Create A Cycle Out Of Scattered Points

I know this sounds trivial, but my head is refusing to give an algorithm for this. I have a bunch of points scattered on a 2-D plane and want to store them in a list such that they

Solution 1:

Here's an idea that will give okay-ish results if your point cloud is already ring-shaped like your example:

• Determine a centre point; this can either be the centre of gravity of all points or the centre of the bounding box.
• Represent all points in radial coordinates (radius, angle) with reference to the centre
• Sort by angle

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, 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, 0for x, y in points:
    x0 += x
    y0 += y

x0 = 1.0 * x0 / len(points)
y0 = 1.0 * y0 / len(points)

# calculate anglesfor i, p inenumerate(points):
    x, y = p
    phi = math.atan2(y - y0, x - x0)

    radial += [(i, phi)]

# sort by angledefrsort(a, b):
    """Sorting criterion for angles"""return cmp(a[1], b[1])

radial.sort(rsort)

# extract indices
ring = [a[0] for a in radial]