435 lines
14 KiB
C++
435 lines
14 KiB
C++
/**
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* @defgroup TIN
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*
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* @brief Generation of a Triangular Irregular Network (TIN) from a dense DEM grid.
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*
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* @author Yi Zhang
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* @date 2021-09-16
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*/
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#ifndef _TIN_DELAUNAY_H
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#define _TIN_DELAUNAY_H
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#include "cmath"
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#include "vector"
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#include "algorithm"
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#define ZERO 1e-5
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// Start vertex definition
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struct vertex2dc
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{
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unsigned int id; // index of the vertex
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double x, y; // position of the vertex
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double elev; // elevation at the vertex
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vertex2dc() : x(NAN), y(NAN), elev(NAN), id(0) {}
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vertex2dc(double inx, double iny, double inelev, unsigned int inid) {set(inx, iny, inelev, inid);}
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void set(double inx, double iny, double inelev, unsigned int inid)
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{
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x = inx; y = iny; elev = inelev; id = inid;
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return;
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}
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};
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bool operator ==(const vertex2dc &a, const vertex2dc &b) // overload the == operator for vertex2dc type
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{
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if(fabs(a.x - b.x) <= ZERO && fabs(a.y - b.y) <= ZERO)
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{
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return true;
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}
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return false;
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}
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bool is_collinear(vertex2dc *a_ptr, vertex2dc *b_ptr, vertex2dc *c_ptr) // Test if the three points are on the same line
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{
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// ｜(y3−y1)(x2−x1)−(y2−y1)(x3−x1)｜
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if (fabs((c_ptr->y - a_ptr->y)*(b_ptr->x - a_ptr->x) - (b_ptr->y - a_ptr->y)*(c_ptr->x - a_ptr->x)) <= ZERO)
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{
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return true;
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}
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return false;
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}
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// End vertex definition
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// Start edge definition
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struct edge
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{
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vertex2dc *vert[2]; // vertex of the edge
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edge() {vert[0] = vert[1] = nullptr;}
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edge(vertex2dc *v0ptr, vertex2dc *v1ptr) {set(v0ptr, v1ptr);}
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void set(vertex2dc *v0ptr, vertex2dc *v1ptr)
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{
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vert[0] = v0ptr; vert[1] = v1ptr;
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return;
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}
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};
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bool operator ==(const edge &a, const edge &b) // overload the == operator for edge type
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{
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if((a.vert[0] == b.vert[0] && a.vert[1] == b.vert[1]) ||
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(a.vert[0] == b.vert[1] && a.vert[1] == b.vert[0]))
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{
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return true;
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}
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return false;
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}
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// End edge definition
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// Start triangle definition
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struct triangle
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{
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vertex2dc *vert[3]; // vertex of the triangle
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double cx, cy; // center of the triangle's circumcircle
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double cr; // radius of the circumcircle
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triangle() {vert[0] = vert[1] = vert[2] = nullptr;}
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triangle(vertex2dc *v0ptr, vertex2dc *v1ptr, vertex2dc *v2ptr) {set(v0ptr, v1ptr, v2ptr);}
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void set(vertex2dc *v0ptr, vertex2dc *v1ptr, vertex2dc *v2ptr)
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{
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vert[0] = v0ptr; vert[1] = v1ptr; vert[2] = v2ptr;
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double s = 0.5 / ((vert[1]->x - vert[0]->x) * (vert[2]->y - vert[0]->y) - (vert[1]->y - vert[0]->y) * (vert[2]->x - vert[0]->x));
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double m = vert[1]->x * vert[1]->x - vert[0]->x * vert[0]->x + vert[1]->y * vert[1]->y - vert[0]->y * vert[0]->y;
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double u = vert[2]->x * vert[2]->x - vert[0]->x * vert[0]->x + vert[2]->y * vert[2]->y - vert[0]->y * vert[0]->y;
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cx = ((vert[2]->y - vert[0]->y) * m + (vert[0]->y - vert[1]->y) * u) * s;
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cy = ((vert[0]->x - vert[2]->x) * m + (vert[1]->x - vert[0]->x) * u) * s;
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cr = (vert[0]->x - cx) * (vert[0]->x - cx) + (vert[0]->y - cy) * (vert[0]->y - cy); // not need to sqrt() here
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return;
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}
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bool bound_location(double inx, double iny) // Test if the location is inside the triangle
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{
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double l1x, l1y, l2x, l2y;
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for (int i = 0; i < 3; i++)
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{
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l1x = vert[(i+1)%3]->x - vert[i]->x;
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l1y = vert[(i+1)%3]->y - vert[i]->y;
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l2x = inx - vert[i]->x;
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l2y = iny - vert[i]->y;
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if ((l1x*l2y - l1y*l2x) < 0) // This condition includes points on the triangle's edge
