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#include <iterator>
#include <iostream>
#include <vector>
#include <Eigen/Dense>
#include "KDTree.h"
using namespace std;
using namespace Eigen;
namespace StOpt
{
/// compare in a given dimension 2 points
class comparePt
{
public:
size_t m_idx;
explicit comparePt(size_t p_idx): m_idx(p_idx) {}
// inline bool compareInDim(
bool operator()(
const pair< ArrayXd, size_t > &a,
const pair< ArrayXd, size_t > &b
)
{
return (a.first(m_idx) < b.first(m_idx));
}
};
inline double dist2(const ArrayXd &a, const ArrayXd &b)
{
double distc = 0;
for (int i = 0; i < a.size(); i++)
{
double di = a(i) - b(i);
distc += di * di;
}
return distc;
}
inline double dist2(const shared_ptr< KDNode > &a, const shared_ptr< KDNode > &b)
{
return dist2(a->getPoint(), b->getPoint());
}
KDTree::KDTree(const ArrayXXd &points)
{
m_leaf = make_shared<KDNode>();
vector< pair< ArrayXd, size_t> > vecPoints(points.cols());
for (int i = 0; i < points.cols(); ++i)
vecPoints[i] = make_pair(points.col(i), i);
auto beg = vecPoints.begin();
auto end = vecPoints.end();
int level = 0;
m_root = createTree(beg, end, vecPoints.size(), level);
}
shared_ptr<KDNode> KDTree::createTree(const vector<pair< ArrayXd, size_t>>::iterator &p_beg,
const vector<pair< ArrayXd, size_t>>::iterator &p_end,
const size_t &p_nbPoints,
const size_t &p_level)
{
if (p_beg == p_end)
{
return shared_ptr< KDNode >(); // empty tree
}
size_t dim = p_beg->first.size();
if (p_nbPoints > 1)
{
sort(p_beg, p_end, comparePt(p_level));
}
auto middle = p_beg + (p_nbPoints / 2);
auto lbeg = p_beg;
auto lend = middle;
auto rbeg = middle + 1;
auto rend = p_end;
size_t llen = p_nbPoints / 2;
size_t rlen = p_nbPoints - llen - 1;
shared_ptr< KDNode > left;
if (llen > 0 && dim > 0)
{
left = createTree(lbeg, lend, llen, (p_level + 1) % dim);
}
else
{
left = m_leaf;
}
shared_ptr< KDNode > right;
if (rlen > 0 && dim > 0)
{
right = createTree(rbeg, rend, rlen, (p_level + 1) % dim);
}
else
{
right = m_leaf;
}
// KDNode result = KDNode();
return make_shared< KDNode >(*middle, left, right);
}
shared_ptr< KDNode > KDTree::nearest(
const shared_ptr< KDNode > &p_branch,
const ArrayXd &p_pt,
const size_t &p_level,
const shared_ptr< KDNode > &p_best,
const double &p_bestDist) const
{
double d, dx, dx2;
if (p_branch->isEmpty())
{
return make_shared<KDNode>(); // basically, null
}
ArrayXd branchPt = p_branch->getPoint();
size_t dim = branchPt.size();
d = dist2(branchPt, p_pt);
dx = branchPt(p_level) - p_pt(p_level);
dx2 = dx * dx;
shared_ptr< KDNode > bestLoc = p_best;
double bestDistLoc = p_bestDist;
if (d < p_bestDist)
{
bestDistLoc = d;
bestLoc = p_branch;
}
size_t nextLevel = (p_level + 1) % dim;
shared_ptr< KDNode > section;
shared_ptr< KDNode > other;
// select which p_branch to check
if (dx > 0)
{
section = p_branch->getLeft();
other = p_branch->getRight();
}
else
{
section = p_branch->getRight();
other = p_branch->getLeft();
}
// keep nearest neighbor from further down the tree
shared_ptr< KDNode > further = nearest(section, p_pt, nextLevel, bestLoc, bestDistLoc);
if (!further->isEmpty())
{
double dl = dist2(further->getPoint(), p_pt);
if (dl < bestDistLoc)
{
bestDistLoc = dl;
bestLoc = further;
}
// only check the other p_branch if it makes sense to do so
if (dx2 < bestDistLoc)
{
further = nearest(other, p_pt, nextLevel, bestLoc, bestDistLoc);
if (!further->isEmpty())
{
dl = dist2(further->getPoint(), p_pt);
if (dl < bestDistLoc)
{
bestDistLoc = dl;
bestLoc = further;
}
}
}
}
return bestLoc;
}
shared_ptr< KDNode > KDTree::nearestNode(const ArrayXd &p_pt) const
{
size_t level = 0;
double branchDist = dist2(m_root->getPoint(), p_pt);
return nearest(m_root, // beginning of tree
p_pt, // point we are querying
level, // start from level 0
m_root, // best is the root
branchDist); // best_dist = branch_dist
}
}
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