segmentation / netmets

  #ifndef STIM_NETWORK_H
  #define STIM_NETWORK_H
  
  #include <stdlib.h>
  #include <assert.h>
  #include <sstream>
  #include <fstream>
  #include <algorithm>
  #include <string.h>
  #include <math.h>
  #include <stim/math/vec3.h>
  #include <stim/visualization/obj.h>
  #include <stim/visualization/swc.h>
  #include "cylinder.h"
  #include <stim/cuda/cudatools/timer.h>
  #include <stim/cuda/cudatools/callable.h>
  #include <stim/structures/kdtree.cuh>
  //********************help function********************
  // gaussian_function
  CUDA_CALLABLE float gaussianFunction(float x, float std = 25) { return exp(-x / (2 * std*std)); }  // std default sigma value is 25
  
  // compute metric in parallel
  #ifdef __CUDACC__
  template <typename T>
  __global__ void find_metric_parallel(T* M, size_t n, T* D, float sigma){
  	size_t x = blockDim.x * blockIdx.x + threadIdx.x;
  	if(x >= n) return;
  	M[x] = 1.0f - gaussianFunction(D[x], sigma);
  }
  
  //find the corresponding edge index from array index
  __global__ void find_edge_index_parallel(size_t* I, size_t n, unsigned* R, size_t* E, size_t ne){
  	size_t x = blockDim.x * blockIdx.x + threadIdx.x;
  	if(x >= n) return;
  	unsigned i = 0;
  	size_t N = 0;
  	for(unsigned e = 0; e < ne; e++){
  		N += E[e];
  		if(I[x] < N){
  			R[x] = i;
  			break;
  		}
  		i++;
  	}
  }
  #endif
  
  //hard-coded factor
  int threshold_fac;
  
  namespace stim{
  /** This is the a class that interfaces with gl_spider in order to store the currently
   *   segmented network. The following data is stored and can be extracted:
   *   1)Network geometry and centerline.
   *   2)Network connectivity (a graph of nodes and edges), reconstructed using kdtree.
  */
  
  template<typename T>
  class network{
  
  	///Each edge is a fiber with two nodes.
  	///Each node is an in index to the endpoint of the fiber in the nodes array.
  	class edge : public cylinder<T>
  	{
  		public:
  	
  		unsigned int v[2];		//unique id's designating the starting and ending
  		// default constructor
  		edge() : cylinder<T>() {
  			v[1] = (unsigned)(-1); v[0] = (unsigned)(-1);
  		}
  		/// Constructor - creates an edge from a list of points by calling the stim::fiber constructor
  /*
  		///@param v0, the starting index.
  		///@param v1, the ending index.
  		///@param sz, the number of point in the fiber.
  		edge(unsigned int v0, unsigned int v1, unsigned int sz) : cylinder<T>(
  		{
  
  		}
  */
  		edge(std::vector<stim::vec3<T> > p, std::vector<T> s)
  			: cylinder<T>(p,s)
  		{
  		}
  		///@param p is an array of positions in space
  		edge(stim::centerline<T> p) : cylinder<T>(p){}
  
  		/// Copy constructor creates an edge from a cylinder
  		edge(stim::cylinder<T> f) : cylinder<T>(f) {}
  
  		/// Resamples an edge by calling the fiber resampling function
  		edge resample(T spacing){
  			edge e(cylinder<T>::resample(spacing));	//call the fiber->edge constructor
  			e.v[0] = v[0];					//copy the vertex data
  			e.v[1] = v[1];
  
  			return e;						//return the new edge
  		}
  
  		/// Output the edge information as a string
  		std::string str(){
  			std::stringstream ss;
  			ss<<"("<<cylinder<T>::size()<<")\tl = "<<this->length()<<"\t"<<v[0]<<"----"<<v[1];
  			return ss.str();
  		}
  
  		std::vector<edge> split(unsigned int idx){
  		
  			std::vector< stim::cylinder<T> > C;
  			C.resize(2);
  			C =	(*this).cylinder<T>::split(idx);
  			std::vector<edge> E(C.size());
  
  			for(unsigned e = 0; e < E.size(); e++){
  				E[e] = C[e];
  			}
  			return E;
  		}
  
  		/// operator for writing the edge information into a binary .nwt file.
  		friend std::ofstream& operator<<(std::ofstream& out, const edge& e)
  		{
  			out.write(reinterpret_cast<const char*>(&e.v[0]), sizeof(unsigned int));	///write the starting point.
  			out.write(reinterpret_cast<const char*>(&e.v[1]), sizeof(unsigned int));	///write the ending point.
  			unsigned int sz = e.size();	///write the number of point in the edge.
  			out.write(reinterpret_cast<const char*>(&sz), sizeof(unsigned int));
  			for(int i = 0; i < sz; i++)	///write each point
  			{
  				stim::vec3<T> point = e[i];
  				out.write(reinterpret_cast<const char*>(&point[0]), 3*sizeof(T));
  			//	for(int j = 0; j < nmags(); j++)	//future code for multiple mags
  			//	{
  				out.write(reinterpret_cast<const char*>(&e.R[i]), sizeof(T));	///write the radius
  				//std::cout << point.str() << " " << e.R[i] << std::endl;
  			//	}
  			}
  			return out;	//return stream
  		}
  
  		/// operator for reading an edge from a binary .nwt file.
  		friend std::ifstream& operator>>(std::ifstream& in, edge& e)
  		{
  			unsigned int v0, v1, sz;
  			in.read(reinterpret_cast<char*>(&v0), sizeof(unsigned int));	//read the staring point.
  			in.read(reinterpret_cast<char*>(&v1), sizeof(unsigned int));	//read the ending point
  			in.read(reinterpret_cast<char*>(&sz), sizeof(unsigned int));	//read the number of points in the edge
  //			stim::centerline<T> temp = stim::centerline<T>(sz);		//allocate the new edge
  //			e = edge(temp);
  			std::vector<stim::vec3<T> > p(sz);
  			std::vector<T> r(sz);
  			for(int i = 0; i < sz; i++)		//set the points and radii to the newly read values
  			{
  				stim::vec3<T> point;
  				in.read(reinterpret_cast<char*>(&point[0]), 3*sizeof(T));
  				p[i] = point;
  				T mag;
  		//				for(int j = 0; j < nmags(); j++)		///future code for mags
  		//				{
  				in.read(reinterpret_cast<char*>(&mag), sizeof(T));	
  				r[i] = mag;
  				//std::cout << point.str() << " " << mag << std::endl;
  		//				}
  			}
  			e = edge(p,r);
  			e.v[0] = v0; e.v[1] = v1;
  			return in;
  		}
  	};
  
  	///Node class that stores the physical position of the node as well as the edges it is connected to (edges that connect to it), As well as any additional data necessary.
  	class vertex : public stim::vec3<T>
  	{
  		public:
  			//std::vector<unsigned int> edges;					//indices of edges connected to this node.
  			std::vector<unsigned int> e[2];						//indices of edges going out (e[0]) and coming in (e[1])
  			//stim::vec3<T> p;							//position of this node in physical space.
  			//default constructor
  			vertex() : stim::vec3<T>()
  			{
  			}
  			//constructor takes a stim::vec
  			vertex(stim::vec3<T> p) : stim::vec3<T>(p){}
  
