Esto podría ser un poco como el uso de una sierra eléctrica para cortar el césped, pero aquí es un extracto de algoritmos en una cáscara de nuez
Creación de una KD-árbol ...
public class KDFactory {
// Known comparators for partitioning points along dimensional axes.
private static Comparator<IMultiPoint> comparators[ ] ;
// Recursively construct KDTree using median method on input points.
public static KDTree generate (IMultiPoint [ ] points) {
if (points. length == 0) { return null; }
// median will be the root.
int maxD = points[ 0] . dimensionality( );
KDTree tree = new KDTree(maxD) ;
// Make dimensional comparators that compare points by ith dimension
comparators = new Comparator[ maxD+1] ;
for (int i = 1; i <= maxD; i++) {
comparators[ i] = new DimensionalComparator(i) ;
}
tree. setRoot(generate (1, maxD, points, 0, points. length-1) ) ;
return tree;
}
// generate the node for the d-th dimension (1 <= d <= maxD)
// for points[ left, right]
private static DimensionalNode generate (int d, int maxD,
IMultiPoint points[ ] ,
int left, int right) {
// Handle the easy cases first
if (right < left) { return null; }
if (right == left) { return new DimensionalNode (d, points[ left] ) ; }
// Order the array[ left, right] so the mth element will be the median
// and the elements prior to it will all be <=, though they won' t
// necessarily be sorted; similarly, the elements after will all be >=
int m = 1+(right-left) /2;
Selection. select(points, m, left, right, comparators[ d] ) ;
// Median point on this dimension becomes the parent
DimensionalNode dm = new DimensionalNode (d, points[ left+m-1] ) ;
// update to the next dimension, or reset back to 1
if (++d > maxD) { d = 1; }
// recursively compute left and right sub-trees, which translate
// into ' below' and ' above' for n-dimensions.
dm. setBelow(maxD, generate (d, maxD, points, left, left+m-2) ) ;
dm. setAbove(maxD, generate (d, maxD, points, left+m, right) ) ;
return dm;
}
}
Encontrar mejores vecinos más cercanos: O (log n) peor O (n)
// method in KDTree
public IMultiPoint nearest (IMultiPoint target) {
if (root == null) return null;
// find parent node to which target would have been inserted. This is our
// best shot at locating closest point; compute best distance guess so far
DimensionalNode parent = parent(target) ;
IMultiPoint result = parent. point;
double smallest = target. distance(result) ;
// now start back at the root, and check all rectangles that potentially
// overlap this smallest distance. If better one is found, return it.
double best[ ] = new double[ ] { smallest };
double raw[ ] = target. raw( );
IMultiPoint betterOne = root. nearest (raw, best) ;
if (betterOne ! = null) { return betterOne; }
return result;
}
// method in DimensionalNode. min[ 0] contains best computed shortest distance.
IMultiPoint nearest (double[ ] rawTarget, double min[ ] ) {
// Update minimum if we are closer.
IMultiPoint result = null;
// If shorter, update minimum
double d = shorter(rawTarget, min[ 0] ) ;
if (d >= 0 && d < min[ 0] ) {
min[ 0] = d;
result = point;
}
// determine if we must dive into the subtrees by computing direct
// perpendicular distance to the axis along which node separates
// the plane. If d is smaller than the current smallest distance,
// we could "bleed" over the plane so we must check both.
double dp = Math. abs(coord - rawTarget[ dimension-1] ) ;
IMultiPoint newResult = null;
if (dp < min[ 0] ) {
// must dive into both. Return closest one.
if (above ! = null) {
newResult = above. nearest (rawTarget, min) ;
if (newResult ! = null) { result = newResult; }
}
if (below ! = null) {
newResult = below. nearest(rawTarget, min) ;
if (newResult ! = null) { result = newResult; }
}
} else {
// only need to go in one! Determine which one now.
if (rawTarget[ dimension-1] < coord) {
if (below ! = null) {
newResult = below. nearest (rawTarget, min) ;
}
} else {
if (above ! = null) {
newResult = above. nearest (rawTarget, min) ;
}
}
// Use smaller result, if found.
if (newResult ! = null) { return newResult; }
}
return result;
}
Más sobre KD-Árboles en la Wikipedia