// Method Nearest Neighbor from Andrew Moore's thesis. Numbered
// comments are direct quotes from there. Step "SDL" is added to
// make the algorithm work correctly. NearestNeighborList solution
// courtesy of Bjoern Heckel.
public static void nnbr(KDNode kd, HPoint target, HRect hr,
float max_dist_sqd, int lev, int K,
NearestNeighborList nnl) {
// 1. if kd is empty then set dist-sqd to infinity and exit.
if (kd == null) {
return;
}
// 2. s := split field of kd
int s = lev % K;
// 3. pivot := dom-elt field of kd
HPoint pivot = kd.k;
float pivot_to_target = HPoint.sqrdist(pivot, target);
// 4. Cut hr into to sub-hyperrectangles left-hr and right-hr.
// The cut plane is through pivot and perpendicular to the s
// dimension.
HRect left_hr = hr; // optimize by not cloning
HRect right_hr = (HRect)hr.clone();
left_hr.max.coord[s] = pivot.coord[s];
right_hr.min.coord[s] = pivot.coord[s];
// 5. target-in-left := target_s <= pivot_s
bool target_in_left = target.coord[s] < pivot.coord[s];
KDNode nearer_kd;
HRect nearer_hr;
KDNode further_kd;
HRect further_hr;
// 6. if target-in-left then
// 6.1. nearer-kd := left field of kd and nearer-hr := left-hr
// 6.2. further-kd := right field of kd and further-hr := right-hr
if (target_in_left) {
nearer_kd = kd.left;
nearer_hr = left_hr;
further_kd = kd.right;
further_hr = right_hr;
}
//
// 7. if not target-in-left then
// 7.1. nearer-kd := right field of kd and nearer-hr := right-hr
// 7.2. further-kd := left field of kd and further-hr := left-hr
else {
nearer_kd = kd.right;
nearer_hr = right_hr;
further_kd = kd.left;
further_hr = left_hr;
}
// 8. Recursively call Nearest Neighbor with paramters
// (nearer-kd, target, nearer-hr, max-dist-sqd), storing the
// results in nearest and dist-sqd
nnbr(nearer_kd, target, nearer_hr, max_dist_sqd, lev + 1, K, nnl);
KDNode nearest = (KDNode)nnl.getHighest();
float dist_sqd;
if (!nnl.isCapacityReached()) {
dist_sqd = float.MaxValue;
}
else {
dist_sqd = nnl.getMaxPriority();
}
// 9. max-dist-sqd := minimum of max-dist-sqd and dist-sqd
max_dist_sqd = Math.Min(max_dist_sqd, dist_sqd);
// 10. A nearer point could only lie in further-kd if there were some
// part of further-hr within distance sqrt(max-dist-sqd) of
// target. If this is the case then
HPoint closest = further_hr.closest(target);
if (HPoint.Distance(ref closest, ref target) < Math.Sqrt(max_dist_sqd)) {
// 10.1 if (pivot-target)^2 < dist-sqd then
if (pivot_to_target < dist_sqd) {
// 10.1.1 nearest := (pivot, range-elt field of kd)
nearest = kd;
// 10.1.2 dist-sqd = (pivot-target)^2
dist_sqd = pivot_to_target;
// add to nnl
if (!kd.deleted) {
nnl.insert(kd, dist_sqd);
}
// 10.1.3 max-dist-sqd = dist-sqd
// max_dist_sqd = dist_sqd;
if (nnl.isCapacityReached()) {
max_dist_sqd = nnl.getMaxPriority();
}
else {
max_dist_sqd = float.MaxValue;
}
}
// 10.2 Recursively call Nearest Neighbor with parameters
// (further-kd, target, further-hr, max-dist_sqd),
// storing results in temp-nearest and temp-dist-sqd
nnbr(further_kd, target, further_hr, max_dist_sqd, lev + 1, K, nnl);
KDNode temp_nearest = (KDNode)nnl.getHighest();
float temp_dist_sqd = nnl.getMaxPriority();
// 10.3 If tmp-dist-sqd < dist-sqd then
if (temp_dist_sqd < dist_sqd) {
// 10.3.1 nearest := temp_nearest and dist_sqd := temp_dist_sqd
nearest = temp_nearest;
dist_sqd = temp_dist_sqd;
}
}
// SDL: otherwise, current point is nearest
else if (pivot_to_target < max_dist_sqd) {
nearest = kd;
dist_sqd = pivot_to_target;
}
}
/**
* Find KD-tree nodes whose keys are <I>n</I> nearest neighbors to
* key. Uses algorithm above. Neighbors are returned in ascending
* order of distance to key.
*
* @param key key for KD-tree node
* @param n how many neighbors to find
*
* @return objects at node nearest to key, or null on failure
*
* @throws KeySizeException if key.length mismatches K
* @throws IllegalArgumentException if <I>n</I> is negative or
* exceeds tree size
*/
public Object[] nearest(float[] key, int n) {
if (n < 0 || n > m_count) {
throw new ArgumentException("Number of neighbors cannot be negative or greater than number of nodes");
}
if (key.Length != m_K) {
throw new ApplicationException("new KeySizeException(");
}
Object[] nbrs = new Object[n];
NearestNeighborList nnl = new NearestNeighborList(n);
// initial call is with infinite hyper-rectangle and max distance
HRect hr = new AABB();
float max_dist_sqd = float.MaxValue;
HPoint keyp = new HPoint(key);
KDNode.nnbr(m_root, keyp, hr, max_dist_sqd, 0, m_K, nnl);
for (int i = 0; i < n; ++i) {
KDNode kd = (KDNode)nnl.removeHighest();
nbrs[n - i - 1] = kd.v;
}
return nbrs;
}