  			/// Output the vertex information as a string
  			std::string 
  			str(){
  				std::stringstream ss;
  				ss<<"\t(x, y, z) = "<<stim::vec3<T>::str();
  
  				if(e[0].size() > 0){
  					ss<<"\t> ";
  					for(unsigned int o = 0; o < e[0].size(); o++)
  						ss<<e[0][o]<<" ";
  				}
  				if(e[1].size() > 0){
  					ss<<"\t< ";
  					for(unsigned int i = 0; i < e[1].size(); i++)
  						ss<<e[1][i]<<" ";
  				}
  
  				return ss.str();
  			}
  			///operator for writing the vector into the stream;
  			friend std::ofstream& operator<<(std::ofstream& out, const vertex& v)
  			{
  				unsigned int s0, s1;
  				s0 = v.e[0].size();
  				s1 = v.e[1].size();
  				out.write(reinterpret_cast<const char*>(&v.ptr[0]), 3*sizeof(T));	///write physical vertex location
  				out.write(reinterpret_cast<const char*>(&s0), sizeof(unsigned int));	///write the number of "outgoing edges"
  				out.write(reinterpret_cast<const char*>(&s1), sizeof(unsigned int));	///write the number of "incoming edges"	
  				if (s0 != 0)
  					out.write(reinterpret_cast<const char*>(&v.e[0][0]), sizeof(unsigned int)*v.e[0].size());	///write the "outgoing edges"
  				if (s1 != 0)
  					out.write(reinterpret_cast<const char*>(&v.e[1][0]), sizeof(unsigned int)*v.e[1].size());	///write the "incoming edges"
  				return out;
  			}
  
  			///operator for reading the vector out of the stream;
  			friend std::ifstream& operator>>(std::ifstream& in, vertex& v)
  			{
  				in.read(reinterpret_cast<char*>(&v[0]), 3*sizeof(T));	///read the physical position
  				unsigned int s[2];					
  				in.read(reinterpret_cast<char*>(&s[0]), 2*sizeof(unsigned int));	///read the sizes of incoming and outgoing edge arrays
  
  				std::vector<unsigned int> one(s[0]);
  				std::vector<unsigned int> two(s[1]);
  				v.e[0] = one;
  				v.e[1] = two;
  				if (one.size() != 0)
  					in.read(reinterpret_cast<char*>(&v.e[0][0]), s[0] * sizeof(unsigned int));		///read the arrays of "outgoing edges"
  				if (two.size() != 0)
  					in.read(reinterpret_cast<char*>(&v.e[1][0]), s[1] * sizeof(unsigned int));		///read the arrays of "incoming edges"
  				return in;
  			}
  
  	};
  
  protected:
  
  	std::vector<edge> E;       //list of edges
  	std::vector<vertex> V;	   //list of vertices.
  
  public:
  
  	///default constructor
  	network()
  	{
  		
  	}
  
  	///constructor with a file to load.
  	network(std::string fileLocation)
  	{
  		load_obj(fileLocation);
  	}
  
  	///Returns the number of edges in the network.
  	unsigned int edges(){
  		return E.size();
  	}
  
  	///Returns the number of nodes in the network.
  	unsigned int vertices(){
  		return V.size();
  	}
  
  	///Returns the radius at specific point in the edge
  	T get_r(unsigned e, unsigned i) {
  		return E[e].r(i);
  	}
  
  	///Returns the average radius of specific edge
  	T get_average_r(unsigned e) {
  		T result = 0.0;
  		unsigned n = E[e].size();
  		for (unsigned p = 0; p < n; p++)
  			result += E[e].r(p);
  
  		return (T)result / n;
  	}
  
  	///Returns the length of current edge
  	T get_l(unsigned e) {
  		return E[e].length();
  	}
  
  	///Returns the start vertex of current edge
  	size_t get_start_vertex(unsigned e) {
  		return E[e].v[0];
  	}
  
  	///Returns the end vertex of current edge
  	size_t get_end_vertex(unsigned e) {
  		return E[e].v[1];
  	}
  
  	///Returns one vertex
  	stim::vec3<T> get_vertex(unsigned i) {
  		return V[i];
  	}
  
  	///Returns the boundary vertices' indices
  	std::vector<unsigned> get_boundary_vertex() {
  		std::vector<unsigned> result;
  
  		for (unsigned v = 0; v < V.size(); v++) {
  			if (V[v].e[0].size() + V[v].e[1].size() == 1) {	// boundary vertex
  				result.push_back(v);
  			}
  		}
  
  		return result;
  	}
  
  	///Set radius
  	void set_r(unsigned e, std::vector<T> radius) {
  		E[e].cylinder<T>::copy_r(radius);
  	}
  
  	void set_r(unsigned e, T radius) {
  		for (size_t i = 0; i < E[e].size(); i++)
  			E[e].cylinder<T>::set_r(i, radius);
  	}
  	//scale the network by some constant value
  	//	I don't think these work??????
  	/*std::vector<vertex> operator*(T s){
  		for (unsigned i=0; i< vertices; i ++ ){
  			V[i] = V[i] * s;
  		}
  		return V;
  	}
  
  	std::vector<vertex> operator*(vec<T> s){
  		for (unsigned i=0; i< vertices; i ++ ){
  			for (unsigned dim = 0 ; dim< 3; dim ++){
  				V[i][dim] = V[i][dim] * s[dim];
  			}
  		}
  		return V;
  	}*/
  
  	// Returns an average of branching index in the network
  	double BranchingIndex(){
  		double B=0;
  		for(unsigned v=0; v < V.size(); v ++){
  			B += ((V[v].e[0].size()) + (V[v].e[1].size()));
  		}
  		B = B / V.size();
  		return B;
  
  	}
  
  	// Returns number of branch points in thenetwork
  	unsigned int BranchP(){
  		unsigned int B=0;
  		unsigned int c;
  		for(unsigned v=0; v < V.size(); v ++){
  			c = ((V[v].e[0].size()) + (V[v].e[1].size()));
  			if (c > 2){
  			B += 1;}
  		}		
  		return B;
  
  	}
  
  	// Returns number of end points (tips) in thenetwork
  	unsigned int EndP(){
  		unsigned int B=0;
  		unsigned int c;
  		for(unsigned v=0; v < V.size(); v ++){
  			c = ((V[v].e[0].size()) + (V[v].e[1].size()));
  			if (c == 1){
  			B += 1;}
  		}		
  		return B;
  
  	}
  
  	//// Returns a dictionary with the key as the vertex
  	//std::map<std::vector<vertex>,unsigned int> DegreeDict(){
  	//	std::map<std::vector<vertex>,unsigned int> dd;
  	//	unsigned int c = 0;
  	//	for(unsigned v=0; v < V.size(); v ++){
  	//		c = ((V[v].e[0].size()) + (V[v].e[1].size()));
  	//		dd[V[v]] = c;
  	//	}
  	//	return dd;
  	//}
  
  	//// Return number of branching stems
  	//unsigned int Stems(){
  	//	unsigned int s = 0;
  	//	std::map<std::vector<vertex>,unsigned int> dd;
  	//	dd = DegreeDict();
  	//	//for(unsigned v=0; v < V.size(); v ++){
  	//	//	V[v].e[0].
  	//	return s;
  	//}
  
  	//Calculate Metrics---------------------------------------------------
  	// Returns an average of fiber/edge lengths in the network
  	double Lengths(){
  		stim::vec<T> L;
  		double sumLength = 0;
  		for(unsigned e = 0; e < E.size(); e++){				//for each edge in the network
  			L.push_back(E[e].length());						//append the edge length
  			sumLength = sumLength + E[e].length();
  		}
  		double avg = sumLength / E.size();
  		return avg;
  	}
  
  
  	// Returns an average of tortuosities in the network
  	double Tortuosities(){
  		stim::vec<T> t;
  		stim::vec<T> id1, id2;                        // starting and ending vertices of the edge
  		double distance;double tortuosity;double sumTortuosity = 0;
  		for(unsigned e = 0; e < E.size(); e++){				//for each edge in the network
  			id1 = E[e][0];									//get the edge starting point
  			id2 = E[e][E[e].size() - 1];					//get the edge ending point
  			distance = (id1 - id2).len();                   //displacement between the starting and ending points
  			if(distance > 0){
  				tortuosity = E[e].length()/	distance	;		// tortuoisty = edge length / edge displacement
  			}
  			else{
  				tortuosity = 0;}
  			t.push_back(tortuosity);
  			sumTortuosity += tortuosity;
  		}
  		double avg = sumTortuosity / E.size();
  		return avg;
  	}
  
