/// <summary>
/// Constructs a new instance of the KDNode.
/// </summary>
/// <param name="key">A Hyper Point representing the key to use for storing this value</param>
/// <param name="value">A valid object value to use for copying this.</param>
/// <remarks>The constructor is used only by class; other methods are static</remarks>
private KdNode(HPoint key, object value)
{
_k = key;
_v = value;
_left = null;
_right = null;
_isDeleted = false;
}
/// <summary>
/// Searches for values in a range
/// </summary>
/// <param name="lowk"></param>
/// <param name="uppk"></param>
/// <param name="t"></param>
/// <param name="lev"></param>
/// <param name="k"></param>
/// <param name="v"></param>
/// <remarks>Method rsearch translated from 352.range.c of Gonnet and Baeza-Yates</remarks>
public static void SearchRange(HPoint lowk, HPoint uppk, KdNode t, int lev,
int k, List<KdNode> v)
{
if (t == null) return;
if (lowk[lev] <= t._k[lev])
{
SearchRange(lowk, uppk, t._left, (lev + 1) % k, k, v);
}
int j;
for (j = 0; j < k && lowk[j] <= t._k[j] &&
uppk[j] >= t._k[j]; j++)
{
}
if (j == k) v.Add(t);
if (uppk[lev] > t._k[lev])
{
SearchRange(lowk, uppk, t._right, (lev + 1) % k, k, v);
}
}
/// <summary>
/// This method was written by Ted Dunsford by restructuring the nearest neighbor
/// algorithm presented by Andrew and Bjoern
/// </summary>
/// <param name="kd">Since this is recursive, this represents the current node</param>
/// <param name="target">The target is the HPoint that we are trying to calculate the farthest distance from</param>
/// <param name="hr">In this case, the hr is the hyper rectangle bounding the region that must contain the furthest point.</param>
/// <param name="maxDistSqd">The maximum distance that we have calculated thus far, and will therefore be testing against.</param>
/// <param name="lev">The integer based level of that we have recursed to in the tree</param>
/// <param name="k">The dimensionality of the kd tree</param>
/// <param name="fnl">A list to contain the output, prioritized by distance</param>
public static void FarthestNeighbor(KdNode kd, HPoint target, HRect hr,
double maxDistSqd, int lev, int k,
FarthestNeighborList fnl)
{
// 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;
double pivotToTarget = HPoint.SquareDistance(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 leftHr = hr; // optimize by not cloning
HRect rightHr = hr.Copy();
leftHr._max[s] = pivot[s];
rightHr._min[s] = pivot[s];
// 5. target-in-left := target_s <= pivot_s
bool targetInLeft = target[s] < pivot[s];
KdNode nearerKd;
HRect nearerHr;
KdNode furtherKd;
HRect furtherHr;
// 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 (targetInLeft)
{
nearerKd = kd._left;
nearerHr = leftHr;
furtherKd = kd._right;
furtherHr = rightHr;
}
//
// 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
{
nearerKd = kd._right;
nearerHr = rightHr;
furtherKd = kd._left;
furtherHr = leftHr;
}
// 8. Recursively call Nearest Neighbor with paramters
// (nearer-kd, target, nearer-hr, max-dist-sqd), storing the
// results in nearest and dist-sqd
//FarthestNeighbor(nearer_kd, target, nearer_hr, max_dist_sqd, lev + 1, K, nnl);
// This line changed by Ted Dunsford to attempt to find the farther point
FarthestNeighbor(furtherKd, target, furtherHr, maxDistSqd, lev + 1, k, fnl);
//KDNode nearest = (KDNode)nnl.Highest;
double distSqd;
if (!fnl.IsCapacityReached)
{
//dist_sqd = 1.79769e+30;// Double.MaxValue;
distSqd = 0;
}
else
{
distSqd = fnl.MinimumPriority;
}
// 9. max-dist-sqd := minimum of max-dist-sqd and dist-sqd
//max_dist_sqd = Math.Min(max_dist_sqd, dist_sqd);
maxDistSqd = Math.Max(maxDistSqd, distSqd);
// 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);
HPoint furthest = nearerHr.Farthest(target);
//if (HPoint.EuclideanDistance(closest, target) < Math.Sqrt(max_dist_sqd))
if(HPoint.EuclideanDistance(furthest, target) > Math.Sqrt(maxDistSqd))
{
// 10.1 if (pivot-target)^2 < dist-sqd then
if (pivotToTarget > distSqd)
{
// 10.1.1 nearest := (pivot, range-elt field of kd)
//nearest = kd;
// 10.1.2 dist-sqd = (pivot-target)^2
distSqd = pivotToTarget;
// add to nnl
if (!kd.IsDeleted)
{
fnl.Insert(kd, distSqd);
}
// 10.1.3 max-dist-sqd = dist-sqd
// max_dist_sqd = dist_sqd;
if (fnl.IsCapacityReached)
{
maxDistSqd = fnl.MinimumPriority;
}
else
{
// max_dist_sqd = 1.79769e+30;//Double.MaxValue;
