "||orth_tau|| = " << sqrt(orth_tau.squared_length()) << "\n"; + FT orth_length = sqrt(orth_tau.squared_length()); + K::Cartesian_const_iterator_d o_it, p_it, s_it, c_it; + // Compute the altitude + FT h = 0; + for (o_it = orth_tau.cartesian_begin(), + p_it = vertices.begin()->cartesian_begin(), + s_it = (vertices.begin()+1)->cartesian_begin(); + o_it != orth_tau.cartesian_end(); + ++o_it, ++p_it, ++s_it) + h += (*o_it)*(*p_it - *s_it)/orth_length; + h = fabs(h); + // Is the center inside the box? + bool inside_the_box = true; + for (c_it = center_cs.cartesian_begin(); c_it != center_cs.cartesian_end(); ++c_it) + if (*c_it > 1.0 || *c_it < -1.0) + { + inside_the_box = false; break; + } + if (inside_the_box && h/r < theta0) + return true; + if (!t.is_infinite(v1)) + { + FT dist2 = Euclidean_distance().transformed_distance(center_cs, v1->point()); + if (!power_protection) + if (dist2 >= r*r-_sfty && dist2 <= (r+delta)*(r+delta)) + return true; + if (power_protection) + if (dist2 >= r*r-_sfty && dist2 <= r*r+delta*delta) + return true; + } + if (!t.is_infinite(v2)) + { + FT dist2 = Euclidean_distance().transformed_distance(center_cs, v2->point()); + if (!power_protection) + if (dist2 >= r*r-_sfty && dist2 <= (r+delta)*(r+delta)) + return true; + if (power_protection) + if (dist2 >= r*r-_sfty && dist2 <= r*r+delta*delta) + return true; + } + } + else + // INFINITE CASE + { + Delaunay_triangulation::Vertex_iterator v = t.vertices_begin(); + while (t.is_infinite(v) || std::find(vertices.begin(), vertices.end(), v->point()) == vertices.end()) + v++; + Hyperplane_d facet_plane(vertices.begin(), vertices.end(), v->point(), CGAL::ON_POSITIVE_SIDE); + Vector_d orth_v = facet_plane.orthogonal_vector(); + /* + for (auto v_it = t.vertices_begin(); v_it != t.vertices_end(); ++v_it) + if (!t.is_infinite(v_it)) + if (std::find(vertices.begin(), vertices.end(), v_it->point()) == vertices.end()) + { + std::vector<FT> coords; + Point_d p = v_it->point(); + auto orth_i = orth_v.cartesian_begin(), p_i = p.cartesian_begin(); + for (; orth_i != orth_v.cartesian_end(); ++orth_i, ++p_i) + coords.push_back((*p_i) - (*orth_i) * delta / sqrt(orth_v.squared_length())); + Point_d p_delta = Point_d(coords); + bool p_is_inside = !Has_on_positive_side_d()(facet_plane, p); + bool p_delta_is_inside = !Has_on_positive_side_d()(facet_plane, p_delta); + if (!p_is_inside && p_delta_is_inside) + return true; + } + */ + if (!t.is_infinite(v1)) + { + std::vector<FT> coords; + Point_d p = v1->point(); + auto orth_i = orth_v.cartesian_begin(), p_i = p.cartesian_begin(); + for (; orth_i != orth_v.cartesian_end(); ++orth_i, ++p_i) + coords.push_back((*p_i) - (*orth_i) * delta / sqrt(orth_v.squared_length())); + Point_d p_delta = Point_d(coords); + bool p_is_inside = !Has_on_positive_side_d()(facet_plane, p); + bool p_delta_is_inside = !Has_on_positive_side_d()(facet_plane, p_delta); + if (!power_protection && !p_is_inside && p_delta_is_inside) + return true; + } + if (!t.is_infinite(v2)) + { + std::vector<FT> coords; + Point_d p = v2->point(); + auto orth_i = orth_v.cartesian_begin(), p_i = p.cartesian_begin(); + for (; orth_i != orth_v.cartesian_end(); ++orth_i, ++p_i) + coords.push_back((*p_i) - (*orth_i) * delta / sqrt(orth_v.squared_length())); + Point_d p_delta = Point_d(coords); + bool p_is_inside = !Has_on_positive_side_d()(facet_plane, p); + bool p_delta_is_inside = !Has_on_positive_side_d()(facet_plane, p_delta); + if (!power_protection && !p_is_inside && p_delta_is_inside) + return true; + } + } + return false; +} + +/** Auxillary recursive function to check if the point p violates the protection of the cell c and + * if there is a violation of an eventual new cell + * + * p is the point to insert + * t is the current triangulation + * c is the current cell (simplex) + * parent_cell is the parent cell (simplex) + * index is the index of the facet between c and parent_cell from parent_cell's point of view + * D is the dimension of the triangulation + * delta is the protection constant + * marked_cells is the vector of all visited cells containing p in their circumscribed ball + * power_protection is true iff you are working with delta-power protection + * + * OUT: true iff inserting p hasn't produced any violation so far + */ + +bool is_violating_protection(Point_d& p, Delaunay_triangulation& t, Full_cell_handle c, Full_cell_handle parent_cell, int index, int D, FT delta, std::vector<Full_cell_handle>& marked_cells, bool power_protection, FT theta0) +{ + Euclidean_distance ed; + std::vector<Point_d> vertices; + if (!t.is_infinite(c)) + { + // if the cell is finite, we look if the protection is violated + for (auto v_it = c->vertices_begin(); v_it != c->vertices_end(); ++v_it) + vertices.push_back((*v_it)->point()); + Sphere_d cs( vertices.begin(), vertices.end()); + Point_d center_cs = cs.center(); + FT r = sqrt(ed.transformed_distance(center_cs, vertices[0])); + FT dist2 = ed.transformed_distance(center_cs, p); + // if the new point is inside the protection ball of a non conflicting simplex + if (!power_protection) + if (dist2 >= r*r-_sfty && dist2 <= (r+delta)*(r+delta)) + return true; + if (power_protection) + if (dist2 >= r*r-_sfty && dist2 <= r*r+delta*delta) + return true; + // if the new point is inside the circumscribing ball : continue violation searching on neighbours + //if (dist2 < r*r) + //if (dist2 < (5*r+delta)*(5*r+delta)) + if (dist2 < r*r) + { + c->tds_data().mark_visited(); + marked_cells.push_back(c); + for (int i = 0; i < D+1; ++i) + { + Full_cell_handle next_c = c->neighbor(i); + if (next_c->tds_data().is_clear() && + is_violating_protection(p, t, next_c, c, i, D, delta, marked_cells, power_protection, theta0)) + return true; + } + } + // if the new point is outside the protection sphere + else + { + // facet f is on the border of the conflict zone : check protection of simplex {p,f} + // the new simplex is guaranteed to be finite + vertices.clear(); vertices.push_back(p); + for (int i = 0; i < D+1; ++i) + if (i != index) + vertices.push_back(parent_cell->vertex(i)->point()); + Delaunay_vertex vertex_to_check = t.infinite_vertex(); + for (auto vh_it = c->vertices_begin(); vh_it != c->vertices_end(); ++vh_it) + if (!vertex_is_in_full_cell(*vh_it, parent_cell)) + { + vertex_to_check = *vh_it; break; + } + if (new_cell_is_violated(t, vertices, vertex_to_check, parent_cell->vertex(index), delta, power_protection, theta0)) + //if (new_cell_is_violated(t, vertices, vertex_to_check->point(), delta)) + return true; + } + } + else + { + // Inside of the convex hull is + side. Outside is - side. + for (auto vh_it = c->vertices_begin(); vh_it != c->vertices_end(); ++vh_it) + if (!t.is_infinite(*vh_it)) + vertices.push_back((*vh_it)->point()); + Delaunay_triangulation::Vertex_iterator v_it = t.vertices_begin(); + while (t.is_infinite(v_it) || vertex_is_in_full_cell(v_it, c)) + v_it++; + Hyperplane_d facet_plane(vertices.begin(), vertices.end(), v_it->point(), CGAL::ON_POSITIVE_SIDE); + //CGAL::Oriented_side outside = Oriented_side_d()(facet_plane, v_it->point()); + Vector_d orth_v = facet_plane.orthogonal_vector(); + std::vector<FT> coords; + auto orth_i = orth_v.cartesian_begin(), p_i = p.cartesian_begin(); + for (; orth_i != orth_v.cartesian_end(); ++orth_i, ++p_i) + coords.push_back((*p_i) - (*orth_i) * delta / sqrt(orth_v.squared_length())); + Point_d p_delta = Point_d(coords); + bool p_is_inside = !Has_on_positive_side_d()(facet_plane, p) && (Oriented_side_d()(facet_plane, p) != CGAL::ZERO); + bool p_delta_is_inside = !Has_on_positive_side_d()(facet_plane, p_delta); + + // If we work with power protection, we just ignore any conflicts + if (!power_protection && !p_is_inside && p_delta_is_inside) + return true; + //if the cell is infinite we look at the neighbours regardless + if (p_is_inside) + { + c->tds_data().mark_visited(); + marked_cells.push_back(c); + for (int i = 0; i < D+1; ++i) + { + Full_cell_handle next_c = c->neighbor(i); + if (next_c->tds_data().is_clear() && + is_violating_protection(p, t, next_c, c, i, D, delta, marked_cells, power_protection, theta0)) + return true; + } + } + else + { + // facet f is on the border of the conflict zone : check protection of simplex {p,f} + // the new simplex is finite if the parent cell is finite + vertices.clear(); vertices.push_back(p); + for (int i = 0; i < D+1; ++i) + if (i != index) + if (!t.is_infinite(parent_cell->vertex(i))) + vertices.push_back(parent_cell->vertex(i)->point()); + Delaunay_vertex vertex_to_check = t.infinite_vertex(); + for (auto vh_it = c->vertices_begin(); vh_it != c->vertices_end(); ++vh_it) + if (!vertex_is_in_full_cell(*vh_it, parent_cell)) + { + vertex_to_check = *vh_it; break; + } + if (new_cell_is_violated(t, vertices, vertex_to_check, parent_cell->vertex(index), delta, power_protection, theta0)) + //if (new_cell_is_violated(t, vertices, vertex_to_check->point(), delta)) + return true; + } + } + //c->tds_data().clear_visited(); + //marked_cells.pop_back(); + return false; +} + +/** Checks if inserting the point p in t will make conflicts + * + * p is the point to insert + * t is the current triangulation + * D is the dimension of triangulation + * delta is the protection constant + * power_protection is true iff you are working with delta-power protection + * OUT: true iff inserting p produces a violation of delta-protection. + */ + +bool is_violating_protection(Point_d& p, Delaunay_triangulation& t, int D, FT delta, bool power_protection, FT theta0) +{ + Euclidean_distance ed; + Delaunay_triangulation::Vertex_handle v; + Delaunay_triangulation::Face f(t.current_dimension()); + Delaunay_triangulation::Facet ft; + Delaunay_triangulation::Full_cell_handle c; + Delaunay_triangulation::Locate_type lt; + std::vector<Full_cell_handle> marked_cells; + c = t.locate(p, lt, f, ft, v); + bool violation_existing_cells = is_violating_protection(p, t, c, c, 0, D, delta, marked_cells, power_protection, theta0); + for (Full_cell_handle fc : marked_cells) + fc->tds_data().clear(); + return violation_existing_cells; +} + +/////////////////////////////////////////////////////////////////////// +/////////////////////////////////////////////////////////////////////// +//!!!!!!!!!!!!! THE INTERFACE FOR LANDMARK CHOICE IS BELOW !!!!!!!!!!// +/////////////////////////////////////////////////////////////////////// +/////////////////////////////////////////////////////////////////////// + +/////////////////////////////////////////////////////////////////////// +// LANDMARK CHOICE PROCEDURE +/////////////////////////////////////////////////////////////////////// + +/** Procedure to compute a maximal protected subset from a point cloud. All OUTs should be empty at call. + * + * IN: W is the initial point cloud having type Epick_d<Dynamic_dimension_tag>::Point_d + * IN: nbP is the size of W + * OUT: landmarks is the output vector for the points + * OUT: landmarks_ind is the output vector for the indices of the selected points in W + * IN: delta is the constant of protection + * OUT: full_cells is the output vector of the simplices in the final Delaunay triangulation + * IN: torus is true iff you are working on a flat torus [-1,1]^d + */ + +void landmark_choice_protected_delaunay(Point_Vector& W, int nbP, Point_Vector& landmarks, std::vector<int>& landmarks_ind, FT delta, std::vector<std::vector<int>>& full_cells, bool torus, bool power_protection, FT theta0) +{ + bool return_ = true; + unsigned D = W[0].size(); + Torus_distance td; + Euclidean_distance ed; + Delaunay_triangulation t(D); + CGAL::Random rand; + int landmark_count = 0; + std::list<int> index_list; + // shuffle the list of indexes (via a vector) + { + std::vector<int> temp_vector; + for (int i = 0; i < nbP; ++i) + temp_vector.push_back(i); + unsigned seed = std::chrono::system_clock::now().time_since_epoch().count(); + std::shuffle(temp_vector.begin(), temp_vector.end(), std::default_random_engine(seed)); + //CGAL::spatial_sort(temp_vector.begin(), temp_vector.end()); + for (std::vector<int>::iterator it = temp_vector.begin(); it != temp_vector.end(); ++it) + index_list.push_front(*it); + } + if (!torus) + for (unsigned pos1 = 0; pos1 < D+1; ++pos1) + { + std::vector<FT> point; + for (unsigned i = 0; i < pos1; ++i) + point.push_back(-1); + if (pos1 != D) + point.push_back(1); + for (unsigned i = pos1+1; i < D; ++i) + point.push_back(0); + assert(point.size() == D); + W[index_list.front()] = Point_d(point); + insert_delaunay_landmark_with_copies(W, index_list.front(), landmarks_ind, t, landmark_count, torus); + index_list.pop_front(); + } + else if (D == 2) + { + for (int i = 0; i < 4; ++i) + for (int j = 0; j < 2; ++j) + { + W[index_list.front()] = Point_d(std::vector<FT>{i*0.5, j*1.0}); + insert_delaunay_landmark_with_copies(W, index_list.front(), landmarks_ind, t, landmark_count, torus); + index_list.pop_front(); + W[index_list.front()] = Point_d(std::vector<FT>{0.25+i*0.5, 0.5+j}); + insert_delaunay_landmark_with_copies(W, index_list.front(), landmarks_ind, t, landmark_count, torus); + index_list.pop_front(); + } + } + else + std::cout << "No torus starter available for dim>2\n"; + std::list<int>::iterator list_it = index_list.begin(); + while (list_it != index_list.end()) + { + if (!is_violating_protection(W[*list_it], t, D, delta, power_protection, theta0)) + { + // If no conflicts then insert in every copy of T^3 + + insert_delaunay_landmark_with_copies(W, *list_it, landmarks_ind, t, landmark_count, torus); + if (return_) + { + index_list.erase(list_it); + list_it = index_list.begin(); + } + else + index_list.erase(list_it++); + /* + // PIECE OF CODE FOR DEBUGGING PURPOSES + + Delaunay_vertex inserted_v = insert_delaunay_landmark_with_copies(W, *list_it, landmarks_ind, t, landmark_count); + if (triangulation_is_protected(t, delta)) + { + index_list.erase(list_it); + list_it = index_list.begin(); + } + else + { //THAT'S WHERE SOMETHING'S WRONG + t.remove(inserted_v); + landmarks_ind.pop_back(); + landmark_count--; + write_delaunay_mesh(t, W[*list_it], is2d); + is_violating_protection(W[*list_it], t_old, D, delta); //Called for encore + } + */ + //std::cout << "index_list_size() = " << index_list.size() << "\n"; + } + else + { + list_it++; + //std::cout << "!!!!!WARNING!!!!! A POINT HAS BEEN OMITTED!!!\n"; + } + //if (list_it != index_list.end()) + // write_delaunay_mesh(t, W[*list_it], is2d); + } + fill_landmarks(W, landmarks, landmarks_ind, torus); + fill_full_cell_vector(t, full_cells); + /* + if (triangulation_is_protected(t, delta)) + std::cout << "Triangulation is ok\n"; + else + { + std::cout << "Triangulation is BAD!! T_T しくしく!\n"; + } + */ + //write_delaunay_mesh(t, W[0], is2d); + //std::cout << t << std::endl; +} + +#endif diff --git a/src/Witness_complex/example/protected_sets/protected_sets_paper.cpp b/src/Witness_complex/example/protected_sets/protected_sets_paper.cpp new file mode 100644 index 00000000..f3df3f1e --- /dev/null +++ b/src/Witness_complex/example/protected_sets/protected_sets_paper.cpp @@ -0,0 +1,610 @@ +#ifndef PROTECTED_SETS_H +#define PROTECTED_SETS_H + +#include <algorithm> +#include <CGAL/Cartesian_d.h> +#include <CGAL/Epick_d.h> +#include <CGAL/Euclidean_distance.h> +#include <CGAL/Kernel_d/Sphere_d.h> +#include <CGAL/Kernel_d/Hyperplane_d.h> +#include <CGAL/Kernel_d/Vector_d.h> + +typedef CGAL::Epick_d<CGAL::Dynamic_dimension_tag> K; +typedef K::Point_d Point_d; +typedef K::Vector_d Vector_d; +typedef K::Oriented_side_d Oriented_side_d; +typedef K::Has_on_positive_side_d Has_on_positive_side_d; +typedef K::Sphere_d Sphere_d; +typedef K::Hyperplane_d Hyperplane_d; + +typedef CGAL::Delaunay_triangulation<K> Delaunay_triangulation; +typedef Delaunay_triangulation::Facet Facet; +typedef Delaunay_triangulation::Vertex_handle Delaunay_vertex; +typedef Delaunay_triangulation::Full_cell_handle Full_cell_handle; + +typedef std::vector<Point_d> Point_Vector; +typedef CGAL::Euclidean_distance<Traits_base> Euclidean_distance; + +FT _sfty = pow(10,-14); + +/////////////////////////////////////////////////////////////////////////////////////////////////////////// +// AUXILLARY FUNCTIONS +/////////////////////////////////////////////////////////////////////////////////////////////////////////// + +/** Insert a point in Delaunay triangulation. If you are working in a flat torus, the procedure adds all the 3^d copies in adjacent cubes as well + * + * W is the initial point vector + * chosen_landmark is the index of the chosen point in W + * landmarks_ind is the vector of indices of already chosen points in W + * delaunay is the Delaunay triangulation + * landmark_count is the current number of chosen vertices + * torus is true iff you are working on a flat torus [-1,1]^d + * OUT: Vertex handle to the newly inserted point + */ +Delaunay_vertex insert_delaunay_landmark_with_copies(Point_d& p, Delaunay_triangulation& delaunay, int& landmark_count, bool torus) +{ + if (!torus) + { + Delaunay_vertex v =delaunay.insert(p); + landmark_count++; + return v; + } + else + { + int D = W[0].size(); + int nb_cells = pow(3, D); + Delaunay_vertex v; + for (int i = 0; i < nb_cells; ++i) + { + std::vector<FT> point; + int cell_i = i; + for (int l = 0; l < D; ++l) + { + point.push_back(p[l] + 2.0*(cell_i%3-1)); + cell_i /= 3; + } + v = delaunay.insert(point); + } + landmark_count++; + return v; + } +} + +/** Small check if the vertex v is in the full cell fc + */ + +bool vertex_is_in_full_cell(Delaunay_triangulation::Vertex_handle v, Full_cell_handle fc) +{ + for (auto v_it = fc->vertices_begin(); v_it != fc->vertices_end(); ++v_it) + if (*v_it == v) + return true; + return false; +} + +/** Fill chosen point vector from indices with copies if you are working on a flat torus + * + * IN: W is the point vector + * OUT: landmarks is the output vector + * IN: landmarks_ind is the vector of indices + * IN: torus is true iff you are working on a flat torus [-1,1]^d + */ + +void fill_landmarks(Point_Vector& W, Point_Vector& landmarks, std::vector<int>& landmarks_ind, bool torus) +{ + if (!torus) + for (unsigned j = 0; j < landmarks_ind.size(); ++j) + landmarks.push_back(W[landmarks_ind[j]]); + else + { + int D = W[0].size(); + int nb_cells = pow(3, D); + int nbL = landmarks_ind.size(); + // Fill landmarks + for (int i = 0; i < nb_cells-1; ++i) + for (int j = 0; j < nbL; ++j) + { + int cell_i = i; + Point_d point; + for (int l = 0; l < D; ++l) + { + point.push_back(W[landmarks_ind[j]][l] + 2.0*(cell_i-1)); + cell_i /= 3; + } + landmarks.push_back(point); + } + } +} + +/** Fill a vector of all simplices in the Delaunay triangulation giving integer indices to vertices + * + * IN: t is the Delaunay triangulation + * OUT: full_cells is the output vector + */ + +void fill_full_cell_vector(Delaunay_triangulation& t, std::vector<std::vector<int>>& full_cells) +{ + // Store vertex indices in a map + int ind = 0; //index of a vertex + std::map<Delaunay_triangulation::Vertex_handle, int> index_of_vertex; + for (auto v_it = t.vertices_begin(); v_it != t.vertices_end(); ++v_it) + if (t.is_infinite(v_it)) + continue; + else + index_of_vertex[v_it] = ind++; + // Write full cells as vectors in full_cells + for (auto fc_it = t.full_cells_begin(); fc_it != t.full_cells_end(); ++fc_it) + { + if (t.is_infinite(fc_it)) + continue; + Point_Vector vertices; + for (auto fc_v_it = fc_it->vertices_begin(); fc_v_it != fc_it->vertices_end(); ++fc_v_it) + vertices.push_back((*fc_v_it)->point()); + Sphere_d cs( vertices.begin(), vertices.end()); + Point_d csc = cs.center(); + bool in_cube = true; + for (auto xi = csc.cartesian_begin(); xi != csc.cartesian_end(); ++xi) + if (*xi > 1.0 || *xi < -1.0) + { + in_cube = false; break; + } + if (!in_cube) + continue; + std::vector<int> cell; + for (auto v_it = fc_it->vertices_begin(); v_it != fc_it->vertices_end(); ++v_it) + cell.push_back(index_of_vertex[*v_it]); + full_cells.push_back(cell); + } +} + +//////////////////////////////////////////////////////////////////////////////////////////////////////////// +// IS VIOLATED TEST +//////////////////////////////////////////////////////////////////////////////////////////////////////////// + +/** Check