major update for tin.h

demo.cpp

@@ -15,9 +15,19 @@ int main(int argc, char const *argv[])
 	}
 	infile.close();
 
+	std::vector<double> err_records;
 	std::vector<vertex2dc*> tin_vert;
 	std::vector<triangle*> tin_ele;
-	dem2tin(topo, 0, 1000, 0, 1000, 10, 10, tin_vert, tin_ele, 1.0);
+	dem2tin(topo, 0, 1000, 0, 1000, 10, 10, tin_vert, tin_ele, 1.0, &err_records);
+
+	// Write a log file
+	std::ofstream logfile("topo_TIN.log");
+	logfile << "# Insertion Maxi-Error\n";
+	for (int i = 0; i < err_records.size(); ++i)
+	{
+		logfile << i+1 << " " << err_records[i] << std::endl;
+	}
+	logfile.close();
 
 	// Write a Gmsh's .msh file
 	std::ofstream outfile("topo_TIN.msh");

tin.h

@@ -1,10 +1,10 @@
 /**
  * @defgroup   TIN
  *
- * @brief      Generation of a Triangular Irregular Network (TIN) from a dense DEM grid
+ * @brief      Generation of a Triangular Irregular Network (TIN) from a dense DEM grid.
  *
  * @author     Yi Zhang
- * @date       2021-09-15
+ * @date       2021-09-16
  */
 
 #ifndef _TIN_DELAUNAY_H
@@ -108,7 +108,7 @@ struct triangle
 			l2x = inx - vert[i]->x;
 			l2y = iny - vert[i]->y;
 
-			if ((l1x*l2y - l1y*l2x) < 0)
+			if ((l1x*l2y - l1y*l2x) < 0) // This condition includes points on the triangle's edge
 			{
 				return false;
 			}
@@ -126,6 +126,25 @@ struct triangle
 };
 // End triangle definition
 
+// Start DEM definition
+struct dem_point
+{
+	double x, y; // position of the DEM location
+	double elev; // elevation at the DEM location
+	triangle *host; // host triangle of the DEM location
+	std::vector<triangle*> circum_host; // triangles which circumcircles include the location
+
+	dem_point() : x(NAN), y(NAN), elev(NAN), host(nullptr) {}
+	dem_point(double inx, double iny, double inelev) {set(inx, iny, inelev);}
+	void set(double inx, double iny, double inelev)
+	{
+		x = inx; y = iny; elev = inelev; host = nullptr;
+		circum_host.clear();
+		return;
+	}
+};
+// End DEM definition
+
 /**
  * @brief      Generate the TIN from the DEM grid
  *
@@ -138,13 +157,16 @@ struct triangle
  * @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
+ * @param[in]  maxi_err     Threshold to quit the algorithm. The default is 1e-0
+ * @param[in]  err_records  If this pointer is not NULL, record maximal error values after each insertion of vertex.
  */
 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)
+	double dx, double dy, std::vector<vertex2dc*> &out_verts, std::vector<triangle*> &out_tris, 
+	double maxi_err = 1e-0, std::vector<double> *err_records = nullptr)
 {
 	if (!out_verts.empty()) out_verts.clear();
 	if (!out_tris.empty())  out_tris.clear();
+	if (err_records != nullptr && !err_records->empty()) err_records->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;
@@ -154,22 +176,37 @@ void dem2tin(const std::vector<double> &dem, double xmin, double xmax, double ym
 
 	if (dem.size() != xnum*ynum) return;
 
+	// Prepare the DEM points
+	std::vector<dem_point> dem_grid(xnum*ynum);
+	std::vector<dem_point>::iterator d_iter;
+	for (int i = 0; i < ynum; ++i)
+	{
+		for (int j = 0; j < xnum; ++j)
+		{
+			dem_grid[j + i*xnum].set(xmin + dx*j, ymin + dy*i, dem[j + i*xnum]);
+		}
+	}
+
 	vertex2dc *tmp_vert = nullptr;
 
-	tmp_vert = new vertex2dc(xmin, ymin, dem[0], out_verts.size()); // lower left corner
+	tmp_vert = new vertex2dc(xmin, ymin, dem_grid[0].elev, out_verts.size()); // lower left corner
 	out_verts.push_back(tmp_vert);
+	d_iter = dem_grid.begin(); dem_grid.erase(d_iter);
 
