From d28c2e867f007309215aadbab570a9fa0beac191 Mon Sep 17 00:00:00 2001 From: Yi Zhang Date: Thu, 16 Sep 2021 11:17:16 +0800 Subject: [PATCH] initial upload --- .gitignore | 2 + README.md | 30 + demo.cpp | 67 + tin.h | 290 ++ topo.txt | 10201 +++++++++++++++++++++++++++++++++++++++++++++++++ topo_TIN.msh | 9348 ++++++++++++++++++++++++++++++++++++++++++++ topo_TIN.png | Bin 0 -> 626554 bytes 7 files changed, 19938 insertions(+) create mode 100644 README.md create mode 100644 demo.cpp create mode 100644 tin.h create mode 100644 topo.txt create mode 100644 topo_TIN.msh create mode 100644 topo_TIN.png diff --git a/.gitignore b/.gitignore index 259148f..6c3feba 100644 --- a/.gitignore +++ b/.gitignore @@ -30,3 +30,5 @@ *.exe *.out *.app + +.DS_Store \ No newline at end of file diff --git a/README.md b/README.md new file mode 100644 index 0000000..f369b18 --- /dev/null +++ b/README.md @@ -0,0 +1,30 @@ +### Generation of a Triangular Irregular Network (TIN) from a dense DEM grid + +topo_TIN + +#### Compile + +```shell +g++ demo.cpp +``` + +#### Run demo + +```shell +./a.out +``` + +#### Visualization + +##### macOS + +```shell +open -a Gmsh topo_TIN.msh +``` + +##### Linux/Unix + +```shell +gmsh topo_TIN.msh +``` + diff --git a/demo.cpp b/demo.cpp new file mode 100644 index 0000000..f52580f --- /dev/null +++ b/demo.cpp @@ -0,0 +1,67 @@ +#include "tin.h" +#include "iostream" +#include "fstream" +#include "iomanip" + +int main(int argc, char const *argv[]) +{ + // read dem grid + std::vector topo(10201); + + std::ifstream infile("topo.txt"); + for (int i = 0; i < 10201; ++i) + { + infile >> topo[i]; + } + infile.close(); + + std::vector tin_vert; + std::vector tin_ele; + dem2tin(topo, 0, 1000, 0, 1000, 10, 10, tin_vert, tin_ele, 1.0); + + // Write a Gmsh's .msh file + std::ofstream outfile("topo_TIN.msh"); + outfile << "$MeshFormat" << std::endl << "2.2 0 8" << std::endl << "$EndMeshFormat "<id + 1 << " " << std::setprecision(16) + << tin_vert[i]->x << " " << tin_vert[i]->y << " " << tin_vert[i]->elev << std::endl; + } + outfile<<"$EndNodes"<vert[j]->id + 1; + } + outfile << std::endl; + } + outfile << "$EndElements"<< std::endl; + outfile<<"$NodeData"<id + 1 << " " << std::setprecision(16) << tin_vert[i]->elev << std::endl; + } + outfile << "$EndNodeData" << std::endl; + outfile.close(); + + // Destroy memories allocated by the dem2tin function + for (int i = 0; i < tin_vert.size(); ++i) + { + delete tin_vert[i]; + } + + for (int i = 0; i < tin_ele.size(); ++i) + { + delete tin_ele[i]; + } + return 0; +} \ No newline at end of file diff --git a/tin.h b/tin.h new file mode 100644 index 0000000..ed0dfef --- /dev/null +++ b/tin.h @@ -0,0 +1,290 @@ +/** + * @defgroup TIN + * + * @brief Generation of a Triangular Irregular Network (TIN) from a dense DEM grid + * + * @author Yi Zhang + * @date 2021-09-15 + */ + +#ifndef _TIN_DELAUNAY_H +#define _TIN_DELAUNAY_H +#include "cmath" +#include "vector" + +#define ZERO 1e-5 + +// Start vertex definition +struct vertex2dc +{ + unsigned int id; // index of the vertex + double x, y; // position of the vertex + double elev; // elevation at the vertex + + vertex2dc() : x(NAN), y(NAN), elev(NAN), id(0) {} + vertex2dc(double inx, double iny, double inelev, unsigned int inid = 0) {set(inx, iny, inelev, inid);} + void set(double inx, double iny, double inelev, unsigned int inid = 0) + { + x = inx; y = iny; elev = inelev; id = inid; + return; + } +}; + +bool operator ==(const vertex2dc &a, const vertex2dc &b) // overload the == operator for vertex2dc type +{ + if(fabs(a.x - b.x) <= ZERO && fabs(a.y - b.y) <= ZERO) + { + return true; + } + return false; +} + +bool is_collinear(vertex2dc *a_ptr, vertex2dc *b_ptr, vertex2dc *c_ptr) // Test if the three points are on the same line +{ + // ｜(y3−y1)(x2−x1)−(y2−y1)(x3−x1)｜ + 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) + { + return true; + } + return false; +} +// End vertex definition + +// Start edge definition +struct edge +{ + vertex2dc *vert[2]; // vertex