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 coo

Answer 1

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]