if a newly created cell is protected from old vertices + * + * t is the Delaunay triangulation + * vertices is the vector containing the point to insert and a facet f in t + * v1 is the vertex of t, such that f and v1 form a simplex + * v2 is the vertex of t, such that f and v2 form another simplex + * delta is the protection constant + * power_protection is true iff the delta-power protection is used + */ + +bool new_cell_is_violated(Delaunay_triangulation& t, std::vector<Point_d>& vertices, const Delaunay_vertex& v1, const Delaunay_vertex v2, FT delta, bool power_protection, FT theta0) +{ + assert(vertices.size() == vertices[0].size() || + vertices.size() == vertices[0].size() + 1); //simplex size = d | d+1 + assert(v1 != v2); + if (vertices.size() == vertices[0].size() + 1) + // FINITE CASE + { + Sphere_d cs(vertices.begin(), vertices.end()); + Point_d center_cs = cs.center(); + FT r = sqrt(Euclidean_distance().transformed_distance(center_cs, vertices[0])); + /* + for (auto v_it = t.vertices_begin(); v_it != t.vertices_end(); ++v_it) + if (!t.is_infinite(v_it)) + { + //CGAL::Oriented_side side = Oriented_side_d()(cs, (v_it)->point()); + if (std::find(vertices.begin(), vertices.end(), v_it->point()) == vertices.end()) + { + FT dist2 = Euclidean_distance().transformed_distance(center_cs, (v_it)->point()); + if (!power_protection) + if (dist2 >= r*r-_sfty && dist2 <= (r+delta)*(r+delta)) + return true; + if (power_protection) + if (dist2 >= r*r-_sfty && dist2 <= r*r+delta*delta) + return true; + } + } + */ + // Check if the simplex is thick enough + Hyperplane_d tau_h(vertices.begin()+1, vertices.end()); + Vector_d orth_tau = tau_h.orthogonal_vector(); + /* + p_s1 = Vector_d(*(vertices.begin()), *(vertices.begin()+1)); + */ + //std::cout << "||orth_tau|| = " << sqrt(orth_tau.squared_length()) << "\n"; + FT orth_length = sqrt(orth_tau.squared_length()); + K::Cartesian_const_iterator_d o_it, p_it, s_it, c_it; + // Compute the altitude + FT h = 0; + for (o_it = orth_tau.cartesian_begin(), + p_it = vertices.begin()->cartesian_begin(), + s_it = (vertices.begin()+1)->cartesian_begin(); + o_it != orth_tau.cartesian_end(); + ++o_it, ++p_it, ++s_it) + h += (*o_it)*(*p_it - *s_it)/orth_length; + h = fabs(h); + // Is the center inside the box? + bool inside_the_box = true; + for (c_it = center_cs.cartesian_begin(); c_it != center_cs.cartesian_end(); ++c_it) + if (*c_it > 1.0 || *c_it < -1.0) + { + inside_the_box = false; break; + } + if (inside_the_box && h/r < theta0) + return true; + if (!t.is_infinite(v1)) + { + FT dist2 = Euclidean_distance().transformed_distance(center_cs, v1->point()); + if (!power_protection) + if (dist2 >= r*r-_sfty && dist2 <= (r+delta)*(r+delta)) + return true; + if (power_protection) + if (dist2 >= r*r-_sfty && dist2 <= r*r+delta*delta) + return true; + } + if (!t.is_infinite(v2)) + { + FT dist2 = Euclidean_distance().transformed_distance(center_cs, v2->point()); + if (!power_protection) + if (dist2 >= r*r-_sfty && dist2 <= (r+delta)*(r+delta)) + return true; + if (power_protection) + if (dist2 >= r*r-_sfty && dist2 <= r*r+delta*delta) + return true; + } + } + else + // INFINITE CASE + { + Delaunay_triangulation::Vertex_iterator v = t.vertices_begin(); + while (t.is_infinite(v) || std::find(vertices.begin(), vertices.end(), v->point()) == vertices.end()) + v++; + Hyperplane_d facet_plane(vertices.begin(), vertices.end(), v->point(), CGAL::ON_POSITIVE_SIDE); + Vector_d orth_v = facet_plane.orthogonal_vector(); + /* + for (auto v_it = t.vertices_begin(); v_it != t.vertices_end(); ++v_it) + if (!t.is_infinite(v_it)) + if (std::find(vertices.begin(), vertices.end(), v_it->point()) == vertices.end()) + { + std::vector<FT> coords; + Point_d p = v_it->point(); + auto orth_i = orth_v.cartesian_begin(), p_i = p.cartesian_begin(); + for (; orth_i != orth_v.cartesian_end(); ++orth_i, ++p_i) + coords.push_back((*p_i) - (*orth_i) * delta / sqrt(orth_v.squared_length())); + Point_d p_delta = Point_d(coords); + bool p_is_inside = !Has_on_positive_side_d()(facet_plane, p); + bool p_delta_is_inside = !Has_on_positive_side_d()(facet_plane, p_delta); + if (!p_is_inside && p_delta_is_inside) + return true; + } + */ + if (!t.is_infinite(v1)) + { + std::vector<FT> coords; + Point_d p = v1->point(); + auto orth_i = orth_v.cartesian_begin(), p_i = p.cartesian_begin(); + for (; orth_i != orth_v.cartesian_end(); ++orth_i, ++p_i) + coords.push_back((*p_i) - (*orth_i) * delta / sqrt(orth_v.squared_length())); + Point_d p_delta = Point_d(coords); + bool p_is_inside = !Has_on_positive_side_d()(facet_plane, p); + bool p_delta_is_inside = !Has_on_positive_side_d()(facet_plane, p_delta); + if (!power_protection && !p_is_inside && p_delta_is_inside) + return true; + } + if (!t.is_infinite(v2)) + { + std::vector<FT> coords; + Point_d p = v2->point(); + auto orth_i = orth_v.cartesian_begin(), p_i = p.cartesian_begin(); + for (; orth_i != orth_v.cartesian_end(); ++orth_i, ++p_i) + coords.push_back((*p_i) - (*orth_i) * delta / sqrt(orth_v.squared_length())); + Point_d p_delta = Point_d(coords); + bool p_is_inside = !Has_on_positive_side_d()(facet_plane, p); + bool p_delta_is_inside = !Has_on_positive_side_d()(facet_plane, p_delta); + if (!power_protection && !p_is_inside && p_delta_is_inside) + return true; + } + } + return false; +} + +/** Auxillary recursive function to check if the point p violates the protection of the cell c and + * if there is a violation of an eventual new cell + * + * p is the point to insert + * t is the current triangulation + * c is the current cell (simplex) + * parent_cell is the parent cell (simplex) + * index is the index of the facet between c and parent_cell from parent_cell's point of view + * D is the dimension of the triangulation + * delta is the protection constant + * marked_cells is the vector of all visited cells containing p in their circumscribed ball + * power_protection is true iff you are working with delta-power protection + * + * OUT: true iff inserting p hasn't produced any violation so far + */ + +bool is_violating_protection(Point_d& p, Delaunay_triangulation& t, Full_cell_handle c, Full_cell_handle parent_cell, int index, int D, FT delta, std::vector<Full_cell_handle>& marked_cells, bool power_protection, FT theta0) +{ + Euclidean_distance ed; + std::vector<Point_d> vertices; + if (!t.is_infinite(c)) + { + // if the cell is finite, we look if the protection is violated + for (auto v_it = c->vertices_begin(); v_it != c->vertices_end(); ++v_it) + vertices.push_back((*v_it)->point()); + Sphere_d cs( vertices.begin(), vertices.end()); + Point_d center_cs = cs.center(); + FT r = sqrt(ed.transformed_distance(center_cs, vertices[0])); + FT dist2 = ed.transformed_distance(center_cs, p); + // if the new point is inside the protection ball of a non conflicting simplex + if (!power_protection) + if (dist2 >= r*r-_sfty && dist2 <= (r+delta)*(r+delta)) + return true; + if (power_protection) + if (dist2 >= r*r-_sfty && dist2 <= r*r+delta*delta) + return true; + // if the new point is inside the circumscribing ball : continue violation searching on neighbours + //if (dist2 < r*r) + //if (dist2 < (5*r+delta)*(5*r+delta)) + if (dist2 < r*r) + { + c->tds_data().mark_visited(); + marked_cells.push_back(c); + for (int i = 0; i < D+1; ++i) + { + Full_cell_handle next_c = c->neighbor(i); + if (next_c->tds_data().is_clear() && + is_violating_protection(p, t, next_c, c, i, D, delta, marked_cells, power_protection, theta0)) + return true; + } + } + // if the new point is outside the protection sphere + else + { + // facet f is on the border of the conflict zone : check protection of simplex {p,f} + // the new simplex is guaranteed to be finite + vertices.clear(); vertices.push_back(p); + for (int i = 0; i < D+1; ++i) + if (i != index) + vertices.push_back(parent_cell->vertex(i)->point()); + Delaunay_vertex vertex_to_check = t.infinite_vertex(); + for (auto vh_it = c->vertices_begin(); vh_it != c->vertices_end(); ++vh_it) + if (!vertex_is_in_full_cell(*vh_it, parent_cell)) + { + vertex_to_check = *vh_it; break; + } + if (new_cell_is_violated(t, vertices, vertex_to_check, parent_cell->vertex(index), delta, power_protection, theta0)) + //if (new_cell_is_violated(t, vertices, vertex_to_check->point(), delta)) + return true; + } + } + else + { + // Inside of the convex hull is + side. Outside is - side. + for (auto vh_it = c->vertices_begin(); vh_it != c->vertices_end(); ++vh_it) + if (!t.is_infinite(*vh_it)) + vertices.push_back((*vh_it)->point()); + Delaunay_triangulation::Vertex_iterator v_it = t.vertices_begin(); + while (t.is_infinite(v_it) || vertex_is_in_full_cell(v_it, c)) + v_it++; + Hyperplane_d facet_plane(vertices.begin(), vertices.end(), v_it->point(), CGAL::ON_POSITIVE_SIDE); + //CGAL::Oriented_side outside = Oriented_side_d()(facet_plane, v_it->point()); + Vector_d orth_v = facet_plane.orthogonal_vector(); + std::vector<FT> coords; + auto orth_i = orth_v.cartesian_begin(), p_i = p.cartesian_begin(); + for (; orth_i != orth_v.cartesian_end(); ++orth_i, ++p_i) + coords.push_back((*p_i) - (*orth_i) * delta / sqrt(orth_v.squared_length())); + Point_d p_delta = Point_d(coords); + bool p_is_inside = !Has_on_positive_side_d()(facet_plane, p) && (Oriented_side_d()(facet_plane, p) != CGAL::ZERO); + bool p_delta_is_inside = !Has_on_positive_side_d()(facet_plane, p_delta); + + // If we work with power protection, we just ignore any conflicts + if (!power_protection && !p_is_inside && p_delta_is_inside) + return true; + //if the cell is infinite we look at the neighbours regardless + if (p_is_inside) + { + c->tds_data().mark_visited(); + marked_cells.push_back(c); + for (int i = 0; i < D+1; ++i) + { + Full_cell_handle next_c = c->neighbor(i); + if (next_c->tds_data().is_clear() && + is_violating_protection(p, t, next_c, c, i, D, delta, marked_cells, power_protection, theta0)) + return true; + } + } + else + { + // facet f is on the border of the conflict zone : check protection of simplex {p,f} + // the new simplex is finite if the parent cell is finite + vertices.clear(); vertices.push_back(p); + for (int i = 0; i < D+1; ++i) + if (i != index) + if (!t.is_infinite(parent_cell->vertex(i))) + vertices.push_back(parent_cell->vertex(i)->point()); + Delaunay_vertex vertex_to_check = t.infinite_vertex(); + for (auto vh_it = c->vertices_begin(); vh_it != c->vertices_end(); ++vh_it) + if (!vertex_is_in_full_cell(*vh_it, parent_cell)) + { + vertex_to_check = *vh_it; break; + } + if (new_cell_is_violated(t, vertices, vertex_to_check, parent_cell->vertex(index), delta, power_protection, theta0)) + //if (new_cell_is_violated(t, vertices, vertex_to_check->point(), delta)) + return true; + } + } + //c->tds_data().clear_visited(); + //marked_cells.pop_back(); + return false; +} + +/** Checks if inserting the point p in t will make conflicts + * + * p is the point to insert + * t is the current triangulation + * D is the dimension of triangulation + * delta is the protection constant + * power_protection is true iff you are working with delta-power protection + * OUT: true iff inserting p produces a violation of delta-protection. + */ + +bool is_violating_protection(Point_d& p, Delaunay_triangulation& t, int D, FT delta, bool power_protection, FT theta0) +{ + Euclidean_distance ed; + Delaunay_triangulation::Vertex_handle v; + Delaunay_triangulation::Face f(t.current_dimension()); + Delaunay_triangulation::Facet ft; + Delaunay_triangulation::Full_cell_handle c; + Delaunay_triangulation::Locate_type lt; + std::vector<Full_cell_handle> marked_cells; + c = t.locate(p, lt, f, ft, v); + bool violation_existing_cells = is_violating_protection(p, t, c, c, 0, D, delta, marked_cells, power_protection, theta0); + for (Full_cell_handle fc : marked_cells) + fc->tds_data().clear(); + return violation_existing_cells; +} + +////////////////////////////////////////////////////////////////////// +// INITIALIZATION +////////////////////////////////////////////////////////////////////// + +void initialize(Search_Tree& W, Delaunay& t, int D, int width, bool torus) +{ + if (!torus) + std::cout << "Non-toric case is not supported\n"; + else + { + if (D == 2) + { + FT stepx = 2.0/width; + FT stepy = sqrt(3)/width; + for (int i = 0; i < width; ++i) + for (int j = 0; j < floor(2*width/sqrt(3)); ++j) + { + insert_delaunay_landmark_with_copies(Point_d(step*i,)) + } + } + else (D == 3) + { + + } + else std::cout << "T^d with d>3 not supported"; + } +} + +/////////////////////////////////////////////////////////////////////// +/////////////////////////////////////////////////////////////////////// +//!!!!!!!!!!!!! THE INTERFACE FOR LANDMARK CHOICE IS BELOW !!!!!!!!!!// +/////////////////////////////////////////////////////////////////////// +/////////////////////////////////////////////////////////////////////// + +/////////////////////////////////////////////////////////////////////// +// LANDMARK CHOICE PROCEDURE AS IN PAPER +/////////////////////////////////////////////////////////////////////// + +/** Procedure to compute a maximal protected subset from a point cloud. All OUTs should be empty at call. + * + * IN: W is the initial point cloud having type Epick_d<Dynamic_dimension_tag>::Point_d + * IN: nbP is the size of W + * OUT: landmarks is the output vector for the points + * OUT: landmarks_ind is the output vector for the indices of the selected points in W + * IN: delta is the constant of protection + * OUT: full_cells is the output vector of the simplices in the final Delaunay triangulation + * IN: torus is true iff you are working on a flat torus [-1,1]^d + */ + +template<class Search_Tree> +void protected_delaunay_refinement(Search_Tree& W, int nbP, Point_Vector& landmarks, FT delta, bool torus, bool power_protection, FT theta0) +{ + bool return_ = true; + unsigned D = W[0].size(); + Torus_distance td; + Euclidean_distance ed; + Delaunay_triangulation t(D); + CGAL::Random rand; + int landmark_count = 0; + //std::list<int> index_list; + // shuffle the list of indexes (via a vector) + // { + // std::vector<int> temp_vector; + // for (int i = 0; i < nbP; ++i) + // temp_vector.push_back(i); + // unsigned seed = std::chrono::system_clock::now().time_since_epoch().count(); + // std::shuffle(temp_vector.begin(), temp_vector.end(), std::default_random_engine(seed)); + // //CGAL::spatial_sort(temp_vector.begin(), temp_vector.end()); + // for (std::vector<int>::iterator it = temp_vector.begin(); it != temp_vector.end(); ++it) + // index_list.push_front(*it); + // } + if (torus) + if (D == 2) + // \T^2 + { + for (int i = 0; i < 4; ++i) + for (int j = 0; j < 2; ++j) + { + W[index_list.front()] = Point_d(std::vector<FT>{i*0.5, j*1.0}); + insert_delaunay_landmark_with_copies(W, index_list.front(), landmarks_ind, t, landmark_count, torus); + index_list.pop_front(); + W[index_list.front()] = Point_d(std::vector<FT>{0.25+i*0.5, 0.5+j}); + insert_delaunay_landmark_with_copies(W, index_list.front(), landmarks_ind, t, landmark_count, torus); + index_list.pop_front(); + } + } + else if (D == 3) + { + + } + //std::cout << "No torus starter available for dim>2\n"; + std::list<int>::iterator list_it = index_list.begin(); + while (list_it != index_list.end()) + { + if (!is_violating_protection(W[*list_it], t, D, delta, power_protection, theta0)) + { + // If no conflicts then insert in every copy of T^3 + + insert_delaunay_landmark_with_copies(W, *list_it, landmarks_ind, t, landmark_count, torus); + if (return_) + { + index_list.erase(list_it); + list_it = index_list.begin(); + } + else + index_list.erase(list_it++); + /* + // PIECE OF CODE FOR DEBUGGING PURPOSES + + Delaunay_vertex inserted_v = insert_delaunay_landmark_with_copies(W, *list_it, landmarks_ind, t, landmark_count); + if (triangulation_is_protected(t, delta)) + { + index_list.erase(list_it); + list_it = index_list.begin(); + } + else + { //THAT'S WHERE SOMETHING'S WRONG + t.remove(inserted_v); + landmarks_ind.pop_back(); + landmark_count--; + write_delaunay_mesh(t, W[*list_it], is2d); + is_violating_protection(W[*list_it], t_old, D, delta); //Called for encore + } + */ + //std::cout << "index_list_size() = " << index_list.size() << "\n"; + } + else + { + list_it++; + //std::cout << "!!!!!WARNING!!!!! A POINT HAS BEEN OMITTED!!!\n"; + } + //if (list_it != index_list.end()) + // write_delaunay_mesh(t, W[*list_it], is2d); + } + fill_landmarks(W, landmarks, landmarks_ind, torus); + fill_full_cell_vector(t, full_cells); + /* + if (triangulation_is_protected(t, delta)) + std::cout << "Triangulation is ok\n"; + else + { + std::cout << "Triangulation is BAD!! T_T しくしく!\n"; + } + */ + //write_delaunay_mesh(t, W[0], is2d); + //std::cout << t << std::endl; +} + +#endif diff --git a/src/Witness_complex/example/protected_sets/protected_sets_paper.h b/src/Witness_complex/example/protected_sets/protected_sets_paper.h new file mode 100644 index 00000000..61fcc75b --- /dev/null +++ b/src/Witness_complex/example/protected_sets/protected_sets_paper.h @@ -0,0 +1,917 @@ +#ifndef PROTECTED_SETS_H +#define PROTECTED_SETS_H + +#include <algorithm> +#include <CGAL/Cartesian_d.h> +#include <CGAL/Epick_d.h> +#include <CGAL/Euclidean_distance.h> +#include <CGAL/Kernel_d/Sphere_d.h> +#include <CGAL/Kernel_d/Hyperplane_d.h> +#include <CGAL/Kernel_d/Vector_d.h> + +#include <CGAL/Orthogonal_k_neighbor_search.h> +#include <CGAL/Kd_tree.h> +#include <CGAL/Fuzzy_sphere.h> + +#include <boost/heap/fibonacci_heap.hpp> +#include <boost/heap/policies.hpp> + +#include "output_tikz.h" + +typedef CGAL::Epick_d<CGAL::Dynamic_dimension_tag> K; +typedef K::Point_d Point_d; +typedef K::Line_d Line_d; +typedef K::Vector_d Vector_d; +typedef K::Oriented_side_d Oriented_side_d; +typedef K::Has_on_positive_side_d Has_on_positive_side_d; +typedef K::Sphere_d Sphere_d; +typedef K::Hyperplane_d Hyperplane_d; + +typedef CGAL::Delaunay_triangulation<K> Delaunay_triangulation; +typedef Delaunay_triangulation::Facet Facet; +typedef Delaunay_triangulation::Vertex_handle Delaunay_vertex; +typedef Delaunay_triangulation::Full_cell_handle Full_cell_handle; + +typedef std::vector<Point_d> Point_Vector; +typedef CGAL::Euclidean_distance<Traits_base> Euclidean_distance; + +typedef CGAL::Search_traits_adapter< + std::ptrdiff_t, Point_d*, Traits_base> STraits; +//typedef K TreeTraits; +//typedef CGAL::Distance_adapter<std::ptrdiff_t,Point_d*,Euclidean_distance > Euclidean_adapter; +//typedef CGAL::Kd_tree<STraits> Kd_tree; +typedef CGAL::Orthogonal_k_neighbor_search<STraits, CGAL::Distance_adapter<std::ptrdiff_t,Point_d*,Euclidean_distance>> K_neighbor_search; +typedef K_neighbor_search::Tree Tree; +typedef K_neighbor_search::Distance Distance; +typedef K_neighbor_search::iterator KNS_iterator; +typedef K_neighbor_search::iterator KNS_range; +typedef CGAL::Fuzzy_sphere<STraits> Fuzzy_sphere; + + +FT _sfty = pow(10,-14); + +bool experiment1, experiment2 = false; + +/* Experiment 1: epsilon as function on time **********************/ +std::vector<FT> eps_vector; + +/* Experiment 2: R/epsilon on delta *******************************/ +std::vector<FT> epsratio_vector; + +/////////////////////////////////////////////////////////////////////////////////////////////////////////// +// AUXILLARY FUNCTIONS +/////////////////////////////////////////////////////////////////////////////////////////////////////////// + +/** Insert a point in Delaunay triangulation. If you are working in a flat torus, the procedure adds all the 3^d copies in adjacent cubes as well + * + * W is the initial point vector + * chosen_landmark is the index of the chosen point in W + * landmarks_ind is the vector of indices of already chosen points in W + * delaunay is the Delaunay triangulation + * landmark_count is the current number of chosen vertices + * torus is true iff you are working on a flat torus [-1,1]^d + * OUT: Vertex handle to the newly inserted point + */ +Delaunay_vertex insert_delaunay_landmark_with_copies(Point_Vector& W, int chosen_landmark, std::vector<int>& landmarks_ind, Delaunay_triangulation& delaunay, int& landmark_count, bool torus) +{ + if (!torus) + { + Delaunay_vertex