Draw source-dual cut on a valid straight-line embedding

Store the combinatorial planar embedding in the result and lay out the
source graph with nx.planar_layout so no primal edges cross and each dual
node sits inside its own triangle, replacing the concentric layout that
produced crossings. Add a committed generate_full_walk.py that reproduces
the walk .md/.pdf/.png outputs, and regenerate the walk 1 and walk 2 dual
figures and PDFs (reports unchanged).

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

papers/medial_tire_cuts/experiments/full_walk/generate_full_walk.py

@@ -0,0 +1,200 @@
+"""Regenerate the ``full_walk`` contents (``.md`` report + ``_dual.png`` +
+``_tires.png`` + combined ``.pdf``) for each configured medial tire cut walk.
+
+Each walk fixes a reproducible source: a base maximal planar 5-connected graph
+``random_maximal_planar_5_connected(n, seed)``, a chosen triangular face, the
+deep-embedding cap vertex placed inside that face as the level source, and a
+root entry tooth.  The source-dual cut, its walk-distance labelling, and the
+figures are all read off the deep embedding ``G'`` (whose dual-cut figure is now
+drawn on a *valid straight-line embedding* of ``G'`` -- see
+``medial_tire_dual_cut_experiment._straight_line_source_layout``).
+
+Run with the repo venv::
+
+    ../../../.venv/bin/python generate_full_walk.py            # all walks
+    ../../../.venv/bin/python generate_full_walk.py --walk 1   # just walk 1
+"""
+
+from __future__ import annotations
+
+import argparse
+import os
+import sys
+
+import networkx as nx
+
+_HERE = os.path.dirname(os.path.abspath(__file__))
+_EXP = os.path.dirname(_HERE)
+sys.path.insert(0, _EXP)
+
+import medial_tire_dual_cut_experiment as E  # noqa: E402
+from run_medial_tire_cut_experiment import (  # noqa: E402
+    random_maximal_planar_5_connected,
+)
+
+
+# --------------------------------------------------------------------------- #
+# Walk configurations.  Each is fully reproducible from (n, seed, face, entry).
+# --------------------------------------------------------------------------- #
+
+WALKS = [
+    {
+        "index": 1,
+        "title": "Full medial tire cut walk 1",
+        "n": 20,
+        "seed": 59,
+        "face": (8, 9, 19),
+        "entry": 2,
+    },
+    {
+        "index": 2,
+        "title": "Full medial tire cut walk 2",
+        "n": 20,
+        "seed": 2,
+        "face": (4, 12, 11),
+        "entry": 3,
+    },
+]
+
+
+def build_result(cfg):
+    """Build the source-dual cut result dict for one walk configuration."""
+    G, graph_seed = random_maximal_planar_5_connected(
+        cfg["n"], cfg["seed"], min_connectivity=5)
+    G_prime, cap, depth = E.deep_embedding(G, cfg["face"])
+    result = E.medial_tire_dual_cut(G_prime, cap, cfg["entry"])
+    result["base_graph"] = G
+    result["chosen_face"] = tuple(cfg["face"])
+    result["cap_vertex"] = cap
+    result["deep_depth"] = depth
+    result["graph_seed"] = graph_seed
+    result["base_min_degree"] = min(dict(G.degree()).values())
+    result["base_connectivity"] = nx.node_connectivity(G)
+    result["min_degree"] = min(dict(G_prime.degree()).values())
+    result["connectivity"] = nx.node_connectivity(G_prime)
+    return result
+
+
+def _tree_report(result):
+    """``(is_tree, n_faces, n_edges, n_components, acyclic)`` for the cut."""
+    cut = E.dual_cut_graph(result)
+    n = cut.number_of_nodes()
+    e = cut.number_of_edges()
+    comps = nx.number_connected_components(cut)
+    return nx.is_tree(cut), n, e, comps, (e == n - comps)
+
+
+def _distance_histogram(dist):
+    """Histogram of dual faces by walk distance, as an ordered dict."""
+    hist = {}
+    for d in dist.values():
+        hist[d] = hist.get(d, 0) + 1
+    return {k: hist[k] for k in sorted(hist)}
+
+
+def render_markdown(result, cfg):
+    """The walk report in the committed ``.md`` format."""
+    G = result["G"]
+    base = result["base_graph"]
+    removed = result["removed_dual_edges"]
+    res = result["results"]