  	// Returns average contraction of the network
  	double Contractions(){
  	stim::vec<T> t;
  	stim::vec<T> id1, id2;                        // starting and ending vertices of the edge
  	double distance;double contraction;double sumContraction = 0;
  	for(unsigned e = 0; e < E.size(); e++){				//for each edge in the network
  		id1 = E[e][0];									//get the edge starting point
  		id2 = E[e][E[e].size() - 1];					//get the edge ending point
  		distance = (id1 - id2).len();                   //displacement between the starting and ending points
  		contraction = distance / E[e].length();		// tortuoisty = edge length / edge displacement
  		t.push_back(contraction);
  		sumContraction += contraction;
  	}
  	double avg = sumContraction / E.size();
  	return avg;
  	}
  
  	// returns average fractal dimension of the branches of the network
  	double FractalDimensions(){
  	stim::vec<T> t;
  	stim::vec<T> id1, id2;                        // starting and ending vertices of the edge
  	double distance;double fract;double sumFractDim = 0;
  	for(unsigned e = 0; e < E.size(); e++){				//for each edge in the network
  		id1 = E[e][0];									//get the edge starting point
  		id2 = E[e][E[e].size() - 1];					//get the edge ending point
  		distance = (id1 - id2).len();                   //displacement between the starting and ending points
  		fract = std::log(distance) / std::log(E[e].length());		// tortuoisty = edge length / edge displacement
  		t.push_back(sumFractDim);
  		sumFractDim += fract;
  	}
  	double avg = sumFractDim / E.size();
  	return avg;
  	}
  
  	//returns a cylinder represented a given fiber (based on edge index)
  	stim::cylinder<T> get_cylinder(unsigned e){
  		return E[e];									//return the specified edge (casting it to a fiber)
  	}
  
  	/// subdivide current network
  	void subdivision() {
  
  		std::vector<unsigned> ori_index;		// original index
  		std::vector<unsigned> new_index;		// new index
  		std::vector<edge> nE;					// new edge
  		std::vector<vertex> nV;					// new vector
  		unsigned id = 0;
  		unsigned num_edge = (*this).E.size();
  
  		for (unsigned i = 0; i < num_edge; i++) {
  			if (E[i].size() == 2) {				// if current edge can't be subdivided
  				stim::centerline<T> line(2);
  				for (unsigned k = 0; k < 2; k++)
  					line[k] = E[i][k];
  				line.update();
  
  				edge new_edge(line);
  
  				vertex new_vertex = new_edge[0];
  				id = E[i].v[0];
  				auto position = std::find(ori_index.begin(), ori_index.end(), id);
  				if (position == ori_index.end()) {		 // new vertex
  					ori_index.push_back(id);
  					new_index.push_back(nV.size());
  
  					new_vertex.e[0].push_back(nE.size());
  					new_edge.v[0] = nV.size();
  					nV.push_back(new_vertex);			// push back vertex as a new vertex
  				}
  				else {									// existing vertex
  					int k = std::distance(ori_index.begin(), position);
  					new_edge.v[0] = new_index[k];
  					nV[new_index[k]].e[0].push_back(nE.size());
  				}
  
  				new_vertex = new_edge[1];
  				id = E[i].v[1];
  				position = std::find(ori_index.begin(), ori_index.end(), id);
  				if (position == ori_index.end()) {		 // new vertex
  					ori_index.push_back(id);
  					new_index.push_back(nV.size());
  
  					new_vertex.e[1].push_back(nE.size());
  					new_edge.v[1] = nV.size();
  					nV.push_back(new_vertex);			// push back vertex as a new vertex
  				}
  				else {									// existing vertex
  					int k = std::distance(ori_index.begin(), position);
  					new_edge.v[1] = new_index[k];
  					nV[new_index[k]].e[1].push_back(nE.size());
  				}
  
  				nE.push_back(new_edge);
  
  				nE[nE.size() - 1].cylinder<T>::set_r(0, E[i].cylinder<T>::r(0));
  				nE[nE.size() - 1].cylinder<T>::set_r(1, E[i].cylinder<T>::r(1));
  			}
  			else {								// subdivide current edge
  				for (unsigned j = 0; j < E[i].size() - 1; j++) {
  					stim::centerline<T> line(2);
  					for (unsigned k = 0; k < 2; k++)
  						line[k] = E[i][j + k];
  					line.update();
  
  					edge new_edge(line);
  
  					if (j == 0) {						// edge contains original starting point
  						vertex new_vertex = new_edge[0];
  						id = E[i].v[0];
  						auto position = std::find(ori_index.begin(), ori_index.end(), id);
  						if (position == ori_index.end()) {		 // new vertex
  							ori_index.push_back(id);
  							new_index.push_back(nV.size());
  
  							new_vertex.e[0].push_back(nE.size());
  							new_edge.v[0] = nV.size();
  							nV.push_back(new_vertex);			// push back vertex as a new vertex
  						}
  						else {									// existing vertex
  							int k = std::distance(ori_index.begin(), position);
  							new_edge.v[0] = new_index[k];
  							nV[new_index[k]].e[0].push_back(nE.size());
  						}
  
  						new_vertex = new_edge[1];
  						new_vertex.e[1].push_back(nE.size());
  						new_edge.v[1] = nV.size();
  						nV.push_back(new_vertex);				// push back internal point as a new vertex
  
  						nE.push_back(new_edge);
  					}
  
  					else if (j == E[i].size() - 2) {	// edge contains original ending point
  
  						vertex new_vertex = new_edge[1];
  						nV[nV.size() - 1].e[0].push_back(nE.size());
  						new_edge.v[0] = nV.size() - 1;
  
  						id = E[i].v[1];
  						auto position = std::find(ori_index.begin(), ori_index.end(), id);
  						if (position == ori_index.end()) {		 // new vertex
  							ori_index.push_back(id);
  							new_index.push_back(nV.size());
  
  							new_vertex.e[1].push_back(nE.size());
  							new_edge.v[1] = nV.size();
  							nV.push_back(new_vertex);			// push back vertex as a new vertex
  						}
  						else {									// existing vertex
  							int k = std::distance(ori_index.begin(), position);
  							new_edge.v[1] = new_index[k];
  							nV[new_index[k]].e[1].push_back(nE.size());
  						}
  
  						nE.push_back(new_edge);
  					}
  
  					else {
  						vertex new_vertex = new_edge[1];
  
  						nV[nV.size() - 1].e[0].push_back(nE.size());
  						new_vertex.e[1].push_back(nE.size());
  						new_edge.v[0] = nV.size() - 1;
  						new_edge.v[1] = nV.size();
  						nV.push_back(new_vertex);
  
  						nE.push_back(new_edge);
  					}
  
  					// get radii
  					nE[nE.size() - 1].cylinder<T>::set_r(0, E[i].cylinder<T>::r(j));
  					nE[nE.size() - 1].cylinder<T>::set_r(1, E[i].cylinder<T>::r(j + 1));
  				}
  			}
  		}
  
  		(*this).E = nE;
  		(*this).V = nV;
  	}
  
  	//load a network from an OBJ file
  	void load_obj(std::string filename){
  
  		stim::obj<T> O;									//create an OBJ object
  		O.load(filename);								//load the OBJ file as an object
  
  		std::vector<unsigned> id2vert;							//this list stores the OBJ vertex ID associated with each network vertex
  
  		unsigned i[2];									//temporary, IDs associated with the first and last points in an OBJ line
  
