stim/biomodels/centerline.h

/*
Copyright <2017> <David Mayerich>
Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*/
#ifndef STIM_CENTERLINE_H
#define STIM_CENTERLINE_H
#include <vector>
#include <stim/math/vec3.h>
#include <stim/structures/kdtree.cuh>
namespace stim{
/**	This class stores information about a single fiber represented as a set of geometric points
 *	between two branch or end points. This class is used as a fundamental component of the stim::network
 *	class to describe an interconnected (often biological) network.
 */
template<typename T>
class centerline : public std::vector< stim::vec3<T> >{
protected:
	std::vector<T> L;										//stores the integrated length along the fiber (used for parameterization)
	///Return the normalized direction vector at point i (average of the incoming and outgoing directions)
	vec3<T> d(size_t i) {
		if (size() <= 1) return vec3<T>(0, 0, 0);						//if there is insufficient information to calculate the direction, return a null vector
		if (size() == 2) return (at(1) - at(0)).norm();					//if there are only two points, the direction vector at both is the direction of the line segment
		if (i == 0) return (at(1) - at(0)).norm();						//the first direction vector is oriented towards the first line segment
		if (i == size() - 1) return (at(size() - 1) - at(size() - 2)).norm();	//the last direction vector is oriented towards the last line segment
		//all other direction vectors are the average direction of the two joined line segments
		vec3<T> a = at(i) - at(i - 1);
		vec3<T> b = at(i + 1) - at(i);
		vec3<T> ab = a.norm() + b.norm();
		return ab.norm();
	}
	//initializes the integrated length vector to make parameterization easier, starting with index idx (all previous indices are assumed to be correct)
	void update_L(size_t start = 0) {
		L.resize(size());									//allocate space for the L array
		if (start == 0) {
			L[0] = 0;											//initialize the length value for the first point to zero (0)
			start++;
		}
		stim::vec3<T> d;
		for (size_t i = start; i < size(); i++) {		//for each line segment in the centerline
			d = at(i) - at(i - 1);
			L[i] = L[i - 1] + d.len();				//calculate the running length total
		}
	}
	void init() {
		if (size() == 0) return;								//return if there aren't any points
		update_L();
	}
	/// Returns a stim::vec representing the point at index i
	/// @param i is an index of the desired centerline point
	stim::vec<T> get_vec(unsigned i){
		return std::vector< stim::vec3<T> >::at(i);
	}
	///finds the index of the point closest to the length l on the lower bound.
	///binary search.
	size_t findIdx(T l) {
		for (size_t i = 1; i < L.size(); i++) {				//for each point in the centerline
			if (L[i] > l) return i - 1;						//if we have passed the desired length value, return i-1
		}
		return L.size() - 1;
		/*size_t i = L.size() / 2;
		size_t max = L.size() - 1;
		size_t min = 0;
		while (i < L.size() - 1){
			if (l < L[i]) {
				max = i;
				i = min + (max - min) / 2;
			}
			else if (L[i] <= l && L[i + 1] >= l) {
				break;
			}
			else {
				min = i;
				i = min + (max - min) / 2;
			}
		}
		return i;*/
	}
	///Returns a position vector at the given length into the fiber (based on the pvalue).
	///Interpolates the radius along the line.
	///@param l: the location of the in the cylinder.
	///@param idx: integer location of the point closest to l but prior to it.
	stim::vec3<T> p(T l, int idx) {
		T rat = (l - L[idx]) / (L[idx + 1] - L[idx]);
		stim::vec3<T> v1 = at(idx);
		stim::vec3<T> v2 = at(idx + 1);
		return(v1 + (v2 - v1)*rat);
	}
public:
	using std::vector< stim::vec3<T> >::at;
	using std::vector< stim::vec3<T> >::size;
	centerline() : std::vector< stim::vec3<T> >() {
		init();
	}
	centerline(size_t n) : std::vector< stim::vec3<T> >(n){
		init();
	}
	centerline(std::vector<stim::vec3<T> > pos) :
		std::vector<stim::vec3<T> > (pos)
	{
		init();
	}
	
	//overload the push_back function to update the length vector
	void push_back(stim::vec3<T> p) {
		std::vector< stim::vec3<T> >::push_back(p);
		update_L(size() - 1);
	}
	///Returns a position vector at the given p-value (p value ranges from 0 to 1).
