"""Utilities for constructing edge graphs from planar graphs."""
from typing import Any, cast
from sage.all import Graph


def get_edge_graph_pos(edge_graph: Graph, pos_src: dict[Any, Any]) -> dict[Any, tuple[Any, Any]]:
    """Return a position dict for edge graph vertices, using midpoints of the source positions."""
    pos: dict[Any, tuple[Any, Any]] = {}
    for e in cast(list[Any], edge_graph.vertices()):  # type: ignore
        pos[e] = (
            (pos_src[e[0]][0] + pos_src[e[1]][0]) / 2,
            (pos_src[e[0]][1] + pos_src[e[1]][1]) / 2
        )
    return pos


def get_edge_graph(graph: Graph, set_pos: bool = True) -> Graph:
    """Return the edge graph of the given graph, optionally setting vertex positions."""
    pos_src: dict[Any, Any] | None = None
    pos: dict[Any, tuple[Any, Any]] = {}
    if set_pos:
        pos_src = cast(dict[Any, Any], graph.get_pos())  # type: ignore

    g = Graph()
    for e in cast(list[Any], graph.edges()):  # type: ignore
        g.add_vertex(e)  # type: ignore
        if pos_src:
            pos[e] = (
                (pos_src[e[0]][0] + pos_src[e[1]][0]) / 2,
                (pos_src[e[0]][1] + pos_src[e[1]][1]) / 2
            )

    for v in cast(list[Any], graph.vertices()):  # type: ignore
        incident_edges = cast(list[Any], graph.edges_incident(v))  # type: ignore
        if len(incident_edges) == 1:
            continue
        for i, e1 in enumerate(incident_edges):
            e2 = incident_edges[(i + 1) % len(incident_edges)]
            g.add_edge(e1, e2)  # type: ignore
    if set_pos:
        g.set_pos(pos)  # type: ignore
    return g