  		//for each line in the OBJ object
  		for(unsigned int l = 1; l <= O.numL(); l++){
  
  			std::vector< stim::vec<T> > c;						//allocate an array of points for the vessel centerline
  			O.getLine(l, c);							//get the fiber centerline
  
  			stim::centerline<T> c3(c.size());
  			for(size_t j = 0; j < c.size(); j++)
  				c3[j] = c[j];
  			c3.update();
  
  	//		edge new_edge = c3;		///This is dangerous.
  			edge new_edge(c3);
  					
  			//create an edge from the given centerline
  			unsigned int I = new_edge.size();					//calculate the number of points on the centerline
  
  			//get the first and last vertex IDs for the line
  			std::vector< unsigned > id;						//create an array to store the centerline point IDs
  			O.getLinei(l, id);							//get the list of point IDs for the line
  			i[0] = id.front();							//get the OBJ ID for the first element of the line
  			i[1] = id.back();							//get the OBJ ID for the last element of the line
  
  			std::vector<unsigned>::iterator it;					//create an iterator for searching the id2vert array
  			unsigned it_idx;							//create an integer for the id2vert entry index
  
  			//find out if the nodes for this fiber have already been created
  			it = find(id2vert.begin(), id2vert.end(), i[0]);	//look for the first node
  			if(it == id2vert.end()){							//if i[0] hasn't already been used
  				vertex new_vertex = new_edge[0];				//create a new vertex, assign it a position
  				bool flag = false;
  				unsigned j = 0;
  				for (; j < V.size(); j++) {						// check whether current vertex is already exist
  					if (new_vertex == V[j]) {
  						flag = true;
  						break;
  					}
  				}
  				if (!flag) {									// unique one
  					new_vertex.e[0].push_back(E.size());				//add the current edge as outgoing
  					new_edge.v[0] = V.size();					//add the new edge to the edge
  					V.push_back(new_vertex);					//add the new vertex to the vertex list
  					id2vert.push_back(i[0]);					//add the ID to the ID->vertex conversion list
  				}
  				else {
  					V[j].e[0].push_back(E.size());
  					new_edge.v[0] = j;
  				}
  			}
  			else{									//if the vertex already exists
  				it_idx = std::distance(id2vert.begin(), it);
  				V[it_idx].e[0].push_back(E.size());				//add the current edge as outgoing
  				new_edge.v[0] = it_idx;
  			}
  
  			it = find(id2vert.begin(), id2vert.end(), i[1]);			//look for the second ID
  			if(it == id2vert.end()){						//if i[1] hasn't already been used
  				vertex new_vertex = new_edge[I-1];				//create a new vertex, assign it a position
  				bool flag = false;
  				unsigned j = 0;
  				for (; j < V.size(); j++) {					// check whether current vertex is already exist
  					if (new_vertex == V[j]) {
  						flag = true;
  						break;
  					}
  				}
  				if (!flag) {
  					new_vertex.e[1].push_back(E.size());				//add the current edge as incoming
  					new_edge.v[1] = V.size();                                  	//add the new vertex to the edge
  					V.push_back(new_vertex);					//add the new vertex to the vertex list
  					id2vert.push_back(i[1]);					//add the ID to the ID->vertex conversion list
  				}
  				else {
  					V[j].e[1].push_back(E.size());
  					new_edge.v[1] = j;
  				}
  			}
  			else{									//if the vertex already exists
  				it_idx = std::distance(id2vert.begin(), it);
  				V[it_idx].e[1].push_back(E.size());				//add the current edge as incoming
  				new_edge.v[1] = it_idx;
  			}
  
  			E.push_back(new_edge);							//push the edge to the list
  
  		}
  
  		// copy the radii information from OBJ
  		/*if (O.numVT()) {
  			unsigned k = 0;
  			for (unsigned i = 0; i < E.size(); i++) {
  				for (unsigned j = 0; j < E[i].size(); j++) {
  					E[i].cylinder<T>::set_r(j, O.getVT(k)[0] / 2);
  					k++;
  				}
  			}
  		}*/
  		// OBJ class assumes that in L the two values are equal
  		if (O.numVT()) {
  			std::vector< unsigned > id;						//create an array to store the centerline point IDs
  			for (unsigned i = 0; i < O.numL(); i++) {
  				id.clear();
  				O.getLinei(i + 1, id);							//get the list of point IDs for the line
  				for (unsigned j = 0; j < id.size(); j++)
  					E[i].cylinder<T>::set_r(j, O.getVT(id[j] - 1)[0] / 2);
  			}
  		}
  	}
  
  	///loads a .nwt file. Reads the header and loads the data into the network according to the header.
  	void
  	loadNwt(std::string filename)
  	{
  		int dims[2];		///number of vertex, number of edges
  		readHeader(filename, &dims[0]);		//read header
  		std::ifstream file;
  		file.open(filename.c_str(), std::ios::in | std::ios::binary);		///skip header information.
  		file.seekg(14+58+4+4, file.beg);
  		vertex v;
  		for(int i = 0; i < dims[0]; i++)		///for every vertex, read vertex, add to network.
  		{
  			file >> v;
  			V.push_back(v);
  //			std::cout << i << " " << v.str() << std::endl;
  		}
  
  		std::cout << std::endl;
  		for(int i = 0; i < dims[1]; i++)		///for every edge, read edge, add to network.
  		{
  			edge e;
  			file >> e;
  			E.push_back(e);
  			//std::cout << i << " " << E[i].str() << std::endl;		// not necessary?
  		}
  		file.close();
  	}
  
  	///saves a .nwt file. Writes the header in raw text format, then saves the network as a binary file.
  	void
  	saveNwt(std::string filename)
  	{
  		writeHeader(filename);
  		std::ofstream file;
  		file.open(filename.c_str(), std::ios::out | std::ios::binary | std::ios::app);	///since we have written the header we are not appending.
  		for(int i = 0; i < V.size(); i++)	///look through the Vertices and write each one.
  		{
  //			std::cout << i << " " << V[i].str() << std::endl;
  			file << V[i];
  		}
  		for(int i = 0; i < E.size(); i++)	///loop through the Edges and write each one.
  		{
  			//std::cout << i << " " << E[i].str() << std::endl;		// not necesarry?
  			file << E[i];
  		}
  		file.close();
  	}
  
  
  	///Writes the header information to a .nwt file.
  	void
  	writeHeader(std::string filename)
  	{
  		std::string magicString = "nwtFileFormat ";		///identifier for the file.
  		std::string desc = "fileid(14B), desc(58B), #vertices(4B), #edges(4B): bindata";
  		int hNumVertices = V.size();		///int byte header storing the number of vertices in the file
  		int hNumEdges = E.size();		///int byte header storing the number of edges.
  		std::ofstream file;
  		file.open(filename.c_str(), std::ios::out | std::ios::binary);
  		std::cout << hNumVertices << " " << hNumEdges << std::endl;
  		file.write(reinterpret_cast<const char*>(&magicString.c_str()[0]), 14);	//write the file id
  		file.write(reinterpret_cast<const char*>(&desc.c_str()[0]), 58);	//write the description
  		file.write(reinterpret_cast<const char*>(&hNumVertices), sizeof(int));	//write #vert.
  		file.write(reinterpret_cast<const char*>(&hNumEdges), sizeof(int));	//write #edges
  //		file << magicString.c_str() << desc.c_str() << hNumVertices << hNumEdges;
  		file.close();
  		
