我如何排序的坐标列表逆时针矩形？ [英] How can I sort a coordinate list for a rectangle counterclockwise?

问题描述

我需要一个坐标列表为矩形整理逆时针，使东北角的第一个坐标。这些地理坐标（即经度，纬度）十进制形式。 ¹

I need to sort a coordinate list for a rectangle counterclockwise, and make the north-east corner the first coordinate. These are geographic coordinates (i.e. Longitude, Latitude) in decimal form.¹

例如，这里有4个角的矩形的，从西北角落，顺时针方向：

For example, here are the 4 corners of a rectangle, starting with the north-west corner and moving clockwise:

[
  { "lat": 34.495239, "lng": -118.127747 }, # north-west
  { "lat": 34.495239, "lng": -117.147217 }, # north-east
  { "lat": 34.095174, "lng": -117.147217 }, # south-east
  { "lat": 34.095174, "lng": -118.127747 }  # south-west
]

我需要梳理这些逆时针和改变锚/起点是东北：

I need to sort these counterclockwise and change the "anchor"/starting point to be north-east:

[
  { "lat": 34.495239, "lng": -117.147217 }, # north-east
  { "lat": 34.495239, "lng": -118.127747 }, # north-west
  { "lat": 34.095174, "lng": -118.127747 }, # south-west
  { "lat": 34.095174, "lng": -117.147217 }  # south-east
]

我不知道什么样的顺序名单将在最初（即顺时针或逆时针）。我不知道哪个角落里重新presents列表中的第一个坐标。

I do not know what order the list will be in initially (i.e. clockwise or counterclockwise). I do not know which corner the first coordinate in the list represents.

---

¹ <子>这不是在映射到地球表面，但因为我有两个相对的角落，我呼吁它的可读性矩形真正的矩形。形状包装+ 180 / -180经度或+ 90 / -90纬度是不是一个问题。

推荐答案

解决方案似乎pretty的简单：

solution seems pretty straightforward:

>>> import math
>>> mlat = sum(x['lat'] for x in l) / len(l)
>>> mlng = sum(x['lng'] for x in l) / len(l)
>>> def algo(x):
    return (math.atan2(x['lat'] - mlat, x['lng'] - mlng) + 2 * math.pi) % (2*math.pi)

>>> l.sort(key=algo)

基本上，算法中正常化输入到 [0，二皮] 的空间，这将是自然排序逆时针。注意，操作者％和*操作具有相同的precedence所以括号周围（2 * math.pi）是重要的，以获得有效结果。

basically, algo normalises the input into the [0, 2pi] space and it would be naturally sorted "counter-clockwise". Note that the % operator and the * operator have the same precedence so the parenthesis around (2*math.pi) are important to get a valid result.

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