Spiral traversal of a list of coordinates

gistfile1.txt

# See https://gist.github.com/mkreyman/1891aaa70e41a3519a7487e7742a5eda
# for a spiral traversal of a matrix.
#
# coordinates =
#   [
#     {0, 0},
#     {1, 0},
#     {2, 0},
#     {3, 0},
#     {0, -1},
#     {1, -1},
#     {2, -1},
#     {3, -1},
#     {0, -2},
#     {1, -2},
#     {2, -2},
#     {3, -2},
#     {0, -3},
#     {1, -3},
#     {2, -3},
#     {3, -3}
#   ]
#
# iex(2)> Spiral.traverse(coordinates, [])
# [
#   {0, 0},
#   {1, 0},
#   {2, 0},
#   {3, 0},
#   {3, -1},
#   {3, -2},
#   {3, -3},
#   {2, -3},
#   {1, -3},
#   {0, -3},
#   {0, -2},
#   {0, -1},
#   {1, -1},
#   {2, -1},
#   {2, -2},
#   {1, -2}
# ]

defmodule Spiral do
  def traverse([], traversed), do: Enum.reverse(traversed)

  def traverse([head|[]], traversed) do
    traversed = [head | traversed]
    traverse([], traversed)
  end

  def traverse(coordinates, traversed) do
    a = anchor(coordinates)
    l = l(coordinates)
    h = h(coordinates)

    {filtered, coordinates} = Enum.split_with(coordinates, &(eastward?(&1, a, l, h)))
    filtered = filtered |> Enum.reverse()
    traversed = [filtered | traversed] |> List.flatten()
    {filtered, coordinates} = Enum.split_with(coordinates, &(southward?(&1, a, l, h)))
    filtered = filtered |> Enum.reverse()
    traversed = [filtered | traversed] |> List.flatten
    {filtered, coordinates} = Enum.split_with(coordinates, &(westward?(&1, a, l, h)))
    traversed = [filtered | traversed] |> List.flatten()
    {filtered, coordinates} = Enum.split_with(coordinates, &(northward?(&1, a, l, h)))
    traversed = [filtered | traversed] |> List.flatten()

    traverse(coordinates, traversed)
  end

  defp anchor(coordinates) do
    coordinates
    |> Enum.sort_by(fn({x, y}) -> {x,-y} end)
    |> Enum.at(0)
  end

  defp eastward?({x, y}, {start_x, start_y}, _l, _h) do
    x >= start_x and y == start_y
  end

  defp southward?({x, y}, {_, start_y}, l, _h) do
    x == l and y < start_y
  end

  defp westward?({x, y}, _, l, h) do
    x < l and y == h
  end

  defp northward?({x, y}, {start_x, _}, _l, h) do
    x == start_x and y > h
  end

  defp l(coordinates) do
    with {length, _} <- Enum.max_by(coordinates, fn({x,_}) -> x end), do: length
  end

  defp h(coordinates) do
    with {_, height} <- Enum.min_by(coordinates, fn({_,y}) -> y end), do: height
  end
end