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
+
+
+
+#### 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
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