KdTree最近邻居搜索算法无法正常工作

Question

I'm implementing a KdTree in java. I have most of the rest of the program done, but I can't seem to get my nearest neighbour search algorithm to work properly. It always returns the root node's values, no matter what. Here is my code:

public Point2D nearest(Point2D p) {

    if (root == null) //if there are no nodes in the tree
        return null;
    else
        return nearest(p, root, root.point);            

}

• rect is a RectHV object that corresponds to the bounds of the node's point.

   public Point2D nearest(Point2D p, Node n, Point2D nearest) { if (n == null) { return nearest; } if (p.distanceSquaredTo(nearest) > p.distanceSquaredTo(n.point)) { nearest = n.point; } if (n.xAxis) { //the xaxis value is a boolean, if it is true, //the node splits on the x axis, false it splits on y if (px() < n.point.x() && p.distanceSquaredTo(nearest) < n.rect.distanceTo(p)) { nearest = nearest(p, n.leftnode, nearest); System.out.println("look left 1"); } else { nearest = nearest(p, n.rightnode, nearest); System.out.println("look right 1"); } } else { if (py() < n.point.y() && p.distanceSquaredTo(nearest) < n.rect.distanceTo(p)) { nearest = nearest(p, n.leftnode, nearest); System.out.println("look left 2"); } else { nearest = nearest(p, n.rightnode, nearest); System.out.println("look right 2"); } } return nearest; 

  }

I'm thinking that my algorithm is too simple for the task. My rationale is that if the distanceSquared between the query point and a candidate point's rectangle is greater than the already established nearest point, then don't search down that tree.

Answer 1

The problems are (1) that the distance from the query point to the point defining a subtree is not a lower bound on the distance to all points in that subtree and (2) that the nearest point may lie in the "other" child.

To get a lower bound, you can track the bounding box of the points in the subtree on descent, and use the distance of the query point to the box. More simplistically, you can use the distance from the point to the half-plane defined by the most recent split. You need to explore both children (unless pruned).