v =delaunay.insert(W[chosen_landmark]); + landmarks_ind.push_back(chosen_landmark); + landmark_count++; + return v; + } + else + { + int D = W[0].size(); + int nb_cells = pow(3, D); + Delaunay_vertex v; + for (int i = 0; i < nb_cells; ++i) + { + std::vector<FT> point; + int cell_i = i; + for (int l = 0; l < D; ++l) + { + point.push_back(W[chosen_landmark][l] + 2.0*(cell_i%3-1)); + cell_i /= 3; + } + if (i == nb_cells/2) + v = delaunay.insert(point); //v = center point + else + delaunay.insert(point); + } + landmarks_ind.push_back(chosen_landmark); + landmark_count++; + return v; + } +} + +/** Small check if the vertex v is in the full cell fc + */ + +bool vertex_is_in_full_cell(Delaunay_triangulation::Vertex_handle v, Full_cell_handle fc) +{ + for (auto v_it = fc->vertices_begin(); v_it != fc->vertices_end(); ++v_it) + if (*v_it == v) + return true; + return false; +} + +/** Fill chosen point vector from indices with copies if you are working on a flat torus + * + * IN: W is the point vector + * OUT: landmarks is the output vector + * IN: landmarks_ind is the vector of indices + * IN: torus is true iff you are working on a flat torus [-1,1]^d + */ + +void fill_landmarks(Point_Vector& W, Point_Vector& landmarks, std::vector<int>& landmarks_ind, bool torus) +{ + if (!torus) + for (unsigned j = 0; j < landmarks_ind.size(); ++j) + landmarks.push_back(W[landmarks_ind[j]]); + else + { + int D = W[0].size(); + int nb_cells = pow(3, D); + int nbL = landmarks_ind.size(); + // Fill landmarks + for (int i = 0; i < nb_cells-1; ++i) + for (int j = 0; j < nbL; ++j) + { + int cell_i = i; + Point_d point; + for (int l = 0; l < D; ++l) + { + point.push_back(W[landmarks_ind[j]][l] + 2.0*(cell_i-1)); + cell_i /= 3; + } + landmarks.push_back(point); + } + } +} + +/** Fill a vector of all simplices in the Delaunay triangulation giving integer indices to vertices + * + * IN: t is the Delaunay triangulation + * OUT: full_cells is the output vector + */ + +void fill_full_cell_vector(Delaunay_triangulation& t, std::vector<std::vector<int>>& full_cells) +{ + // Store vertex indices in a map + int ind = 0; //index of a vertex + std::map<Delaunay_triangulation::Vertex_handle, int> index_of_vertex; + for (auto v_it = t.vertices_begin(); v_it != t.vertices_end(); ++v_it) + if (t.is_infinite(v_it)) + continue; + else + index_of_vertex[v_it] = ind++; + // Write full cells as vectors in full_cells + for (auto fc_it = t.full_cells_begin(); fc_it != t.full_cells_end(); ++fc_it) + { + if (t.is_infinite(fc_it)) + continue; + Point_Vector vertices; + for (auto fc_v_it = fc_it->vertices_begin(); fc_v_it != fc_it->vertices_end(); ++fc_v_it) + vertices.push_back((*fc_v_it)->point()); + Sphere_d cs( vertices.begin(), vertices.end()); + Point_d csc = cs.center(); + bool in_cube = true; + for (auto xi = csc.cartesian_begin(); xi != csc.cartesian_end(); ++xi) + if (*xi > 1.0 || *xi < -1.0) + { + in_cube = false; break; + } + if (!in_cube) + continue; + std::vector<int> cell; + for (auto v_it = fc_it->vertices_begin(); v_it != fc_it->vertices_end(); ++v_it) + cell.push_back(index_of_vertex[*v_it]); + full_cells.push_back(cell); + } +} + +bool sphere_intersects_cube(Point_d& c, FT r) +{ + bool in_cube = true; + // int i = 0, D = p.size(); + for (auto xi = c.cartesian_begin(); xi != c.cartesian_end(); ++xi) + // if ((*xi < 1.0 || *xi > -1.0) && + // (*xi-r < 1.0 || *xi-r > -1.0) && + // (*xi+r < 1.0 || *xi+r > -1.0)) + + if ((*xi-r < -1.0 && *xi+r < -1.0) || + (*xi-r > 1.0 && *xi+r > 1.0 )) + { + in_cube = false; break; + } + return in_cube; +} + +/** Recursive function for checking if the simplex is good, + * meaning it does not contain a k-face, which is not theta0^(k-1) thick + */ + +bool is_theta0_good(std::vector<Point_d>& vertices, FT theta0) +{ + if (theta0 > 1) + { + std::cout << "Warning! theta0 is set > 1\n"; + return false; + } + int D = vertices.size()-1; + if (D <= 1) + return true; // Edges are always good + //******** Circumscribed sphere + Euclidean_distance ed; + Sphere_d cs(vertices.begin(), vertices.end()); + FT r = sqrt(cs.squared_radius()); + for (std::vector<Point_d>::iterator v_it = vertices.begin(); v_it != vertices.end(); ++v_it) + { + std::vector<Point_d> facet; + for (std::vector<Point_d>::iterator f_it = vertices.begin(); f_it != vertices.end(); ++f_it) + if (f_it != v_it) + facet.push_back(*f_it); + // Compute the altitude + + if (vertices[0].size() == 3 && D == 2) + { + //Vector_d l = facet[0] - facet[1]; + FT orth_length2 = ed.transformed_distance(facet[0],facet[1]); + K::Cartesian_const_iterator_d l_it, p_it, s_it, c_it; + FT h = 0; + // Scalar product = <sp,l> + FT scalar = 0; + for (p_it = v_it->cartesian_begin(), + s_it = facet[0].cartesian_begin(), + l_it = facet[1].cartesian_begin(); + p_it != v_it->cartesian_end(); + ++l_it, ++p_it, ++s_it) + scalar += (*l_it - *s_it)*(*p_it - *s_it); + // Gram-Schmidt for one vector + for (p_it = v_it->cartesian_begin(), + s_it = facet[0].cartesian_begin(), + l_it = facet[1].cartesian_begin(); + p_it != v_it->cartesian_end(); + ++l_it, ++p_it, ++s_it) + { + FT hx = (*p_it - *s_it) - scalar*(*l_it - *s_it)/orth_length2; + h += hx*hx; + } + h = sqrt(h); + + if (h/(2*r) < pow(theta0, D-1)) + return false; + if (!is_theta0_good(facet, theta0)) + return false; + } + else + { + Hyperplane_d tau_h(facet.begin(), facet.end(), *v_it); + Vector_d orth_tau = tau_h.orthogonal_vector(); + FT orth_length = sqrt(orth_tau.squared_length()); + K::Cartesian_const_iterator_d o_it, p_it, s_it, c_it; + FT h = 0; + for (o_it = orth_tau.cartesian_begin(), + p_it = v_it->cartesian_begin(), + s_it = (facet.begin())->cartesian_begin(); + o_it != orth_tau.cartesian_end(); + ++o_it, ++p_it, ++s_it) + h += (*o_it)*(*p_it - *s_it)/orth_length; + h = fabs(h); + if (h/(2*r) < pow(theta0, D-1)) + return false; + if (!is_theta0_good(facet, theta0)) + return false; + } + } + return true; +} + + +//////////////////////////////////////////////////////////////////////////////////////////////////////////// +// IS VIOLATED TEST +//////////////////////////////////////////////////////////////////////////////////////////////////////////// + +/** Check if a newly created cell is protected from old vertices + * + * t is the Delaunay triangulation + * vertices is the vector containing the point to insert and a facet f in t + * v1 is the vertex of t, such that f and v1 form a simplex + * v2 is the vertex of t, such that f and v2 form another simplex + * delta is the protection constant + * power_protection is true iff the delta-power protection is used + */ + +bool new_cell_is_violated(Delaunay_triangulation& t, std::vector<Point_d>& vertices, const Delaunay_vertex& v1, const Delaunay_vertex v2, FT delta, bool power_protection, FT theta0) +{ + assert(vertices.size() == vertices[0].size() || + vertices.size() == vertices[0].size() + 1); //simplex size = d | d+1 + assert(v1 != v2); + if (vertices.size() == vertices[0].size() + 1) + // FINITE CASE + { + Sphere_d cs(vertices.begin(), vertices.end()); + Point_d center_cs = cs.center(); + FT r = sqrt(Euclidean_distance().transformed_distance(center_cs, vertices[0])); + /* + for (auto v_it = t.vertices_begin(); v_it != t.vertices_end(); ++v_it) + if (!t.is_infinite(v_it)) + { + //CGAL::Oriented_side side = Oriented_side_d()(cs, (v_it)->point()); + if (std::find(vertices.begin(), vertices.end(), v_it->point()) == vertices.end()) + { + FT dist2 = Euclidean_distance().transformed_distance(center_cs, (v_it)->point()); + if (!power_protection) + if (dist2 >= r*r-_sfty && dist2 <= (r+delta)*(r+delta)) + return true; + if (power_protection) + if (dist2 >= r*r-_sfty && dist2 <= r*r+delta*delta) + return true; + } + } + */ + // Check if the simplex is theta0-good + if (!is_theta0_good(vertices, theta0)) + return true; + // Is the center inside the box? (only Euclidean case) + // if (!torus) + // { + // bool inside_the_box = true; + // for (c_it = center_cs.cartesian_begin(); c_it != center_cs.cartesian_end(); ++c_it) + // if (*c_it > 1.0 || *c_it < -1.0) + // { + // inside_the_box = false; break; + // } + // if (inside_the_box && h/r < theta0) + // return true; + // } + // Check the two vertices (if not infinite) + if (!t.is_infinite(v1)) + { + FT dist2 = Euclidean_distance().transformed_distance(center_cs, v1->point()); + if (!power_protection) + if (dist2 >= r*r-_sfty && dist2 <= (r+delta)*(r+delta)) + return true; + if (power_protection) + if (dist2 >= r*r-_sfty && dist2 <= r*r+delta*delta) + return true; + } + if (!t.is_infinite(v2)) + { + FT dist2 = Euclidean_distance().transformed_distance(center_cs, v2->point()); + if (!power_protection) + if (dist2 >= r*r-_sfty && dist2 <= (r+delta)*(r+delta)) + return true; + if (power_protection) + if (dist2 >= r*r-_sfty && dist2 <= r*r+delta*delta) + return true; + } + } + else + // INFINITE CASE + { + Delaunay_triangulation::Vertex_iterator v = t.vertices_begin(); + while (t.is_infinite(v) || std::find(vertices.begin(), vertices.end(), v->point()) == vertices.end()) + v++; + Hyperplane_d facet_plane(vertices.begin(), vertices.end(), v->point(), CGAL::ON_POSITIVE_SIDE); + Vector_d orth_v = facet_plane.orthogonal_vector(); + /* + for (auto v_it = t.vertices_begin(); v_it != t.vertices_end(); ++v_it) + if (!t.is_infinite(v_it)) + if (std::find(vertices.begin(), vertices.end(), v_it->point()) == vertices.end()) + { + std::vector<FT> coords; + Point_d p = v_it->point(); + auto orth_i = orth_v.cartesian_begin(), p_i = p.cartesian_begin(); + for (; orth_i != orth_v.cartesian_end(); ++orth_i, ++p_i) + coords.push_back((*p_i) - (*orth_i) * delta / sqrt(orth_v.squared_length())); + Point_d p_delta = Point_d(coords); + bool p_is_inside = !Has_on_positive_side_d()(facet_plane, p); + bool p_delta_is_inside = !Has_on_positive_side_d()(facet_plane, p_delta); + if (!p_is_inside && p_delta_is_inside) + return true; + } + */ + if (!t.is_infinite(v1)) + { + std::vector<FT> coords; + Point_d p = v1->point(); + auto orth_i = orth_v.cartesian_begin(), p_i = p.cartesian_begin(); + for (; orth_i != orth_v.cartesian_end(); ++orth_i, ++p_i) + coords.push_back((*p_i) - (*orth_i) * delta / sqrt(orth_v.squared_length())); + Point_d p_delta = Point_d(coords); + bool p_is_inside = !Has_on_positive_side_d()(facet_plane, p); + bool p_delta_is_inside = !Has_on_positive_side_d()(facet_plane, p_delta); + if (!power_protection && !p_is_inside && p_delta_is_inside) + return true; + } + if (!t.is_infinite(v2)) + { + std::vector<FT> coords; + Point_d p = v2->point(); + auto orth_i = orth_v.cartesian_begin(), p_i = p.cartesian_begin(); + for (; orth_i != orth_v.cartesian_end(); ++orth_i, ++p_i) + coords.push_back((*p_i) - (*orth_i) * delta / sqrt(orth_v.squared_length())); + Point_d p_delta = Point_d(coords); + bool p_is_inside = !Has_on_positive_side_d()(facet_plane, p); + bool p_delta_is_inside = !Has_on_positive_side_d()(facet_plane, p_delta); + if (!power_protection && !p_is_inside && p_delta_is_inside) + return true; + } + } + return false; +} + +/** Auxillary recursive function to check if the point p violates the protection of the cell c and + * if there is a violation of an eventual new cell + * + * p is the point to insert + * t is the current triangulation + * c is the current cell (simplex) + * parent_cell is the parent cell (simplex) + * index is the index of the facet between c and parent_cell from parent_cell's point of view + * D is the dimension of the triangulation + * delta is the protection constant + * marked_cells is the vector of all visited cells containing p in their circumscribed ball + * power_protection is true iff you are working with delta-power protection + * + * OUT: true iff inserting p hasn't produced any violation so far + */ + +bool is_violating_protection(Point_d& p, Delaunay_triangulation& t, Full_cell_handle c, Full_cell_handle parent_cell, int index, int D, FT delta, std::vector<Full_cell_handle>& marked_cells, bool power_protection, FT theta0) +{ + Euclidean_distance ed; + std::vector<Point_d> vertices; + if (!t.is_infinite(c)) + { + // if the cell is finite, we look if the protection is violated + for (auto v_it = c->vertices_begin(); v_it != c->vertices_end(); ++v_it) + vertices.push_back((*v_it)->point()); + Sphere_d cs( vertices.begin(), vertices.end()); + Point_d center_cs = cs.center(); + FT r = sqrt(ed.transformed_distance(center_cs, vertices[0])); + FT dist2 = ed.transformed_distance(center_cs, p); + // if the new point is inside the protection ball of a non conflicting simplex + if (!power_protection) + if (dist2 >= r*r-_sfty && dist2 <= (r+delta)*(r+delta)) + return true; + if (power_protection) + if (dist2 >= r*r-_sfty && dist2 <= r*r+delta*delta) + return true; + // if the new point is inside the circumscribing ball : continue violation searching on neighbours + //if (dist2 < r*r) + //if (dist2 < (5*r+delta)*(5*r+delta)) + if (dist2 < r*r) + { + c->tds_data().mark_visited(); + marked_cells.push_back(c); + for (int i = 0; i < D+1; ++i) + { + Full_cell_handle next_c = c->neighbor(i); + if (next_c->tds_data().is_clear() && + is_violating_protection(p, t, next_c, c, i, D, delta, marked_cells, power_protection, theta0)) + return true; + } + } + // if the new point is outside the protection sphere + else + { + // facet f is on the border of the conflict zone : check protection of simplex {p,f} + // the new simplex is guaranteed to be finite + vertices.clear(); vertices.push_back(p); + for (int i = 0; i < D+1; ++i) + if (i != index) + vertices.push_back(parent_cell->vertex(i)->point()); + Delaunay_vertex vertex_to_check = t.infinite_vertex(); + for (auto vh_it = c->vertices_begin(); vh_it != c->vertices_end(); ++vh_it) + if (!vertex_is_in_full_cell(*vh_it, parent_cell)) + { + vertex_to_check = *vh_it; break; + } + if (new_cell_is_violated(t, vertices, vertex_to_check, parent_cell->vertex(index), delta, power_protection, theta0)) + //if (new_cell_is_violated(t, vertices, vertex_to_check->point(), delta)) + return true; + } + } + else + { + // Inside of the convex hull is + side. Outside is - side. + for (auto vh_it = c->vertices_begin(); vh_it != c->vertices_end(); ++vh_it) + if (!t.is_infinite(*vh_it)) + vertices.push_back((*vh_it)->point()); + Delaunay_triangulation::Vertex_iterator v_it = t.vertices_begin(); + while (t.is_infinite(v_it) || vertex_is_in_full_cell(v_it, c)) + v_it++; + Hyperplane_d facet_plane(vertices.begin(), vertices.end(), v_it->point(), CGAL::ON_POSITIVE_SIDE); + //CGAL::Oriented_side outside = Oriented_side_d()(facet_plane, v_it->point()); + Vector_d orth_v = facet_plane.orthogonal_vector(); + std::vector<FT> coords; + auto orth_i = orth_v.cartesian_begin(), p_i = p.cartesian_begin(); + for (; orth_i != orth_v.cartesian_end(); ++orth_i, ++p_i) + coords.push_back((*p_i) - (*orth_i) * delta / sqrt(orth_v.squared_length())); + Point_d p_delta = Point_d(coords); + bool p_is_inside = !Has_on_positive_side_d()(facet_plane, p) && (Oriented_side_d()(facet_plane, p) != CGAL::ZERO); + bool p_delta_is_inside = !Has_on_positive_side_d()(facet_plane, p_delta); + + // If we work with power protection, we just ignore any conflicts + if (!power_protection && !p_is_inside && p_delta_is_inside) + return true; + //if the cell is infinite we look at the neighbours regardless + if (p_is_inside) + { + c->tds_data().mark_visited(); + marked_cells.push_back(c); + for (int i = 0; i < D+1; ++i) + { + Full_cell_handle next_c = c->neighbor(i); + if (next_c->tds_data().is_clear() && + is_violating_protection(p, t, next_c, c, i, D, delta, marked_cells, power_protection, theta0)) + return true; + } + } + else + { + // facet f is on the border of the conflict zone : check protection of simplex {p,f} + // the new simplex is finite if the parent cell is finite + vertices.clear(); vertices.push_back(p); + for (int i = 0; i < D+1; ++i) + if (i != index) + if (!t.is_infinite(parent_cell->vertex(i))) + vertices.push_back(parent_cell->vertex(i)->point()); + Delaunay_vertex vertex_to_check = t.infinite_vertex(); + for (auto vh_it = c->vertices_begin(); vh_it != c->vertices_end(); ++vh_it) + if (!vertex_is_in_full_cell(*vh_it, parent_cell)) + { + vertex_to_check = *vh_it; break; + } + if (new_cell_is_violated(t, vertices, vertex_to_check, parent_cell->vertex(index), delta, power_protection, theta0)) + //if (new_cell_is_violated(t, vertices, vertex_to_check->point(), delta)) + return true; + } + } + //c->tds_data().clear_visited(); + //marked_cells.pop_back(); + return false; +} + +/** Checks if inserting the point p in t will make conflicts + * + * p is the point to insert + * t is the current triangulation + * D is the dimension of triangulation + * delta is the protection constant + * power_protection is true iff you are working with delta-power protection + * OUT: true iff inserting p produces a violation of delta-protection. + */ + +bool is_violating_protection(Point_d& p, Delaunay_triangulation& t, int D, FT delta, bool power_protection, FT theta0) +{ + Euclidean_distance ed; + Delaunay_triangulation::Vertex_handle v; + Delaunay_triangulation::Face f(t.current_dimension()); + Delaunay_triangulation::Facet ft; + Delaunay_triangulation::Full_cell_handle c; + Delaunay_triangulation::Locate_type lt; + std::vector<Full_cell_handle> marked_cells; + //c = t.locate(p, lt, f, ft, v); + c = t.locate(p); + bool violation_existing_cells = is_violating_protection(p, t, c, c, 0, D, delta, marked_cells, power_protection, theta0); + for (Full_cell_handle fc : marked_cells) + fc->tds_data().clear(); + return violation_existing_cells; +} + + +//////////////////////////////////////////////////////////////////////// +// INITIALIZATION +//////////////////////////////////////////////////////////////////////// + +// Query for a sphere near a cite in all copies of a torus +// OUT points_inside +void torus_search(Tree& treeW, int D, Point_d cite, FT r, std::vector<int>& points_inside) +{ + int nb_cells = pow(3, D); + Delaunay_vertex v; + for (int i = 0; i < nb_cells; ++i) + { + std::vector<FT> cite_copy; + int cell_i = i; + for (int l = 0; l < D; ++l) + { + cite_copy.push_back(cite[l] + 2.0*(cell_i%3-1)); + cell_i /= 3; + } + Fuzzy_sphere fs(cite_copy, r, 0, treeW.traits()); + treeW.search(std::insert_iterator<std::vector<int>>(points_inside, points_inside.end()), fs); + } +} + + +void initialize_torus(Point_Vector& W, Tree& treeW, Delaunay_triangulation& t, FT epsilon, std::vector<int>& landmarks_ind, int& landmark_count) +{ + int D = W[0].size(); + if (D == 2) + { + int xw = 6, yw = 4; + // Triangular lattice close to regular triangles h=0.866a ~ 0.875a : 48p + for (int i = 0; i < xw; ++i) + for (int j = 0; j < yw; ++j) + { + Point_d cite1(std::vector<FT>{2.0/xw*i, 1.0/yw*j}); + std::vector<int> points_inside; + torus_search(treeW, D, cite1, epsilon, points_inside); + assert(points_inside.size() > 0); + insert_delaunay_landmark_with_copies(W, *(points_inside.begin()), + landmarks_ind, t, landmark_count, true); + Point_d cite2(std::vector<FT>{2.0/xw*(i+0.5), 1.0/yw*(j+0.5)}); + points_inside.clear(); + torus_search(treeW, D, cite2, epsilon, points_inside); + assert(points_inside.size() > 0); + insert_delaunay_landmark_with_copies(W, *(points_inside.begin()), + landmarks_ind, t, landmark_count, true); + } + } + else if (D == 3) + { + int wd = 3; + // Body-centered cubic lattice : 54p + for (int i = 0; i < wd; ++i) + for (int j = 0; j < wd; ++j) + for (int k = 0; k < wd; ++k) + { + Point_d cite1(std::vector<FT>{2.0/wd*i, 2.0/wd*j, 2.0/wd*k}); + std::vector<int> points_inside; + torus_search(treeW, D, cite1, epsilon, points_inside); + assert(points_inside.size() > 0); + insert_delaunay_landmark_with_copies(W, *(points_inside.begin()), + landmarks_ind, t, landmark_count, true); + Point_d cite2(std::vector<FT>{2.0/wd*(i+0.5), 2.0/wd*(j+0.5), 2.0/wd*(k+0.5)}); + points_inside.clear(); + torus_search(treeW, D, cite2, epsilon, points_inside); + assert(points_inside.size() > 0); + insert_delaunay_landmark_with_copies(W, *(points_inside.begin()), + landmarks_ind, t, landmark_count, true); + } + } +} + +/////////////////////////////////////////////////////////////////////// +/////////////////////////////////////////////////////////////////////// +//!!!!!!!!!!!!! THE INTERFACE FOR LANDMARK CHOICE IS BELOW !!!!!!!!!!