public KDNode(int index, KDNode parent = null, KDNode left = null, KDNode right = null)
{
this.ElementIndex = index;
this.Left = left;
this.Right = right;
this.Parent = parent;
}
public KDTreeNavigator(KDTree <TNode> tree, KDNode node)
{
this.tree = tree;
this.node = node;
}
/// <summary>
/// A top-down recursive method to find the nearest neighbors of a given point.
/// </summary>
/// <param name="node">The index of the node for the current recursion branch.</param>
/// <param name="target">The point whose neighbors we are trying to find.</param>
/// <param name="rect">The <see cref="HyperRect{T}"/> containing the possible nearest neighbors.</param>
/// <param name="dimension">The current splitting dimension for this recursion branch.</param>
/// <param name="nearestNeighbors">The <see cref="BoundedPriorityList{TElement,TPriority}"/> containing the nearest neighbors already discovered.</param>
/// <param name="maxSearchRadius">The radius of the current largest distance to search from the <paramref name="target"/></param>
private void SearchForNearestNeighbors(
KDNode node,
double[] target,
HyperRect <double> rect,
int dimension,
BoundablePriorityList <int, double> nearestNeighbors,
double maxSearchRadius)
{
if (node == null)
{
return;
}
// Work out the current dimension
var dim = dimension % this.Dimensions;
// Get the coordinate of the current node.
var coordinate = this.PointSelector(this.InternalList[node.ElementIndex]);
// Split our hyper-rectangle into 2 sub rectangles along the current
// node's point on the current dimension
var leftRect = rect.Clone();
leftRect.MaxPoint[dim] = coordinate[dim];
var rightRect = rect.Clone();
rightRect.MinPoint[dim] = coordinate[dim];
// Determine which side the target resides in
var comparison = target[dim] <= coordinate[dim];
var nearerRect = comparison ? leftRect : rightRect;
var furtherRect = comparison ? rightRect : leftRect;
var nearerNode = comparison ? node.Left : node.Right;
var furtherNode = comparison ? node.Right : node.Left;
// Move down into the nearer branch
this.SearchForNearestNeighbors(
nearerNode,
target,
nearerRect,
dimension + 1,
nearestNeighbors,
maxSearchRadius);
// Walk down into the further branch but only if our capacity hasn't been reached
// OR if there's a region in the further rectangle that's closer to the target than our
// current furtherest nearest neighbor
var closestPointInFurtherRect = furtherRect.GetClosestPoint(target);
var distanceToTarget = this.Metric(closestPointInFurtherRect, target);
if (distanceToTarget.CompareTo(maxSearchRadius) <= 0)
{
if (nearestNeighbors.IsFull)
{
if (distanceToTarget.CompareTo(nearestNeighbors.MaxPriority) < 0)
{
this.SearchForNearestNeighbors(
furtherNode,
target,
furtherRect,
dimension + 1,
nearestNeighbors,
maxSearchRadius);
}
}
else
{
this.SearchForNearestNeighbors(
furtherNode,
target,
furtherRect,
dimension + 1,
nearestNeighbors,
maxSearchRadius);
}
}
// Try to add the current node to our nearest neighbors list
distanceToTarget = this.Metric(coordinate, target);
if (distanceToTarget.CompareTo(maxSearchRadius) <= 0)
{
nearestNeighbors.Add(node.ElementIndex, distanceToTarget);
}
}
/// <summary>
/// Grows a KD tree recursively via median splitting. We find the median by doing a full sort.
/// </summary>
/// <param name="currentNode">The array index for the current node.</param>
/// <param name="dim">The current splitting dimension.</param>
/// <param name="points">The set of points remaining to be added to the KDTree.</param>
/// <param name="nodes">The set of nodes RE</param>
private void GenerateTree(
ref KDNode currentNode,
KDNode previousNode,
int dim,
IReadOnlyCollection <CoordinateWithIndex> points)
{
// See wikipedia for a good explanation KDTree construction.
// https://en.wikipedia.org/wiki/K-d_tree
// sort the points along the current dimension
var sortedPoints = points.OrderBy(z => z.Coordinate[dim]).ToArray();
// get the point which has the median value of the current dimension.
var medianPoint = sortedPoints[points.Count / 2];
var medianPointIdx = sortedPoints.Length / 2;
// The point with the median value all the current dimension now becomes the value of the current tree node
// The previous node becomes the parents of the current node.
currentNode = new KDNode(medianPoint.Index, previousNode);
previousNode = currentNode;
// We now split the sorted points into 2 groups
// 1st group: points before the median
var leftPoints = new CoordinateWithIndex[medianPointIdx];
Array.Copy(sortedPoints, leftPoints, leftPoints.Length);
// 2nd group: Points after the median
var rightPoints = new CoordinateWithIndex[sortedPoints.Length - (medianPointIdx + 1)];
Array.Copy(
sortedPoints,
medianPointIdx + 1,
rightPoints,
0,
rightPoints.Length);
// We new recurse, passing the left and right arrays for arguments.
// The current node's left and right values become the "roots" for
// each recursion call. We also forward cycle to the next dimension.
var nextDim = (dim + 1) % this.Dimensions; // select next dimension
// We only need to recurse if the point array contains more than one point
// If the array has no points then the node stay a null value
if (leftPoints.Length <= 1)
{
if (leftPoints.Length == 1)
{
currentNode.Left = new KDNode(leftPoints[0].Index, previousNode);
}
}
else
{
this.GenerateTree(ref currentNode.Left, currentNode, nextDim, leftPoints);
}
// Do the same for the right points
if (rightPoints.Length <= 1)
{
if (rightPoints.Length == 1)
{
currentNode.Right = new KDNode(rightPoints[0].Index, previousNode);
}
}
else
{
this.GenerateTree(ref currentNode.Right, currentNode, nextDim, rightPoints);
}
}