  	}
  
  	///Reads the header information from a .nwt file.
  	void
  	readHeader(std::string filename, int *dims)
  	{
  		char magicString[14];		///id
  		char desc[58];			///description
  		int hNumVertices;		///#vert
  		int hNumEdges;			///#edges
  		std::ifstream file;		////create stream
  		file.open(filename.c_str(), std::ios::in | std::ios::binary);
  		file.read(reinterpret_cast<char*>(&magicString[0]), 14);	///read the file id.
  		file.read(reinterpret_cast<char*>(&desc[0]), 58);		///read the description
  		file.read(reinterpret_cast<char*>(&hNumVertices), sizeof(int));	///read the number of vertices
  		file.read(reinterpret_cast<char*>(&hNumEdges), sizeof(int));	///read the number of edges
  //		std::cout << magicString << desc << hNumVertices << " " <<  hNumEdges << std::endl;
  		file.close();							///close the file.
  		dims[0] = hNumVertices;						///fill the returned reference.
  		dims[1] = hNumEdges;
  	}
  
  	//load a network from an SWC file
  	void load_swc(std::string filename) {
  		stim::swc<T> S;										// create swc variable
  		S.load(filename);									// load the node information
  		S.create_tree();									// link those node according to their linking relationships as a tree
  		S.resample();
  
  		//NT.push_back(S.node[0].type);						// set the neuronal_type value to the first vertex in the network
  		std::vector<unsigned> id2vert;						// this list stores the SWC vertex ID associated with each network vertex
  		unsigned i[2];										// temporary, IDs associated with the first and last points
  
  		for (unsigned int l = 0; l < S.numE(); l++) {		// for every edge
  			//NT.push_back(S.node[l].type);
  
  			std::vector< stim::vec3<T> > c;
  			S.get_points(l, c);
  
  			stim::centerline<T> c3(c.size());				// new fiber
  			
  			for (unsigned j = 0; j < c.size(); j++)
  				c3[j] = c[j];								// copy the points
  		
  			c3.update();									// update the L information
  			
  			stim::cylinder<T> C3(c3);						// create a new cylinder in order to copy the origin radius information
  			// upadate the R information
  			std::vector<T> radius;
  			S.get_radius(l, radius);
  
  			C3.copy_r(radius);
  
  			edge new_edge(C3);								// new edge	
  
  			//create an edge from the given centerline
  			unsigned int I = (unsigned)new_edge.size();				//calculate the number of points on the centerline
  			
  			//get the first and last vertex IDs for the line
  			i[0] = S.E[l].front();
  			i[1] = S.E[l].back();
  
  			std::vector<unsigned>::iterator it;				//create an iterator for searching the id2vert array
  			unsigned it_idx;								//create an integer for the id2vert entry index
  
  			//find out if the nodes for this fiber have already been created
  			it = find(id2vert.begin(), id2vert.end(), i[0]);	//look for the first node
  			if (it == id2vert.end()) {							//if i[0] hasn't already been used
  				vertex new_vertex = new_edge[0];				//create a new vertex, assign it a position
  				new_vertex.e[0].push_back(E.size());			//add the current edge as outgoing
  				new_edge.v[0] = V.size();						//add the new edge to the edge
  				V.push_back(new_vertex);						//add the new vertex to the vertex list
  				id2vert.push_back(i[0]);						//add the ID to the ID->vertex conversion list
  			}
  			else {									//if the vertex already exists
  				it_idx = std::distance(id2vert.begin(), it);
  				V[it_idx].e[0].push_back(E.size());				//add the current edge as outgoing
  				new_edge.v[0] = it_idx;
  			}
  
  			it = find(id2vert.begin(), id2vert.end(), i[1]);	//look for the second ID
  			if (it == id2vert.end()) {							//if i[1] hasn't already been used
  				vertex new_vertex = new_edge[I - 1];			//create a new vertex, assign it a position
  				new_vertex.e[1].push_back(E.size());			//add the current edge as incoming
  				new_edge.v[1] = V.size();                       //add the new vertex to the edge
  				V.push_back(new_vertex);						//add the new vertex to the vertex list
  				id2vert.push_back(i[1]);						//add the ID to the ID->vertex conversion list
  			}
  			else {									//if the vertex already exists
  				it_idx = std::distance(id2vert.begin(), it);
  				V[it_idx].e[1].push_back(E.size());				//add the current edge as incoming
  				new_edge.v[1] = it_idx;
  			}
  
  			E.push_back(new_edge);								//push the edge to the list
  		}
  	}
  
  	/// Get adjacency matrix of the network
  	std::vector< typename std::vector<int> > get_adj_mat() {
  		
  		unsigned n = V.size();		// get the number of vertices in the networks
  
  		std::vector< typename std::vector<int> > result(n, std::vector<int>(n, 0));	// initialize every entry in the matrix to be 0
  		result.resize(n);			// resize rows
  		for (unsigned i = 0; i < n; i++)
  			result[i].resize(n);	// resize columns
  		
  		for (unsigned i = 0; i < n; i++) {			// for every vertex
  			unsigned num_out = V[i].e[0].size();	// number of outgoing edges of current vertex
  			if (num_out != 0) {
  				for (unsigned j = 0; j < num_out; j++) {
  					int edge_idx = V[i].e[0][j];		// get the jth out-going edge index of current vertex
  					int vertex_idx = E[edge_idx].v[1];	// get the ending vertex of specific out-going edge
  					result[i][vertex_idx] = 1;			// can simply set to 1 if it is simple-graph
  					result[vertex_idx][i] = 1;			// symmetric
  				}
  			}
  		}
  
  		return result;
  	}
  
  	/// Output the network as a string
  	std::string str(){
  
  		std::stringstream ss;
  		ss<<"Nodes ("<<V.size()<<")--------"<<std::endl;
  		for(unsigned int v = 0; v < V.size(); v++){
  			ss<<"\t"<<v<<V[v].str()<<std::endl;
  		}
  
  		ss<<"Edges ("<<E.size()<<")--------"<<std::endl;
  		for(unsigned e = 0; e < E.size(); e++){
  			ss<<"\t"<<e<<E[e].str()<<std::endl;
  		}
  
  		return ss.str();
  	}
  
  	/// This function resamples all fibers in a network given a desired minimum spacing
  	/// @param spacing is the minimum distance between two points on the network
  	stim::network<T> resample(T spacing){
  		stim::network<T> n;								//create a new network that will be an exact copy, with resampled fibers
  		n.V = V;									//copy all vertices
  		//n.NT = NT;										//copy all the neuronal type information
  		n.E.resize(edges());								//allocate space for the edge list
  
  		//copy all fibers, resampling them in the process
  		for(unsigned e = 0; e < edges(); e++){						//for each edge in the edge list
  			n.E[e] = E[e].resample(spacing);					//resample the edge and copy it to the new network
  		}
  
  		return n;							              	//return the resampled network
  	}
  
  	/// Calculate the total number of points on all edges.
  	unsigned total_points(){
  		unsigned n = 0;
  		for(unsigned e = 0; e < E.size(); e++)
  			n += E[e].size();
  		return n;
  	}
  
  	//Copy the point cloud representing the centerline for the network into an array
  	void centerline_cloud(T* dst) {
  		size_t p;										//stores the current edge point
  		size_t P;										//stores the number of points in an edge
  		size_t i = 0;									//index into the output array of points
  		for (size_t e = 0; e < E.size(); e++) {			//for each edge in the network
  			P = E[e].size();							//get the number of points in this edge
  			for (p = 0; p < P; p++) {
  				dst[i * 3 + 0] = E[e][p][0];		
  				dst[i * 3 + 1] = E[e][p][1];
  				dst[i * 3 + 2] = E[e][p][2];
  				i++;
  			}
  		}
  	}
  
      // convert vec3 to array
  	void stim2array(float *a, stim::vec3<T> b){
  		a[0] = b[0];
  		a[1] = b[1];
  		a[2] = b[2];
  	}
  