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{
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return false;
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}
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}
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return true;
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}
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double interpolate(double inx, double iny) // Interpolate the elevation of the given location inside the triangle
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{
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double a1 = 0.5 * ((vert[1]->x - inx)*(vert[2]->y - iny) - (vert[1]->y - iny)*(vert[2]->x - inx));
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double a2 = 0.5 * ((vert[2]->x - inx)*(vert[0]->y - iny) - (vert[2]->y - iny)*(vert[0]->x - inx));
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double a3 = 0.5 * ((vert[0]->x - inx)*(vert[1]->y - iny) - (vert[0]->y - iny)*(vert[1]->x - inx));
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return (a1*vert[0]->elev + a2*vert[1]->elev + a3*vert[2]->elev)/(a1 + a2 + a3);
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}
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};
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// End triangle definition
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// Start DEM definition
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struct dem_point
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{
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double x, y; // position of the DEM location
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double elev; // elevation at the DEM location
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double err; // error of the TIN with respect to the elevation
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triangle *host; // host triangle of the DEM location
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std::vector<triangle*> circum_host; // triangles which circumcircles include the location
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dem_point() : x(NAN), y(NAN), elev(NAN), host(nullptr) {}
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dem_point(double inx, double iny, double inelev) {set(inx, iny, inelev);}
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void set(double inx, double iny, double inelev)
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{
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x = inx; y = iny; elev = inelev; host = nullptr;
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return;
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}
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};
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bool compare_dem_point(dem_point *a, dem_point *b)
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{
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if (a->err > b->err) return true;
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return false;
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}
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// End DEM definition
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/**
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* @brief Generate the TIN from the DEM grid
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*
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* @param[in] dem Input DEM grid (Ordered from lower left corner to the upper right corner)
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* @param[in] xmin The minimal coordinate of the DEM grid on the x-axis
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* @param[in] xmax The maximal coordinate of the DEM grid on the x-axis
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* @param[in] ymin The minimal coordinate of the DEM grid on the y-axis
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* @param[in] ymax The maximal coordinate of the DEM grid on the y-axis
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* @param[in] dx Data spacing of the DEM grid on the x-axis
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* @param[in] dy Data spacing of the DEM grid on the y-axis
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* @param out_verts The output vector of vertex's pointers. The user need to destroy the memories allocated by the function before destroy the vector
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* @param out_tris The output vector of triangle's pointers. The user need to destroy the memories allocated by the function before destroy the vector
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* @param[in] maxi_err Threshold to quit the algorithm. The default is 1e-0
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* @param[in] err_records If this pointer is not NULL, record maximal error values after each insertion of vertex.
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*/
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void dem2tin(const std::vector<double> &dem, double xmin, double xmax, double ymin, double ymax,
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double dx, double dy, std::vector<vertex2dc*> &out_verts, std::vector<triangle*> &out_tris,
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double maxi_err = 1e-0, std::vector<double> *err_records = nullptr)
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{
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if (!out_verts.empty()) out_verts.clear();
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if (!out_tris.empty()) out_tris.clear();
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if (err_records != nullptr && !err_records->empty()) err_records->clear();
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if (dx <= 0.0 || dy <= 0.0 || maxi_err <= 0.0) return;
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if (xmin >= xmax || ymin >= ymax || (xmin + dx) > xmax || (ymin + dy) > ymax) return;
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int xnum = round((xmax - xmin)/dx) + 1;
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int ynum = round((ymax - ymin)/dy) + 1;
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if (dem.size() != xnum*ynum) return;
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// Prepare the DEM points
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dem_point *tmp_dem = nullptr;;
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std::vector<dem_point*> dem_grid(xnum*ynum);
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std::vector<dem_point*>::iterator d_iter;
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for (int i = 0; i < ynum; ++i)
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{
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for (int j = 0; j < xnum; ++j)
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{
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dem_grid[j + i*xnum] = new dem_point(xmin + dx*j, ymin + dy*i, dem[j + i*xnum]);
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}
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}
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vertex2dc *tmp_vert = nullptr;
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tmp_vert = new vertex2dc(xmin, ymin, dem_grid[0]->elev, out_verts.size()); // lower left corner
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out_verts.push_back(tmp_vert);
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d_iter = dem_grid.begin();
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tmp_dem = *d_iter; delete tmp_dem;
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dem_grid.erase(d_iter);
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tmp_vert = new vertex2dc(xmax, ymin, dem_grid[xnum-2]->elev, out_verts.size()); // lower right corner. Note the first location is already erased
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out_verts.push_back(tmp_vert);
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d_iter = dem_grid.begin() + (xnum - 2);
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tmp_dem = *d_iter; delete tmp_dem;
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dem_grid.erase(d_iter);