	///interpolates the position along the line.
	///@param pvalue: the location of the in the cylinder, from 0 (beginning to 1).
	stim::vec3<T> p(T pvalue) {
		if (pvalue <= 0.0) return at(0);			//return the first element
		if (pvalue >= 1.0) return back();			//return the last element
		T l = pvalue*L[L.size() - 1];
		int idx = findIdx(l);
		return p(l, idx);
	}
	///Update centerline internal parameters (currently the L vector)
	void update() {
		init();
	}
	///Return the length of the entire centerline
	T length() {
		return L.back();
	}
	/// stitch two centerlines
	///@param c1, c2: two centerlines
	///@param sigma: sample rate
	static std::vector< stim::centerline<T> > stitch(stim::centerline<T> c1, stim::centerline<T> c2 = stim::centerline<T>()) {
		
		std::vector< stim::centerline<T> > result;
		stim::centerline<T> new_centerline;
		stim::vec3<T> new_vertex;
		// if only one centerline, stitch itself!
		if (c2.size() == 0) {
			size_t num = c1.size();
			size_t id = 100000;							// store the downsample start position
			T threshold;
			if (num < 4) {								// if the number of vertex is less than 4, do nothing
				result.push_back(c1);
				return result;
			}
			else {
				// test geometry start vertex
				stim::vec3<T> v1 = c1[1] - c1[0];		// vector from c1[0] to c1[1]
				for (size_t p = 2; p < num; p++) {		// 90° standard???
					stim::vec3<T> v2 = c1[p] - c1[0];
					float cosine = v2.dot(v1);
					if (cosine < 0) {
						id = p;
						threshold = v2.len();
						break;
					}
				}
				if (id != 100000) {						// find a downsample position on the centerline
					T* c;
					c = (T*)malloc(sizeof(T) * (num - id) * 3);
					for (size_t p = id; p < num; p++) {
						for (size_t d = 0; d < 3; d++) {
							c[p * 3 + d] = c1[p][d];
						}
					}
					stim::kdtree<T, 3> kdt;
					kdt.create(c, num - id, 5);			// create tree
					T* query = (T*)malloc(sizeof(T) * 3);
					for (size_t d = 0; d < 3; d++)
						query[d] = c1[0][d];
					size_t index;
					T dist;
					kdt.search(query, 1, &index, &dist);
					free(query);
					free(c);
					if (dist > threshold) {
						result.push_back(c1);
					}
					else {
						// the loop part
						new_vertex = c1[index];
						new_centerline.push_back(new_vertex);
						for (size_t p = 0; p < index + 1; p++) {
							new_vertex = c1[p];
							new_centerline.push_back(new_vertex);
						}
						result.push_back(new_centerline);
						new_centerline.clear();
						// the tail part
						for (size_t p = index; p < num; p++) {
							new_vertex = c1[p];
							new_centerline.push_back(new_vertex);
						}
						result.push_back(new_centerline);
					}
				}
				else {	// there is one potential problem that two positions have to be stitched
						// test geometry end vertex
					stim::vec3<T> v1 = c1[num - 2] - c1[num - 1];
					for (size_t p = num - 2; p > 0; p--) {		// 90° standard
						stim::vec3<T> v2 = c1[p - 1] - c1[num - 1];
						float cosine = v2.dot(v1);
						if (cosine < 0) {
							id = p;
							threshold = v2.len();
							break;
						}
					}
					if (id != 100000) {						// find a downsample position
						T* c;
						c = (T*)malloc(sizeof(T) * (id + 1) * 3);
						for (size_t p = 0; p < id + 1; p++) {
							for (size_t d = 0; d < 3; d++) {
								c[p * 3 + d] = c1[p][d];
							}
						}
						stim::kdtree<T, 3> kdt;
						kdt.create(c, id + 1, 5);				// create tree
						T* query = (T*)malloc(sizeof(T) * 1 * 3);
						for (size_t d = 0; d < 3; d++)
							query[d] = c1[num - 1][d];
						size_t index;
						T dist;
						kdt.search(query, 1, &index, &dist);
						free(query);
						free(c);
						if (dist > threshold) {
							result.push_back(c1);
						}
						else {
							// the tail part
							for (size_t p = 0; p < index + 1; p++) {
								new_vertex = c1[p];
								new_centerline.push_back(new_vertex);
							}
							result.push_back(new_centerline);
							new_centerline.clear();
