libtin/tin_backup.h

/**
 * @defgroup   TIN
 *
 * @brief      Generation of a Triangular Irregular Network (TIN) from a dense DEM grid.
 *
 * @author     Yi Zhang
 * @date       2021-09-16
 */

#ifndef _TIN_DELAUNAY_H
#define _TIN_DELAUNAY_H
#include "cmath"
#include "vector"
#include "algorithm"

#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) {set(inx, iny, inelev, inid);}
	void set(double inx, double iny, double inelev, unsigned int inid)
	{
		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 dem_point;

struct triangle
{
	vertex2dc *vert[3]; // vertex of the triangle
	double cx, cy; // center of the triangle's circumcircle
	double cr; // radius of the circumcircle
	std::vector<dem_point*> circum_dem;

	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) // This condition includes points on the triangle's edge
			{
				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

// Start DEM definition
struct dem_point
{
	double x, y; // position of the DEM location
	double elev; // elevation at the DEM location
	double err; // error of the TIN with respect to the elevation 
	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;
		return;
	}
};

bool compare_dem_point(dem_point *a, dem_point *b)
{
	if (a->err > b->err) return true;
	return false;
}
// End DEM 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-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-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;

	int xnum = round((xmax - xmin)/dx) + 1;
	int ynum = round((ymax - ymin)/dy) + 1;

	if (dem.size() != xnum*ynum) return;

	// Prepare the DEM points
	dem_point *tmp_dem = nullptr;;
	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] = new dem_point(xmin + dx*j, ymin + dy*i, dem[j + i*xnum]);
		}
	}

	vertex2dc *tmp_vert = nullptr;
	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();
	tmp_dem = *d_iter; delete tmp_dem;
	dem_grid.erase(d_iter);

	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);
	tmp_dem = *d_iter; delete tmp_dem;
	dem_grid.erase(d_iter);

	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);
	tmp_dem = *d_iter; delete tmp_dem;
	dem_grid.erase(d_iter);

	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);
	tmp_dem = *d_iter; delete tmp_dem;
	dem_grid.erase(d_iter);

	triangle *tmp_tri = nullptr;
	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
	{
		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);
	}

	// 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]);
				out_tris[t]->circum_dem.push_back(dem_grid[i]);
				// no beak here. There might be more than one triangle's circumcircle includes the DEM location
			}
		}
	}

	// loop all DEM data to find the location with maximal error
	for (int i = 0; i < dem_grid.size(); ++i)
	{
		dem_grid[i]->err = fabs(dem_grid[i]->host->interpolate(dem_grid[i]->x, dem_grid[i]->y) - dem_grid[i]->elev);
	}

	// Sort dem_grid in the desceding order with respect to the error
	std::sort(dem_grid.begin(), dem_grid.end(), compare_dem_point);

	bool removed;
	edge tmp_edge;
	std::vector<edge> cnst_edge;
	std::vector<edge>::iterator e_iter;

	while (dem_grid[0]->err >= maxi_err) // quit til the threshold is meet
	{
		if (err_records != nullptr)
		{
			err_records->push_back(dem_grid[0]->err);
		}

		// create a new vertex
		tmp_vert = new vertex2dc(dem_grid[0]->x, dem_grid[0]->y, dem_grid[0]->elev, out_verts.size());
		out_verts.push_back(tmp_vert);

		// Move triangles which circumcircles include the new vertex to the cnst_tri and remove it from out_tris
		cnst_tri.clear();
		for (int i = 0; i < dem_grid[0]->circum_host.size(); ++i)
		{
			cnst_tri.push_back(dem_grid[0]->circum_host[i]);
		}

		for (int c = 0; c < cnst_tri.size(); ++c)
		{
			for (t_iter = out_tris.begin(); t_iter != out_tris.end(); )
			{
				tmp_tri = *t_iter;
				if (cnst_tri[c] == tmp_tri)
				{
					t_iter = out_tris.erase(t_iter);
					break; // no need to search more
				}
				else t_iter++;
			}
		}

		// remove cnst_tri from its circumed DEM's circum triangle list
		for (int c = 0; c < cnst_tri.size(); ++c)
		{
			for (int i = 0; i < cnst_tri[c]->circum_dem.size(); ++i)
			{
				tmp_dem = cnst_tri[c]->circum_dem[i];
				for (t_iter = tmp_dem->circum_host.begin(); t_iter != tmp_dem->circum_host.end(); )
				{
					if (cnst_tri[c] == *t_iter)
					{
						t_iter = tmp_dem->circum_host.erase(t_iter);
						break;
					}
					else t_iter++;
				}
			}
		}

		// remove dem_grid[0] from its circumed triangle's circum DEM list
		for (int c = 0; c < cnst_tri.size(); ++c)
		{
			for (d_iter = cnst_tri[c]->circum_dem.begin(); d_iter != cnst_tri[c]->circum_dem.end(); )
			{
				if (dem_grid[0] == *d_iter)
				{
					d_iter = cnst_tri[c]->circum_dem.erase(d_iter);
					break;
				}
				else d_iter++;
			}
		}

		// clear host and circumcircle triangles for the used DEM location
		d_iter = dem_grid.begin();
		tmp_dem = *d_iter; tmp_dem->circum_host.clear(); delete tmp_dem;
		dem_grid.erase(d_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
		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);
			}
		}

		// loop all DEM data to update host triangles
		for (int c = 0; c < cnst_tri.size(); ++c)
		{
			for (int i = 0; i < cnst_tri[c]->circum_dem.size(); ++i)
			{
				tmp_dem = cnst_tri[c]->circum_dem[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(tmp_dem->x, tmp_dem->y))
					{
						tmp_dem->host = new_tri[n];
						tmp_dem->err = fabs(new_tri[n]->interpolate(tmp_dem->x, tmp_dem->y) - tmp_dem->elev);
						break; // already found, no need to search more
					}
				}
			}
		}

		// Find circum_host triangles for all DEM locations
		// cnst_tri's circum area doesn't over cover new_tri's circum area
		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
				{
					new_tri[n]->circum_dem.push_back(dem_grid[i]);
					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
				}
			}
		}
		

		// destroy memories used by cnst_edge
		for (int c = 0; c < cnst_tri.size(); ++c)
		{
			tmp_tri = cnst_tri[c];
			tmp_tri->circum_dem.clear();
			delete tmp_tri; tmp_tri = nullptr;
		}

		// Sort dem_grid in the desceding order with respect to the error
		std::sort(dem_grid.begin(), dem_grid.end(), compare_dem_point);
	}

	if (err_records != nullptr)
	{
		err_records->push_back(dem_grid[0]->err);
	}

	// destroy remaining DEM data
	for (int i = 0; i < dem_grid.size(); ++i)
	{
		tmp_dem = dem_grid[i];
		delete tmp_dem; tmp_dem = nullptr;
	}

	return;
}

#endif // _TIN_DELAUNAY_H