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Diffstat (limited to 'src/Witness_complex/example/protected_sets/protected_sets_paper.h')
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diff --git a/src/Witness_complex/example/protected_sets/protected_sets_paper.h b/src/Witness_complex/example/protected_sets/protected_sets_paper.h deleted file mode 100644 index 61fcc75b..00000000 --- a/src/Witness_complex/example/protected_sets/protected_sets_paper.h +++ /dev/null @@ -1,917 +0,0 @@ -#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 |