							// the loop part
							for (size_t p = index; p < num; p++) {
								new_vertex = c1[p];
								new_centerline.push_back(new_vertex);
							}
							new_vertex = c1[index];
							new_centerline.push_back(new_vertex);
							result.push_back(new_centerline);
						}
					}
					else {	// no stitch position
						result.push_back(c1);
					}
				}
			}
		}
		// two centerlines
		else {
			// find stitch position based on nearest neighbors												
			size_t num1 = c1.size();
			T* c = (T*)malloc(sizeof(T) * num1 * 3);		// c1 as reference point
			for (size_t p = 0; p < num1; p++)				// centerline to array
				for (size_t d = 0; d < 3; d++)				// because right now my kdtree code is a relatively close code, it has its own structure
					c[p * 3 + d] = c1[p][d];				// I will merge it into stimlib totally in the near future
			stim::kdtree<T, 3> kdt;							// kdtree object
			kdt.create(c, num1, 5);							// create tree
			size_t num2 = c2.size();						
			T* query = (T*)malloc(sizeof(T) * num2 * 3);	// c2 as query point
			for (size_t p = 0; p < num2; p++) {
				for (size_t d = 0; d < 3; d++) {
					query[p * 3 + d] = c2[p][d];
				}
			}
			std::vector<size_t> index(num2);
			std::vector<T> dist(num2);
			kdt.search(query, num2, &index[0], &dist[0]);	// find the nearest neighbors in c1 for c2
			// clear up
			free(query);
			free(c);
			// find the average vertex distance of one centerline
			T sigma1 = 0;
			T sigma2 = 0;
			for (size_t p = 0; p < num1 - 1; p++) 
				sigma1 += (c1[p] - c1[p + 1]).len();
			for (size_t p = 0; p < num2 - 1; p++)
				sigma2 += (c2[p] - c2[p + 1]).len();
			sigma1 /= (num1 - 1);
			sigma2 /= (num2 - 1);
			float threshold = 4 * (sigma1 + sigma2) / 2;			// better way to do this?
			T min_d = *std::min_element(dist.begin(), dist.end());	// find the minimum distance between c1 and c2
			if (min_d > threshold) {								// if the minimum distance is too large
				result.push_back(c1);
				result.push_back(c2);
#ifdef DEBUG
				std::cout << "The distance between these two centerlines is too large" << std::endl;
#endif
			}
			else {
			//	auto smallest = std::min_element(dist.begin(), dist.end());
				unsigned int smallest = std::min_element(dist.begin(), dist.end());
			//	auto i = std::distance(dist.begin(), smallest);		// find the index of min-distance in distance list
				unsigned int i = std::distance(dist.begin(), smallest);		// find the index of min-distance in distance list
				// stitch position in c1 and c2
				int id1 = index[i];
				int id2 = i;
				// actually there are two cases
				// first one inacceptable
				// second one acceptable
				if (id1 != 0 && id1 != num1 - 1 && id2 != 0 && id2 != num2 - 1) {		// only stitch one end vertex to another centerline
					result.push_back(c1);
					result.push_back(c2);
				}
				else {
					if (id1 == 0 || id1 == num1 - 1) {			// if the stitch vertex is the first or last vertex of c1
						// for c2, consider two cases(one degenerate case)
						if (id2 == 0 || id2 == num2 - 1) {		// case 1, if stitch position is also on the end of c2
							// we have to decide which centerline get a new vertex, based on direction
							// for c1, computer the direction change angle
							stim::vec3<T> v1, v2;
							float alpha1, alpha2;				// direction change angle
							if (id1 == 0)
								v1 = (c1[1] - c1[0]).norm();
							else
								v1 = (c1[num1 - 2] - c1[num1 - 1]).norm();
							v2 = (c2[id2] - c1[id1]).norm();
							alpha1 = v1.dot(v2);
							if (id2 == 0)
								v1 = (c2[1] - c2[0]).norm();
							else
								v1 = (c2[num2 - 2] - c2[num2 - 1]).norm();
							v2 = (c1[id1] - c2[id2]).norm();
							alpha2 = v1.dot(v2);
							if (abs(alpha1) > abs(alpha2)) {					// add the vertex to c1 in order to get smooth connection
								// push back c1
								if (id1 == 0) {									// keep geometry information
									new_vertex = c2[id2];
									new_centerline.push_back(new_vertex);