-	tmp_vert = new vertex2dc(xmax, ymin, dem[xnum-1], out_verts.size()); // lower right corner
+	tmp_vert = new vertex2dc(xmax, ymin, dem_grid[xnum-2].elev, out_verts.size()); // lower right corner. Note the first location is already erased
 	out_verts.push_back(tmp_vert);
+	d_iter = dem_grid.begin() + (xnum - 2); dem_grid.erase(d_iter);
 
-	tmp_vert = new vertex2dc(xmax, ymax, dem[xnum*ynum-1], out_verts.size()); // upper right corner
+	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
 	out_verts.push_back(tmp_vert);
+	d_iter = dem_grid.begin() + (xnum*ynum - 3); dem_grid.erase(d_iter);
 
-	tmp_vert = new vertex2dc(xmin, ymax, dem[xnum*(ynum-1)], out_verts.size()); // upper left corner
+	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
 	out_verts.push_back(tmp_vert);
+	d_iter = dem_grid.begin() + (xnum*(ynum-1) - 2); dem_grid.erase(d_iter);
 
 	triangle *tmp_tri = nullptr;
-	std::vector<triangle*> cnst_tri;
+	std::vector<triangle*> cnst_tri, new_tri;
 	std::vector<triangle*>::iterator t_iter;
 
 	if (!is_collinear(out_verts[0], out_verts[1], out_verts[2])) // Do not create triangle if the vertexes are collinear
@@ -184,12 +221,39 @@ void dem2tin(const std::vector<double> &dem, double xmin, double xmax, double ym
 		out_tris.push_back(tmp_tri);
 	}
 
+	// Find host triangle for all DEM locations
+	for (int i = 0; i < dem_grid.size(); ++i)
+	{
+		for (int t = 0; t < out_tris.size(); ++t)
+		{
+			if (out_tris[t]->bound_location(dem_grid[i].x, dem_grid[i].y))
+			{
+				dem_grid[i].host = out_tris[t];
+				break; // already found, no need to search more
+			}
+		}
+	}
+
+	// Find circum_host triangles for all DEM locations
+	double dist;
+	for (int i = 0; i < dem_grid.size(); ++i)
+	{
+		for (int t = 0; t < out_tris.size(); ++t)
+		{
+			dist = (out_tris[t]->cx - dem_grid[i].x) * (out_tris[t]->cx - dem_grid[i].x) 
+				+ (out_tris[t]->cy - dem_grid[i].y) * (out_tris[t]->cy - dem_grid[i].y);
+			if ((dist - out_tris[t]->cr) <= ZERO) // Points on the circumcircle are also included
+			{
+				dem_grid[i].circum_host.push_back(out_tris[t]);
+				// no beak here. There might be more than one triangle's circumcircle includes the DEM location
+			}
+		}
+	}
+
 	int now_maxi_id;
-	double now_x, now_y, now_err;
+	double now_err, now_maxi_err;
-	double now_maxi_err;
 
 	bool removed;
-	double dist;
 	edge tmp_edge;
 	std::vector<edge> cnst_edge;
 	std::vector<edge>::iterator e_iter;
@@ -197,47 +261,51 @@ void dem2tin(const std::vector<double> &dem, double xmin, double xmax, double ym
 	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)
+		for (int i = 0; i < dem_grid.size(); ++i)
 		{
-			now_x = (i%xnum)*dx + xmin;
+			now_err = fabs(dem_grid[i].host->interpolate(dem_grid[i].x, dem_grid[i].y) - dem_grid[i].elev);
-			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;
-				}
 		}
+
+		if (err_records != nullptr)
+		{
+			err_records->push_back(now_maxi_err);
 		}
 
 		// create a new vertex
-		now_x = (now_maxi_id%xnum)*dx + xmin;
+		tmp_vert = new vertex2dc(dem_grid[now_maxi_id].x, dem_grid[now_maxi_id].y, dem_grid[now_maxi_id].elev, out_verts.size());
-		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
+		// Move triangles which circumcircles include the new vertex 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 (int i = 0; i < dem_grid[now_maxi_id].circum_host.size(); ++i)
+		{
+			cnst_tri.push_back(dem_grid[now_maxi_id].circum_host[i]);
+		}
+
+		for (int i = 0; i < cnst_tri.size(); ++i)
+		{
 			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 (cnst_tri[i] == tmp_tri)
-			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);
+					break; // no need to search more
 				}
 				else t_iter++;
 			}
+		}
+
+		// clear host and circumcircle triangles for the used DEM location
+		dem_grid[now_maxi_id].host = nullptr;
+		dem_grid[now_maxi_id].circum_host.clear();
+		d_iter = dem_grid.begin() + now_maxi_id; dem_grid.erase(d_iter);
 