of the edge + + edge() {vert[0] = vert[1] = nullptr;} + edge(vertex2dc *v0ptr, vertex2dc *v1ptr) {set(v0ptr, v1ptr);} + void set(vertex2dc *v0ptr, vertex2dc *v1ptr) + { + vert[0] = v0ptr; vert[1] = v1ptr; + return; + } +}; + +bool operator ==(const edge &a, const edge &b) // overload the == operator for edge type +{ + if((a.vert[0] == b.vert[0] && a.vert[1] == b.vert[1]) || + (a.vert[0] == b.vert[1] && a.vert[1] == b.vert[0])) + { + return true; + } + return false; +} +// End edge definition + +// Start triangle definition +struct triangle +{ + vertex2dc *vert[3]; // vertex of the triangle + double cx, cy; // center of the triangle's circumcircle + double cr; // radius of the circumcircle + + triangle() {vert[0] = vert[1] = vert[2] = nullptr;} + triangle(vertex2dc *v0ptr, vertex2dc *v1ptr, vertex2dc *v2ptr) {set(v0ptr, v1ptr, v2ptr);} + void set(vertex2dc *v0ptr, vertex2dc *v1ptr, vertex2dc *v2ptr) + { + vert[0] = v0ptr; vert[1] = v1ptr; vert[2] = v2ptr; + + 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)); + 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; + 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; + + cx = ((vert[2]->y - vert[0]->y) * m + (vert[0]->y - vert[1]->y) * u) * s; + cy = ((vert[0]->x - vert[2]->x) * m + (vert[1]->x - vert[0]->x) * u) * s; + cr = (vert[0]->x - cx) * (vert[0]->x - cx) + (vert[0]->y - cy) * (vert[0]->y - cy); // not need to sqrt() here + return; + } + + bool bound_location(double inx, double iny) // Test if the location is inside the triangle + { + double l1x, l1y, l2x, l2y; + for (int i = 0; i < 3; i++) + { + l1x = vert[(i+1)%3]->x - vert[i]->x; + l1y = vert[(i+1)%3]->y - vert[i]->y; + l2x = inx - vert[i]->x; + l2y = iny - vert[i]->y; + + if ((l1x*l2y - l1y*l2x) < 0) + { + return false; + } + } + return true; + } + + double interpolate(double inx, double iny) // Interpolate the elevation of the given location inside the triangle + { + double a1 = 0.5 * ((vert[1]->x - inx)*(vert[2]->y - iny) - (vert[1]->y - iny)*(vert[2]->x - inx)); + double a2 = 0.5 * ((vert[2]->x - inx)*(vert[0]->y - iny) - (vert[2]->y - iny)*(vert[0]->x - inx)); + double a3 = 0.5 * ((vert[0]->x - inx)*(vert[1]->y - iny) - (vert[0]->y - iny)*(vert[1]->x - inx)); + return (a1*vert[0]->elev + a2*vert[1]->elev + a3*vert[2]->elev)/(a1 + a2 + a3); + } +}; +// End triangle definition + +/** + * @brief Generate the TIN from the DEM grid + * + * @param[in] dem Input DEM grid (Ordered from lower left corner to the upper right corner) + * @param[in] xmin The minimal coordinate of the DEM grid on the x-axis + * @param[in] xmax The maximal coordinate of the DEM grid on the x-axis + * @param[in] ymin The minimal coordinate of the DEM grid on the y-axis + * @param[in] ymax The maximal coordinate of the DEM grid on the y-axis + * @param[in] dx Data spacing of the DEM grid on the x-axis + * @param[in] dy Data spacing of the DEM grid on the y-axis + * @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 + * @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 + * @param[in] maxi_err Threshold to quit the algorithm. The default is 1e-2 + */ +void dem2tin(const std::vector &dem, double xmin, double xmax, double ymin, double ymax, + double dx, double dy, std::vector &out_verts, std::vector &out_tris, double maxi_err = 1e-2) +{ + if (!out_verts.empty()) out_verts.clear(); + if (!out_tris.empty()) out_tris.clear(); + + if (dx <= 0.0 || dy <= 0.0 || maxi_err <= 0.0) return; + if (xmin >= xmax || ymin >= ymax || (xmin + dx) > xmax || (ymin + dy) > ymax) return; + + int xnum = round((xmax - xmin)/dx) + 1; + int ynum = round((ymax - ymin)/dy) + 1; + + if (dem.size() != xnum*ynum) return; + + vertex2dc *tmp_vert = nullptr; + + tmp_vert = new vertex2dc(xmin, ymin, dem[0], out_verts.size()); // lower left corner + out_verts.push_back(tmp_vert); + + tmp_vert = new vertex2dc(xmax, ymin, dem[xnum-1], out_verts.size()); // lower right corner + out_verts.push_back(tmp_vert); + + tmp_vert = new vertex2dc(xmax, ymax, dem[xnum*ynum-1], out_verts.size()); // upper