// +/////////////////////////////////////////////////////////////////////// +/////////////////////////////////////////////////////////////////////// + +// Struct for R_max_heap elements + +struct R_max_handle +{ + FT value; + Point_d center; + + R_max_handle(FT value_, Point_d c): value(value_), center(c) + {} +}; + +struct R_max_compare +{ + bool operator()(const R_max_handle& rmh1, const R_max_handle& rmh2) const + { + return rmh1.value < rmh2.value; + } +}; + +// typedef boost::heap::fibonacci_heap<R_max_handle, boost::heap::compare<R_max_compare>> Heap; + +// void make_heap(Delaunay_triangulation& t, Heap& R_max_heap) +// { +// R_max_heap.clear(); +// for (auto fc_it = t.full_cells_begin(); fc_it != t.full_cells_end(); ++fc_it) +// { +// if (t.is_infinite(fc_it)) +// continue; +// Point_Vector vertices; +// for (auto fc_v_it = fc_it->vertices_begin(); fc_v_it != fc_it->vertices_end(); ++fc_v_it) +// vertices.push_back((*fc_v_it)->point()); +// Sphere_d cs( vertices.begin(), vertices.end()); +// Point_d csc = cs.center(); +// FT r = sqrt(cs.squared_radius()); +// // A ball is in the heap, if it intersects the cube +// bool accepted = sphere_intersects_cube(csc, sqrt(r)); +// if (!accepted) +// continue; +// R_max_heap.push(R_max_handle(r, fc_it, csc)); +// } +// } + +////////////////////////////////////////////////////////////////////////////////////////////////////////// +// SAMPLING RADIUS +////////////////////////////////////////////////////////////////////////////////////////////////////////// + +R_max_handle sampling_radius(Delaunay_triangulation& t) +{ + FT epsilon2 = 0; + Point_d final_center; + Point_d control_point; + for (auto fc_it = t.full_cells_begin(); fc_it != t.full_cells_end(); ++fc_it) + { + if (t.is_infinite(fc_it)) + continue; + Point_Vector vertices; + for (auto fc_v_it = fc_it->vertices_begin(); fc_v_it != fc_it->vertices_end(); ++fc_v_it) + vertices.push_back((*fc_v_it)->point()); + Sphere_d cs( vertices.begin(), vertices.end()); + Point_d csc = cs.center(); + bool in_cube = true; + for (auto xi = csc.cartesian_begin(); xi != csc.cartesian_end(); ++xi) + if (*xi > 1.0 || *xi < -1.0) + { + in_cube = false; break; + } + if (!in_cube) + continue; + FT r2 = Euclidean_distance().transformed_distance(cs.center(), *(vertices.begin())); + if (epsilon2 < r2) + { + epsilon2 = r2; + final_center = csc; + control_point = (*vertices.begin()); + } + } + return R_max_handle(sqrt(epsilon2), final_center); +} + +/////////////////////////////////////////////////////////////////////// +// LANDMARK CHOICE PROCEDURE +/////////////////////////////////////////////////////////////////////// + +/** Procedure to compute a maximal protected subset from a point cloud. All OUTs should be empty at call. + * + * IN: W is the initial point cloud having type Epick_d<Dynamic_dimension_tag>::Point_d + * IN: nbP is the size of W + * OUT: landmarks is the output vector for the points + * OUT: landmarks_ind is the output vector for the indices of the selected points in W + * IN: delta is the constant of protection + * OUT: full_cells is the output vector of the simplices in the final Delaunay triangulation + * IN: torus is true iff you are working on a flat torus [-1,1]^d + */ + +void protected_delaunay(Point_Vector& W, + //Point_Vector& landmarks, + std::vector<int>& landmarks_ind, + FT delta, + FT epsilon, + FT alpha, + FT theta0, + //std::vector<std::vector<int>>& full_cells, + bool torus, + bool power_protection + ) +{ + //bool return_ = true; + unsigned D = W[0].size(); + int nbP = W.size(); + Torus_distance td; + Euclidean_distance ed; + Delaunay_triangulation t(D); + CGAL::Random rand; + int landmark_count = 0; + std::list<int> index_list; + //****************** Kd Tree W + STraits traits(&(W[0])); + Tree treeW(boost::counting_iterator<std::ptrdiff_t>(0), + boost::counting_iterator<std::ptrdiff_t>(nbP), + typename Tree::Splitter(), + traits); + // shuffle the list of indexes (via a vector) + { + std::vector<int> temp_vector; + for (int i = 0; i < nbP; ++i) + temp_vector.push_back(i); + unsigned seed = std::chrono::system_clock::now().time_since_epoch().count(); + std::shuffle(temp_vector.begin(), temp_vector.end(), std::default_random_engine(seed)); + //CGAL::spatial_sort(temp_vector.begin(), temp_vector.end()); + for (std::vector<int>::iterator it = temp_vector.begin(); it != temp_vector.end(); ++it) + index_list.push_front(*it); + } + //******************** Initialize point set + if (!torus) + for (unsigned pos1 = 0; pos1 < D+1; ++pos1) + { + std::vector<FT> point; + for (unsigned i = 0; i < pos1; ++i) + point.push_back(-1); + if (pos1 != D) + point.push_back(1); + for (unsigned i = pos1+1; i < D; ++i) + point.push_back(0); + assert(point.size() == D); + W[index_list.front()] = Point_d(point); + insert_delaunay_landmark_with_copies(W, index_list.front(), landmarks_ind, t, landmark_count, torus); + index_list.pop_front(); + } + else + initialize_torus(W, treeW, t, epsilon, landmarks_ind, landmark_count); + //std::cout << "Size of treeW: " << treeW.size() << "\n"; + //std::cout << "Size of t: " << t.number_of_vertices() << "\n"; + //******************* Initialize heap for R_max + //Heap R_max_heap; + //make_heap(t, R_max_heap); + + + R_max_handle rh = sampling_radius(t); + FT epsilon0 = rh.value; + if (experiment1) eps_vector.push_back(pow(1/rh.value,D)); + //******************** Iterative algorithm + std::vector<int> candidate_points; + torus_search(treeW, D, + rh.center, + alpha*rh.value, + candidate_points); + std::list<int>::iterator list_it; + std::vector<int>::iterator cp_it = candidate_points.begin(); + while (cp_it != candidate_points.end()) + { + if (!is_violating_protection(W[*cp_it], t, D, delta, power_protection, theta0)) + { + insert_delaunay_landmark_with_copies(W, *cp_it, landmarks_ind, t, landmark_count, torus); + //make_heap(t, R_max_heap); + rh = sampling_radius(t); + if (experiment1) eps_vector.push_back(pow(1/rh.value,D)); + //std::cout << "rhvalue = " << rh.value << "\n"; + //std::cout << "D = " << + candidate_points.clear(); + torus_search(treeW, D, + rh.center, + alpha*rh.value, + candidate_points); + /* + // PIECE OF CODE FOR DEBUGGING PURPOSES + + Delaunay_vertex inserted_v = insert_delaunay_landmark_with_copies(W, *list_it, landmarks_ind, t, landmark_count); + if (triangulation_is_protected(t, delta)) + { + index_list.erase(list_it); + list_it = index_list.begin(); + } + else + { //THAT'S WHERE SOMETHING'S WRONG + t.remove(inserted_v); + landmarks_ind.pop_back(); + landmark_count--; + write_delaunay_mesh(t, W[*list_it], is2d); + is_violating_protection(W[*list_it], t_old, D, delta); //Called for encore + } + */ + //std::cout << "index_list_size() = " << index_list.size() << "\n"; + } + else + { + cp_it++; + //std::cout << "!!!!!WARNING!!!!! A POINT HAS BEEN OMITTED!!!\n"; + } + //if (list_it != index_list.end()) + // write_delaunay_mesh(t, W[*list_it], is2d); + } + if (experiment2) epsratio_vector.push_back(rh.value/epsilon0); + std::cout << "The iteration ended when cp_count = " << candidate_points.size() << "\n"; + std::cout << "alphaRmax = " << alpha*rh.value << "\n"; + std::cout << "epsilon' = " << rh.value << "\n"; + std::cout << "nbL = " << landmarks_ind.size() << "\n"; + //fill_landmarks(W, landmarks, landmarks_ind, torus); + //fill_full_cell_vector(t, full_cells); + /* + if (triangulation_is_protected(t, delta)) + std::cout << "Triangulation is ok\n"; + else + { + std::cout << "Triangulation is BAD!! T_T しくしく!\n"; + } + */ + //write_delaunay_mesh(t, W[0], is2d); + //std::cout << t << std::endl; +} + +/////////////////////////////////////////////////////////////////////////////////////////////////////////// +// Series of experiments +/////////////////////////////////////////////////////////////////////////////////////////////////////////// + +void start_experiments(Point_Vector& W, FT theta0, std::vector<int>& landmarks_ind, FT epsilon) +{ + // Experiment 1 + experiment1 = true; + protected_delaunay(W, landmarks_ind, 0.1*epsilon, epsilon, 0.5, 0, true, true); + write_tikz_plot(eps_vector,"epstime.tikz"); + experiment1 = false; + + // Experiment 2 + // experiment2 = true; + // for (FT delta = 0; delta < epsilon; delta += 0.1*epsilon) + // protected_delaunay(W, landmarks_ind, delta, epsilon, 0.5, 0, true, true); + // write_tikz_plot(epsratio_vector,"epsratio_delta.tikz"); + // experiment2 = false; + +} + +#endif diff --git a/src/Witness_complex/example/protected_sets/protected_sets_paper2.h b/src/Witness_complex/example/protected_sets/protected_sets_paper2.h new file mode 100644 index 00000000..04b5e3bc --- /dev/null +++ b/src/Witness_complex/example/protected_sets/protected_sets_paper2.h @@ -0,0 +1,1384 @@ +#ifndef PROTECTED_SETS_H +#define PROTECTED_SETS_H + +#include <algorithm> +#include <CGAL/Cartesian_d.h> +#include <CGAL/Epick_d.h> +#include <CGAL/Euclidean_distance.h> +#include <CGAL/Kernel_d/Sphere_d.h> +#include <CGAL/Kernel_d/Hyperplane_d.h> +#include <CGAL/Kernel_d/Vector_d.h> + +#include <CGAL/Orthogonal_k_neighbor_search.h> +#include <CGAL/Kd_tree.h> +#include <CGAL/Fuzzy_sphere.h> + +#include <boost/heap/fibonacci_heap.hpp> +#include <boost/heap/policies.hpp> + +#include "output_tikz.h" +#include "../output.h" +#include "../generators.h" + +#include <CGAL/point_generators_d.h> + + +typedef CGAL::Epick_d<CGAL::Dynamic_dimension_tag> K; +typedef K::Point_d Point_d; +typedef K::Line_d Line_d; +typedef K::Vector_d Vector_d; +typedef K::Oriented_side_d Oriented_side_d; +typedef K::Has_on_positive_side_d Has_on_positive_side_d; +typedef K::Sphere_d Sphere_d; +typedef K::Hyperplane_d Hyperplane_d; + +typedef CGAL::Delaunay_triangulation<K> Delaunay_triangulation; +typedef Delaunay_triangulation::Facet Facet; +typedef Delaunay_triangulation::Vertex_handle Delaunay_vertex; +typedef Delaunay_triangulation::Full_cell_handle Full_cell_handle; + +typedef std::vector<Point_d> Point_Vector; +typedef CGAL::Euclidean_distance<Traits_base> Euclidean_distance; + +typedef CGAL::Search_traits_adapter< + std::ptrdiff_t, Point_d*, Traits_base> STraits; +//typedef K TreeTraits; +//typedef CGAL::Distance_adapter<std::ptrdiff_t,Point_d*,Euclidean_distance > Euclidean_adapter; +//typedef CGAL::Kd_tree<STraits> Kd_tree; +typedef CGAL::Orthogonal_k_neighbor_search<STraits, CGAL::Distance_adapter<std::ptrdiff_t,Point_d*,Euclidean_distance>> K_neighbor_search; +typedef K_neighbor_search::Tree Tree; +typedef K_neighbor_search::Distance Distance; +typedef K_neighbor_search::iterator KNS_iterator; +typedef K_neighbor_search::iterator KNS_range; +typedef CGAL::Fuzzy_sphere<STraits> Fuzzy_sphere; + +typedef CGAL::Random_points_in_ball_d<Point_d> Random_point_iterator; + + +FT _sfty = pow(10,-14); + +bool experiment1, experiment2, experiment3, experiment5 = false; + +/* Experiment 1: epsilon as function on time **********************/ +std::vector<FT> eps_vector; + +/* Experiment 2: R/epsilon on alpha *******************************/ +std::vector<FT> epsratio_vector; +std::vector<FT> epsslope_vector; + +/* Experiment 3: theta on delta ***********************************/ +std::vector<FT> thetamin_vector; FT curr_theta; +std::vector<FT> gammamin_vector; + +/* Statistical data ***********************************************/ +int refused_case1, refused_case2, refused_bad, refused_centers1, refused_centers2; + +void initialize_statistics() +{ + refused_case1 = 0; + refused_case2 = 0; + refused_bad = 0; + refused_centers1 = 0; + refused_centers2 = 0; +} + +void print_statistics() +{ + std::cout << " * Old simplex not protected: " << refused_case1 << "\n"; + std::cout << " * New simplex not protected: " << refused_case2 << "\n"; + std::cout << " * New simplex not good: " << refused_bad << "\n"; + std::cout << " * New-old centers too close: " << refused_centers1 << "\n"; + std::cout << " * New-new centers too close: " << refused_centers2 << "\n"; +} + +/////////////////////////////////////////////////////////////////////////////////////////////////////////// +// AUXILLARY FUNCTIONS +/////////////////////////////////////////////////////////////////////////////////////////////////////////// + +/** Insert a point in Delaunay triangulation. If you are working in a flat torus, the procedure adds all the 3^d copies in adjacent cubes as well + * + * W is the initial point vector + * chosen_landmark is the index of the chosen point in W + * landmarks_ind is the vector of indices of already chosen points in W + * delaunay is the Delaunay triangulation + * landmark_count is the current number of chosen vertices + * torus is true iff you are working on a flat torus [-1,1]^d + * OUT: Vertex handle to the newly inserted point + */ +Delaunay_vertex insert_delaunay_landmark_with_copies(Point_Vector& W, int chosen_landmark, std::vector<int>& landmarks_ind, Delaunay_triangulation& delaunay, int& landmark_count, bool torus) +{ + if (!torus) + { + Delaunay_vertex v =delaunay.insert(W[chosen_landmark]); + landmarks_ind.push_back(chosen_landmark); + landmark_count++; + return v; + } + else + { + int D = W[0].size(); + int nb_cells = pow(3, D); + Delaunay_vertex v; + for (int i = 0; i < nb_cells; ++i) + { + std::vector<FT> point; + int cell_i = i; + for (int l = 0; l < D; ++l) + { + point.push_back(W[chosen_landmark][l] + 2.0*(cell_i%3-1)); + cell_i /= 3; + } + if (i == nb_cells/2) + v = delaunay.insert(point); //v = center point + else + delaunay.insert(point); + } + landmarks_ind.push_back(chosen_landmark); + landmark_count++; + return v; + } +} + +/** Small check if the vertex v is in the full cell fc + */ + +bool vertex_is_in_full_cell(Delaunay_triangulation::Vertex_handle v, Full_cell_handle fc) +{ + for (auto v_it = fc->vertices_begin(); v_it != fc->vertices_end(); ++v_it) + if (*v_it == v) + return true; + return false; +} + +/** Fill chosen point vector from indices with copies if you are working on a flat torus + * + * IN: W is the point vector + * OUT: landmarks is the output vector + * IN: landmarks_ind is the vector of indices + * IN: torus is true iff you are working on a flat torus [-1,1]^d + */ + +void fill_landmarks(Point_Vector& W, Point_Vector& landmarks, std::vector<int>& landmarks_ind, bool torus) +{ + if (!torus) + for (unsigned j = 0; j < landmarks_ind.size(); ++j) + landmarks.push_back(W[landmarks_ind[j]]); + else + { + int D = W[0].size(); + int nb_cells = pow(3, D); + int nbL = landmarks_ind.size(); + // Fill landmarks + for (int i = 0; i < nb_cells-1; ++i) + for (int j = 0; j < nbL; ++j) + { + int cell_i = i; + Point_d point; + for (int l = 0; l < D; ++l) + { + point.push_back(W[landmarks_ind[j]][l] + 2.0*(cell_i-1)); + cell_i /= 3; + } + landmarks.push_back(point); + } + } +} + +/** Fill a vector of all simplices in the Delaunay triangulation giving integer indices to vertices + * + * IN: t is the Delaunay triangulation + * OUT: full_cells is the output vector + */ + +void fill_full_cell_vector(Delaunay_triangulation& t, std::vector<std::vector<int>>& full_cells) +{ + // Store vertex indices in a map + int ind = 0; //index of a vertex + std::map<Delaunay_triangulation::Vertex_handle, int> index_of_vertex; + for (auto v_it = t.vertices_begin(); v_it != t.vertices_end(); ++v_it) + if (t.is_infinite(v_it)) + continue; + else + index_of_vertex[v_it] = ind++; + // Write full cells as vectors in full_cells + for (auto fc_it = t.full_cells_begin(); fc_it != t.full_cells_end(); ++fc_it) + { + if (t.is_infinite(fc_it)) + continue; + Point_Vector vertices; + for (auto fc_v_it = fc_it->vertices_begin(); fc_v_it != fc_it->vertices_end(); ++fc_v_it) + vertices.push_back((*fc_v_it)->point()); + Sphere_d cs( vertices.begin(), vertices.end()); + Point_d csc = cs.center(); + bool in_cube = true; + for (auto xi = csc.cartesian_begin(); xi != csc.cartesian_end(); ++xi) + if (*xi > 1.0 || *xi < -1.0) + { + in_cube = false; break; + } + if (!in_cube) + continue; + std::vector<int> cell; + for (auto v_it = fc_it->vertices_begin(); v_it != fc_it->vertices_end(); ++v_it) + cell.push_back(index_of_vertex[*v_it]); + full_cells.push_back(cell); + } +} + +bool sphere_intersects_cube(Point_d& c, FT r) +{ + bool in_cube = true; + // int i = 0, D = p.size(); + for (auto xi = c.cartesian_begin(); xi != c.cartesian_end(); ++xi) + // if ((*xi < 1.0 || *xi > -1.0) && + // (*xi-r < 1.0 || *xi-r > -1.0) && + // (*xi+r < 1.0 || *xi+r > -1.0)) + + if ((*xi-r < -1.0 && *xi+r < -1.0) || + (*xi-r > 1.0 && *xi+r > 1.0 )) + { + in_cube = false; break; + } + return in_cube; +} + +/** Recursive function for checking if the simplex is good, + * meaning it does not contain a k-face, which is not theta0^(k-1) thick + */ + +bool is_theta0_good(std::vector<Point_d>& vertices, FT theta0) +{ + if (theta0 > 1) + { + std::cout << "Warning! theta0 is set > 1\n"; + return false; + } + int D = vertices.size()-1; + if (D <= 1) + return true; // Edges are always good + //******** Circumscribed sphere + Euclidean_distance ed; + Sphere_d cs(vertices.begin(), vertices.end()); + FT r = sqrt(cs.squared_radius()); + for (std::vector<Point_d>::iterator v_it = vertices.begin(); v_it != vertices.end(); ++v_it) + { + std::vector<Point_d> facet; + for (std::vector<Point_d>::iterator f_it = vertices.begin(); f_it != vertices.end(); ++f_it) + if (f_it != v_it) + facet.push_back(*f_it); + // Compute the altitude + + if (vertices[0].size() == 3 && D == 2) + { + //Vector_d l = facet[0] - facet[1]; + FT orth_length2 = ed.transformed_distance(facet[0],facet[1]); + K::Cartesian_const_iterator_d l_it, p_it, s_it, c_it; + FT h = 0; + // Scalar product = <sp,l> + FT scalar = 0; + for (p_it = v_it->cartesian_begin(), + s_it = facet[0].cartesian_begin(), + l_it = facet[1].cartesian_begin(); + p_it != v_it->cartesian_end(); + ++l_it, ++p_it, ++s_it) + scalar += (*l_it - *s_it)*(*p_it - *s_it); + // Gram-Schmidt for one vector + for (p_it = v_it->cartesian_begin(), + s_it = facet[0].cartesian_begin(), + l_it = facet[1].cartesian_begin(); + p_it != v_it->cartesian_end(); + ++l_it, ++p_it, ++s_it) + { + FT hx = (*p_it - *s_it) - scalar*(*l_it - *s_it)/orth_length2; + h += hx*hx; + } + h = sqrt(h); + + if (h/(2*r) < pow(theta0, D-1)) + return false; + if (!is_theta0_good(facet, theta0)) + return false; + } + else + { + Hyperplane_d tau_h(facet.begin(), facet.end(), *v_it); + Vector_d orth_tau = tau_h.orthogonal_vector(); + FT orth_length = sqrt(orth_tau.squared_length()); + K::Cartesian_const_iterator_d o_it, p_it, s_it, c_it; + FT h = 0; + for (o_it = orth_tau.cartesian_begin(), + p_it = v_it->cartesian_begin(), + s_it = (facet.begin())->cartesian_begin(); + o_it != orth_tau.cartesian_end(); + ++o_it, ++p_it, ++s_it) + h += (*o_it)*(*p_it - *s_it)/orth_length; + h = fabs(h); + if (experiment3 && thetamin_vector[thetamin_vector.size()-1] > pow(h/(2*r), 1.0/(D-1))) + { + thetamin_vector[thetamin_vector.size()-1] = pow(h/(2*r), 1.0/(D-1)); + //std::cout << "theta=" << h/(2*r) << ", "; + } + if (h/(2*r) < pow(theta0, D-1)) + return false; + if (!is_theta0_good(facet, theta0)) + return false; + } + } + return true; +} + +/** Recursive function for checking the goodness of a simplex, + * meaning it does not contain a k-face, which is not theta0^(k-1) thick + */ + +FT theta(std::vector<Point_d>& vertices) +{ + FT curr_value = 1.0; + int D = vertices.size()-1; + if (D <= 1) + return 1; // Edges are always good + //******** Circumscribed sphere + Euclidean_distance ed; + Sphere_d cs(vertices.begin(), vertices.end()); + FT r = sqrt(cs.squared_radius()); + for (std::vector<Point_d>::iterator v_it = vertices.begin(); v_it != vertices.end(); ++v_it) + { + std::vector<Point_d> facet; + for (std::vector<Point_d>::iterator f_it = vertices.begin(); f_it != vertices.end(); ++f_it) + if (f_it != v_it) + facet.push_back(*f_it); + // Compute the altitude + curr_value = std::min(curr_value, theta(facet)); // Check the corresponding facet + if (vertices[0].size() == 3 && D == 2) + { + //Vector_d l = facet[0] - facet[1]; + FT orth_length2 = ed.transformed_distance(facet[0],facet[1]); + K::Cartesian_const_iterator_d