  	// convert vec3 to array in bunch
  	void edge2array(T* a, edge b){
  		size_t n = b.size();
  		for(size_t i = 0; i < n; i++){
  			a[i * 3 + 0] = b[i][0];
  			a[i * 3 + 1] = b[i][1];
  			a[i * 3 + 2] = b[i][2];	 
  		}
  	}
  
  	// get list of metric
  	std::vector<T> metric() {
  		std::vector<T> result;
  		T m;
  		for (size_t e = 0; e < E.size(); e++) {
  			for (size_t p = 0; p < E[e].size(); p++) {
  				m = E[e].r(p);
  				result.push_back(m);
  			}
  		}
  		return result;
  	}
  
  	/// Calculate the average magnitude across the entire network.
  	/// @param m is the magnitude value to use. The default is 0 (usually radius).
  	T average(unsigned m = 0){
  
  		T M, L;										//allocate space for the total magnitude and length
  		M = L = 0;									//initialize both the initial magnitude and length to zero
  		for(unsigned e = 0; e < E.size(); e++){						//for each edge in the network
  			M += E[e].integrate();							//get the integrated magnitude
  			L += E[e].length();							//get the edge length
  		}
  
  		return M / L;									//return the average magnitude
  	}
  
  	/// This function compares two networks and returns the percentage of the current network that is missing from A.
  	/// @param A is the network to compare to - the field is generated for A
  	/// @param sigma is the user-defined tolerance value - smaller values provide a stricter comparison
  	stim::network<T> compare(stim::network<T> A, float sigma, int device = -1){
  
  		stim::network<T> R;										//generate a network storing the result of the comparison
  		R = (*this);											//initialize the result with the current network
  
  		T *c;						                 			// centerline (array of double pointers) - points on kdtree must be double
  		size_t n_data = A.total_points();          				// set the number of points
  		c = (T*) malloc(sizeof(T) * n_data * 3);				// allocate an array to store all points in the data set				
  
  		unsigned t = 0;
  		for(unsigned e = 0; e < A.E.size(); e++){				//for each edge in the network
  			for(unsigned p = 0; p < A.E[e].size(); p++){		//for each point in the edge
  				for(unsigned d = 0; d < 3; d++){				//for each coordinate
  
  					c[t * 3 + d] = A.E[e][p][d];				//copy the point into the array c
  				}
  				t++;
  			}
  		}
  
  		//generate a KD-tree for network A
  		size_t MaxTreeLevels = 3;								// max tree level
  		
  #ifdef __CUDACC__
  		cudaSetDevice(device);
  		int current_device;
  		if (cudaGetDevice(&current_device) == device) {
  			std::cout << "Using CUDA device " << device << " for calculations..." << std::endl;
  		}
  		stim::kdtree<T, 3> kdt;								// initialize a pointer to a kd tree
  
  		kdt.create(c, n_data, MaxTreeLevels);				// build a KD tree
  
  		for(unsigned e = 0; e < R.E.size(); e++){					//for each edge in A
  			//R.E[e].add_mag(0);							//add a new magnitude for the metric
  			//size_t errormag_id = R.E[e].nmags() - 1;		//get the id for the new magnitude
  			
  			size_t n = R.E[e].size();						// the number of points in current edge
  			T* queryPt = new T[3 * n];
  			T* m1 = new T[n];
  			T* dists = new T[n];
  			size_t* nnIdx = new size_t[n];
  
  			T* d_dists;										
  			T* d_m1;										
  			cudaMalloc((void**)&d_dists, n * sizeof(T));
  			cudaMalloc((void**)&d_m1, n * sizeof(T));
  
  			edge2array(queryPt, R.E[e]);
  			kdt.search(queryPt, n, nnIdx, dists);		
  
  			cudaMemcpy(d_dists, dists, n * sizeof(T), cudaMemcpyHostToDevice);					// copy dists from host to device
  
  			// configuration parameters
  			size_t threads = (1024>n)?n:1024;
  			size_t blocks = n/threads + (n%threads)?1:0;
  
  			find_metric_parallel<<<blocks, threads>>>(d_m1, n, d_dists, sigma);					//calculate the metric value based on the distance
  
  			cudaMemcpy(m1, d_m1, n * sizeof(T), cudaMemcpyDeviceToHost);
  
  			for(unsigned p = 0; p < n; p++){
  				R.E[e].set_r(p, m1[p]);
  			}
  
  			//d_set_mag<<<blocks, threads>>>(R.E[e].M, errormag_id, n, m1);
  		}
  
  #else
  		stim::kdtree<T, 3> kdt;
  		kdt.create(c, n_data, MaxTreeLevels);
  	
  		for(unsigned e = 0; e < R.E.size(); e++){			//for each edge in A
  
  			size_t n = R.E[e].size();						// the number of points in current edge
  			T* query = new T[3 * n];
  			T* m1 = new T[n];
  			T* dists = new T[n];
  			size_t* nnIdx = new size_t[n];
  
  			edge2array(query, R.E[e]);
  
  			kdt.cpu_search(query, n, nnIdx, dists);			//find the distance between A and the current network
  
  			for(unsigned p = 0; p < R.E[e].size(); p++){
  				m1[p] = 1.0f - gaussianFunction((T)dists[p], sigma);	//calculate the metric value based on the distance
  				R.E[e].set_r(p, m1[p]);					//set the error for the second point in the segment
  			}
  		}
  #endif
  		return R;		//return the resulting network
  	}
  
  	/// This function compares two networks and split the current one according to the nearest neighbor of each point in each edge
  	/// @param A is the network to split
  	/// @param B is the corresponding mapping network
  	/// @param sigma is the user-defined tolerance value - smaller values provide a stricter comparison
  	/// @param device is the device that user want to use
  	void split(stim::network<T> A, stim::network<T> B, float sigma, int device, float threshold){
  
  		T *c;						                 	
  		size_t n_data = B.total_points();          				
  		c = (T*) malloc(sizeof(T) * n_data * 3); 				
  
  		size_t NB = B.E.size();								// the number of edges in B
  		unsigned t = 0;
  		for(unsigned e = 0; e < NB; e++){					// for every edge in B			
  			for(unsigned p = 0; p < B.E[e].size(); p++){	// for every points in B.E[e]
  				for(unsigned d = 0; d < 3; d++){				
  
  					c[t * 3 + d] = B.E[e][p][d];			// convert to array
  				}
  				t++;
  			}
  		}
  		size_t MaxTreeLevels = 3;							// max tree level
  
  #ifdef __CUDACC__
  		cudaSetDevice(device);
  		stim::kdtree<T, 3> kdt;								// initialize a pointer to a kd tree
  	
  		//compare each point in the current network to the field produced by A
  		kdt.create(c, n_data, MaxTreeLevels);				// build a KD tree
  
  		std::vector<std::vector<unsigned> > relation;		// the relationship between GT and T corresponding to NN
  		relation.resize(A.E.size());										
  
  		for(unsigned e = 0; e < A.E.size(); e++){			//for each edge in A
  			//A.E[e].add_mag(0);								//add a new magnitude for the metric
  			//size_t errormag_id = A.E[e].nmags() - 1;
  			
  			size_t n = A.E[e].size();						// the number of edges in A
  
  			T* queryPt = new T[3 * n];							// set of all the points in current edge
  			T* m1 = new T[n];								// array of metrics for every point in current edge
  			T* dists = new T[n];							// store the distances for every point in current edge
  			size_t* nnIdx = new size_t[n];					// store the indices for every point in current edge
  			
  			// define pointers in device
  			T* d_dists;														
  			T* d_m1;
  			size_t* d_nnIdx;
  