									for (size_t p = 0; p < num1; p++) {			// stitch vertex on c2 -> geometry start vertex on c1 -> geometry end vertex on c1
										new_vertex = c1[p];
										new_centerline.push_back(new_vertex);
									}
								}
								else {
									for (size_t p = 0; p < num1; p++) {			// stitch vertex on c2 -> geometry end vertex on c1 -> geometry start vertex on c1
										new_vertex = c1[p];
										new_centerline.push_back(new_vertex);
									}
									new_vertex = c2[id2];
									new_centerline.push_back(new_vertex);
								}
								result.push_back(new_centerline);
								new_centerline.clear();
								// push back c2
								for (size_t p = 0; p < num2; p++) {
									new_vertex = c2[p];
									new_centerline.push_back(new_vertex);
								}
								result.push_back(new_centerline);
							}
							else {												// add the vertex to c2 in order to get smooth connection
								// push back c1
								for (size_t p = 0; p < num1; p++) {
									new_vertex = c1[p];
									new_centerline.push_back(new_vertex);
								}
								result.push_back(new_centerline);
								new_centerline.clear();
								// push back c2
								if (id2 == 0) {									// keep geometry information
									new_vertex = c1[id1];
									new_centerline.push_back(new_vertex);
									for (size_t p = 0; p < num2; p++) {			// stitch vertex on c2 -> geometry start vertex on c1 -> geometry end vertex on c1
										new_vertex = c2[p];
										new_centerline.push_back(new_vertex);
									}
								}
								else {
									for (size_t p = 0; p < num2; p++) {			// stitch vertex on c2 -> geometry end vertex on c1 -> geometry start vertex on c1
										new_vertex = c2[p];
										new_centerline.push_back(new_vertex);
									}
									new_vertex = c1[id1];
									new_centerline.push_back(new_vertex);
								}
								result.push_back(new_centerline);
							}
						}
						else {												// case 2, the stitch position is on c2
							// push back c1
							if (id1 == 0) {									// keep geometry information
								new_vertex = c2[id2];
								new_centerline.push_back(new_vertex);
								for (size_t p = 0; p < num1; p++) {			// stitch vertex on c2 -> geometry start vertex on c1 -> geometry end vertex on c1
									new_vertex = c1[p];
									new_centerline.push_back(new_vertex);
								}
							}
							else {
								for (size_t p = 0; p < num1; p++) {			// geometry end vertex on c1 -> geometry start vertex on c1 -> stitch vertex on c2
									new_vertex = c1[p];
									new_centerline.push_back(new_vertex);
								}
								new_vertex = c2[id2];
								new_centerline.push_back(new_vertex);
							}
							result.push_back(new_centerline);
							new_centerline.clear();
							// push back c2
							for (size_t p = 0; p < id2 + 1; p++) {			// first part
								new_vertex = c2[p];
								new_centerline.push_back(new_vertex);
							}
							result.push_back(new_centerline);
							new_centerline.clear();
							for (size_t p = id2; p < num2; p++) {			// second part
								new_vertex = c2[p];
								new_centerline.push_back(new_vertex);
							}
							result.push_back(new_centerline);
						}
					}
					else {							// if the stitch vertex is the first or last vertex of c2
						// push back c2
						if (id2 == 0) {										// keep geometry information
							new_vertex = c1[id1];
							new_centerline.push_back(new_vertex);
							for (size_t p = 0; p < num2; p++) {				// stitch vertex on c1 -> geometry start vertex on c2 -> geometry end vertex on c2
								new_vertex = c2[p];
								new_centerline.push_back(new_vertex);
							}
						}
						else {
							for (size_t p = 0; p < num2; p++) {				// geometry end vertex on c2 -> geometry start vertex on c2 -> stitch vertex on c1
								new_vertex = c2[p];
								new_centerline.push_back(new_vertex);
							}
							new_vertex = c1[id1];
							new_centerline.push_back(new_vertex);