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tmp_vert = new vertex2dc(xmax, ymax, dem_grid[xnum*ynum-3]->elev, out_verts.size()); // upper right corner. Note the first two locations are already erased
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out_verts.push_back(tmp_vert);
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d_iter = dem_grid.begin() + (xnum*ynum - 3);
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tmp_dem = *d_iter; delete tmp_dem;
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dem_grid.erase(d_iter);
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tmp_vert = new vertex2dc(xmin, ymax, dem_grid[xnum*(ynum-1) - 2]->elev, out_verts.size()); // upper left corner. Note the first two locations are already erased
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out_verts.push_back(tmp_vert);
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d_iter = dem_grid.begin() + (xnum*(ynum-1) - 2);
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tmp_dem = *d_iter; delete tmp_dem;
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dem_grid.erase(d_iter);
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triangle *tmp_tri = nullptr;
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std::vector<triangle*> cnst_tri, new_tri;
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std::vector<triangle*>::iterator t_iter;
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if (!is_collinear(out_verts[0], out_verts[1], out_verts[2])) // Do not create triangle if the vertexes are collinear
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{
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tmp_tri = new triangle(out_verts[0], out_verts[1], out_verts[2]); // order the vertex anti-clock wise
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out_tris.push_back(tmp_tri);
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}
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if (!is_collinear(out_verts[0], out_verts[2], out_verts[3]))
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{
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tmp_tri = new triangle(out_verts[0], out_verts[2], out_verts[3]); // order the vertex anti-clock wise
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out_tris.push_back(tmp_tri);
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}
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// Find host triangle for all DEM locations
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for (int i = 0; i < dem_grid.size(); ++i)
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{
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for (int t = 0; t < out_tris.size(); ++t)
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{
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if (out_tris[t]->bound_location(dem_grid[i]->x, dem_grid[i]->y))
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{
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dem_grid[i]->host = out_tris[t];
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break; // already found, no need to search more
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}
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}
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}
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// Find circum_host triangles for all DEM locations
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double dist;
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for (int i = 0; i < dem_grid.size(); ++i)
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{
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for (int t = 0; t < out_tris.size(); ++t)
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{
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dist = (out_tris[t]->cx - dem_grid[i]->x) * (out_tris[t]->cx - dem_grid[i]->x)
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+ (out_tris[t]->cy - dem_grid[i]->y) * (out_tris[t]->cy - dem_grid[i]->y);
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if ((dist - out_tris[t]->cr) <= ZERO) // Points on the circumcircle are also included
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{
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dem_grid[i]->circum_host.push_back(out_tris[t]);
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// no beak here. There might be more than one triangle's circumcircle includes the DEM location
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}
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}
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}
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// loop all DEM data to find the location with maximal error
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for (int i = 0; i < dem_grid.size(); ++i)
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{
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dem_grid[i]->err = fabs(dem_grid[i]->host->interpolate(dem_grid[i]->x, dem_grid[i]->y) - dem_grid[i]->elev);
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}
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// Sort dem_grid in the desceding order with respect to the error
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std::sort(dem_grid.begin(), dem_grid.end(), compare_dem_point);
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bool removed;
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edge tmp_edge;
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std::vector<edge> cnst_edge;
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std::vector<edge>::iterator e_iter;
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while (dem_grid[0]->err >= maxi_err) // quit til the threshold is meet
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{
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if (err_records != nullptr)
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{
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err_records->push_back(dem_grid[0]->err);
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}
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// create a new vertex
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tmp_vert = new vertex2dc(dem_grid[0]->x, dem_grid[0]->y, dem_grid[0]->elev, out_verts.size());
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out_verts.push_back(tmp_vert);
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// Move triangles which circumcircles include the new vertex to the cnst_tri and remove it from out_tris
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cnst_tri.clear();
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for (int i = 0; i < dem_grid[0]->circum_host.size(); ++i)
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{
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cnst_tri.push_back(dem_grid[0]->circum_host[i]);
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}
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for (int i = 0; i < cnst_tri.size(); ++i)
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{
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for (t_iter = out_tris.begin(); t_iter != out_tris.end(); )
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{
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tmp_tri = *t_iter;
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if (cnst_tri[i] == tmp_tri)
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{
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t_iter = out_tris.erase(t_iter);
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break; // no need to search more
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}
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else t_iter++;
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}
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}
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// clear host and circumcircle triangles for the used DEM location
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dem_grid[0]->circum_host.clear();
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d_iter = dem_grid.begin();
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tmp_dem = *d_iter; delete tmp_dem;