 		// loop to remove duplicate edges
 		cnst_edge.clear();
@@ -267,12 +335,59 @@ void dem2tin(const std::vector<double> &dem, double xmin, double xmax, double ym
 		}
 
 		// construct new triangles and add to out_tris
+		new_tri.clear();
 		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);
+				new_tri.push_back(tmp_tri);
+			}
+		}
+
+		// purge circumcircle triangles for all DEM data
+		for (int c = 0; c < cnst_tri.size(); ++c)
+		{
+			for (int i = 0; i < dem_grid.size(); ++i)
+			{
+				for (t_iter = dem_grid[i].circum_host.begin(); t_iter != dem_grid[i].circum_host.end(); )
+				{
+					if (cnst_tri[c] == *t_iter)
+					{
+						t_iter = dem_grid[i].circum_host.erase(t_iter);
+						break; // no need to search more
+					}
+					else t_iter++;
+				}
+			}
+		}
+
+		// loop all DEM data to update host and circumcircle triangles
+		for (int i = 0; i < dem_grid.size(); ++i)
+		{
+			for (int n = 0; n < new_tri.size(); ++n) // search in newly created triangles to find new host
+			{
+				if (new_tri[n]->bound_location(dem_grid[i].x, dem_grid[i].y))
+				{
+					dem_grid[i].host = new_tri[n];
+					break; // already found, no need to search more
+				}
+			}
+		}
+
+		// Find circum_host triangles for all DEM locations
+		for (int i = 0; i < dem_grid.size(); ++i)
+		{
+			for (int n = 0; n < new_tri.size(); ++n) // search in newly created triangles to find new circumcircle triangles
+			{
+				dist = (new_tri[n]->cx - dem_grid[i].x) * (new_tri[n]->cx - dem_grid[i].x) 
+					+ (new_tri[n]->cy - dem_grid[i].y) * (new_tri[n]->cy - dem_grid[i].y);
+				if ((dist - new_tri[n]->cr) <= ZERO) // Points on the circumcircle are also included
+				{
+					dem_grid[i].circum_host.push_back(new_tri[n]);
+					// no beak here. There might be more than one triangle's circumcircle includes the DEM location
+				}
 			}
 		}
 
@@ -282,6 +397,7 @@ void dem2tin(const std::vector<double> &dem, double xmin, double xmax, double ym
 			tmp_tri = cnst_tri[c];
 			delete tmp_tri; tmp_tri = nullptr;
 		}
+
 	} while (now_maxi_err >= maxi_err);
 
 	return;

topo_TIN.msh

@@ -2339,9 +2339,9 @@ $Nodes
 2334 850 360 40.4211
 2335 830 360 45.5722
 2336 340 630 112.757
-2337 300 190 15.6154
+2337 350 260 26.3352
-2338 350 260 26.3352
+2338 340 260 24.4764
-2339 340 260 24.4764
+2339 300 190 15.6154
 2340 540 1000 1.93313
 2341 480 1000 2.29036
 2342 440 920 15.8236
@@ -6944,20 +6944,20 @@ $Elements
 4590 2 0 2253 342 2336
 4591 2 0 336 2011 2336
 4592 2 0 2011 2253 2336
-4593 2 0 1175 61 2337
+4593 2 0 441 1735 2337
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+4595 2 0 1735 1641 2337
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+4597 2 0 2337 1641 2338
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+4598 2 0 2101 2103 2338
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+4599 2 0 2103 2337 2338
-4600 2 0 2103 441 2338
+4600 2 0 2266 2101 2338
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+4601 2 0 1175 61 2339
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+4602 2 0 1575 1175 2339
-4603 2 0 2338 1641 2339
+4603 2 0 2251 1575 2339
-4604 2 0 2101 2103 2339
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+4606 2 0 1749 2251 2339
 4607 2 0 1728 100 2340
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 4609 2 0 1986 2030 2341
@@ -9335,9 +9335,9 @@ $NodeData
 2334 40.4211
 2335 45.5722
 2336 112.757
-2337 15.6154
+2337 26.3352
-2338 26.3352
+2338 24.4764
-2339 24.4764
+2339 15.6154
 2340 1.93313
 2341 2.29036
 2342 15.8236