							result.push_back(new_centerline);
							new_centerline.clear();
							// push back c1
							for (size_t p = 0; p < id1 + 1; p++) {			// first part
								new_vertex = c1[p];
								new_centerline.push_back(new_vertex);
							}
							result.push_back(new_centerline);
							new_centerline.clear();
							for (size_t p = id1; p < num1; p++) {			// second part
								new_vertex = c1[p];
								new_centerline.push_back(new_vertex);
							}
							result.push_back(new_centerline);
						}
					}
				}
			}
		}
		return result;
	}
	/// Split the fiber at the specified index. If the index is an end point, only one fiber is returned
	std::vector< stim::centerline<T> > split(unsigned int idx){
		std::vector< stim::centerline<T> > fl;				//create an array to store up to two fibers
		size_t N = size();
		//if the index is an end point, only the existing fiber is returned
		if(idx == 0 || idx == N-1){
			fl.resize(1);							//set the size of the fiber to 1
			fl[0] = *this;							//copy the current fiber
		}
		//if the index is not an end point
		else{
			unsigned int N1 = idx + 1;					//calculate the size of both fibers
			unsigned int N2 = N - idx;
			fl.resize(2);								//set the array size to 2
			fl[0] = stim::centerline<T>(N1);			//set the size of each fiber
			fl[1] = stim::centerline<T>(N2);
			//copy both halves of the fiber
			unsigned int i;
			//first half
			for(i = 0; i < N1; i++)					//for each centerline point
				fl[0][i] = std::vector< stim::vec3<T> >::at(i);
			fl[0].init();							//initialize the length vector
			//second half
			for(i = 0; i < N2; i++)
				fl[1][i] = std::vector< stim::vec3<T> >::at(idx+i);
			fl[1].init();							//initialize the length vector
		}
		return fl;										//return the array
	}
	/// Outputs the fiber as a string
	std::string str(){
		std::stringstream ss;
		size_t N = std::vector< stim::vec3<T> >::size();
		ss << "---------[" << N << "]---------" << std::endl;
		for (size_t i = 0; i < N; i++)
			ss << std::vector< stim::vec3<T> >::at(i) << std::endl;
		ss << "--------------------" << std::endl;
		return ss.str();
	}
	/// Back method returns the last point in the fiber
	stim::vec3<T> back(){
		return std::vector< stim::vec3<T> >::back();
	}
		////resample a fiber in the network
	stim::centerline<T> resample(T spacing)
	{	
		//std::cout<<"fiber::resample()"<<std::endl;
		stim::vec3<T> v;    //v-direction vector of the segment
		stim::vec3<T> p;      //- intermediate point to be added
		stim::vec3<T> p1;   // p1 - starting point of an segment on the fiber,
		stim::vec3<T> p2;   // p2 - ending point,
		//double sum=0;  //distance summation
		size_t N = size();
		centerline<T> new_c; // initialize list of new resampled points on the fiber
		// for each point on the centerline (skip if it is the last point on centerline)
		for(unsigned int f=0; f< N-1; f++)
		{			
			p1 = at(f); 
			p2 = at(f+1);
			v = p2 - p1;
			
			T lengthSegment = v.len();			//find Length of the segment as distance between the starting and ending points of the segment
			if(lengthSegment >= spacing){ // if length of the segment is greater than standard deviation resample
				
				// repeat resampling until accumulated stepsize is equsl to length of the segment
				for(T step=0.0; step<lengthSegment; step+=spacing){
					// calculate the resampled point by travelling step size in the direction of normalized gradient vector
					p = p1 + v * (step / lengthSegment);
					
					// add this resampled points to the new fiber list
					new_c.push_back(p);
				}
			}
			else       // length of the segment is now less than standard deviation, push the ending point of the segment and proceed to the next point in the fiber
				new_c.push_back(at(f));
		}
		new_c.push_back(at(N-1));   //add the last point on the fiber to the new fiber list
		//centerline newFiber(newPointList);
		return new_c;
	}
};
}	//end namespace stim
#endif