ordering shuffled points that can be joined to form a polygon (in python)

Question

I have a collection of points that join to form a polygon in 2D cartesian space. It is in the form of a python list of tuples

[(x1, y1), (x2, y2), ... , (xn, yn)]

the problem is the join them and form a polygon in a graph. (I'm using matplotlib.path)

I made a function to do this. It works as follows:

it goes to first point ie (x1, y1) and joins a line to next point ie (x2, y2) and a line from (x2, y2) to (x3, y3) and so on .. till the end which is (xn, yn). It closes the polygon by joining (xn, yn) to (x1, y1).

The problem is the list containing these points does not contain the points in the right order so that results in bad drawings like these(Every closed polygon is colored automatically).

Example:

for this list of vertices = `[(-0.500000050000005, -0.5), (-0.499999950000005, 0.5), (-0.500000100000005, -1.0), (-0.49999990000000505, 1.0), (0.500000050000005, -0.5), (-1.0000000250000025, -0.5), (1.0000000250000025, -0.5), (0.499999950000005, 0.5), (-0.9999999750000024, 0.5), (0.9999999750000024, 0.5), (0.500000100000005, -1.0), (0.49999990000000505, 1.0), (-1.0, 0.0), (-0.0, -1.0), (0.0, 1.0), (1.0, 0.0), (-0.500000050000005, -0.5)]

The points: enter image description here

Bad order of points results in: enter image description here

Correct way to join: enter image description here

Is there any good (and easy if possible) algorithm to reorder the points to correct order? `

This doesn't sound like the most general solution, but have you tried connecting each point to the closest neighbor? — Lev Levitsky
yea I"ve tried connecting points to closest neighbour. It didn't work. Because there have been closest points but when we join them they lead to an intersections or points which are not so close but should be joined together — user5198

eudoxos eudoxos · Accepted Answer · 2012-06-01T09:39:57

This sorts your points according to polar coordinates:

import math
import matplotlib.patches as patches
import pylab
pp=[(-0.500000050000005, -0.5), (-0.499999950000005, 0.5), (-0.500000100000005, -1.0), (-0.49999990000000505, 1.0), (0.500000050000005, -0.5), (-1.0000000250000025, -0.5), (1.0000000250000025, -0.5), (0.499999950000005, 0.5), (-0.9999999750000024, 0.5), (0.9999999750000024, 0.5), (0.500000100000005, -1.0), (0.49999990000000505, 1.0), (-1.0, 0.0), (-0.0, -1.0), (0.0, 1.0), (1.0, 0.0), (-0.500000050000005, -0.5)]
# compute centroid
cent=(sum([p[0] for p in pp])/len(pp),sum([p[1] for p in pp])/len(pp))
# sort by polar angle
pp.sort(key=lambda p: math.atan2(p[1]-cent[1],p[0]-cent[0]))
# plot points
pylab.scatter([p[0] for p in pp],[p[1] for p in pp])
# plot polyline
pylab.gca().add_patch(patches.Polygon(pp,closed=False,fill=False))
pylab.grid()
pylab.show()

resulting polygon

ordering shuffled points that can be joined to form a polygon (in python)

2 Answers