diff --git a/demo.cpp b/demo.cpp
index 9f3688f..b8418f1 100644
--- a/demo.cpp
+++ b/demo.cpp
@@ -1,8 +1,67 @@
 #include "tin.h"
 #include "iostream"
+#include "fstream"
+#include "iomanip"
 
 int main(int argc, char const *argv[])
 {
-	
+	// read dem grid
+	std::vector<double> topo(10201);
+
+	std::ifstream infile("topo.txt");
+	for (int i = 0; i < 10201; ++i)
+	{
+		infile >> topo[i];
+	}
+	infile.close();
+
+	std::vector<vertex2dc*> tin_vert;
+	std::vector<triangle*> tin_ele;
+	dem2tin(topo, 0, 1000, 0, 1000, 10, 10, tin_vert, tin_ele, 3.0);
+
+	// Write a Gmsh's .msh file
+	std::ofstream outfile("topo_TIN.msh");
+	outfile << "$MeshFormat" << std::endl << "2.2 0 8" << std::endl << "$EndMeshFormat "<<std::endl;
+	outfile << "$Nodes" << std::endl << tin_vert.size() << std::endl;
+	for (int i = 0; i < tin_vert.size(); i++)
+	{
+		outfile << tin_vert[i]->id + 1 << " " << std::setprecision(16) 
+			<< tin_vert[i]->x << " " << tin_vert[i]->y << " " << tin_vert[i]->elev << std::endl;
+	}
+	outfile<<"$EndNodes"<<std::endl;
+	outfile << "$Elements" << std::endl << tin_ele.size() <<std::endl;
+	for (int i = 0; i < tin_ele.size(); i++)
+	{
+		outfile << i + 1 << " 2 0";
+		for (int j = 0; j < 3; j++)
+		{
+			outfile << " " << tin_ele[i]->vert[j]->id + 1;
+		}
+		outfile << std::endl;
+	}
+	outfile << "$EndElements"<< std::endl;
+	outfile<<"$NodeData"<<std::endl;
+	outfile<<1<<std::endl
+		<<"\"Topography (m)\"" <<std::endl
+		<< 1 <<std::endl<< 0.0 <<std::endl
+		<< 3 <<std::endl<< 0<<std::endl
+		<< 1 <<std::endl<< tin_vert.size() <<std::endl;
+	for (int i = 0; i < tin_vert.size(); i++)
+	{
+		outfile << tin_vert[i]->id + 1 << " " << std::setprecision(16) << tin_vert[i]->elev << std::endl;
+	}
+	outfile << "$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
index 59bf523..a0c97d7 100644
--- a/tin.h
+++ b/tin.h
@@ -12,6 +12,8 @@
 #include "cmath"
 #include "vector"
 
+#include "iostream"
+
 #define ZERO 1e-5
 
 // Start vertex definition
@@ -19,12 +21,13 @@ 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), id(0) {}
-	vertex2dc(double inx, double iny, unsigned int inid = 0) {set(inx, iny, inid);}
-	void set(double inx, double iny, unsigned int inid = 0)
+	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; id = inid;
+		x = inx; y = iny; elev = inelev; id = inid;
 		return;
 	}
 };
@@ -86,81 +89,136 @@ struct triangle
 		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)
+	{
+		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)
+	{
+		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      2D Delaunay triangulation of some given points using the Bowyer-Watson algorithm.
+ * @brief      Generate the TIN from the DEM grid
  *
- * @param      in_verts  Input vertexes. Defined by the user.
- * @param      out_tris  Output triangles. Compute by the function.
+ * @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 triangulation(std::vector<vertex2dc> &in_verts, std::vector<triangle> &out_tris)
+void dem2tin(const std::vector<double> &dem, double xmin, double xmax, double ymin, double ymax, 
+	double dx, double dy, std::vector<vertex2dc*> &out_verts, std::vector<triangle*> &out_tris, double maxi_err = 1e-2)
 {
-	if (!out_tris.empty()) out_tris.clear();
-	if (in_verts.size() < 3) return;
+	if (!out_verts.empty()) out_verts.clear();
+	if (!out_tris.empty())  out_tris.clear();
 
-	// locate the surrounding box and initiate the staring two triangles
-	double xmin = in_verts[0].x, xmax = in_verts[0].x;
-	double ymin = in_verts[0].y, ymax = in_verts[0].y;
-	for (int i = 0; i < in_verts.size(); ++i)
-	{
-		xmin = std::min(xmin, in_verts[i].x);
-		xmax = std::max(xmax, in_verts[i].x);
-		ymin = std::min(ymin, in_verts[i].y);
-		ymax = std::max(ymax, in_verts[i].y);
-	}
+	if (xmin >= xmax || ymin >= ymax || (xmin + dx) > xmax || (ymin + dy) > ymax) return;
 
-	double midx = 0.5*(xmin + xmax);
-	double midy = 0.5*(ymin + ymax);
-	double maxi_s = std::max(xmax - xmin, ymax - ymin); // use an four times bigger rectangle to include all points
+	int xnum = round((xmax - xmin)/dx) + 1;
+	int ynum = round((ymax - ymin)/dy) + 1;
+
+	if (dem.size() != xnum*ynum) return;
 
 	vertex2dc *tmp_vert = nullptr;
-	std::vector<vertex2dc*> assit_vert;
 