right corner + out_verts.push_back(tmp_vert); + + tmp_vert = new vertex2dc(xmin, ymax, dem[xnum*(ynum-1)], out_verts.size()); // upper left corner + out_verts.push_back(tmp_vert); + + triangle *tmp_tri = nullptr; + std::vector cnst_tri; + std::vector::iterator t_iter; + + if (!is_collinear(out_verts[0], out_verts[1], out_verts[2])) // Do not create triangle if the vertexes are collinear + { + tmp_tri = new triangle(out_verts[0], out_verts[1], out_verts[2]); // order the vertex anti-clock wise + out_tris.push_back(tmp_tri); + } + + if (!is_collinear(out_verts[0], out_verts[2], out_verts[3])) + { + tmp_tri = new triangle(out_verts[0], out_verts[2], out_verts[3]); // order the vertex anti-clock wise + out_tris.push_back(tmp_tri); + } + + int now_maxi_id; + double now_x, now_y, now_err; + double now_maxi_err; + + bool removed; + double dist; + edge tmp_edge; + std::vector cnst_edge; + std::vector::iterator e_iter; + + do // quit til the threshold is meet + { + // loop all DEM data to find the location with maximal error + // this part is very time consuming. We will fix it later + now_maxi_err = -1.0; + for (int i = 0; i < xnum*ynum; ++i) + { + now_x = (i%xnum)*dx + xmin; + now_y = (i/xnum)*dy + ymin; + for (int e = 0; e < out_tris.size(); ++e) + { + if (out_tris[e]->bound_location(now_x, now_y)) + { + now_err = fabs(out_tris[e]->interpolate(now_x, now_y) - dem[i]); + if (now_err > now_maxi_err) + { + now_maxi_err = now_err; + now_maxi_id = i; + } + break; + } + } + } + + // create a new vertex + now_x = (now_maxi_id%xnum)*dx + xmin; + now_y = (now_maxi_id/xnum)*dy + ymin; + tmp_vert = new vertex2dc(now_x, now_y, dem[now_maxi_id], out_verts.size()); + out_verts.push_back(tmp_vert); + + // determine triangles that include the point and add the triangle to the cnst_tri and remove it from out_tris + // this is also a part that could take a lot of time if we are working with a large amount of points. We will fix it later + cnst_tri.clear(); + for (t_iter = out_tris.begin(); t_iter != out_tris.end(); ) + { + tmp_tri = *t_iter; + dist = (tmp_tri->cx - now_x) * (tmp_tri->cx - now_x) + (tmp_tri->cy - now_y) * (tmp_tri->cy - now_y); + if ((dist - tmp_tri->cr) <= ZERO) // Points on the circumcircle are also included + { + t_iter = out_tris.erase(t_iter); + cnst_tri.push_back(tmp_tri); + } + else t_iter++; + } + + // loop to remove duplicate edges + cnst_edge.clear(); + for (int c = 0; c < cnst_tri.size(); ++c) + { + for (int e = 0; e < 3; ++e) + { + tmp_edge.set(cnst_tri[c]->vert[e], cnst_tri[c]->vert[(e+1)%3]); + + removed = false; + for (e_iter = cnst_edge.begin(); e_iter != cnst_edge.end(); ) + { + if (tmp_edge == *e_iter) // duplicate edge, remove from cnst_edge + { + e_iter = cnst_edge.erase(e_iter); + removed = true; + break; // no need to search more + } + else e_iter++; + } + + if (!removed) // not a duplicate edge, add to the cnst_edge + { + cnst_edge.push_back(tmp_edge); + } + } + } + + // construct new triangles and add to out_tris + for (int c = 0; c < cnst_edge.size(); ++c) + { + if (!is_collinear(cnst_edge[c].vert[0], cnst_edge[c].vert[1], tmp_vert)) // Do not create triangle if the vertexes are collinear + { + tmp_tri = new triangle(cnst_edge[c].vert[0], cnst_edge[c].vert[1], tmp_vert); // order the vertex anti-clock wise + out_tris.push_back(tmp_tri); + } + } + + // destroy memories used by cnst_edge + for (int c = 0; c < cnst_tri.size(); ++c) + { + tmp_tri = cnst_tri[c]; + delete tmp_tri; tmp_tri = nullptr; + } + } while (now_maxi_err >= maxi_err); + + return; +} + +#endif // _TIN_DELAUNAY_H \ No newline at end of file diff --git a/topo.txt b/topo.txt new file mode 100644 index 0000000..1cd854b --- /dev/null +++ b/topo.txt @@ -0,0 +1,10201 @@ +0 +1.10988 +2.04267 +2.83746 +3.40047 +3.87157 +4.4515 +5.03463 +5.77806 +6.53316 +7.232 +8.01455 +8.89201 +9.25172 +10.0051 +10.3978 +11.119 +10.8091 +10.7428 +10.6482 +10.6109 +10.2784 +10.0918 +10.2771 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