l_it, p_it, s_it, c_it; + FT h = 0; + // Scalar product = <sp,l> + FT scalar = 0; + for (p_it = v_it->cartesian_begin(), + s_it = facet[0].cartesian_begin(), + l_it = facet[1].cartesian_begin(); + p_it != v_it->cartesian_end(); + ++l_it, ++p_it, ++s_it) + scalar += (*l_it - *s_it)*(*p_it - *s_it); + // Gram-Schmidt for one vector + for (p_it = v_it->cartesian_begin(), + s_it = facet[0].cartesian_begin(), + l_it = facet[1].cartesian_begin(); + p_it != v_it->cartesian_end(); + ++l_it, ++p_it, ++s_it) + { + FT hx = (*p_it - *s_it) - scalar*(*l_it - *s_it)/orth_length2; + h += hx*hx; + } + h = sqrt(h); + curr_value = std::min(curr_value, std::pow(h/(2*r), 1.0/(D-1))); + } + else + { + Hyperplane_d tau_h(facet.begin(), facet.end(), *v_it); + Vector_d orth_tau = tau_h.orthogonal_vector(); + FT orth_length = sqrt(orth_tau.squared_length()); + K::Cartesian_const_iterator_d o_it, p_it, s_it, c_it; + FT h = 0; + for (o_it = orth_tau.cartesian_begin(), + p_it = v_it->cartesian_begin(), + s_it = (facet.begin())->cartesian_begin(); + o_it != orth_tau.cartesian_end(); + ++o_it, ++p_it, ++s_it) + h += (*o_it)*(*p_it - *s_it)/orth_length; + h = fabs(h); + curr_value = std::min(curr_value, pow(h/(2*r), 1.0/(D-1))); + } + } + return curr_value; +} + +// Doubling in a way 1->2->5->10 +void double_round(int& i) +{ + FT order10 = pow(10,std::floor(std::log10(i))); + int digit = std::floor( i / order10); + std::cout << digit; + if (digit == 1) + i *= 2; + else if (digit == 2) + i = 5*i/2; + else if (digit == 5) + i *= 2; + else + std::cout << "digit not correct. digit = " << digit << std::endl; +} + +//////////////////////////////////////////////////////////////////////////////////////////////////////////// +// IS VIOLATED TEST +//////////////////////////////////////////////////////////////////////////////////////////////////////////// + +/** Check if a newly created cell is protected from old vertices + * + * t is the Delaunay triangulation + * vertices is the vector containing the point to insert and a facet f in t + * v1 is the vertex of t, such that f and v1 form a simplex + * v2 is the vertex of t, such that f and v2 form another simplex + * delta is the protection constant + * power_protection is true iff the delta-power protection is used + */ + +bool new_cell_is_violated(Delaunay_triangulation& t, std::vector<Point_d>& vertices, const Delaunay_vertex& v1, const Delaunay_vertex v2, FT delta0, bool power_protection, FT theta0, FT gamma0) +{ + assert(vertices.size() == vertices[0].size() || + vertices.size() == vertices[0].size() + 1); //simplex size = d | d+1 + assert(v1 != v2); + if (vertices.size() == vertices[0].size() + 1) + // FINITE CASE + { + Sphere_d cs(vertices.begin(), vertices.end()); + Point_d center_cs = cs.center(); + FT r = sqrt(Euclidean_distance().transformed_distance(center_cs, vertices[0])); + /* + for (auto v_it = t.vertices_begin(); v_it != t.vertices_end(); ++v_it) + if (!t.is_infinite(v_it)) + { + //CGAL::Oriented_side side = Oriented_side_d()(cs, (v_it)->point()); + if (std::find(vertices.begin(), vertices.end(), v_it->point()) == vertices.end()) + { + FT dist2 = Euclidean_distance().transformed_distance(center_cs, (v_it)->point()); + if (!power_protection) + if (dist2 >= r*r-_sfty && dist2 <= (r+delta)*(r+delta)) + return true; + if (power_protection) + if (dist2 >= r*r-_sfty && dist2 <= r*r+delta*delta) + return true; + } + } + */ + // Is the center inside the box? (only Euclidean case) + // if (!torus) + // { + // bool inside_the_box = true; + // for (c_it = center_cs.cartesian_begin(); c_it != center_cs.cartesian_end(); ++c_it) + // if (*c_it > 1.0 || *c_it < -1.0) + // { + // inside_the_box = false; break; + // } + // if (inside_the_box && h/r < theta0) + // return true; + // } + // Check the two vertices (if not infinite) + if (!t.is_infinite(v1)) + { + FT dist2 = Euclidean_distance().transformed_distance(center_cs, v1->point()); + if (!power_protection) + if (dist2 >= r*r-_sfty && dist2 <= (r+r*delta0)*(r+r*delta0)) + { refused_case2++; return true;} + if (power_protection) + if (dist2 >= r*r-_sfty && dist2 <= r*r+r*r*delta0*delta0) + { refused_case2++; return true;} + // Check if the centers are not too close + std::vector<Point_d> sigma(vertices); + sigma[0] = v1->point(); + Sphere_d cs_sigma(sigma.begin(), sigma.end()); + Point_d csc_sigma = cs_sigma.center(); + FT r_sigma = sqrt(cs_sigma.squared_radius()); + FT dcc = sqrt(Euclidean_distance().transformed_distance(center_cs, csc_sigma)); + if (experiment3 && dcc/r < gammamin_vector[gammamin_vector.size()-1]) + gammamin_vector[gammamin_vector.size()-1] = dcc/r; + if (experiment3 && dcc/r_sigma < gammamin_vector[gammamin_vector.size()-1]) + gammamin_vector[gammamin_vector.size()-1] = dcc/r_sigma; + if (dcc < r*gamma0 || dcc < r_sigma*gamma0) + { refused_centers1++; return true; } + } + if (!t.is_infinite(v2)) + { + FT dist2 = Euclidean_distance().transformed_distance(center_cs, v2->point()); + if (!power_protection) + if (dist2 >= r*r-_sfty && dist2 <= (r+r*delta0)*(r+r*delta0)) + { refused_case2++; return true;} + if (power_protection) + if (dist2 >= r*r-_sfty && dist2 <= r*r+r*r*delta0*delta0) + { refused_case2++; return true;} + // Check if the centers are not too close + std::vector<Point_d> sigma(vertices); + sigma[0] = v2->point(); + Sphere_d cs_sigma(sigma.begin(), sigma.end()); + Point_d csc_sigma = cs_sigma.center(); + FT r_sigma = sqrt(cs_sigma.squared_radius()); + FT dcc = sqrt(Euclidean_distance().transformed_distance(center_cs, csc_sigma)); + if (experiment3 && dcc/r < gammamin_vector[gammamin_vector.size()-1]) + gammamin_vector[gammamin_vector.size()-1] = dcc/r; + if (experiment3 && dcc/r_sigma < gammamin_vector[gammamin_vector.size()-1]) + gammamin_vector[gammamin_vector.size()-1] = dcc/r_sigma; + if (dcc < r*gamma0 || dcc < r_sigma*gamma0) + { refused_centers1++; return true; } + } + // Check if the simplex is theta0-good + if (!is_theta0_good(vertices, theta0)) + { refused_bad++; return true;} + + } + else + // INFINITE CASE + { + Delaunay_triangulation::Vertex_iterator v = t.vertices_begin(); + while (t.is_infinite(v) || std::find(vertices.begin(), vertices.end(), v->point()) == vertices.end()) + v++; + Hyperplane_d facet_plane(vertices.begin(), vertices.end(), v->point(), CGAL::ON_POSITIVE_SIDE); + Vector_d orth_v = facet_plane.orthogonal_vector(); + /* + for (auto v_it = t.vertices_begin(); v_it != t.vertices_end(); ++v_it) + if (!t.is_infinite(v_it)) + if (std::find(vertices.begin(), vertices.end(), v_it->point()) == vertices.end()) + { + std::vector<FT> coords; + Point_d p = v_it->point(); + auto orth_i = orth_v.cartesian_begin(), p_i = p.cartesian_begin(); + for (; orth_i != orth_v.cartesian_end(); ++orth_i, ++p_i) + coords.push_back((*p_i) - (*orth_i) * delta / sqrt(orth_v.squared_length())); + Point_d p_delta = Point_d(coords); + bool p_is_inside = !Has_on_positive_side_d()(facet_plane, p); + bool p_delta_is_inside = !Has_on_positive_side_d()(facet_plane, p_delta); + if (!p_is_inside && p_delta_is_inside) + return true; + } + */ + if (!t.is_infinite(v1)) + { + std::vector<FT> coords; + Point_d p = v1->point(); + auto orth_i = orth_v.cartesian_begin(), p_i = p.cartesian_begin(); + for (; orth_i != orth_v.cartesian_end(); ++orth_i, ++p_i) + coords.push_back((*p_i) - (*orth_i) * delta0 / sqrt(orth_v.squared_length())); + Point_d p_delta = Point_d(coords); + bool p_is_inside = !Has_on_positive_side_d()(facet_plane, p); + bool p_delta_is_inside = !Has_on_positive_side_d()(facet_plane, p_delta); + if (!power_protection && !p_is_inside && p_delta_is_inside) + return true; + } + if (!t.is_infinite(v2)) + { + std::vector<FT> coords; + Point_d p = v2->point(); + auto orth_i = orth_v.cartesian_begin(), p_i = p.cartesian_begin(); + for (; orth_i != orth_v.cartesian_end(); ++orth_i, ++p_i) + coords.push_back((*p_i) - (*orth_i) * delta0 / sqrt(orth_v.squared_length())); + Point_d p_delta = Point_d(coords); + bool p_is_inside = !Has_on_positive_side_d()(facet_plane, p); + bool p_delta_is_inside = !Has_on_positive_side_d()(facet_plane, p_delta); + if (!power_protection && !p_is_inside && p_delta_is_inside) + return true; + } + } + return false; +} + +/** Auxillary recursive function to check if the point p violates the protection of the cell c and + * if there is a violation of an eventual new cell + * + * p is the point to insert + * t is the current triangulation + * c is the current cell (simplex) + * parent_cell is the parent cell (simplex) + * index is the index of the facet between c and parent_cell from parent_cell's point of view + * D is the dimension of the triangulation + * delta is the protection constant + * marked_cells is the vector of all visited cells containing p in their circumscribed ball + * power_protection is true iff you are working with delta-power protection + * + * OUT: true iff inserting p hasn't produced any violation so far + */ + +bool is_violating_protection(Point_d& p, Delaunay_triangulation& t, Full_cell_handle c, Full_cell_handle parent_cell, int index, int D, FT delta0, std::vector<Full_cell_handle>& marked_cells, bool power_protection, FT theta0, FT gamma0) +{ + Euclidean_distance ed; + std::vector<Point_d> vertices; + if (!t.is_infinite(c)) + { + // if the cell is finite, we look if the protection is violated + for (auto v_it = c->vertices_begin(); v_it != c->vertices_end(); ++v_it) + vertices.push_back((*v_it)->point()); + Sphere_d cs( vertices.begin(), vertices.end()); + Point_d center_cs = cs.center(); + FT r = sqrt(ed.transformed_distance(center_cs, vertices[0])); + FT dist2 = ed.transformed_distance(center_cs, p); + // if the new point is inside the protection ball of a non conflicting simplex + if (!power_protection) + if (dist2 >= r*r-_sfty && dist2 <= (r+r*delta0)*(r+r*delta0)) + { refused_case1++; return true;} + if (power_protection) + if (dist2 >= r*r-_sfty && dist2 <= r*r+delta0*delta0*r*r) + { refused_case1++; return true;} + // if the new point is inside the circumscribing ball : continue violation searching on neighbours + //if (dist2 < r*r) + //if (dist2 < (5*r+delta)*(5*r+delta)) + if (dist2 < r*r) + { + c->tds_data().mark_visited(); + marked_cells.push_back(c); + for (int i = 0; i < D+1; ++i) + { + Full_cell_handle next_c = c->neighbor(i); + if (next_c->tds_data().is_clear() && + is_violating_protection(p, t, next_c, c, i, D, delta0, marked_cells, power_protection, theta0, gamma0)) + return true; + } + } + // if the new point is outside the protection sphere + else + { + // facet f is on the border of the conflict zone : check protection of simplex {p,f} + // the new simplex is guaranteed to be finite + vertices.clear(); vertices.push_back(p); + for (int i = 0; i < D+1; ++i) + if (i != index) + vertices.push_back(parent_cell->vertex(i)->point()); + Delaunay_vertex vertex_to_check = t.infinite_vertex(); + for (auto vh_it = c->vertices_begin(); vh_it != c->vertices_end(); ++vh_it) + if (!vertex_is_in_full_cell(*vh_it, parent_cell)) + { + vertex_to_check = *vh_it; break; + } + if (new_cell_is_violated(t, vertices, vertex_to_check, parent_cell->vertex(index), delta0, power_protection, theta0, gamma0)) + //if (new_cell_is_violated(t, vertices, vertex_to_check->point(), delta)) + return true; + } + } + else + { + // Inside of the convex hull is + side. Outside is - side. + for (auto vh_it = c->vertices_begin(); vh_it != c->vertices_end(); ++vh_it) + if (!t.is_infinite(*vh_it)) + vertices.push_back((*vh_it)->point()); + Delaunay_triangulation::Vertex_iterator v_it = t.vertices_begin(); + while (t.is_infinite(v_it) || vertex_is_in_full_cell(v_it, c)) + v_it++; + Hyperplane_d facet_plane(vertices.begin(), vertices.end(), v_it->point(), CGAL::ON_POSITIVE_SIDE); + //CGAL::Oriented_side outside = Oriented_side_d()(facet_plane, v_it->point()); + Vector_d orth_v = facet_plane.orthogonal_vector(); + std::vector<FT> coords; + auto orth_i = orth_v.cartesian_begin(), p_i = p.cartesian_begin(); + for (; orth_i != orth_v.cartesian_end(); ++orth_i, ++p_i) + coords.push_back((*p_i) - (*orth_i) * delta0 / sqrt(orth_v.squared_length())); + Point_d p_delta = Point_d(coords); + bool p_is_inside = !Has_on_positive_side_d()(facet_plane, p) && (Oriented_side_d()(facet_plane, p) != CGAL::ZERO); + bool p_delta_is_inside = !Has_on_positive_side_d()(facet_plane, p_delta); + + // If we work with power protection, we just ignore any conflicts + if (!power_protection && !p_is_inside && p_delta_is_inside) + return true; + //if the cell is infinite we look at the neighbours regardless + if (p_is_inside) + { + c->tds_data().mark_visited(); + marked_cells.push_back(c); + for (int i = 0; i < D+1; ++i) + { + Full_cell_handle next_c = c->neighbor(i); + if (next_c->tds_data().is_clear() && + is_violating_protection(p, t, next_c, c, i, D, delta0, marked_cells, power_protection, theta0, gamma0)) + return true; + } + } + else + { + // facet f is on the border of the conflict zone : check protection of simplex {p,f} + // the new simplex is finite if the parent cell is finite + vertices.clear(); vertices.push_back(p); + for (int i = 0; i < D+1; ++i) + if (i != index) + if (!t.is_infinite(parent_cell->vertex(i))) + vertices.push_back(parent_cell->vertex(i)->point()); + Delaunay_vertex vertex_to_check = t.infinite_vertex(); + for (auto vh_it = c->vertices_begin(); vh_it != c->vertices_end(); ++vh_it) + if (!vertex_is_in_full_cell(*vh_it, parent_cell)) + { + vertex_to_check = *vh_it; break; + } + if (new_cell_is_violated(t, vertices, vertex_to_check, parent_cell->vertex(index), delta0, power_protection, theta0, gamma0)) + //if (new_cell_is_violated(t, vertices, vertex_to_check->point(), delta)) + return true; + } + } + //c->tds_data().clear_visited(); + //marked_cells.pop_back(); + return false; +} + +/** Checks if inserting the point p in t will make conflicts + * + * p is the point to insert + * t is the current triangulation + * D is the dimension of triangulation + * delta is the protection constant + * power_protection is true iff you are working with delta-power protection + * OUT: true iff inserting p produces a violation of delta-protection. + */ + +bool is_violating_protection(Point_d& p, Delaunay_triangulation& t, int D, FT delta0, bool power_protection, FT theta0, FT gamma0) +{ + Euclidean_distance ed; + Delaunay_triangulation::Vertex_handle v; + Delaunay_triangulation::Face f(t.current_dimension()); + Delaunay_triangulation::Facet ft; + Delaunay_triangulation::Full_cell_handle c; + Delaunay_triangulation::Locate_type lt; + std::vector<Full_cell_handle> marked_cells; + //c = t.locate(p, lt, f, ft, v); + c = t.locate(p); + bool violation_existing_cells = is_violating_protection(p, t, c, c, 0, D, delta0, marked_cells, power_protection, theta0, gamma0); + for (Full_cell_handle fc : marked_cells) + fc->tds_data().clear(); + return violation_existing_cells; +} + + +//////////////////////////////////////////////////////////////////////// +// INITIALIZATION +//////////////////////////////////////////////////////////////////////// + +// Query for a sphere near a cite in all copies of a torus +// OUT points_inside +void torus_search(Tree& treeW, int D, Point_d cite, FT r, std::vector<int>& points_inside) +{ + int nb_cells = pow(3, D); + Delaunay_vertex v; + for (int i = 0; i < nb_cells; ++i) + { + std::vector<FT> cite_copy; + int cell_i = i; + for (int l = 0; l < D; ++l) + { + cite_copy.push_back(cite[l] + 2.0*(cell_i%3-1)); + cell_i /= 3; + } + Fuzzy_sphere fs(cite_copy, r, 0, treeW.traits()); + treeW.search(std::insert_iterator<std::vector<int>>(points_inside, points_inside.end()), fs); + } +} + + +void initialize_torus(Point_Vector& W, Tree& treeW, Delaunay_triangulation& t, FT epsilon, std::vector<int>& landmarks_ind, int& landmark_count, std::vector<bool>& point_taken) +{ + initialize_statistics(); + int D = W[0].size(); + if (D == 2) + { + int xw = 6, yw = 4; + // Triangular lattice close to regular triangles h=0.866a ~ 0.875a : 48p + for (int i = 0; i < xw; ++i) + for (int j = 0; j < yw; ++j) + { + Point_d cite1(std::vector<FT>{2.0/xw*i, 2.0/yw*j}); + std::vector<int> points_inside; + torus_search(treeW, D, cite1, epsilon, points_inside); + //std::cout << "i=" << i << ", j=" << j << " "; print_vector(points_inside); std::cout << "\n"; + std::vector<int>::iterator p_it = points_inside.begin(); + while (p_it != points_inside.end() && point_taken[*p_it]) + ++p_it; + assert(p_it != points_inside.end()); + //W[*p_it] = cite1; // debug purpose + insert_delaunay_landmark_with_copies(W, *p_it, + landmarks_ind, t, landmark_count, true); + point_taken[*p_it] = true; + + Point_d cite2(std::vector<FT>{2.0/xw*(i+0.5), 2.0/yw*(j+0.5)}); + points_inside.clear(); + torus_search(treeW, D, cite2, epsilon, points_inside); + //std::cout << "i=" << i << ", j=" << j << " "; print_vector(points_inside); std::cout << "\n"; + p_it = points_inside.begin(); + while (p_it != points_inside.end() && point_taken[*p_it]) + ++p_it; + assert(p_it != points_inside.end()); + //W[*p_it] = cite2; // debug purpose + insert_delaunay_landmark_with_copies(W, *p_it, + landmarks_ind, t, landmark_count, true); + point_taken[*p_it] = true; + } + } + else if (D == 3) + { + int wd = 3; + // Body-centered cubic lattice : 54p + for (int i = 0; i < wd; ++i) + for (int j = 0; j < wd; ++j) + for (int k = 0; k < wd; ++k) + { + Point_d cite1(std::vector<FT>{2.0/wd*i, 2.0/wd*j, 2.0/wd*k}); + std::vector<int> points_inside; + torus_search(treeW, D, cite1, epsilon, points_inside); + std::vector<int>::iterator p_it = points_inside.begin(); + while (p_it != points_inside.end() && point_taken[*p_it]) + ++p_it; + assert(p_it != points_inside.end()); + insert_delaunay_landmark_with_copies(W, *(points_inside.begin()), + landmarks_ind, t, landmark_count, true); + point_taken[*p_it] = true; + + Point_d cite2(std::vector<FT>{2.0/wd*(i+0.5), 2.0/wd*(j+0.5), 2.0/wd*(k+0.5)}); + points_inside.clear(); + torus_search(treeW, D, cite2, epsilon, points_inside); + p_it = points_inside.begin(); + while (p_it != points_inside.end() && point_taken[*p_it]) + ++p_it; + assert(p_it != points_inside.end()); + insert_delaunay_landmark_with_copies(W, *(points_inside.begin()), + landmarks_ind, t, landmark_count, true); + point_taken[*p_it] = true; + } + } + //write_mesh +} + +/////////////////////////////////////////////////////////////////////// +/////////////////////////////////////////////////////////////////////// +//!!!!!!!!!!!!! THE INTERFACE FOR LANDMARK CHOICE IS BELOW !!!!!!!!!!