  			// allocate memory for defined pointers
  			cudaMalloc((void**)&d_dists, n * sizeof(T));
  			cudaMalloc((void**)&d_m1, n * sizeof(T));
  			cudaMalloc((void**)&d_nnIdx, n * sizeof(size_t));
  
  			edge2array(queryPt, A.E[e]);						// convert edge to array
  			kdt.search(queryPt, n, nnIdx, dists);				// search the tree to find the NN for every point in current edge
  
  			cudaMemcpy(d_dists, dists, n * sizeof(T), cudaMemcpyHostToDevice);					// copy dists from host to device
  			cudaMemcpy(d_nnIdx, nnIdx, n * sizeof(size_t), cudaMemcpyHostToDevice);				// copy Idx from host to device
  
  			// configuration parameters
  			size_t threads = (1024>n)?n:1024;													// test to see whether the number of point in current edge is more than 1024
  			size_t blocks = n/threads + (n%threads)?1:0;
  
  			find_metric_parallel<<<blocks, threads>>>(d_m1, n, d_dists, sigma);								// calculate the metrics in parallel
  
  			cudaMemcpy(m1, d_m1, n * sizeof(T), cudaMemcpyDeviceToHost);
  
  			for(unsigned p = 0; p < n; p++){
  				A.E[e].set_r(p, m1[p]);											// set the error(radius) value to every point in current edge
  			}
  
  			relation[e].resize(n);																// resize every edge relation size
  
  			unsigned* d_relation;
  			cudaMalloc((void**)&d_relation, n * sizeof(unsigned));								// allocate memory
  
  			std::vector<size_t> edge_point_num(NB);												// %th element is the number of points that %th edge has
  			for(unsigned ee = 0; ee < NB; ee++)
  				edge_point_num[ee] = B.E[ee].size();
  
  			size_t* d_edge_point_num;
  			cudaMalloc((void**)&d_edge_point_num, NB * sizeof(size_t));
  			cudaMemcpy(d_edge_point_num, &edge_point_num[0], NB * sizeof(size_t), cudaMemcpyHostToDevice);
  
  			find_edge_index_parallel<<<blocks, threads>>>(d_nnIdx, n, d_relation, d_edge_point_num, NB);			// find the edge corresponding to the array index in parallel
  
  			cudaMemcpy(&relation[e][0], d_relation, n * sizeof(unsigned), cudaMemcpyDeviceToHost);	//copy relationship from device to host
  		}
  #else
  		stim::kdtree<T, 3> kdt;
  		kdt.create(c, n_data, MaxTreeLevels);
  	
  		std::vector<std::vector<unsigned>> relation;		// the mapping relationship between two networks
  		relation.resize(A.E.size());										
  		for(unsigned i = 0; i < A.E.size(); i++)
  			relation[i].resize(A.E[i].size());
  
  		std::vector<size_t> edge_point_num(NB);				//%th element is the number of points that %th edge has
  		for(unsigned ee = 0; ee < NB; ee++)
  			edge_point_num[ee] = B.E[ee].size();
  
  		for(unsigned e = 0; e < A.E.size(); e++){			//for each edge in A
  			
  			size_t n = A.E[e].size();						//the number of edges in A
  
  			T* queryPt = new T[3 * n];
  			T* m1 = new T[n];
  			T* dists = new T[n];							//store the distances
  			size_t* nnIdx = new size_t[n];					//store the indices
  			
  			edge2array(queryPt, A.E[e]);
  			kdt.search(queryPt, n, nnIdx, dists);		
  
  			for(unsigned p = 0; p < A.E[e].size(); p++){
  				m1[p] = 1.0f - gaussianFunction((T)dists[p], sigma);	//calculate the metric value based on the distance
  				A.E[e].set_r(p, m1[p]);									//set the error for the second point in the segment
  				
  				unsigned id = 0;																	//mapping edge's idx
  				size_t num = 0;																		//total number of points before #th edge
  				for(unsigned i = 0; i < NB; i++){
  					num += B.E[i].size();
  					if(nnIdx[p] < num){																//find the edge it belongs to
  						relation[e][p] = id;
  						break;
  					}
  					id++;																			//current edge won't be the one, move to next edge
  				}
  			}
  		}
  #endif
  		E = A.E;
  		V = A.V;
  
  		unsigned int id = 0;									// split value								
  		for(unsigned e = 0; e < E.size(); e++){					// for every edge
  			for(unsigned p = 0; p < E[e].size() - 1; p++){		// for every point in each edge
  				int t = (int)(E[e].length() / sigma * 2);
  				if (t <= 20)
  					threshold_fac = E[e].size();
  				else
  					threshold_fac = (E[e].length() / sigma * 2)/10;
  				if(relation[e][p] != relation[e][p + 1]){		// find the nearest edge changing point
  					id = p + 1;									// if there is no change in NN
  					if(id < threshold_fac || (E[e].size() - id) < threshold_fac)				
  						id = E[e].size() - 1;																			// extreme situation is not acceptable
  					else
  						break;
  				}
  				if(p == E[e].size() - 2)																// if there is no splitting index, set the id to the last point index of current edge
  					id = E[e].size() - 1;
  			}
  			//unsigned errormag_id = E[e].nmags() - 1;
  			T G = 0;																					// test to see whether it has its nearest neighbor
  			for(unsigned i = 0; i < E[e].size(); i++)
  				G += E[e].r(i);																			// won't split special edges
  			if(G / E[e].size() > threshold)															// should based on the color map
  				id = E[e].size() - 1;																	// set split idx to outgoing direction vertex
  
  			std::vector<edge> tmpe;
  			tmpe.resize(2);
  			tmpe = E[e].split(id);
  			vertex tmpv = stim::vec3<T>(-1, -1, 0);														// store the split point as vertex
  			if(tmpe.size() == 2){
  				relation.resize(relation.size() + 1);
  				for(unsigned d = id; d < E[e].size(); d++)
  					relation[relation.size() - 1].push_back(relation[e][d]);
  				tmpe[0].v[0] = E[e].v[0];																// begining vertex of first half edge -> original begining vertex
  				tmpe[1].v[1] = E[e].v[1];																// ending vertex of second half edge -> original ending vertex
  				tmpv = E[e][id];
  				V.push_back(tmpv);
  				tmpe[0].v[1] = (unsigned)V.size() - 1;													// ending vertex of first half edge -> new vertex
  				tmpe[1].v[0] = (unsigned)V.size() - 1;													// begining vertex of second half edge -> new vertex
  				edge tmp(E[e]);
  				E[e] = tmpe[0];																			// replace original edge by first half edge
  				E.push_back(tmpe[1]);																	// push second half edge to the last
  				V[V.size() - 1].e[1].push_back(e);														// push first half edge to the incoming of new vertex
  				V[V.size() - 1].e[0].push_back((unsigned)E.size() - 1);									// push second half edge to the outgoing of new vertex
  				for(unsigned i = 0; i < V[tmp.v[1]].e[1].size(); i++)									// find the incoming edge of original ending vertex
  					if(V[tmp.v[1]].e[1][i] == e)
  						V[tmp.v[1]].e[1][i] = (unsigned)E.size() - 1;									// set to new edge
  			}
  		}
  	}
  
  	/// This function compares two splitted networks and yields a mapping relationship between them according to NN
  	/// @param B is the network that the current network is going to map to
  	/// @param C is the mapping relationship: C[e1] = _e1 means e1 edge in current network is mapping the _e1 edge in B
  	/// @param device is the device that user want to use
  	void mapping(stim::network<T> B, std::vector<unsigned> &C, int device, float threshold){
  		stim::network<T> A;								//generate a network storing the result of the comparison
  		A = (*this);
  
  		size_t n = A.E.size();							// the number of edges in A
  		size_t NB = B.E.size();							// the number of edges in B
  
  		C.resize(A.E.size());	
  
