Move outer_face and get_embedding_from_pos to lib/planar_embedding

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

lib/planar_embedding.py

@@ -0,0 +1,51 @@
+"""Utilities for working with planar embeddings of graphs."""
+import math
+from typing import Any
+
+from sage.all import Graph  # type: ignore
+
+
+def outer_face(g: Graph) -> list[Any]:
+    """Return the vertices of the outer (unbounded) face of g using its planar embedding and positions."""
+    pos = g.get_pos()
+    embedding = g.get_embedding()
+    if not pos or not embedding:
+        raise Exception("Position and embedding required to find outer face")
+
+    visited: set[tuple[Any, Any]] = set()
+    faces: list[list[Any]] = []
+
+    for u in g.vertices():
+        for v in embedding[u]:
+            if (u, v) not in visited:
+                face: list[Any] = []
+                cu, cv = u, v
+                while (cu, cv) not in visited:
+                    visited.add((cu, cv))
+                    face.append(cu)
+                    neighbors = embedding[cv]
+                    cw = neighbors[(neighbors.index(cu) + 1) % len(neighbors)]
+                    cu, cv = cv, cw
+                faces.append(face)
+
+    def signed_area(face: list[Any]) -> float:
+        coords = [pos[v] for v in face]
+        n = len(coords)
+        return sum(
+            coords[i][0] * coords[(i + 1) % n][1] - coords[(i + 1) % n][0] * coords[i][1]
+            for i in range(n)
+        ) / 2
+
+    return min(faces, key=signed_area)
+
+
+def get_embedding_from_pos(g: Graph) -> dict[Any, list[Any]]:
+    """Compute a combinatorial planar embedding by sorting each vertex's neighbors by angle."""
+    pos_or_none = g.get_pos()
+    if pos_or_none is None:
+        raise Exception("Cannot get embedding without position")
+    pos: dict[Any, Any] = pos_or_none
+    return {
+        v: sorted(g.neighbors(v), key=lambda w: math.atan2(pos[w][1] - pos[v][1], pos[w][0] - pos[v][0]))
+        for v in g.vertices()
+    }