-	tmp_vert = new vertex2dc(midx - maxi_s, midy - maxi_s); // lower left corner
-	assit_vert.push_back(tmp_vert);
+	tmp_vert = new vertex2dc(xmin, ymin, dem[0], out_verts.size()); // lower left corner
+	out_verts.push_back(tmp_vert);
 
-	tmp_vert = new vertex2dc(midx + maxi_s, midy - maxi_s); // lower right corner
-	assit_vert.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(midx + maxi_s, midy + maxi_s); // upper right corner
-	assit_vert.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(midx - maxi_s, midy + maxi_s); // upper left corner
-	assit_vert.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<triangle*>  exist_tri, cnst_tri;
+	std::vector<triangle*> cnst_tri;
 	std::vector<triangle*>::iterator t_iter;
 
-	tmp_tri = new triangle(assit_vert[0], assit_vert[1], assit_vert[2]); // order the vertex anti-clock wise
-	exist_tri.push_back(tmp_tri);
+	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);
 
-	tmp_tri = new triangle(assit_vert[0], assit_vert[2], assit_vert[3]); // order the vertex anti-clock wise
-	exist_tri.push_back(tmp_tri);
+	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;
 
-	// loop all input vertice
 	bool removed;
 	double dist;
 	edge tmp_edge;
 	std::vector<edge> cnst_edge;
 	std::vector<edge>::iterator e_iter;
-	for (int i = 0; i < in_verts.size(); ++i)
+
+	do // quit til the threshold is meet
 	{
-		// determine triangles that include the point and add the triangle to the cnst_tri and remove the triangle from exist_tri
-		// this is the part that could take a lot of time if we are working with a large amount of points. We will fix this later
+		// 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 the triangle 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 this later
 		cnst_tri.clear();
-		for (t_iter = exist_tri.begin(); t_iter != exist_tri.end(); )
+		for (t_iter = out_tris.begin(); t_iter != out_tris.end(); )
 		{
 			tmp_tri = *t_iter;
-
-			dist = (tmp_tri->cx - in_verts[i].x) * (tmp_tri->cx - in_verts[i].x) + 
-				(tmp_tri->cy - in_verts[i].y) * (tmp_tri->cy - in_verts[i].y);
-
+			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 = exist_tri.erase(t_iter);
+				t_iter = out_tris.erase(t_iter);
 				cnst_tri.push_back(tmp_tri);
 			}
 			else t_iter++;
@@ -193,11 +251,11 @@ void triangulation(std::vector<vertex2dc> &in_verts, std::vector<triangle> &out_
 			}
 		}
 
-		// construct new triangles and add to exist_tri
+		// construct new triangles and add to out_tris
 		for (int c = 0; c < cnst_edge.size(); ++c)
 		{
-			tmp_tri = new triangle(cnst_edge[c].vert[0], cnst_edge[c].vert[1], &in_verts[i]); // order the vertex anti-clock wise
-			exist_tri.push_back(tmp_tri);
+			tmp_tri = new triangle(cnst_edge[c].vert[0], cnst_edge[c].vert[1], out_verts.back()); // order the vertex anti-clock wise
+			out_tris.push_back(tmp_tri);
 		}
 
 		// destroy memories used by cnst_edge
@@ -206,36 +264,8 @@ void triangulation(std::vector<vertex2dc> &in_verts, std::vector<triangle> &out_
 			tmp_tri = cnst_tri[c];
 			delete tmp_tri; tmp_tri = nullptr;
 		}
-	}
+	} while (now_maxi_err >= maxi_err);
 
-	// remove any triangles has an assistant vertex from exist_tri
-	for (t_iter = exist_tri.begin(); t_iter != exist_tri.end(); )
-	{
-		tmp_tri = *t_iter;
-		if (tmp_tri->vert[0] == assit_vert[0] || tmp_tri->vert[0] == assit_vert[1] || tmp_tri->vert[0] == assit_vert[2] || tmp_tri->vert[0] == assit_vert[3] || 
-			tmp_tri->vert[1] == assit_vert[0] || tmp_tri->vert[1] == assit_vert[1] || tmp_tri->vert[1] == assit_vert[2] || tmp_tri->vert[1] == assit_vert[3] || 
-			tmp_tri->vert[2] == assit_vert[0] || tmp_tri->vert[2] == assit_vert[1] || tmp_tri->vert[2] == assit_vert[2] || tmp_tri->vert[2] == assit_vert[3])
-		{
-			// destroy the memories located and remove from the vector
-			t_iter = exist_tri.erase(t_iter);
-			delete tmp_tri; tmp_tri = nullptr;
-		}
-		else t_iter++;
-	}
-
-	// copy exist_tri to out_tris and destroy memories located
-	out_tris.resize(exist_tri.size());
-	for (int i = 0; i < exist_tri.size(); ++i)
-	{
-		out_tris[i].set(exist_tri[i]->vert[0], exist_tri[i]->vert[1], exist_tri[i]->vert[2]);
-		delete exist_tri[i]; exist_tri[i] = nullptr;
-	}
-
-	// destroy memories located for assit_vert
-	for (int i = 0; i < 4; ++i)
-	{
-		delete assit_vert[i]; assit_vert[i] = nullptr;
-	}
 	return;
 }
 
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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