问题描述
我知道这听起来微不足道，但我的头被拒绝给出一个算法这一点。
I know this sounds trivial, but my head is refusing to give an algorithm for this.
我有一堆散落在一个2-D平面上的点，并希望将它们存储在一个列表中，这样他们创造一个环。点不属于上一周期。
I have a bunch of points scattered on a 2-D plane and want to store them in a list such that they create a ring. The points do not belong on a cycle.
开始从该列表中的第一个点（红在这个图），并依次基于其距离其余添加
Start from the first point in the list (red in this pic) and sequentially add the rest based on their distance.
因为我不能回答我的问题，我会在这里发表一个可能的答案。
Since I cannot answer my question I will post here a possible answer.
这是似乎做这项工作的方法。V.pos保持节点和距离的位置（）仅仅是一个函数，返回两个点之间的欧几里得距离。更快的方法也将其附加到环后删除next_node，这样你就不必去通过已连接点
This is an approach that seems to do the job.V.pos holds the positions of the nodes and distance() is just a function that returns the Euclidean distance between two points. A faster approach would also delete the next_node after appending it to the ring so that you don't have to go through the already connected points
圈= [节点[0] 而LEN（圈）＆LT;的len（节点）： MINL = 99999 因为我在范围内（LEN（节点））： DIST =距离（V.pos [圈[-1]，V.pos [节点[I]） 如果DIST＆LT; MINL和节点[我]不响： MINL = DIST next_node =节点[I] ring.append（next_node）
ring = [nodes[0]] while len(ring) < len(nodes): minl=99999 for i in range(len(nodes)): dist = distance(V.pos[ring[-1]],V.pos[nodes[i]]) if dist<minl and nodes[i] not in ring: minl = dist next_node = nodes[i] ring.append(next_node)
推荐答案
下面有一个想法，这将使好吗杂交的结果，如果你的点云已经环形喜欢你的例子：
Here's an idea that will give okay-ish results if your point cloud is already ring-shaped like your example:
- 确定中心点;这既可以是中心的所有点的重心或边界框的中心。
- 重新present径向坐标（半径，角度）参照所有点到中心
- 排序角度
这当然会，产生锯齿星为随机的云彩，但目前尚不清楚，到底什么是环是。你也许可以用这个作为一个初稿，并开始交换节点，如果说给你一个较短的总距离。也许这种简单的code是所有你需要实现短的最小距离过图的所有节点。
This will, of course, produce jagged stars for random clouds, but it is not clear, what exactly a "ring" is. You could probably use this as a first draft and start swapping nodes if that gives you a shorter overall distance. Maybe this simple code is all you need short of implementing the minimum distance over all nodes of a graph.
Anayway，这里有云：
Anayway, here goes:
import math
points = [(0, 4), (2, 2), ...] # original points in Cartesian coords
radial = [] # list of tuples(index, angle)
# find centre point (centre of gravity)
x0, y0 = 0, 0
for x, y in points:
x0 += x
y0 += y
x0 = 1.0 * x0 / len(points)
y0 = 1.0 * y0 / len(points)
# calculate angles
for i, p in enumerate(points):
x, y = p
phi = math.atan2(y - y0, x - x0)
radial += [(i, phi)]
# sort by angle
def rsort(a, b):
"""Sorting criterion for angles"""
return cmp(a[1], b[1])
radial.sort(rsort)
# extract indices
ring = [a[0] for a in radial]
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