+    i = cfg["index"]
+    em = result["entry_medial_vertex"]
+
+    is_tree, n_faces, n_edges, comps, acyclic = _tree_report(result)
+    dist, root = E.dual_cut_distances(result)
+    root_face = result["faces"][root]
+    hist = _distance_histogram(dist)
+    max_dist = max(dist.values()) if dist else 0
+
+    lines = [
+        f"# {cfg['title']}",
+        "",
+        f"- base vertices: {base.number_of_nodes()}",
+        f"- deep-embedded vertices: {G.number_of_nodes()}",
+        f"- deep-embedded edges: {G.number_of_edges()}",
+        f"- graph seed: {result['graph_seed']}",
+        f"- deep-embedded minimum degree: {result['min_degree']}",
+        f"- chosen face: {result['chosen_face']}",
+        f"- chosen source cap vertex: {result['source']}",
+        f"- root entry tooth: e{result['entry_edge']} "
+        f"(apex medial vertex = level-1 edge {em})",
+        f"- recognised treads: {len(res)}",
+        f"- skipped treads: {result['skipped']}",
+        f"- removed source-dual edges: {len(removed)}",
+        f"- annular/cap cuts: {len(result['annular_cut_edges'])}",
+        f"- up-apex cuts: {len(result['apex_cut_edges'])}",
+        "",
+        f"- **source-dual cut is a tree: {is_tree}** ({n_faces} dual faces, "
+        f"{n_edges} edges, {comps} component(s), acyclic={acyclic})",
+        "",
+        "## Walk-distance labelling of the source-dual cut",
+        "",
+        "Each dual face (vertex of the source-dual cut) is labelled by its "
+        "distance, within the cut, from the **cap down tooth of the first "
+        f"entry**: the triangular face `{root_face}` = "
+        f"`{{source {result['source']}, edge {em}}}` (dual node {root}).",
+        "",
+        f"- maximum distance: {max_dist}",
+        f"- distance histogram (faces by distance): `{hist}`",
+        "",
+        f"- dual cut figure: `full_medial_tire_cut_walk_{i}_dual.png`",
+        f"- tire cut grid: `full_medial_tire_cut_walk_{i}_tires.png`",
+        f"- combined PDF: `full_medial_tire_cut_walk_{i}.pdf`",
+        "",
+        "| tread | depth | component | annular | up | singleton down | "
+        "bite apexes | entry | closing cuts | up-apex cuts | "
+        "shared/entry skipped |",
+        "|--:|--:|--:|--:|--:|--:|--:|--:|--:|--:|--:|",
+    ]
+    for idx, key in enumerate(sorted(res), start=1):
+        d, comp = key
+        rec = res[key]
+        g, bij, entry = rec["g"], rec["bij"], rec["entry_edge"]
+        up = len(g.up_edges)
+        apex = len(E.up_apex_cuts(g, entry, bij))
+        lines.append(
+            f"| T{idx} | {d} | {comp} | {g.n} | {up} | "
+            f"{len(g.singleton_down_edges)} | {len(g.bites)} | e{entry} | "
+            f"{len(rec['cuts'])} | {apex} | {up - apex} |")
+    lines += [
+        "",
+        "## Removed Source-Dual Edges",
+        "",
+        f"- annular/cap: `{sorted(result['annular_cut_edges'])}`",
+        f"- up apexes: `{sorted(result['apex_cut_edges'])}`",
+        "",
+    ]
+    return "\n".join(lines)
+
+
+def generate(cfg):
+    """Build one walk and write its ``.md`` report and three figures."""
+    result = build_result(cfg)
+    i = cfg["index"]
+    stem = os.path.join(_HERE, f"full_medial_tire_cut_walk_{i}")
+
+    with open(f"{stem}.md", "w") as fh:
+        fh.write(render_markdown(result, cfg))
+    E.draw_png(result, f"{stem}_dual.png")
+    E.draw_tire_cuts_png(result, f"{stem}_tires.png")
+    E.draw_combined_pdf(result, f"{stem}.pdf")
+
+    print(f"walk {i}: wrote {stem}.md + _dual.png + _tires.png + .pdf")
+
+
+def main():
+    parser = argparse.ArgumentParser(
+        description=__doc__,
+        formatter_class=argparse.RawDescriptionHelpFormatter)
+    parser.add_argument("--walk", type=int, default=None,
+                        help="regenerate only this walk index (default: all)")
+    args = parser.parse_args()
+
+    for cfg in WALKS:
+        if args.walk is None or cfg["index"] == args.walk:
+            generate(cfg)
+
+
+if __name__ == "__main__":
+    main()