// +/////////////////////////////////////////////////////////////////////// +/////////////////////////////////////////////////////////////////////// + +// Struct for R_max_heap elements + +struct R_max_handle +{ + FT value; + Point_d center; + + R_max_handle(FT value_, Point_d c): value(value_), center(c) + {} +}; + +struct R_max_compare +{ + bool operator()(const R_max_handle& rmh1, const R_max_handle& rmh2) const + { + return rmh1.value < rmh2.value; + } +}; + +// typedef boost::heap::fibonacci_heap<R_max_handle, boost::heap::compare<R_max_compare>> Heap; + +// void make_heap(Delaunay_triangulation& t, Heap& R_max_heap) +// { +// R_max_heap.clear(); +// for (auto fc_it = t.full_cells_begin(); fc_it != t.full_cells_end(); ++fc_it) +// { +// if (t.is_infinite(fc_it)) +// continue; +// Point_Vector vertices; +// for (auto fc_v_it = fc_it->vertices_begin(); fc_v_it != fc_it->vertices_end(); ++fc_v_it) +// vertices.push_back((*fc_v_it)->point()); +// Sphere_d cs( vertices.begin(), vertices.end()); +// Point_d csc = cs.center(); +// FT r = sqrt(cs.squared_radius()); +// // A ball is in the heap, if it intersects the cube +// bool accepted = sphere_intersects_cube(csc, sqrt(r)); +// if (!accepted) +// continue; +// R_max_heap.push(R_max_handle(r, fc_it, csc)); +// } +// } + +////////////////////////////////////////////////////////////////////////////////////////////////////////// +// SAMPLING RADIUS +////////////////////////////////////////////////////////////////////////////////////////////////////////// + +R_max_handle sampling_radius(Delaunay_triangulation& t) +{ + FT epsilon2 = 0; + Point_d final_center; + Point_d control_point; + for (auto fc_it = t.full_cells_begin(); fc_it != t.full_cells_end(); ++fc_it) + { + if (t.is_infinite(fc_it)) + continue; + Point_Vector vertices; + for (auto fc_v_it = fc_it->vertices_begin(); fc_v_it != fc_it->vertices_end(); ++fc_v_it) + vertices.push_back((*fc_v_it)->point()); + Sphere_d cs( vertices.begin(), vertices.end()); + Point_d csc = cs.center(); + bool in_cube = true; + for (auto xi = csc.cartesian_begin(); xi != csc.cartesian_end(); ++xi) + if (*xi > 1.0 || *xi < -1.0) + { + in_cube = false; break; + } + if (!in_cube) + continue; + FT r2 = Euclidean_distance().transformed_distance(cs.center(), *(vertices.begin())); + if (epsilon2 < r2) + { + epsilon2 = r2; + final_center = csc; + control_point = (*vertices.begin()); + } + } + return R_max_handle(sqrt(epsilon2), final_center); +} + +FT sampling_fatness(Delaunay_triangulation& t) +{ + FT curr_theta = 1.0; + for (auto fc_it = t.full_cells_begin(); fc_it != t.full_cells_end(); ++fc_it) + { + if (t.is_infinite(fc_it)) + continue; + Point_Vector vertices; + for (auto fc_v_it = fc_it->vertices_begin(); fc_v_it != fc_it->vertices_end(); ++fc_v_it) + vertices.push_back((*fc_v_it)->point()); + Sphere_d cs( vertices.begin(), vertices.end()); + Point_d csc = cs.center(); + bool in_cube = true; + for (auto xi = csc.cartesian_begin(); xi != csc.cartesian_end(); ++xi) + if (*xi > 1.0 || *xi < -1.0) + { + in_cube = false; break; + } + if (!in_cube) + continue; + FT theta_f = theta(vertices); + curr_theta = std::min(curr_theta, theta_f); + //std::cout << "theta(sigma) = " << theta_f << "\n"; + } + return curr_theta; +} + +// Generate an epsilon sample for a given epsilon +void generate_epsilon_sample_torus(Point_Vector& W, FT epsilon, int dim, Delaunay_triangulation& t) +{ + W.clear(); + t.clear(); + int point_count = 0; + std::vector<int> point_ind; + // std::vector<FT> coords; + FT curr_eps = 2*dim; + // Initialize + // for (int i = 0; i < dim; ++i) + // coords.push_back(-1); + // R_max_handle rmh(2*sqrt(dim), Point_d(coords)); + // int N = dim; std::floor(std::pow(1/epsilon,dim)); + // std::cout << N << "\n"; + typedef CGAL::Random_points_in_cube_d<Point_d> Random_cube_iterator; + Random_cube_iterator rp(dim, 1.0); + W.push_back(*rp++); + insert_delaunay_landmark_with_copies(W, W.size()-1, point_ind, t, point_count, true); + curr_eps = sampling_radius(t).value; + while (curr_eps > epsilon) + { + + W.push_back(*rp++); + insert_delaunay_landmark_with_copies(W, W.size()-1, point_ind, t, point_count, true); + + Point_d c = sampling_radius(t).center; + W.push_back(c); + insert_delaunay_landmark_with_copies(W, W.size()-1, point_ind, t, point_count, true); + curr_eps = sampling_radius(t).value; + + std::cout << "curr_eps = " << curr_eps << "\n"; + } + // Iterate and insert in a torus + // while (rmh.value > epsilon) + // { + // W.push_back(rmh.center); + // insert_delaunay_landmark_with_copies(W, W.size()-1, point_ind, t, point_count, true); + // rmh = sampling_radius(t); + // //std::cout << rmh.value; + // } +} + +/////////////////////////////////////////////////////////////////////// +// LANDMARK CHOICE PROCEDURE +/////////////////////////////////////////////////////////////////////// + +/** Procedure to compute a maximal protected subset from a point cloud. All OUTs should be empty at call. + * + * IN: W is the initial point cloud having type Epick_d<Dynamic_dimension_tag>::Point_d + * IN: nbP is the size of W + * OUT: landmarks is the output vector for the points + * OUT: landmarks_ind is the output vector for the indices of the selected points in W + * IN: delta is the constant of protection + * OUT: full_cells is the output vector of the simplices in the final Delaunay triangulation + * IN: torus is true iff you are working on a flat torus [-1,1]^d + */ + +void protected_delaunay(Point_Vector& W, + //Point_Vector& landmarks, + std::vector<int>& landmarks_ind, + FT alpha, + FT epsilon, + FT delta0, + FT theta0, + FT gamma0, + //std::vector<std::vector<int>>& full_cells, + bool torus, + bool power_protection + ) +{ + //bool return_ = true; + unsigned D = W[0].size(); + int nbP = W.size(); + //FT beta = 1/(1-alpha); + //FT Ad = pow((4*alpha + 8*beta)/alpha, D); + //FT theta0 = 1/Ad; + //FT delta0 = pow(1/Ad,D); + Torus_distance td; + Euclidean_distance ed; + Delaunay_triangulation t(D); + std::vector<bool> point_taken(nbP,false); + CGAL::Random rand; + int landmark_count = 0; + std::list<int> index_list; + //****************** Kd Tree W + STraits traits(&(W[0])); + Tree treeW(boost::counting_iterator<std::ptrdiff_t>(0), + boost::counting_iterator<std::ptrdiff_t>(nbP), + typename Tree::Splitter(), + traits); + // shuffle the list of indexes (via a vector) + { + std::vector<int> temp_vector; + for (int i = 0; i < nbP; ++i) + temp_vector.push_back(i); + unsigned seed = std::chrono::system_clock::now().time_since_epoch().count(); + std::shuffle(temp_vector.begin(), temp_vector.end(), std::default_random_engine(seed)); + //CGAL::spatial_sort(temp_vector.begin(), temp_vector.end()); + for (std::vector<int>::iterator it = temp_vector.begin(); it != temp_vector.end(); ++it) + index_list.push_front(*it); + } + //******************** Initialize point set + if (!torus) + for (unsigned pos1 = 0; pos1 < D+1; ++pos1) + { + std::vector<FT> point; + for (unsigned i = 0; i < pos1; ++i) + point.push_back(-1); + if (pos1 != D) + point.push_back(1); + for (unsigned i = pos1+1; i < D; ++i) + point.push_back(0); + assert(point.size() == D); + W[index_list.front()] = Point_d(point); + insert_delaunay_landmark_with_copies(W, index_list.front(), landmarks_ind, t, landmark_count, torus); + index_list.pop_front(); + } + else + initialize_torus(W, treeW, t, epsilon, landmarks_ind, landmark_count, point_taken); + //std::cout << "Size of treeW: " << treeW.size() << "\n"; + //std::cout << "Size of t: " << t.number_of_vertices() << "\n"; + //******************* Initialize heap for R_max + //Heap R_max_heap; + //make_heap(t, R_max_heap); + + + R_max_handle rh = sampling_radius(t); + FT epsilon0 = rh.value; + if (experiment1) eps_vector.push_back(pow(1/rh.value,D)); + //******************** Iterative algorithm + std::vector<int> candidate_points; + torus_search(treeW, D, + rh.center, + alpha*rh.value, + candidate_points); + std::list<int>::iterator list_it; + std::vector<int>::iterator cp_it = candidate_points.begin(); + while (cp_it != candidate_points.end()) + { + if (!point_taken[*cp_it] && !is_violating_protection(W[*cp_it], t, D, delta0, power_protection, theta0, gamma0)) + { + Delaunay_vertex v = insert_delaunay_landmark_with_copies(W, *cp_it, landmarks_ind, t, landmark_count, torus); + { + // Simple check if the new cells don't have centers too close one to another + std::vector<Full_cell_handle> inc_cells; + std::back_insert_iterator<std::vector<Full_cell_handle>> out(inc_cells); + t.tds().incident_full_cells(v, out); + + std::vector<Sphere_d> spheres; + for (auto i_it = inc_cells.begin(); i_it != inc_cells.end(); ++i_it) + { + std::vector<Point_d> vertices; + for (auto v_it = (*i_it)->vertices_begin(); v_it != (*i_it)->vertices_end(); ++v_it) + vertices.push_back((*v_it)->point()); + spheres.push_back(Sphere_d(vertices.begin(), vertices.end())); + } + for (auto s_it = spheres.begin(); s_it != spheres.end(); ++s_it) + for (auto t_it = s_it+1; t_it != spheres.end(); ++t_it) + { + FT ddc2 = ed.transformed_distance(s_it->center(),t_it->center()); + if (ddc2 < gamma0*gamma0*s_it->squared_radius() || + ddc2 < gamma0*gamma0*t_it->squared_radius()) + { refused_centers2++; } + } + } + + //std::cout << *cp_it << ",\n"; + //make_heap(t, R_max_heap); + point_taken[*cp_it] = true; + rh = sampling_radius(t); + if (experiment1) eps_vector.push_back(pow(1/rh.value,D)); + //std::cout << "rhvalue = " << rh.value << "\n"; + //std::cout << "D = " << + candidate_points.clear(); + torus_search(treeW, D, + rh.center, + alpha*rh.value, + candidate_points); + cp_it = candidate_points.begin(); + /* + // PIECE OF CODE FOR DEBUGGING PURPOSES + + Delaunay_vertex inserted_v = insert_delaunay_landmark_with_copies(W, *list_it, landmarks_ind, t, landmark_count); + if (triangulation_is_protected(t, delta)) + { + index_list.erase(list_it); + list_it = index_list.begin(); + } + else + { //THAT'S WHERE SOMETHING'S WRONG + t.remove(inserted_v); + landmarks_ind.pop_back(); + landmark_count--; + write_delaunay_mesh(t, W[*list_it], is2d); + is_violating_protection(W[*list_it], t_old, D, delta); //Called for encore + } + */ + //std::cout << "index_list_size() = " << index_list.size() << "\n"; + } + else + { + cp_it++; + //std::cout << "!!!!!WARNING!!!!! A POINT HAS BEEN OMITTED!!!\n"; + } + //if (list_it != index_list.end()) + // write_delaunay_mesh(t, W[*list_it], is2d); + } + + if (experiment2) epsratio_vector.push_back(rh.value/epsilon0); + if (experiment2) epsslope_vector.push_back( (pow(1/rh.value,D)-pow(1/epsilon0,D))/(landmarks_ind.size() - 48) ); + std::cout << "The iteration ended when cp_count = " << candidate_points.size() << "\n"; + std::cout << "alphaRmax = " << alpha*rh.value << "\n"; + std::cout << "epsilon' = " << rh.value << "\n"; + std::cout << "nbL = " << landmarks_ind.size() << "\n"; + print_statistics(); + //print_vector(landmarks_ind); std::cout << std::endl; + //std::sort(landmarks_ind.begin(), landmarks_ind.end()); + print_vector(landmarks_ind); std::cout << std::endl; + if (experiment3) thetamin_vector[thetamin_vector.size()-1] = sampling_fatness(t); + std::cout << "theta = " << sampling_fatness(t) << "\n"; + //fill_landmarks(W, landmarks, landmarks_ind, torus); + //fill_full_cell_vector(t, full_cells); + /* + if (triangulation_is_protected(t, delta)) + std::cout << "Triangulation is ok\n"; + else + { + std::cout << "Triangulation is BAD!! T_T しくしく!\n"; + } + */ + write_delaunay_mesh(t, W[0], true); + //std::cout << t << std::endl; +} + +void run_experiment5(Point_Vector& W, + int D, + FT alpha, + FT epsilon, + FT delta0, + FT theta0, + FT gamma0, + //std::vector<std::vector<int>>& full_cells, + bool torus, + bool power_protection + ) +{ + // INITIALIZATION + Delaunay_triangulation t(D); + std::vector<int> landmarks_ind; + int landmark_count = 0; + initialize_statistics(); + if (D == 2) + { + int xw = 6, yw = 4; + // Triangular lattice close to regular triangles h=0.866a ~ 0.875a : 48p + for (int i = 0; i < xw; ++i) + for (int j = 0; j < yw; ++j) + { + Point_d cite1(std::vector<FT>{2.0/xw*i, 2.0/yw*j}); + W.push_back(cite1); // debug purpose + insert_delaunay_landmark_with_copies(W, W.size()-1, + landmarks_ind, t, landmark_count, true); + + Point_d cite2(std::vector<FT>{2.0/xw*(i+0.5), 2.0/yw*(j+0.5)}); + W.push_back(cite2); // debug purpose + insert_delaunay_landmark_with_copies(W, W.size()-1, + landmarks_ind, t, landmark_count, true); + } + } + else if (D == 3) + { + int wd = 3; + // Body-centered cubic lattice : 54p + for (int i = 0; i < wd; ++i) + for (int j = 0; j < wd; ++j) + for (int k = 0; k < wd; ++k) + { + Point_d cite1(std::vector<FT>{2.0/wd*i, 2.0/wd*j, 2.0/wd*k}); + W.push_back(cite1); // debug purpose + insert_delaunay_landmark_with_copies(W, W.size()-1, + landmarks_ind, t, landmark_count, true); + + Point_d cite2(std::vector<FT>{2.0/wd*(i+0.5), 2.0/wd*(j+0.5), 2.0/wd*(k+0.5)}); + W.push_back(cite2); // debug purpose + insert_delaunay_landmark_with_copies(W, W.size()-1, + landmarks_ind, t, landmark_count, true); + } + } + + // ITERATIONS + R_max_handle rh = sampling_radius(t); + Point_d rp = *(Random_point_iterator(D, alpha*rh.value)); + int death_count = 0; + std::cout << "death count " << death_count << " rp = " << rp << "\n"; + while (death_count < 100) + { + std::vector<FT> coords; + for (auto c_it = rh.center.cartesian_begin(), + r_it = rp.cartesian_begin(); + c_it != rh.center.cartesian_end(); + ++c_it, ++r_it) + coords.push_back(*c_it + *r_it); + Point_d new_p(coords); + if (!is_violating_protection(new_p, t, D, delta0, power_protection, theta0, gamma0)) + { + W.push_back(new_p); + insert_delaunay_landmark_with_copies(W, W.size()-1, landmarks_ind, t, landmark_count, torus); + rh = sampling_radius(t); + rp = *(Random_point_iterator(D, alpha*rh.value)); + death_count = 0; + std::cout << "death count " << death_count << " rp = " << rp << "\n"; + } + else + { + rp = *(Random_point_iterator(D, alpha*rh.value)); + death_count++; + std::cout << "death count " << death_count << " rp = " << rp << "\n"; + } + //Point_d new_p = (*rp++) + Vector_d; + } +} + +/////////////////////////////////////////////////////////////////////////////////////////////////////////// +// Series of experiments +/////////////////////////////////////////////////////////////////////////////////////////////////////////// + +void start_experiments(Point_Vector& W, FT alpha, std::vector<int>& landmarks_ind, FT epsilon) +{ + int experiment_no = 1; + FT delta0 = 0.1; + FT theta0 = 0.1; + FT gamma0 = 0.01; + std::string suffix; + //std::cout << "ようこそジプシー我が神秘の部屋へ:\n"; + while (experiment_no != 0) + { + std::cout << "Enter experiment no (0 to exit): "; + std::cin >> experiment_no; + switch (experiment_no) + { + case 1: + // Experiment 1 + experiment1 = true; + eps_vector = {}; + std::cout << "Enter delta0: "; std::cin >> delta0; + std::cout << "Enter theta0: "; std::cin >> theta0; + std::cout << "Enter gamma0: "; std::cin >> gamma0; + protected_delaunay(W, landmarks_ind, alpha, epsilon, delta0, theta0, gamma0, true, true); + write_tikz_plot(eps_vector,"epstime.tikz"); + experiment1 = false; + break; + + case 2: + // Experiment 2 + suffix = ""; + experiment2 = true; + epsratio_vector = {0}; + epsslope_vector = {0}; + std::cout << "File name suffix: "; + std::cin >> suffix; + for (FT alpha = 0.01; alpha < 0.999; alpha += 0.01) + { + landmarks_ind.clear(); + std::cout << "Test for alpha = " << alpha << "\n"; + protected_delaunay(W, landmarks_ind, alpha, epsilon, delta0, theta0, gamma0, true, true); + } + write_tikz_plot(epsratio_vector,"epsratio_alpha." + suffix + ".tex"); + write_tikz_plot(epsslope_vector,"epsslope_alpha." + suffix + ".tex"); + experiment2 = false; + break; + + case 3: + // Experiment 3 + experiment3 = true; + thetamin_vector = {}; + gammamin_vector = {}; + theta0 = 0; + gamma0 = 0; + for (FT delta0 = 0; delta0 < 0.999; delta0 += 0.05) + { + landmarks_ind.clear(); + thetamin_vector.push_back(1.0); //0.7489 fatness of the initialization + gammamin_vector.push_back(10); + std::cout << "Test for delta0 = " << delta0 << "\n"; + protected_delaunay(W, landmarks_ind, alpha, epsilon, delta0, theta0, gamma0, true, true); + } + write_tikz_plot(thetamin_vector,"thetamin_delta.tex"); + write_tikz_plot(gammamin_vector,"gammamin_delta.tex"); + experiment3 = false; + break; + + // case 4: + // // Experiment 4 + // { + // int dim; + // std::cout << "Enter dimension: "; + // std::cin >> dim; + // Delaunay_triangulation t(dim); + // // for (FT eps = 0.7; eps < 1.1; eps += 0.1) + // // { + // // generate_epsilon_sample_torus(W, eps, dim, t); + // // for (auto v_it = t.vertices_begin(); v_it != t.vertices_end(); ++v_it) + // // { + // // if (t.is_infinite(v_it)) + // // continue; + // // bool in_cube = true; + // // for (auto xi = v_it->cartesian_begin(); xi != v_it->cartesian_end(); ++xi) + // // if (*xi > 1.0 || *xi < -1.0) + // // { + // // in_cube = false; break; + // // } + // // if (!in_cube) + // // continue; + // // for (auto t.tds().incident_full_cells()) + // // } + // // std::cout << "eps = " << eps << ", real epsilon = " << sampling_radius(t).value << "\n"; + // // } + // // } + // break; + + + case 5: + // Experiment 5 + experiment5 = true; + // std::cout << "Enter dimension: "; + // std::cin >> dim; + + landmarks_ind.clear(); + W.clear(); + run_experiment5(W, alpha, epsilon, delta0, theta0, gamma0, true, true); + experiment5 = false; + break; + } + + } + +} + +#endif diff --git a/src/Witness_complex/example/witness_complex_cube.cpp b/src/Witness_complex/example/witness_complex_cube.cpp index a9a2959b..e448c55d 100644 --- a/src/Witness_complex/example/witness_complex_cube.cpp +++ b/src/Witness_complex/example/witness_complex_cube.cpp @@ -20,6 +20,11 @@ * along with this program. If not, see <http://www.gnu.org/licenses/>. */ +// Avoiding the max arity issue with CGAL +#ifndef BOOST_PARAMETER_MAX_ARITY +# define BOOST_PARAMETER_MAX_ARITY 12 +#endif + #include <iostream> #include <fstream> #include <ctime> @@ -37,6 +42,10 @@ #include "gudhi/Witness_complex.h" #include "gudhi/reader_utils.h" #include "Torus_distance.h" +#include "generators.h" +#include "output.h" +//#include "protected_sets/protected_sets.h" +#include "protected_sets/protected_sets_paper2.h" #include <CGAL/Cartesian_d.h> #include <CGAL/Search_traits.h> @@ -106,8 +115,6 @@ typedef std::vector<Point_d> Point_Vector; //typedef K::Equal_d Equal_d; //typedef CGAL::Random_points_in_cube_d<CGAL::Point_d<CGAL::Cartesian_d<FT> > > Random_cube_iterator; -typedef CGAL::Random_points_in_cube_d<Point_d> Random_cube_iterator; -typedef CGAL::Random_points_in_ball_d<Point_d> Random_point_iterator; typedef CGAL::Delaunay_triangulation<K> Delaunay_triangulation; typedef Delaunay_triangulation::Facet Facet; @@ -117,449 +124,84 @@ typedef Delaunay_triangulation::Full_cell_handle Full_cell_handle; typedef K::Sphere_d Sphere_d; typedef K::Hyperplane_d Hyperplane_d; +/*////////////////////////////////////// + * GLOBAL VARIABLES ******************** + *////////////////////////////////////// -bool toric=false; - - -/** - * \brief Customized version of read_points - * which takes into account a possible nbP first line - * - */ -inline void -read_points_cust ( std::string file_name , Point_Vector & points) -{ - std::ifstream in_file (file_name.c_str(),std::ios::in); - if(!in_file.is_open()) - { - std::cerr << "Unable to open file " << file_name << std::endl; - return; - } - std::string line; - double x; - while( getline ( in_file , line ) ) - { - std::vector< double > point; - std::istringstream iss( line ); - while(iss >> x) { point.push_back(x); } - Point_d p(point.begin(), point.end()); - if (point.size() != 1) - points.push_back(p); - } - in_file.close(); -} - -void generate_points_grid(Point_Vector& W, int width, int D) -{ - int nb_points = 1; - for (int i = 0; i < D; ++i) - nb_points *= width; - for (int i = 0; i < nb_points; ++i) - { - std::vector<double> point; - int cell_i = i; - for (int l = 0; l < D; ++l) - { - point.push_back(0.01*(cell_i%width)); - cell_i /= width; - } - W.push_back(point); - } -} - -void generate_points_random_box(Point_Vector& W, int nbP, int dim) -{ - /* - Random_cube_iterator rp(dim, 1); - for (int i = 0; i < nbP; i++) - { - std::vector<double> point; - for (auto it = rp->cartesian_begin(); it != rp->cartesian_end(); ++it) - point.push_back(*it); - W.push_back(Point_d(point)); - rp++; - } - */ - Random_cube_iterator rp(dim, 1.0); - for (int i = 0; i < nbP; i++) - { - W.push_back(*rp++); - } -} - - -void write_wl( std::string file_name, std::vector< std::vector <int> > & WL) -{ - std::ofstream ofs (file_name, std::ofstream::out); - for (auto w : WL) - { - for (auto l: w) - ofs << l << " "; - ofs << "\n"; - } - ofs.close(); -} +//NA bool toric=false; +bool power_protection = true; +bool grid_points = true; +bool is2d = true; +//FT _sfty = pow(10,-14); +bool torus = false; -void write_points( std::string file_name, std::vector< Point_d > & points) -{ - std::ofstream ofs (file_name, std::ofstream::out); - for (auto w : points) - { - for (auto it = w.cartesian_begin(); it != w.cartesian_end(); ++it) - ofs << *it << " "; - ofs << "\n"; - } - ofs.close(); -} - -void write_edges(std::string file_name, Witness_complex<>& witness_complex, Point_Vector& landmarks) -{ - std::ofstream ofs (file_name, std::ofstream::out); - for (auto u: witness_complex.complex_vertex_range()) - for (auto v: witness_complex.complex_vertex_range()) - { - typeVectorVertex edge = {u,v}; - if (u < v && witness_complex.find(edge) != witness_complex.null_simplex()) - { - for (auto it = landmarks[u].cartesian_begin(); it != landmarks[u].cartesian_end(); ++it) - ofs << *it << " "; - ofs << "\n"; - for (auto it = landmarks[v].cartesian_begin(); it != landmarks[v].cartesian_end(); ++it) - ofs << *it << " "; - ofs << "\n\n\n"; - } - } - ofs.close(); -} - - -void insert_delaunay_landmark_with_copies(Point_Vector& W, int chosen_landmark, std::vector<int>& landmarks_ind, Delaunay_triangulation& delaunay, int& landmark_count) -{ - delaunay.insert(W[chosen_landmark]); - landmarks_ind.push_back(chosen_landmark); - landmark_count++; -} - -bool vertex_is_in_full_cell(Delaunay_triangulation::Vertex_handle v, Full_cell_handle fc) -{ - for (auto v_it = fc->vertices_begin(); v_it != fc->vertices_end(); ++v_it) - if (*v_it == v) - return true; - return false; -} - -bool new_cell_is_violated(Delaunay_triangulation& t, std::vector<Point_d>& vertices, bool is_infinite, const Point_d& p, FT delta) -{ - if (!is_infinite) - // FINITE CASE - { - Sphere_d cs(vertices.begin(), vertices.end()); - Point_d center_cs = cs.center(); - FT r = sqrt(Euclidean_distance().transformed_distance(center_cs, vertices[0])); - for (auto v_it = t.vertices_begin(); v_it != t.vertices_end(); ++v_it) - if (!t.is_infinite(v_it)) - { - //CGAL::Oriented_side side = Oriented_side_d()(cs, (v_it)->point()); - if (std::find(vertices.begin(), vertices.end(), v_it->point()) == vertices.end()) - { - FT dist2 = Euclidean_distance().transformed_distance(center_cs, (v_it)->point()); - //if (dist2 >= r*r && dist2 <= (r+delta)*(r+delta)) - if (dist2 >= r*r && dist2 <= r*r+delta*delta) - return true; - } - } - } - else - // INFINITE CASE - { - Delaunay_triangulation::Vertex_iterator v = t.vertices_begin(); - while (t.is_infinite(v) || std::find(vertices.begin(), vertices.end(), v->point()) == vertices.end()) - v++; - Hyperplane_d facet_plane(vertices.begin(), vertices.end(), v->point(), CGAL::ON_POSITIVE_SIDE); - Vector_d orth_v = facet_plane.orthogonal_vector(); - for (auto v_it = t.vertices_begin(); v_it != t.vertices_end(); ++v_it) - if (!t.is_infinite(v_it)) - if (std::find(vertices.begin(), vertices.end(), v_it->point()) == vertices.end()) - { - std::vector<FT> coords; - Point_d p = v_it->point(); - auto orth_i = orth_v.cartesian_begin(), p_i = p.cartesian_begin(); - for (; orth_i != orth_v.cartesian_end(); ++orth_i, ++p_i) - coords.push_back((*p_i) - (*orth_i) * delta / sqrt(orth_v.squared_length())); - Point_d p_delta = Point_d(coords); - bool p_is_inside = !Has_on_positive_side_d()(facet_plane, p); - bool p_delta_is_inside = !Has_on_positive_side_d()(facet_plane, p_delta); - if (!p_is_inside && p_delta_is_inside) - return true; - } - } - return false; -} - - -bool is_violating_protection(Point_d& p, Delaunay_triangulation& t, Full_cell_handle c, Full_cell_handle parent_cell, int index, int D, FT delta, std::vector<Full_cell_handle>& marked_cells) -{ - Euclidean_distance ed; - std::vector<Point_d> vertices; - if (!t.is_infinite(c)) - { - // if the cell is finite, we look if the protection is violated - for (auto v_it = c->vertices_begin(); v_it != c->vertices_end(); ++v_it) - vertices.push_back((*v_it)->point()); - Sphere_d cs( vertices.begin(), vertices.end()); - Point_d center_cs = cs.center(); - FT r = sqrt(ed.transformed_distance(center_cs, vertices[0])); - FT dist2 = ed.transformed_distance(center_cs, p); - // if the new point is inside the protection ball of a non conflicting simplex - //if (dist2 >= r*r && dist2 <= (r+delta)*(r+delta)) - if (dist2 >= r*r && dist2 <= r*r+delta*delta) - return true; - c->tds_data().mark_visited(); - marked_cells.push_back(c); - // if the new point is inside the circumscribing ball : continue violation searching on neughbours - if (dist2 < r*r) - for (int i = 0; i < D+1; ++i) - { - Full_cell_handle next_c = c->neighbor(i); - if (next_c->tds_data().is_clear() && - is_violating_protection(p, t, next_c, c, i, D, delta, marked_cells)) - return true; - } - // if the new point is outside the protection sphere - else - { - // facet f is on the border of the conflict zone : check protection of simplex {p,f} - // the new simplex is guaranteed to be finite - vertices.clear(); vertices.push_back(p); - for (int i = 0; i < D+1; ++i) - if (i != index) - vertices.push_back(parent_cell->vertex(i)->point()); - Delaunay_vertex vertex_to_check; - for (auto vh_it = c->vertices_begin(); vh_it != c->vertices_end(); ++vh_it) - if (!vertex_is_in_full_cell(*vh_it, parent_cell)) - { - vertex_to_check = *vh_it; break; - } - if (new_cell_is_violated(t, vertices, false, vertex_to_check->point(), delta)) - return true; - } - } - else - { - // Inside of the convex hull is + side. Outside is - side. - for (auto vh_it = c->vertices_begin(); vh_it != c->vertices_end(); ++vh_it) - if (!t.is_infinite(*vh_it)) - vertices.push_back((*vh_it)->point()); - Delaunay_triangulation::Vertex_iterator v_it = t.vertices_begin(); - while (t.is_infinite(v_it) || vertex_is_in_full_cell(v_it, c)) - v_it++; - Hyperplane_d facet_plane(vertices.begin(), vertices.end(), v_it->point(), CGAL::ON_POSITIVE_SIDE); - //CGAL::Oriented_side outside = Oriented_side_d()(facet_plane, v_it->point()); - Vector_d orth_v = facet_plane.orthogonal_vector(); - std::vector<FT> coords; - auto orth_i = orth_v.cartesian_begin(), p_i = p.cartesian_begin(); - for (; orth_i != orth_v.cartesian_end(); ++orth_i, ++p_i) - coords.push_back((*p_i) - (*orth_i) * delta / sqrt(orth_v.squared_length())); - Point_d p_delta = Point_d(coords); - bool p_is_inside = !Has_on_positive_side_d()(facet_plane, p); - bool p_delta_is_inside = !Has_on_positive_side_d()(facet_plane, p_delta); - - if (!p_is_inside && p_delta_is_inside) - return true; - //if the cell is infinite we look at the neighbours regardless - c->tds_data().mark_visited(); - marked_cells.push_back(c); - if (p_is_inside) - for (int i = 0; i < D+1; ++i) - { - Full_cell_handle next_c = c->neighbor(i); - if (next_c->tds_data().is_clear() && - is_violating_protection(p, t, next_c, c, i, D, delta, marked_cells)) - return true; - } - else - { - // facet f is on the border of the conflict zone : check protection of simplex {p,f} - // the new simplex is finite if the parent cell is finite - vertices.clear(); vertices.push_back(p); - bool new_simplex_is_finite = false; - for (int i = 0; i < D+1; ++i) - if (i != index) - { - if (t.is_infinite(parent_cell->vertex(i))) - new_simplex_is_finite = true; - else - vertices.push_back(parent_cell->vertex(i)->point()); - } - Delaunay_vertex vertex_to_check; - for (auto vh_it = c->vertices_begin(); vh_it != c->vertices_end(); ++vh_it) - if (!vertex_is_in_full_cell(*vh_it, parent_cell)) - { - vertex_to_check = *vh_it; break; - } - if (new_cell_is_violated(t, vertices, new_simplex_is_finite, vertex_to_check->point(), delta)) - return true; - } - } - return false; -} - -bool is_violating_protection(Point_d& p, Delaunay_triangulation& t, int D, FT delta) -{ - Euclidean_distance ed; - Delaunay_triangulation::Vertex_handle v; - Delaunay_triangulation::Face f(t.current_dimension()); - Delaunay_triangulation::Facet ft; - Delaunay_triangulation::Full_cell_handle c; - Delaunay_triangulation::Locate_type lt; - std::vector<Full_cell_handle> marked_cells; - c = t.locate(p, lt, f, ft, v); - bool violation_existing_cells = is_violating_protection(p, t, c, c, 0, D, delta, marked_cells); - for (Full_cell_handle fc : marked_cells) - fc->tds_data().clear(); - return violation_existing_cells; -} - -bool old_is_violating_protection(Point_d& p, Delaunay_triangulation& t, int D, FT delta) +bool triangulation_is_protected(Delaunay_triangulation& t, FT delta) { + std::cout << "Start protection verification\n"; Euclidean_distance ed; - Delaunay_triangulation::Vertex_handle v; - Delaunay_triangulation::Face f(t.current_dimension()); - Delaunay_triangulation::Facet ft; - Delaunay_triangulation::Full_cell_handle c; - Delaunay_triangulation::Locate_type lt; - c = t.locate(p, lt, f, ft, v); - for (auto fc_it = t.full_cells_begin(); fc_it != t.full_cells_end(); ++fc_it) - if (!t.is_infinite(fc_it)) - { - std::vector<Point_d> vertices; - for (auto v_it = fc_it->vertices_begin(); v_it != fc_it->vertices_end(); ++v_it) - vertices.push_back((*v_it)->point()); - Sphere_d cs( vertices.begin(), vertices.end()); - Point_d center_cs = cs.center(); - FT r = sqrt(ed.transformed_distance(center_cs, fc_it->vertex(1)->point())); - FT dist2 = ed.transformed_distance(center_cs, p); - //if the new point is inside the protection ball of a non conflicting simplex - if (dist2 >= r*r && dist2 <= (r+delta)*(r+delta)) - return true; - } - t.insert(p, c); - return false; -} - -void write_delaunay_mesh(Delaunay_triangulation& t, const Point_d& p) -{ - std::ofstream ofs ("delaunay.mesh", std::ofstream::out); - int nbV = t.number_of_vertices()+1; - ofs << "MeshVersionFormatted 1\nDimension 2\n"; - ofs << "Vertices\n" << nbV << "\n"; - int ind = 1; //index of a vertex + // Fill the map Vertices -> Numbers std::map<Delaunay_triangulation::Vertex_handle, int> index_of_vertex; + int ind = 0; for (auto v_it = t.vertices_begin(); v_it != t.vertices_end(); ++v_it) { if (t.is_infinite(v_it)) continue; - for (auto coord = v_it->point().cartesian_begin(); coord != v_it->point().cartesian_end(); ++coord) - ofs << *coord << " "; - ofs << "508\n"; index_of_vertex[v_it] = ind++; } - for (auto coord = p.cartesian_begin(); coord != p.cartesian_end(); ++coord) - ofs << *coord << " "; - ofs << "208\n"; - /* - int nbFacets = 0; - for (auto ft_it = t.finite_facets_begin(); ft_it != t.finite_facets_end(); ++ft_it) - nbFacets++; - ofs << "\nEdges\n" << nbFacets << "\n\n"; - for (auto ft_it = t.facets_begin(); ft_it != t.facets_end(); ++ft_it) - { - if (t.is_infinite(ft_it)) - continue; - for (auto vh_it = ft_it->vertices_begin(); vh_it != ft_it->vertices_end(); ++vh_it) - ofs << index_of_vertex[*vh_it] << " "; - } - */ - ofs << "Triangles " << t.number_of_finite_full_cells()+1 << "\n"; - for (auto fc_it = t.full_cells_begin(); fc_it != t.full_cells_end(); ++fc_it) - { - if (t.is_infinite(fc_it)) - continue; - for (auto vh_it = fc_it->vertices_begin(); vh_it != fc_it->vertices_end(); ++vh_it) - ofs << index_of_vertex[*vh_it] << " "; - ofs << "508\n"; - } - ofs << nbV << " " << nbV << " " << nbV << " " << 208 << "\n"; - ofs << "End\n"; - ofs.close(); -} - -bool triangulation_is_protected(Delaunay_triangulation& t, FT delta) -{ - // Verification part - Euclidean_distance ed; for (auto fc_it = t.full_cells_begin(); fc_it != t.full_cells_end(); ++fc_it) if (!t.is_infinite(fc_it)) - for (auto v_it = t.vertices_begin(); v_it != t.vertices_end(); ++v_it) - if (!t.is_infinite(v_it)) + { + std::vector<Point_d> vertices; + for (auto fc_v_it = fc_it->vertices_begin(); fc_v_it != fc_it->vertices_end(); ++fc_v_it) + vertices.push_back((*fc_v_it)->point()); + Sphere_d cs( vertices.begin(), vertices.end()); + Point_d center_cs = cs.center(); + FT r = sqrt(ed.transformed_distance(center_cs, fc_it->vertex(0)->point())); + for (auto v_it = t.vertices_begin(); v_it != t.vertices_end(); ++v_it) + if (!t.is_infinite(v_it)) //check if vertex belongs to the face - if (!vertex_is_in_full_cell(v_it, fc_it)) - { - std::vector<Point_d> vertices; - for (auto fc_v_it = fc_it->vertices_begin(); fc_v_it != fc_it->vertices_end(); ++fc_v_it) - vertices.push_back((*fc_v_it)->point()); - Sphere_d cs( vertices.begin(), vertices.end()); - Point_d center_cs = cs.center(); - FT r = sqrt(ed.transformed_distance(center_cs, fc_it->vertex(0)->point())); - FT dist2 = ed.transformed_distance(center_cs, v_it->point()); - //if the new point is inside the protection ball of a non conflicting simplex - //std::cout << "Dist^2 = " << dist2 << " (r+delta)*(r+delta) = " << (r+delta)*(r+delta) << " r^2 = " << r*r <<"\n"; - //if (dist2 <= (r+delta)*(r+delta) && dist2 >= r*r) - if (dist2 <= r*r+delta*delta && dist2 >= r*r) - { - write_delaunay_mesh(t, v_it->point()); - std::cout << "Problematic vertex " << *v_it << " "; - std::cout << "Problematic cell " << *fc_it << "\n"; - std::cout << "r^2 = " << r*r << ", d^2 = " << dist2 << ", r^2+delta^2 = " << r*r+delta*delta << "\n"; - return false; - } - } - + if (!vertex_is_in_full_cell(v_it, fc_it)) + { + FT dist2 = ed.transformed_distance(center_cs, v_it->point()); + //if the new point is inside the protection ball of a non conflicting simplex + //std::cout << "Dist^2 = " << dist2 << " (r+delta)*(r+delta) = " << (r+delta)*(r+delta) << " r^2 = " << r*r <<"\n"; + if (!power_protection) + if (dist2 <= (r+delta)*(r+delta) && dist2 >= r*r) + { + write_delaunay_mesh(t, v_it->point(), is2d); + // Output the problems + std::cout << "Problematic vertex " << index_of_vertex[v_it] << " "; + std::cout << "Problematic cell "; + for (auto vh_it = fc_it->vertices_begin(); vh_it != fc_it->vertices_end(); ++vh_it) + if (!t.is_infinite(*vh_it)) + std::cout << index_of_vertex[*vh_it] << " "; + std::cout << "\n"; + std::cout << "r^2 = " << r*r << ", d^2 = " << dist2 << ", (r+delta)^2 = " << (r+delta)*(r+delta) << "\n"; + return false; + } + if (power_protection) + if (dist2 <= r*r+delta*delta && dist2 >= r*r) + { + write_delaunay_mesh(t, v_it->point(), is2d); + std::cout << "Problematic vertex " << *v_it << " "; + std::cout << "Problematic cell " << *fc_it << "\n"; + std::cout << "r^2 = " << r*r << ", d^2 = " << dist2 << ", r^2+delta^2 = " << r*r+delta*delta << "\n"; + return false; + } + } + } return true; } -void fill_landmarks(Point_Vector& W, Point_Vector& landmarks, std::vector<int>& landmarks_ind) -{ - for (unsigned j = 0; j < landmarks_ind.size(); ++j) - landmarks.push_back(W[landmarks_ind[j]]); -} - -void fill_full_cell_vector(Delaunay_triangulation& t, std::vector<std::vector<int>>& full_cells) -{ - // Store vertex indices in a map - int ind = 0; //index of a vertex - std::map<Delaunay_triangulation::Vertex_handle, int> index_of_vertex; - for (auto v_it = t.vertices_begin(); v_it != t.vertices_end(); ++v_it) - if (t.is_infinite(v_it)) - continue; - else - index_of_vertex[v_it] = ind++; - // Write full cells as vectors in full_cells - for (auto fc_it = t.full_cells_begin(); fc_it != t.full_cells_end(); ++fc_it) - { - if (t.is_infinite(fc_it)) - continue; - std::vector<int> cell; - for (auto v_it = fc_it->vertices_begin(); v_it != fc_it->vertices_end(); ++v_it) - cell.push_back(index_of_vertex[*v_it]); - full_cells.push_back(cell); - } -} +////////////////////////////////////////////////////////////////////////////////////////////////////////// +// SAMPLING RADIUS +////////////////////////////////////////////////////////////////////////////////////////////////////////// -FT sampling_radius(Delaunay_triangulation& t) +FT sampling_radius(Delaunay_triangulation& t, FT epsilon0) { - FT epsilon2 = 4.0; + FT epsilon2 = 0; + Point_d control_point; for (auto fc_it = t.full_cells_begin(); fc_it != t.full_cells_end(); ++fc_it) { if (t.is_infinite(fc_it)) @@ -578,134 +220,106 @@ FT sampling_radius(Delaunay_triangulation& t) if (!in_cube) continue; FT r2 = Euclidean_distance().transformed_distance(cs.center(), *(vertices.begin())); - if (epsilon2 > r2) - epsilon2 = r2; + if (epsilon2 < r2) + { + epsilon2 = r2; + control_point = (*vertices.begin()); + } + } + if (epsilon2 < epsilon0*epsilon0) + { + std::cout << "ACHTUNG! E' < E\n"; + std::cout << "eps = " << epsilon0 << " eps' = " << sqrt(epsilon2) << "\n"; + write_delaunay_mesh(t, control_point, is2d); } return sqrt(epsilon2); } -FT point_sampling_radius_by_delaunay(Point_Vector& points) +FT point_sampling_radius_by_delaunay(Point_Vector& points, FT epsilon0) { Delaunay_triangulation t(points[0].size()); t.insert(points.begin(), points.end()); - return sampling_radius(t); + return sampling_radius(t, epsilon0); } -void landmark_choice_protected_delaunay(Point_Vector& W, int nbP, Point_Vector& landmarks, std::vector<int>& landmarks_ind, FT delta, std::vector<std::vector<int>>& full_cells) +// A little script to make a tikz histogram of epsilon distribution +// Returns the average epsilon +FT epsilon_histogram(Delaunay_triangulation& t, int n) { - unsigned D = W[0].size(); - Torus_distance td; - Euclidean_distance ed; - Delaunay_triangulation t(D); - CGAL::Random rand; - int landmark_count = 0; - std::list<int> index_list; - // shuffle the list of indexes (via a vector) - { - std::vector<int> temp_vector; - for (int i = 0; i < nbP; ++i) - temp_vector.push_back(i); - unsigned seed = std::chrono::system_clock::now().time_since_epoch().count(); - std::shuffle(temp_vector.begin(), temp_vector.end(), std::default_random_engine(seed)); - //CGAL::spatial_sort(temp_vector.begin(), temp_vector.end()); - for (std::vector<int>::iterator it = temp_vector.begin(); it != temp_vector.end(); ++it) - index_list.push_front(*it); - } - for (unsigned pos1 = 0; pos1 < D+1; ++pos1) - { - std::vector<FT> point; - for (unsigned i = 0; i < pos1; ++i) - point.push_back(-1); - if (pos1 != D) - point.push_back(1); - for (unsigned i = pos1+1; i < D; ++i) - point.push_back(0); - assert(point.size() == D); - W[index_list.front()] = Point_d(point); - insert_delaunay_landmark_with_copies(W, index_list.front(), landmarks_ind, t, landmark_count); - index_list.pop_front(); - } - // add the first D+1 vertices to form one finite cell - /* - for (int i = 0; i <= D+1; ++i) - { - t.insert(W[index_list.front()]); - insert_delaunay_landmark_with_copies(W, index_list.front(), landmarks_ind, t, landmark_count); - index_list.pop_front(); - } - */ - /* - { - std::vector<FT> coords; - for (int i = 0; i < D; ++i) - coords.push_back(-1); - W[index_list.front()] = Point_d(coords); - insert_delaunay_landmark_with_copies(W, index_list.front(), landmarks_ind, t, landmark_count); - index_list.pop_front(); - for (int i = 0; i < D; ++i) - { - coords.clear(); - for (int j = 0; j < D; ++j) - if (i == j) - coords.push_back(1); - else - coords.push_back(-1); - W[index_list.front()] = Point_d(coords); - insert_delaunay_landmark_with_copies(W, index_list.front(), landmarks_ind, t, landmark_count); - index_list.pop_front(); - } - } - */ - //std::cout << t; - //assert(t.number_of_vertices() == D+1); - //assert(landmarks_ind.size() == D+1); - //assert(W[landmarks_ind[0]][0] == 0); - // add other vertices if they don't violate protection - std::list<int>::iterator list_it = index_list.begin(); - while (list_it != index_list.end()) + FT epsilon_max = 0; //sampling_radius(t,0); + FT sum_epsilon = 0; + int count_simplices = 0; + std::vector<int> histo(n+1, 0); + for (auto fc_it = t.full_cells_begin(); fc_it != t.full_cells_end(); ++fc_it) { - if (!is_violating_protection(W[*list_it], t, D, delta)) - { - // If no conflicts then insert in every copy of T^3 - is_violating_protection(W[*list_it], t, D, delta); - insert_delaunay_landmark_with_copies(W, *list_it, landmarks_ind, t, landmark_count); - index_list.erase(list_it); - list_it = index_list.begin(); - //std::cout << "index_list_size() = " << index_list.size() << "\n"; - } - else - { - list_it++; - //std::cout << "!!!!!WARNING!!!!! A POINT HAS BEEN OMITTED!!!\n"; - } - //write_delaunay_mesh(t, W[*list_it]); + if (t.is_infinite(fc_it)) + continue; + Point_Vector vertices; + for (auto fc_v_it = fc_it->vertices_begin(); fc_v_it != fc_it->vertices_end(); ++fc_v_it) + vertices.push_back((*fc_v_it)->point()); + Sphere_d cs( vertices.begin(), vertices.end()); + Point_d csc = cs.center(); + bool in_cube = true; + for (auto xi = csc.cartesian_begin(); xi != csc.cartesian_end(); ++xi) + if (*xi > 1.0 || *xi < -1.0) + { + in_cube = false; break; + } + if (!in_cube) + continue; + FT r = sqrt(Euclidean_distance().transformed_distance(cs.center(), *(vertices.begin()))); + if (r > epsilon_max) + epsilon_max = r; + sum_epsilon += r; + count_simplices++; + histo[floor(r/epsilon_max*n)]++; } - fill_landmarks(W, landmarks, landmarks_ind); - fill_full_cell_vector(t, full_cells); - if (triangulation_is_protected(t, delta)) - std::cout << "Triangulation is ok\n"; - else - std::cout << "Triangulation is BAD!! T_T しくしく!