centerline.h
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#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();
}
//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++) { // 90ยฐ 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--) { // 90ยฐ 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());
auto 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