  		T *c;						                 	// centerline (array of double pointers) - points on kdtree must be double
  		size_t n_data = B.total_points();          		// set the number of points
  		c = (T*) malloc(sizeof(T) * n_data * 3); 				
  
  		unsigned t = 0;
  		for(unsigned e = 0; e < NB; e++){					// for each edge in the network
  			for(unsigned p = 0; p < B.E[e].size(); p++){	// for each point in the edge
  				for(unsigned d = 0; d < 3; d++){			// for each coordinate
  
  					c[t * 3 + d] = B.E[e][p][d];
  				}
  				t++;
  			}
  		}
  
  		//generate a KD-tree for network A
  		//float metric = 0.0;                               		// initialize metric to be returned after comparing the network
  		size_t MaxTreeLevels = 3;									// max tree level
  		
  #ifdef __CUDACC__
  		cudaSetDevice(device);
  		stim::kdtree<T, 3> kdt;								// initialize a pointer to a kd tree
  	
  		kdt.create(c, n_data, MaxTreeLevels);				// build a KD tree
  
  		for(unsigned e = 0; e < n; e++){					//for each edge in A
  			//size_t errormag_id = A.E[e].nmags() - 1;		//get the id for the new magnitude
  			
  			//pre-judge to get rid of impossibly mapping edges
  			T M = 0;
  			for(unsigned p = 0; p < A.E[e].size(); p++)
  				M += A.E[e].r(p);
  			M = M / A.E[e].size();
  			if(M > threshold)
  				C[e] = (unsigned)-1;						//set the nearest edge of impossibly mapping edges to maximum of unsigned
  			else{
  				T* queryPt = new T[3];
  				T* dists = new T[1];
  				size_t* nnIdx = new size_t[1];
  
  				stim2array(queryPt, A.E[e][A.E[e].size()/2]);
  				kdt.search(queryPt, 1, nnIdx, dists);
  				
  				unsigned id = 0;							//mapping edge's idx
  				size_t num = 0;								//total number of points before #th edge
  				for(unsigned i = 0; i < NB; i++){
  					num += B.E[i].size();
  					if(nnIdx[0] < num){
  						C[e] = id;
  						break;
  					}
  					id++;
  				}
  			}
  		}
  #else
  		stim::kdtree<T, 3> kdt;
  		kdt.create(c, n_data, MaxTreeLevels);
  		T *dists = new T[1];								// near neighbor distances
  		size_t *nnIdx = new size_t[1];						// near neighbor indices // allocate near neigh indices
  
  		stim::vec3<T> p0, p1;
  		T* queryPt = new T[3];
  
  		for(unsigned int e = 0; e < R.E.size(); e++){			// for each edge in A
  			T M;											// the sum of metrics of current edge
  			for(unsigned p = 0; p < R.E[e].size(); p++)
  				M += A.E[e].r(p);
  			M = M / A.E[e].size();
  			if(M > threshold)								
  				C[e] = (unsigned)-1;
  			else{											// if it should have corresponding edge in B, then...
  				p1 = R.E[e][R.E[e].size()/2];							
  				stim2array(queryPt, p1);
  				kdt.cpu_search(queryPt, 1, nnIdx, dists);	// search the tree		
  				
  				unsigned id = 0;							//mapping edge's idx
  				size_t num = 0;								//total number of points before #th edge
  				for(unsigned i = 0; i < NB; i++){
  					num += B.E[i].size();
  					if(nnIdx[0] < num){
  						C[e] = id;
  						break;
  					}
  					id++;
  				}
  			}
  		}
  #endif
  	}
  
  	/// Returns the number of magnitude values stored in each edge. This should be uniform across the network.
  	//unsigned nmags(){
  	//	return E[0].nmags();
  	//}
  	// split a string in text by the character sep
  	stim::vec<T> split(std::string &text, char sep) 
  	{
  		stim::vec<T> tokens;
  		std::size_t start = 0, end = 0;
  		while ((end = text.find(sep, start)) != std::string::npos) {
  		tokens.push_back(atof(text.substr(start, end - start).c_str()));
  		start = end + 1;
  		}
  		tokens.push_back(atof(text.substr(start).c_str()));
  		return tokens;
  	}
  	// load a network in text file to a network class
  	void load_txt(std::string filename)
  	{
  		std::vector <std::string> file_contents;
  		std::ifstream file(filename.c_str());
  		std::string line;
  		std::vector<unsigned> id2vert;	//this list stores the vertex ID associated with each network vertex
  		//for each line in the text file, store them as strings in file_contents
  		while (std::getline(file, line))
  		{
  			std::stringstream ss(line);
  			file_contents.push_back(ss.str());
  		}
  		unsigned int numEdges = atoi(file_contents[0].c_str()); //number of edges in the network
  		unsigned int I = atoi(file_contents[1].c_str()) ;		//calculate the number of points3d on the first edge
  		unsigned int count = 1; unsigned int k = 2; // count is global counter through the file contents, k is for the vertices on the edges
  		// for each edge in the network.
  		for (unsigned int i = 0; i < numEdges; i ++ )
  		{
  			// pre allocate a position vector p with number of points3d on the edge p
  			std::vector< stim::vec<T> > p(0, I);
  			// for each point on the nth edge
  		  for (unsigned int j = k; j < I + k; j++)
  		  {
  			 // split the points3d of floats with separator space and form a float3 position vector out of them
  			  p.push_back(split(file_contents[j], ' '));
  		  }
  			count += p.size() + 1; // increment count to point at the next edge in the network
  			I = atoi(file_contents[count].c_str()); // read in the points3d at the next edge and convert it to an integer
  			k = count + 1;
  			edge new_edge = p; // create an edge with a vector of points3d  on the edge
  			E.push_back(new_edge); // push the edge into the network
  		}
  		unsigned int numVertices = atoi(file_contents[count].c_str()); // this line in the text file gives the number of distinct vertices
  		count = count + 1; // this line of text file gives the first verrtex
  		// push each vertex into V
  		for (unsigned int i = 0; i < numVertices; i ++)
  		{
  			vertex new_vertex = split(file_contents[count], ' ');
  			V.push_back(new_vertex);
  			count += atoi(file_contents[count + 1].c_str()) + 2; // Skip number of edge ids + 2 to point to the next vertex
  		}
  	} // end load_txt function
  
  	// strTxt returns a string of edges
  	std::string
  	strTxt(std::vector< stim::vec<T> > p)
  	{
  		std::stringstream ss;
  		std::stringstream oss;
  		for(unsigned int i = 0; i < p.size(); i++){
  			ss.str(std::string());
  			for(unsigned int d = 0; d < 3; d++){
  				ss<<p[i][d];
  			}
  			ss << "\n";
  		}
  		return ss.str();
  	}
  	// removes specified character from string
  	void removeCharsFromString(std::string &str, char* charsToRemove ) {
  	   for ( unsigned int i = 0; i < strlen(charsToRemove); ++i ) {
  		  str.erase( remove(str.begin(), str.end(), charsToRemove[i]), str.end() );
  	   }
  	}
  	//exports network to txt file
  	void
  	to_txt(std::string filename)
  	{
  		std::ofstream ofs(filename.c_str(), std::ofstream::out | std::ofstream::app);
  		//int num;
  		ofs << (E.size()).str() << "\n";
  		for(unsigned int i = 0; i < E.size(); i++)
  		{
  			 std::string str;
  			 ofs << (E[i].size()).str() << "\n";
  			 str = E[i].strTxt();
               ofs << str << "\n";
  		} 
  		for(int i = 0; i < V.size(); i++)
  		{
  			std::string str;
  			str = V[i].str();
  			char temp[4] = "[],";
  			removeCharsFromString(str, temp);
  			ofs << str << "\n";
  		}
  		ofs.close();
  	}
  };		//end stim::network class
  };		//end stim namespace
  #endif