\n"; - write_delaunay_mesh(t, Point_d(std::vector<FT>({0,0}))); - //std::cout << t << std::endl; + std::ofstream ofs ("histogram.tikz", std::ofstream::out); + FT barwidth = 20.0/n; + int max_value = *(std::max_element(histo.begin(), histo.end())); + std::cout << max_value << std::endl; + FT ten_power = pow(10, ceil(log10(max_value))); + FT max_histo = ten_power; + if (max_value/ten_power < 2) + max_histo = 0.2*ten_power; + if (max_value/ten_power < 5) + max_histo = 0.5*ten_power; + std::cout << ceil(log10(max_value)) << std::endl << max_histo << std::endl; + FT unitht = max_histo/10.0; + + ofs << "\\draw[->] (0,0) -- (0,11);\n" << + "\\draw[->] (0,0) -- (21,0);\n" << + "\\foreach \\i in {1,...,10}\n" << + "\\draw (0,\\i) -- (-0.1,\\i);\n" << + "\\foreach \\i in {1,...,20}\n" << + "\\draw (\\i,0) -- (\\i,-0.1);\n" << + + "\\node at (-1,11) {$\\epsilon$};\n" << + "\\node at (22,-1) {$\\epsilon/\\epsilon_{max}$};\n" << + "\\node at (-0.5,-0.5) {0};\n" << + "\\node at (-0.5,10) {" << max_histo << "};\n" << + "\\node at (20,-0.5) {1};\n"; + + + for (int i = 0; i < n; ++i) + ofs << "\\draw (" << barwidth*i << "," << histo[i]/unitht << ") -- (" + << barwidth*(i+1) << "," << histo[i]/unitht << ") -- (" + << barwidth*(i+1) << ",0) -- (" << barwidth*i << ",0) -- cycle;\n"; + + ofs.close(); + + //return sum_epsilon/count_simplices; + return epsilon_max; } -template <typename T> -void print_vector(std::vector<T> v) +FT epsilon_histogram_by_delaunay(Point_Vector& points, int n) { - std::cout << "["; - if (!v.empty()) - { - std::cout << *(v.begin()); - for (auto it = v.begin()+1; it != v.end(); ++it) - { - std::cout << ","; - std::cout << *it; - } - } - std::cout << "]"; + Delaunay_triangulation t(points[0].size()); + t.insert(points.begin(), points.end()); + return epsilon_histogram(t, n); } + int landmark_perturbation(Point_Vector &W, int nbL, Point_Vector& landmarks, std::vector<int>& landmarks_ind, std::vector<std::vector<int>>& full_cells) { //******************** Preface: origin point @@ -764,7 +378,7 @@ int landmark_perturbation(Point_Vector &W, int nbL, Point_Vector& landmarks, std } } std::string out_file = "wl_result"; - write_wl(out_file,WL); + //write_wl(out_file,WL); //******************** Constructng a witness complex std::cout << "Entered witness complex construction\n"; @@ -787,7 +401,7 @@ int landmark_perturbation(Point_Vector &W, int nbL, Point_Vector& landmarks, std not_in << " are not.\n"; //******************** Making a set of bad link landmarks - /* + std::cout << "Entered bad links\n"; std::set< int > perturbL; int count_badlinks = 0; @@ -814,7 +428,7 @@ int landmark_perturbation(Point_Vector &W, int nbL, Point_Vector& landmarks, std if (count_bad[i] != 0) std::cout << "count_bad[" << i << "] = " << count_bad[i] << std::endl; std::cout << "\nBad links total: " << count_badlinks << " Points to perturb: " << perturbL.size() << std::endl; - */ + //*********************** Perturb bad link landmarks /* for (auto u: perturbL) @@ -848,16 +462,19 @@ int landmark_perturbation(Point_Vector &W, int nbL, Point_Vector& landmarks, std ofs.close(); } - write_edges("landmarks/edges", witnessComplex, landmarks); + //write_edges("landmarks/edges", witnessComplex, landmarks); /* return count_badlinks; */ return 0; } - int main (int argc, char * const argv[]) { + power_protection = true;//false; + grid_points = false;//true; + torus = true; + if (argc != 4) { std::cerr << "Usage: " << argv[0] @@ -866,40 +483,98 @@ int main (int argc, char * const argv[]) } int nbP = atoi(argv[1]); int dim = atoi(argv[2]); - double delta = atof(argv[3]); + double theta0 = atof(argv[3]); + //double delta = atof(argv[3]); + + is2d = (dim == 2); std::cout << "Let the carnage begin!\n"; Point_Vector point_vector; - generate_points_random_box(point_vector, nbP, dim); - FT epsilon = point_sampling_radius_by_delaunay(point_vector); + if (grid_points) + { + generate_points_grid(point_vector, (int)pow(nbP, 1.0/dim), dim, torus); + nbP = (int)pow((int)pow(nbP, 1.0/dim), dim); + } + else + generate_points_random_box(point_vector, nbP, dim); + FT epsilon = point_sampling_radius_by_delaunay(point_vector, 0); + //FT epsilon = epsilon_histogram_by_delaunay(point_vector,50); std::cout << "Initial epsilon = " << epsilon << std::endl; Point_Vector L; std::vector<int> chosen_landmarks; //write_points("landmarks/initial_pointset",point_vector); //write_points("landmarks/initial_landmarks",L); CGAL::Timer timer; + + int n = 1; + std::vector<FT> values(n,0); + std::vector<FT> time(n,0); + + //FT step = 0.001; + //FT delta = 0.01*epsilon; + //FT alpha = 0.5; + //FT step = atof(argv[3]); + + start_experiments(point_vector, theta0, chosen_landmarks, epsilon); + + // for (int i = 0; i < n; i++) + // //for (int i = 0; bl > 0; i++) + // { + // //std::cout << "========== Start iteration " << i << "== curr_min(" << curr_min << ")========\n"; + // //double delta = pow(10, -(1.0*i)/2); + // //delta = step*i*epsilon; + // //theta0 = step*i; + // std::cout << "delta/epsilon = " << delta/epsilon << std::endl; + // std::cout << "theta0 = " << theta0 << std::endl; + // // Averaging the result + // int sum_values = 0; + // int nb_iterations = 1; + // std::vector<std::vector<int>> full_cells; + // for (int i = 0; i < nb_iterations; ++i) + // { + // //L = {}; + // chosen_landmarks = {}; + // //full_cells = {}; + // //timer.start(); + // //protected_delaunay(point_vector, nbP, L, chosen_landmarks, delta, epsilon, alpha, theta0, full_cells, torus, power_protection); + // protected_delaunay(point_vector, chosen_landmarks, delta, epsilon, alpha, theta0, torus, power_protection); + // //timer.stop(); + // sum_values += chosen_landmarks.size(); + // } + // //FT epsilon2 = point_sampling_radius_by_delaunay(L, epsilon); + // //std::cout << "Final epsilon = " << epsilon2 << ". Ratio = " << epsilon2/epsilon << std::endl; + // //write_points("landmarks/initial_landmarks",L); + // //std::cout << "delta/epsilon' = " << delta/epsilon2 << std::endl; + // FT nbL = (sum_values*1.0)/nb_iterations; + // //values[i] = pow((1.0*nbL)/nbP, -1.0/dim); + // values[i] = (1.0*nbL)/nbP; + // std::cout << "Number of landmarks = " << nbL << ", time= " << timer.time() << "s"<< std::endl; + // //landmark_perturbation(point_vector, nbL, L, chosen_landmarks, full_cells); + // time[i] = timer.time(); + // timer.reset(); + // //write_points("landmarks/landmarks0",L); + // } + + // // OUTPUT A PLOT + // FT hstep = 20.0/(n-1); + // FT wstep = 10.0; + + // std::ofstream ofs("N'Nplot.tikz", std::ofstream::out); + // ofs << "\\draw[red] (0," << wstep*values[0] << ")"; + // for (int i = 1; i < n; ++i) + // ofs << " -- (" << hstep*i << "," << wstep*values[i] << ")"; + // ofs << ";\n"; + // ofs.close(); /* - for (int i = 0; i < 11; i++) - //for (int i = 0; bl > 0; i++) - { - //std::cout << "========== Start iteration " << i << "== curr_min(" << curr_min << ")========\n"; - double delta = pow(10, -(1.0*i)/2); - std::cout << "delta = " << delta << std::endl; - L = {}; chosen_landmarks = {}; - std::vector<std::vector<int>> full_cells; - timer.start(); - landmark_choice_protected_delaunay(point_vector, nbP, L, chosen_landmarks, delta, full_cells); - timer.stop(); - FT epsilon2 = point_sampling_radius_by_delaunay(L); - std::cout << "Final epsilon = " << epsilon2 << ". Ratio = " << epsilon/epsilon2 << std::endl; - write_points("landmarks/initial_landmarks",L); - int nbL = chosen_landmarks.size(); - std::cout << "Number of landmarks = " << nbL << ", time= " << timer.time() << "s"<< std::endl; - landmark_perturbation(point_vector, nbL, L, chosen_landmarks, full_cells); - timer.reset(); - //write_points("landmarks/landmarks0",L); - } - */ + wstep = 0.1; + ofs = std::ofstream("time.tikz", std::ofstream::out); + ofs << "\\draw[red] (0," << wstep*time[0] << ")"; + for (int i = 1; i < n; ++i) + ofs << " -- (" << hstep*i << "," << wstep*time[i] << ")"; + ofs << ";\n"; + ofs.close(); + + std::vector<std::vector<int>> full_cells; timer.start(); landmark_choice_protected_delaunay(point_vector, nbP, L, chosen_landmarks, delta, full_cells); @@ -909,6 +584,7 @@ int main (int argc, char * const argv[]) write_points("landmarks/initial_landmarks",L); int nbL = chosen_landmarks.size(); std::cout << "Number of landmarks = " << nbL << ", time= " << timer.time() << "s"<< std::endl; - landmark_perturbation(point_vector, nbL, L, chosen_landmarks, full_cells); + //landmark_perturbation(point_vector, nbL, L, chosen_landmarks, full_cells); timer.reset(); + */ } diff --git a/src/Witness_complex/example/witness_complex_flat_torus.cpp b/src/Witness_complex/example/witness_complex_flat_torus.cpp index 69ef5fbf..49383154 100644 --- a/src/Witness_complex/example/witness_complex_flat_torus.cpp +++ b/src/Witness_complex/example/witness_complex_flat_torus.cpp @@ -776,8 +776,8 @@ int main (int argc, char * const argv[]) std::cout << "Let the carnage begin!\n"; Point_Vector point_vector; //read_points_cust(file_name, point_vector); - generate_points_random_box(point_vector, nbP, dim); - //generate_points_grid(point_vector, (int)pow(nbP, 1.0/dim), dim); + //generate_points_random_box(point_vector, nbP, dim); + generate_points_grid(point_vector, (int)pow(nbP, 1.0/dim), dim); //nbP = (int)(pow((int)pow(nbP, 1.0/dim), dim)); /* for (auto &p: point_vector) diff --git a/src/Witness_complex/example/witness_complex_knn_landmarks.cpp b/src/Witness_complex/example/witness_complex_knn_landmarks.cpp index e4a1c324..c45bc0c1 100644 --- a/src/Witness_complex/example/witness_complex_knn_landmarks.cpp +++ b/src/Witness_complex/example/witness_complex_knn_landmarks.cpp @@ -32,6 +32,8 @@ //#include "gudhi/graph_simplicial_complex.h" #include "gudhi/Witness_complex.h" #include "gudhi/reader_utils.h" +#include "generators.h" +#include "output.h" //#include <boost/filesystem.hpp> //#include <CGAL/Delaunay_triangulation.h> @@ -73,60 +75,6 @@ typedef K_neighbor_search::iterator KNS_range; typedef boost::container::flat_map<int, int> Point_etiquette_map; typedef std::vector<Point_d> Point_Vector; -/** - * \brief Customized version of read_points - * which takes into account a possible nbP first line - * - */ -inline void -read_points_cust ( std::string file_name , Point_Vector & points) -{ - std::ifstream in_file (file_name.c_str(),std::ios::in); - if(!in_file.is_open()) - { - std::cerr << "Unable to open file " << file_name << std::endl; - return; - } - std::string line; - double x; - while( getline ( in_file , line ) ) - { - std::vector< double > point; - std::istringstream iss( line ); - while(iss >> x) { point.push_back(x); } - Point_d p(point.begin(), point.end()); - if (point.size() != 1) - points.push_back(p); - } - in_file.close(); -} - -/* -void read_points_to_tree (std::string file_name, Tree& tree) -{ - //I assume here that tree is empty - std::ifstream in_file (file_name.c_str(),std::ios::in); - if(!in_file.is_open()) - { - std::cerr << "Unable to open file " << file_name << std::endl; - return; - } - std::string line; - double x; - while( getline ( in_file , line ) ) - { - std::vector<double> coords; - std::istringstream iss( line ); - while(iss >> x) { coords.push_back(x); } - if (coords.size() != 1) - { - Point_d point(coords.begin(), coords.end()); - tree.insert(point); - } - } - in_file.close(); -} -*/ /** Function that chooses landmarks from W and place it in the kd-tree L. * Note: nbL hould be removed if the code moves to Witness_complex @@ -184,19 +132,6 @@ void d_nearest_landmarks(Point_Vector &W, Tree &L, Point_etiquette_map &L_i, std } } - -void write_wl( std::string file_name, std::vector< std::vector <int> > & WL) -{ - std::ofstream ofs (file_name, std::ofstream::out); - for (auto w : WL) - { - for (auto l: w) - ofs << l << " "; - ofs << "\n"; - } - ofs.close(); -} - int main (int argc, char * const argv[]) { if (argc != 3) @@ -270,6 +205,6 @@ int main (int argc, char * const argv[]) out_file = "output/"+file_name+"_"+argv[2]+".badlinks"; std::ofstream ofs2(out_file, std::ofstream::out); - witnessComplex.write_bad_links(ofs2); + //witnessComplex.write_bad_links(ofs2); ofs2.close(); } diff --git a/src/Witness_complex/example/witness_complex_protected_delaunay.cpp b/src/Witness_complex/example/witness_complex_protected_delaunay.cpp index 2f795a5f..77a167a5 100644 --- a/src/Witness_complex/example/witness_complex_protected_delaunay.cpp +++ b/src/Witness_complex/example/witness_complex_protected_delaunay.cpp @@ -268,6 +268,15 @@ void insert_delaunay_landmark_with_copies(Point_Vector& W, int chosen_landmark, landmark_count++; } + + + +//////////////////////////////////////////////////////////////////////// +// OLD CODE VVVVVVVV +//////////////////////////////////////////////////////////////////////// + + +/* bool is_violating_protection(Point_d& p, Delaunay_triangulation& t, int D, FT delta) { Euclidean_distance ed; @@ -592,3 +601,4 @@ int main (int argc, char * const argv[]) } } +*/ diff --git a/src/Witness_complex/example/witness_complex_sphere.cpp b/src/Witness_complex/example/witness_complex_sphere.cpp index 550c9392..bf3015fa 100644 --- a/src/Witness_complex/example/witness_complex_sphere.cpp +++ b/src/Witness_complex/example/witness_complex_sphere.cpp @@ -35,6 +35,8 @@ //#include "gudhi/graph_simplicial_complex.h" #include "gudhi/Witness_complex.h" #include "gudhi/reader_utils.h" +#include "generators.h" +#include "output.h" //#include <boost/filesystem.hpp> //#include <CGAL/Delaunay_triangulation.h> @@ -94,101 +96,9 @@ typedef CGAL::Fuzzy_sphere<STraits> Fuzzy_sphere; typedef std::vector<Point_d> Point_Vector; //typedef K::Equal_d Equal_d; -typedef CGAL::Random_points_in_cube_d<Point_d> Random_cube_iterator; -typedef CGAL::Random_points_in_ball_d<Point_d> Random_point_iterator; bool toric=false; -/** - * \brief Customized version of read_points - * which takes into account a possible nbP first line - * - */ -inline void -read_points_cust ( std::string file_name , Point_Vector & points) -{ - std::ifstream in_file (file_name.c_str(),std::ios::in); - if(!in_file.is_open()) - { - std::cerr << "Unable to open file " << file_name << std::endl; - return; - } - std::string line; - double x; - while( getline ( in_file , line ) ) - { - std::vector< double > point; - std::istringstream iss( line ); - while(iss >> x) { point.push_back(x); } - Point_d p(point.begin(), point.end()); - if (point.size() != 1) - points.push_back(p); - } - in_file.close(); -} - -void generate_points_grid(Point_Vector& W, int width, int D) -{ - -} - -void generate_points_random_box(Point_Vector& W, int nbP, int dim) -{ - Random_cube_iterator rp(dim, 1); - for (int i = 0; i < nbP; i++) - { - W.push_back(*rp++); - } -} - -/* NOT TORUS RELATED - */ -void generate_points_sphere(Point_Vector& W, int nbP, int dim) -{ - CGAL::Random_points_on_sphere_d<Point_d> rp(dim,1); - for (int i = 0; i < nbP; i++) - W.push_back(*rp++); -} -/* -void read_points_to_tree (std::string file_name, Tree& tree) -{ - //I assume here that tree is empty - std::ifstream in_file (file_name.c_str(),std::ios::in); - if(!in_file.is_open()) - { - std::cerr << "Unable to open file " << file_name << std::endl; - return; - } - std::string line; - double x; - while( getline ( in_file , line ) ) - { - std::vector<double> coords; - std::istringstream iss( line ); - while(iss >> x) { coords.push_back(x); } - if (coords.size() != 1) - { - Point_d point(coords.begin(), coords.end()); - tree.insert(point); - } - } - in_file.close(); -} -*/ - -void write_wl( std::string file_name, std::vector< std::vector <int> > & WL) -{ - std::ofstream ofs (file_name, std::ofstream::out); - for (auto w : WL) - { - for (auto l: w) - ofs << l << " "; - ofs << "\n"; - } - ofs.close(); -} - - std::vector<Point_d> convert_to_torus(std::vector< Point_d>& points) { std::vector< Point_d > points_torus; @@ -205,82 +115,6 @@ std::vector<Point_d> convert_to_torus(std::vector< Point_d>& points) return points_torus; } -void write_points_torus( std::string file_name, std::vector< Point_d > & points) -{ - std::ofstream ofs (file_name, std::ofstream::out); - std::vector<Point_d> points_torus = convert_to_torus(points); - for (auto w : points_torus) - { - for (auto it = w.cartesian_begin(); it != w.cartesian_end(); ++it) - ofs << *it << " "; - ofs << "\n"; - } - ofs.close(); -} - -void write_points( std::string file_name, std::vector< Point_d > & points) -{ - if (toric) write_points_torus(file_name, points); - else - { - std::ofstream ofs (file_name, std::ofstream::out); - for (auto w : points) - { - for (auto it = w.cartesian_begin(); it != w.cartesian_end(); ++it) - ofs << *it << " "; - ofs << "\n"; - } - ofs.close(); - } -} - - -void write_edges_torus(std::string file_name, Witness_complex<>& witness_complex, Point_Vector& landmarks) -{ - std::ofstream ofs (file_name, std::ofstream::out); - Point_Vector l_torus = convert_to_torus(landmarks); - for (auto u: witness_complex.complex_vertex_range()) - for (auto v: witness_complex.complex_vertex_range()) - { - typeVectorVertex edge = {u,v}; - if (u < v && witness_complex.find(edge) != witness_complex.null_simplex()) - { - for (auto it = l_torus[u].cartesian_begin(); it != l_torus[u].cartesian_end(); ++it) - ofs << *it << " "; - ofs << "\n"; - for (auto it = l_torus[v].cartesian_begin(); it != l_torus[v].cartesian_end(); ++it) - ofs << *it << " "; - ofs << "\n\n\n"; - } - } - ofs.close(); -} - -void write_edges(std::string file_name, Witness_complex<>& witness_complex, Point_Vector& landmarks) -{ - std::ofstream ofs (file_name, std::ofstream::out); - if (toric) write_edges_torus(file_name, witness_complex, landmarks); - else - { - for (auto u: witness_complex.complex_vertex_range()) - for (auto v: witness_complex.complex_vertex_range()) - { - typeVectorVertex edge = {u,v}; - if (u < v && witness_complex.find(edge) != witness_complex.null_simplex()) - { - for (auto it = landmarks[u].cartesian_begin(); it != landmarks[u].cartesian_end(); ++it) - ofs << *it << " "; - ofs << "\n"; - for (auto it = landmarks[v].cartesian_begin(); it != landmarks[v].cartesian_end(); ++it) - ofs << *it << " "; - ofs << "\n\n\n"; - } - } - ofs.close(); - } -} - - /** Function that chooses landmarks from W and place it in the kd-tree L. * Note: nbL hould be removed if the code moves to Witness_complex */ @@ -356,6 +190,7 @@ void landmark_choice_600cell(Point_Vector&W, int nbP, int nbL, Point_Vector& lan int landmark_perturbation(Point_Vector &W, Point_Vector& landmarks, std::vector<int>& landmarks_ind) { //********************Preface: origin point + clock_t start, end; int D = W[0].size(); std::vector<FT> orig_vector; for (int i=0; i<D; i++) @@ -383,6 +218,7 @@ int landmark_perturbation(Point_Vector &W, Point_Vector& landmarks, std::vector< */ std::cout << "Enter (D+1) nearest landmarks\n"; //std::cout << "Size of the tree is " << L.size() << std::endl; + start = clock(); for (int i = 0; i < nbP; i++) { //std::cout << "Entered witness number " << i << std::endl; @@ -416,7 +252,9 @@ int landmark_perturbation(Point_Vector &W, Point_Vector& landmarks, std::vector< } } //std::cout << "\n"; - + end = clock(); + std::cout << "Landmark choice for " << nbL << " landmarks took " + << (double)(end-start)/CLOCKS_PER_SEC << " s. \n"; std::string out_file = "wl_result"; write_wl(out_file,WL); @@ -424,14 +262,19 @@ int landmark_perturbation(Point_Vector &W, Point_Vector& landmarks, std::vector< std::cout << "Entered witness complex construction\n"; Witness_complex<> witnessComplex; witnessComplex.setNbL(nbL); + start = clock(); witnessComplex.witness_complex(WL); + // + end = clock(); + std::cout << "Howdy world! The process took " + << (double)(end-start)/CLOCKS_PER_SEC << " s. \n"; + //witnessComplex.witness_complex(WL); /* if (witnessComplex.is_witness_complex(WL)) std::cout << "!!YES. IT IS A WITNESS COMPLEX!!\n"; else std::cout << "??NO. IT IS NOT A WITNESS COMPLEX??\n"; */ - */ //******************** Making a set of bad link landmarks std::cout << "Entered bad links\n"; std::set< int > perturbL; @@ -575,8 +418,8 @@ int main (int argc, char * const argv[]) */ } int bl = nbL, curr_min = bl; - write_points("landmarks/initial_pointset",point_vector); - write_points("landmarks/initial_landmarks",L); + //write_points("landmarks/initial_pointset",point_vector); + //write_points("landmarks/initial_landmarks",L); for (int i = 0; bl > 0; i++) //for (int i = 0; i < 1; i++) @@ -585,7 +428,7 @@ int main (int argc, char * const argv[]) bl=landmark_perturbation(point_vector, L, chosen_landmarks); if (bl < curr_min) curr_min=bl; - write_points("landmarks/landmarks0",L); + //write_points("landmarks/landmarks0",L); } //end = clock(); |