maxDistSqd = 0;
}
}
// 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
FarthestNeighbor(nearerKd, target, nearerHr, maxDistSqd, lev + 1, k, fnl);
KdNode tempFarthest = (KdNode)fnl.Farthest;
double tempDistSqd = fnl.MinimumPriority;
// 10.3 If tmp-dist-sqd < dist-sqd then
if (tempDistSqd > distSqd)
{
// 10.3.1 nearest := temp_nearest and dist_sqd := temp_dist_sqd
distSqd = tempDistSqd;
}
}
// SDL: otherwise, current point is nearest
else if (pivotToTarget < maxDistSqd)
{
distSqd = pivotToTarget;
}
}
/// <summary>
/// Inserts a
/// </summary>
/// <param name="key"></param>
/// <param name="value"></param>
/// <param name="t"></param>
/// <param name="lev"></param>
/// <param name="k"></param>
/// <returns></returns>
/// <remarks> Method ins translated from 352.ins.c of Gonnet and Baeza-Yates</remarks>
public static KdNode Insert(HPoint key, object value, KdNode t, int lev, int k)
{
if (t == null)
{
t = new KdNode(key, value);
}
else if (key.Equals(t._k))
{
// "re-insert"
if (t.IsDeleted)
{
t.IsDeleted = false;
t._v = value;
}
else
{
throw (new KeyDuplicateException());
}
}
else if (key[lev] > t._k[lev])
{
t._right = Insert(key, value, t._right, (lev + 1) % k, k);
}
else
{
t._left = Insert(key, value, t._left, (lev + 1) % k, k);
}
return t;
}
/// <summary>
/// Searches for a specific value
/// </summary>
/// <param name="key"></param>
/// <param name="t"></param>
/// <param name="k"></param>
/// <returns></returns>
/// <remarks>Method srch translated from 352.srch.c of Gonnet and Baeza-Yates</remarks>
public static KdNode Search(HPoint key, KdNode t, int k)
{
for (int lev = 0; t != null; lev = (lev + 1) % k)
{
if (!t.IsDeleted && key.Equals(t._k))
{
return t;
}
t = key[lev] > t._k[lev] ? t._right : t._left;
}
return null;
}
/// <summary>
/// Calculates the distance in comparison with any coordinate. The coordinate with fewer dimensions
/// will determine the dimensionality for the comparison.
/// </summary>
/// <param name="p"></param>
/// <returns></returns>
public double HyperDistance(HPoint p)
{
return Math.Sqrt(SquareHyperDistance(p));
}
/// <summary>
/// Calculates the square of the Euclidean distance between this point and the other point.
/// </summary>
/// <param name="p">Any valid implementation of ICoordinate</param>
/// <returns>A double representing the distances.</returns>
public double SquareHyperDistance(HPoint p)
{
int maxOrdinate = Math.Min(p.NumOrdinates, NumOrdinates);
double dist = 0;
for (int i = 0; i < maxOrdinate; i++)
{
double diff = (p[i] - this[i]);
dist += (diff * diff);
}
return dist;
}
/// <summary>
/// A Static method for returning the square distance between two coordinates
/// </summary>
/// <param name="x">One coordinate</param>
/// <param name="y">A second coordinate</param>
/// <returns>A double representing the square distance</returns>
public static double SquareDistance(HPoint x, HPoint y)
{
HPoint a = x;
HPoint b = y;
int minOrdinate = Math.Min(x.NumOrdinates, y.NumOrdinates);
double dist = 0;
if (a != null && b != null)
{
// if we can calculate using direct access to the internal coord variable,
// it will be slightly faster.
for (int i = 0; i < minOrdinate; ++i)
{
double diff = (a[i] - b[i]);
dist += (diff * diff);
}
}
else
{
// otherwise, just use the standard ICoordinate accessors
for (int i = 0; i < minOrdinate; ++i)
{
double diff = (x[i] - y[i]);
dist += (diff * diff);
}
}
return dist;
}
/// <summary>
/// Calculates the Euclidean distance between the two coordinates
/// </summary>
/// <param name="x">An ICoordinate</param>
/// <param name="y">Another ICoordinate</param>
/// <returns>A double representing the distance</returns>
public static double EuclideanDistance(HPoint x, HPoint y)
{
return Math.Sqrt(SquareDistance(x, y));
}
/// <summary>
/// Calculates the closest point on the hyper-extent to the specified point.
/// from Moore's eqn. 6.6
/// </summary>
/// <param name="t"></param>
/// <returns></returns>
public HPoint Closest(HPoint t)
{
int len = t.NumOrdinates;
HPoint p = new HPoint(len);
for (int i = 0; i < len; ++i)
{
if (t[i] <= _min[i])
{
p[i] = _min[i];
}
else if (t[i] >= _max[i])
{
p[i] = _max[i];
}
else
{
p[i] = t[i];
}
}
return p;
}
/// <summary>
/// Find KD-tree nodes whose keys are <I>n</I> farthest neighbors from
/// key. Neighbors are returned in descending order of distance to key.
