52 lines
1.8 KiB
Python
52 lines
1.8 KiB
Python
"""Utilities for working with planar embeddings of graphs."""
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import math
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from typing import Any
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from sage.all import Graph # type: ignore
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def outer_face(g: Graph) -> list[Any]:
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"""Return the vertices of the outer (unbounded) face of g using its planar embedding and positions."""
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pos = g.get_pos()
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embedding = g.get_embedding()
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if not pos or not embedding:
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raise Exception("Position and embedding required to find outer face")
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visited: set[tuple[Any, Any]] = set()
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faces: list[list[Any]] = []
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for u in g.vertices():
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for v in embedding[u]:
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if (u, v) not in visited:
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face: list[Any] = []
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cu, cv = u, v
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while (cu, cv) not in visited:
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visited.add((cu, cv))
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face.append(cu)
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neighbors = embedding[cv]
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cw = neighbors[(neighbors.index(cu) + 1) % len(neighbors)]
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cu, cv = cv, cw
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faces.append(face)
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def signed_area(face: list[Any]) -> float:
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coords = [pos[v] for v in face]
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n = len(coords)
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return sum(
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coords[i][0] * coords[(i + 1) % n][1] - coords[(i + 1) % n][0] * coords[i][1]
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for i in range(n)
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) / 2
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return min(faces, key=signed_area)
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def get_embedding_from_pos(g: Graph) -> dict[Any, list[Any]]:
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"""Compute a combinatorial planar embedding by sorting each vertex's neighbors by angle."""
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pos_or_none = g.get_pos()
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if pos_or_none is None:
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raise Exception("Cannot get embedding without position")
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pos: dict[Any, Any] = pos_or_none
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return {
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v: sorted(g.neighbors(v), key=lambda w: math.atan2(pos[w][1] - pos[v][1], pos[w][0] - pos[v][0]))
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for v in g.vertices()
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}
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