Python 如何在kd树实现中包含同一分割线上的点

下面是KD树实现的python代码，代码如下：

from random import seed, random
from time import clock
from operator import itemgetter
from collections import namedtuple
from math import sqrt
from copy import deepcopy


def sqd(p1, p2):
    return sum((c1 - c2) ** 2 for c1, c2 in zip(p1, p2))


class KdNode(object):
    __slots__ = ("dom_elt", "split", "left", "right")

    def __init__(self, dom_elt, split, left, right):
        self.dom_elt = dom_elt
        self.split = split
        self.left = left
        self.right = right


class Orthotope(object):
    __slots__ = ("min", "max")

    def __init__(self, mi, ma):
        self.min, self.max = mi, ma


class KdTree(object):
    __slots__ = ("n", "bounds")

    def __init__(self, pts, bounds):
        def nk2(split, exset):
            if not exset:
                return None
            exset.sort(key=itemgetter(split))
            print('-------------------------------')
            print('set: ',exset, 'split: ',split)
            m = len(exset) // 2
            d = exset[m]
            print('pivot point:', d, 'm: ',m)
            while m + 1 < len(exset) and exset[m + 1][split] == d[split]:
                m += 1
            print('pivot point:', d, 'm: ',m)
            s2 = (split + 1) % len(d)  # cycle coordinates
            return KdNode(d, split, nk2(s2, exset[:m]),
                                    nk2(s2, exset[m + 1:]))
        self.n = nk2(0, pts)
        self.bounds = bounds


if __name__ == "__main__":
    seed(1)
    P = lambda *coords: list(coords)
    kd1 = KdTree([P(2, 3), P(5, 4), P(9, 6), P(4, 7), P(8, 1), P(7, 2)],
                  Orthotope(P(0, 0), P(10, 10)))

我稍微改变了这个例子，p（8,1）到p（7,1）（我画了下面的点）并发现p（7,2）不会变成KdNode，因为第一个轴心点是（7,1），KdNode将把集合分割成{[2,3]，[4,7]，[5,4]，[7,1]}和{[9,6]}，根据代码，这将使p（7,2）消失

我想知道在旋转点的同一条分割线上是否还有其他点（这里是垂直线交叉点（7,1）），应该包括哪一组p（7,2），以及何时必须将其作为KdNode

感谢您的阅读和帮助，我们将不胜感激

代码更改

返回KdNode（d，split，self.nk2（s2，exset[：m]），self.nk2（s2，exset[m+1:]）

到

返回KdNode（exset[m]，split，self.nk2（s2，exset[：m]），self.nk2（s2，exset[m+1:]）

虽然split对我来说看起来很奇怪，但我正在努力包含缺失的一点。不过我还是希望听到更好的答案！谢谢大家!

-------------------------------
set:  [[2, 3], [4, 7], [5, 4], [7, 1], [7, 2], [9, 6]] split:  0
pivot point: [7, 1] m:  3
pivot point: [7, 1] m:  4
-------------------------------
set:  [[7, 1], [2, 3], [5, 4], [4, 7]] split:  1
pivot point: [5, 4] m:  2
pivot point: [5, 4] m:  2
-------------------------------
set:  [[2, 3], [7, 1]] split:  0
pivot point: [7, 1] m:  1
pivot point: [7, 1] m:  1
-------------------------------
set:  [[2, 3]] split:  1
pivot point: [2, 3] m:  0
pivot point: [2, 3] m:  0
-------------------------------
set:  [[4, 7]] split:  0
pivot point: [4, 7] m:  0
pivot point: [4, 7] m:  0
-------------------------------
set:  [[9, 6]] split:  1
pivot point: [9, 6] m:  0
pivot point: [9, 6] m:  0