/// </summary>
/// <param name="key">key for KD-tree node</param>
/// <param name="numNeighbors">The Integer showing how many neighbors to find</param>
/// <returns>An array of objects at the node nearest to the key</returns>
/// <exception cref="KeySizeException">Mismatch if key length doesn't match the dimension for the tree</exception>
/// <exception cref="NeighborsOutOfRangeException">if <I>n</I> is negative or exceeds tree size </exception>
public object[] Farthest(double[] key, int numNeighbors)
{
if (numNeighbors < 0 || numNeighbors > _count) throw new NeighborsOutOfRangeException();
if (key.Length != _k) throw new KeySizeException();
object[] neighbors = new object[numNeighbors];
FarthestNeighborList fnl = new FarthestNeighborList(numNeighbors);
// initial call is with infinite hyper-rectangle and max distance
HRect hr = HRect.InfiniteHRect(key.Length);
//double max_dist_sqd = 1.79769e+30;//Double.MaxValue;
HPoint keyp = new HPoint(key);
KdNode.FarthestNeighbor(_root, keyp, hr, 0, 0, _k, fnl);
//KDNode.nnbr(_root, keyp, hr, max_dist_sqd, 0, _k, nnl);
for (int i = 0; i < numNeighbors; ++i)
{
KdNode kd = (KdNode)fnl.RemoveFarthest();
neighbors[numNeighbors - i - 1] = kd._v;
}
return neighbors;
}
/// <summary>
/// Creates a new bounding rectangle based on the two coordinates specified. It is assumed that
/// the vmin and vmax coordinates have already been correctly calculated.
/// </summary>
/// <param name="vmin"></param>
/// <param name="vmax"></param>
public HRect(HPoint vmin, HPoint vmax)
{
_min = vmin.Copy();
_max = vmax.Copy();
}
/// <summary>
/// Constructs a new instance of a rectangle binding structure based on a specified number of dimensions
/// </summary>
/// <param name="numDimensions">An integer representing the number of dimensions. For X, Y coordinates, this should be 2.</param>
public HRect(int numDimensions)
{
_min = new HPoint(numDimensions);
_max = new HPoint(numDimensions);
}
/// <summary>
/// If the specified HRect does not intersect this HRect, this returns null. Otherwise,
/// this will return a smaller rectangular region that represents the intersection
/// of the two bounding regions.
/// </summary>
/// <param name="region">Another HRect object to intersect with this one.</param>
/// <returns>The HRect that represents the intersection area for the two bounding boxes.</returns>
/// <remarks>currently unused</remarks>
public HRect Intersection(HRect region)
{
HPoint newmin = new HPoint(_min.NumOrdinates);
HPoint newmax = new HPoint(_min.NumOrdinates);
for (int i = 0; i < _min.NumOrdinates; ++i)
{
newmin[i] = Math.Max(_min[i], region._min[i]);
newmax[i] = Math.Min(_max[i], region._max[i]);
if (newmin[i] >= newmax[i]) return null;
}
return new HRect(newmin, newmax);
}
/// <summary>
/// Calculates a new HRect object that has a nearly infinite bounds.
/// </summary>
/// <param name="d">THe number of dimensions to use</param>
/// <returns>A new HRect where the minimum is negative infinity, and the maximum is positive infinity</returns>
/// <remarks>Used in initial conditions of KDTree.nearest()</remarks>
public static HRect InfiniteHRect(int d)
{
HPoint vmin = new HPoint(d);
HPoint vmax = new HPoint(d);
for (int i = 0; i < d; ++i)
{
vmin[i] = Double.NegativeInfinity;
vmax[i] = Double.PositiveInfinity;
}
return new HRect(vmin, vmax);
}
/// <summary>
/// This method calculates the furthest point on the rectangle
/// from the specified point. This is to determine if it is
/// possible for any of the members of the closer rectangle
/// to be positioned further away from the test point than
/// the points in the hyper-extent that is further from the point.
/// </summary>
/// <param name="t"></param>
/// <returns></returns>
public HPoint Farthest(HPoint t)
{
int len = t.NumOrdinates;
HPoint p = new HPoint(len);
for (int i = 0; i < len; ++i)
{
if (t[i] <= _min[i])
{
p[i] = _max[i];
}
else if (t[i] >= _max[i])
{
p[i] = _min[i];
}
else
{
// Calculating the closest position always uses the point, but
// to calculate the furthest position, we actually want to
// pick the furhter of two extremes, in order to pick up the
// diagonal distance.
// p[i] = t[i];
if (t[i] - _min[i] > _max[i] - t[i])
{
p[i] = _min[i];
}
else
{
p[i] = _max[i];
}
}
}
return p;
}