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dem_grid.erase(d_iter);
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// loop to remove duplicate edges
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cnst_edge.clear();
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for (int c = 0; c < cnst_tri.size(); ++c)
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{
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for (int e = 0; e < 3; ++e)
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{
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tmp_edge.set(cnst_tri[c]->vert[e], cnst_tri[c]->vert[(e+1)%3]);
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removed = false;
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for (e_iter = cnst_edge.begin(); e_iter != cnst_edge.end(); )
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{
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if (tmp_edge == *e_iter) // duplicate edge, remove from cnst_edge
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{
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e_iter = cnst_edge.erase(e_iter);
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removed = true;
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break; // no need to search more
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}
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else e_iter++;
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}
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if (!removed) // not a duplicate edge, add to the cnst_edge
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{
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cnst_edge.push_back(tmp_edge);
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}
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}
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}
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// construct new triangles and add to out_tris
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new_tri.clear();
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for (int c = 0; c < cnst_edge.size(); ++c)
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{
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if (!is_collinear(cnst_edge[c].vert[0], cnst_edge[c].vert[1], tmp_vert)) // Do not create triangle if the vertexes are collinear
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{
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tmp_tri = new triangle(cnst_edge[c].vert[0], cnst_edge[c].vert[1], tmp_vert); // order the vertex anti-clock wise
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out_tris.push_back(tmp_tri);
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new_tri.push_back(tmp_tri);
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}
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}
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// purge circumcircle triangles for all DEM data
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for (int c = 0; c < cnst_tri.size(); ++c)
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{
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for (int i = 0; i < dem_grid.size(); ++i)
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{
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for (t_iter = dem_grid[i]->circum_host.begin(); t_iter != dem_grid[i]->circum_host.end(); )
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{
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if (cnst_tri[c] == *t_iter)
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{
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t_iter = dem_grid[i]->circum_host.erase(t_iter);
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break; // no need to search more
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}
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else t_iter++;
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}
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}
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}
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// loop all DEM data to update host and circumcircle triangles
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for (int i = 0; i < dem_grid.size(); ++i)
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{
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for (int n = 0; n < new_tri.size(); ++n) // search in newly created triangles to find new host
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{
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if (new_tri[n]->bound_location(dem_grid[i]->x, dem_grid[i]->y))
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{
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dem_grid[i]->host = new_tri[n];
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dem_grid[i]->err = fabs(new_tri[n]->interpolate(dem_grid[i]->x, dem_grid[i]->y) - dem_grid[i]->elev);
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break; // already found, no need to search more
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}
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}
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}
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// Find circum_host triangles for all DEM locations
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for (int i = 0; i < dem_grid.size(); ++i)
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{
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for (int n = 0; n < new_tri.size(); ++n) // search in newly created triangles to find new circumcircle triangles
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{
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dist = (new_tri[n]->cx - dem_grid[i]->x) * (new_tri[n]->cx - dem_grid[i]->x)
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+ (new_tri[n]->cy - dem_grid[i]->y) * (new_tri[n]->cy - dem_grid[i]->y);
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if ((dist - new_tri[n]->cr) <= ZERO) // Points on the circumcircle are also included
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{
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dem_grid[i]->circum_host.push_back(new_tri[n]);
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// no beak here. There might be more than one triangle's circumcircle includes the DEM location
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}
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}
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}
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// destroy memories used by cnst_edge
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for (int c = 0; c < cnst_tri.size(); ++c)
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{
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tmp_tri = cnst_tri[c];
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delete tmp_tri; tmp_tri = nullptr;
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}
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// Sort dem_grid in the desceding order with respect to the error
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std::sort(dem_grid.begin(), dem_grid.end(), compare_dem_point);
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}
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if (err_records != nullptr)
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{
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err_records->push_back(dem_grid[0]->err);
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}
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// destroy remaining DEM data
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for (int i = 0; i < dem_grid.size(); ++i)
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{
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tmp_dem = dem_grid[i];
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delete tmp_dem; tmp_dem = nullptr;
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}
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return;
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}
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#endif // _TIN_DELAUNAY_H
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