"""Module for performing tutte embeddings"""
from typing import Iterable, cast, Any
from sage.all import vector, Graph, cos, pi, sin # type: ignore


def create_tutte_embedding(
    graph: Graph,
    outer_face: list[Any],
    max_iter: int=50,
    set_pos: bool = True) -> dict[Any, Any]:
    """
    Performs a tutte force embedding with a prescribed outer face on
    a given sage graph.

    For a description on tutte embeddings, see the video [here](\
    https://www.youtube.com/watch?v=mEzPPMhR8XE).
    """
    radius = 1000
    pos: dict[Any, Any] = {}
    num_outer_points = len(outer_face)
    for i, v in enumerate(outer_face):
        pos[v] = (
            radius * cos((i / num_outer_points) * 2 * pi),
            radius * sin((i / num_outer_points) * 2 * pi)
        )

    # start off setting all other points to (0, 0)
    num_inner_points = cast(int, graph.order()) - num_outer_points

    for i, v in enumerate(cast(Iterable[Any], graph.vertices())): # type: ignore
        if v in pos:
            continue
        pos[v] = (
            radius/3 * cos((i / num_inner_points) * 2 * pi),
            radius/3 * sin((i / num_inner_points) * 2 * pi)
        )

    i = 0
    while i < max_iter:
        for v in cast(Iterable[Any], graph.vertices()): # type: ignore
            if v in outer_face:
                continue
            neighbors = cast(list[Any], graph.neighbors(v)) # type: ignore
            deg = len(neighbors)
            x_desired = sum(map(lambda n: pos[n][0], neighbors)) / deg
            y_desired = sum(map(lambda n: pos[n][1], neighbors)) / deg
            pos[v] = tuple(
                vector(pos[v]) - vector([  # type: ignore
                    pos[v][0] - x_desired, pos[v][1] - y_desired
                ])
            )
        i += 1

    if set_pos:
        graph.set_pos(pos) # type: ignore

    return pos