Sorting according to clockwise point coordinates

Question

Given a list in Python containing 8 x, y coordinate values (all positive) of 4 points as [x1, x2, x3, x4, y1, y2, y3, y4] ((xi, yi) are x and y coordinates of ith point ),

How can I sort it such that new list [a1, a2, a3, a4, b1, b2, b3, b4] is such that coordinates (ai, bi) of 1 2 3 4 are clockwise in order with 1 closest to origin of xy plane, i.e. something like

          2--------3
          |        |
          |        |
          |        |
          1--------4

Points will roughly form a parallelogram.

Currently, I am thinking of finding point with least value of (x+y) as 1, then 2 by the point with least x in remaining coordinates, 3 by largest value of (x + y) and 4 as the remaining point

Answer 1

import math

def centeroidpython(data):
    x, y = zip(*data)
    l = len(x)
    return sum(x) / l, sum(y) / l

xy = [405952.0, 408139.0, 407978.0, 405978.0, 6754659.0, 6752257.0, 6754740.0, 6752378.0]
xy_pairs = list(zip(xy[:int(len(xy)/2)], xy[int(len(xy)/2):]))

centroid_x, centroid_y = centeroidpython(xy_pairs)
xy_sorted = sorted(xy_pairs, key = lambda x: math.atan2((x[1]-centroid_y),(x[0]-centroid_x)))
xy_sorted_x_first_then_y = [coord for pair in list(zip(*xy_sorted)) for coord in pair]

Answer 2

As suggested by IgnacioVazquez-Abrams, we can also do sorting according to atan2 angles:

Code:

import math
import copy
import matplotlib.pyplot as plt

a = [2, 4, 5, 1, 0.5, 4, 0, 4]
print(a)


def clock(a):
    angles = []
    (x0, y0) = ((a[0]+a[1]+a[2]+a[3])/4, (a[4]+ a[5] + a[6] + a[7])/4)  # centroid
    for j in range(4):
        (dx, dy) = (a[j] - x0, a[j+4] - y0)
        angles.append(math.degrees(math.atan2(float(dy), float(dx))))
    for k in range(4):
        angles.append(angles[k] + 800)
    # print(angles)

    z = [copy.copy(x) for (y,x) in sorted(zip(angles,a), key=lambda pair: pair[0])]
    print("z is: ", z)

plt.scatter(a[:4], a[4:8])
plt.show()

clock(a)

Output is :

[2, 4, 5, 1, 0.5, 4, 0, 4]
[-121.60750224624891, 61.92751306414704, -46.73570458892839, 136.8476102659946, 678.3924977537511, 861.9275130641471, 753.2642954110717, 936.8476102659946]
z is:  [2, 5, 4, 1, 0.5, 0, 4, 4]

Answer 3

You should use a list of 2-item tuples as your data structure to represent a variable number of coordinates in a meaningful way.

from functools import reduce
import operator
import math
coords = [(0, 1), (1, 0), (1, 1), (0, 0)]
center = tuple(map(operator.truediv, reduce(lambda x, y: map(operator.add, x, y), coords), [len(coords)] * 2))
print(sorted(coords, key=lambda coord: (-135 - math.degrees(math.atan2(*tuple(map(operator.sub, coord, center))[::-1]))) % 360))

This outputs:

[(0, 0), (0, 1), (1, 1), (1, 0)]

Answer 4

# P4=8,10 P1=3,5   P2=8,5   P3=3,10
points=[8,3,8,3,10,5,5,10]
k=0
#we know these numbers are extreme and data won't be bigger than these
xmin=1000
xmax=-1000
ymin=1000
ymax=-1000
#finding min and max values of x and y
for i in points:
    if  k<4:
        if (xmin>i): xmin=i
        if (xmax<i): xmax=i        
    else:
        if (ymin>i): ymin=i
        if (ymax<i): ymax=i        
    k +=1

sortedlist=[xmin,xmin,xmax,xmax,ymin,ymax,ymax,ymin]
print(sortedlist)

output:[3, 3, 8, 8, 5, 10, 10, 5] for other regions you need to change sortedlist line. if center is inside the box then it will require more condition controlling

Answer 5

What we want to sort by is the angle from the start coordinate. I've used numpy here to interpret each vector from the starting coordinate as a complex number, for which there is an easy way of computing the angle (counterclockwise along the unit sphere)

def angle_with_start(coord, start):
    vec = coord - start
    return np.angle(np.complex(vec[0], vec[1]))

Full code:

import itertools
import numpy as np


def angle_with_start(coord, start):
    vec = coord - start
    return np.angle(np.complex(vec[0], vec[1]))


def sort_clockwise(points):
    # convert into a coordinate system
    # (1, 1, 1, 2) -> (1, 1), (1, 2)
    coords = [np.array([points[i], points[i+4]]) for i in range(len(points) // 2)]

    # find the point closest to the origin,
    # this becomes our starting point
    coords = sorted(coords, key=lambda coord: np.linalg.norm(coord))
    start = coords[0]
    rest = coords[1:]

    # sort the remaining coordinates by angle
    # with reverse=True because we want to sort by clockwise angle
    rest = sorted(rest, key=lambda coord: angle_with_start(coord, start), reverse=True)

    # our first coordinate should be our starting point
    rest.insert(0, start)
    # convert into the proper coordinate format
    # (1, 1), (1, 2) -> (1, 1, 1, 2)
    return list(itertools.chain.from_iterable(zip(*rest)))

Behavior on some sample inputs:

In [1]: a
Out[1]: [1, 1, 2, 2, 1, 2, 1, 2]

In [2]: sort_clockwise(a)
Out[2]: [1, 1, 2, 2, 1, 2, 2, 1]

In [3]: b
Out[3]: [1, 2, 0, 2, 1, 2, 3, 1]

In [4]: sort_clockwise(b)
Out[4]: [1, 0, 2, 2, 1, 3, 2, 1]