papers/medial_tire_cuts/experiments/medial_tire_dual_cut_experiment.py

@@ -304,7 +304,7 @@ def medial_tire_dual_cut(G, source, entry_edge):
     return {
         "G": G, "M": M, "source": source, "entry_edge": entry_edge,
         "entry_medial_vertex": entry_medial,
-        "faces": faces, "outer_face": 0,
+        "faces": faces, "embedding": emb, "outer_face": 0,
         "levels": levels, "treads": treads, "tread_meta": tread_meta,
         "skipped": skipped,
         "results": results, "cap_cuts": cap_cuts, "cut_graph": cut_graph,
@@ -415,40 +415,23 @@ def summary(result):
     return "\n".join(lines)
 
 
-def _radial_source_layout(G, source, levels):
+def _straight_line_source_layout(result):
-    """Concentric ('onion') layout rooted at the cap ``source``: radius grows
+    """A valid straight-line embedding of the source graph: vertex positions
-    with BFS level so the depth rings are actual circles, and each ring's
+    with no edge crossings.
-    angular order is inherited from its lower-level neighbours to keep the
+
-    nesting legible.  This matches the cap-source construction, where the BFS
+    Computed from the *same* combinatorial planar embedding that defines
-    rings are exactly the plane-depth rings."""
+    ``result["faces"]`` (stored as ``result["embedding"]``), so every dual face
-    import math
+    centroid lands strictly inside its triangle and the dual edges cross only
-    max_level = max(levels.values()) or 1
+    their own primal edge.  ``nx.planar_layout`` realises that embedding as a
-    ring = defaultdict(list)
+    crossing-free straight-line drawing via a canonical ordering; we tried a
-    for v, d in levels.items():
+    Tutte barycentric embedding instead, but the high-degree cap hub collapses
-        ring[d].append(v)
+    it into an unreadable sliver, whereas the canonical drawing spreads the
-    angle = {source: 0.0}
+    triangulation out legibly.  Falls back to recomputing the embedding for
-    pos = {source: (0.0, 0.0)}
+    older results that predate the stored ``embedding`` key."""
-    for d in range(1, max_level + 1):
+    emb = result.get("embedding")
-        verts = ring[d]
+    if emb is None:
-        prov = {}
+        _faces, emb = triangular_faces(result["G"])
-        for v in verts:
+    return nx.planar_layout(emb)
-            pa = [angle[w] for w in G.neighbors(v)
-                  if levels.get(w) == d - 1 and w in angle]
-            if pa:
-                sx = sum(math.cos(a) for a in pa)
-                sy = sum(math.sin(a) for a in pa)
-                prov[v] = math.atan2(sy, sx)
-            else:
-                prov[v] = 0.0
-        verts.sort(key=lambda v: prov[v] % (2 * math.pi))
-        k = len(verts)
-        base = prov[verts[0]] if verts else 0.0
-        r = d / max_level
-        for i, v in enumerate(verts):
-            a = base + 2 * math.pi * i / k
-            angle[v] = a
-            pos[v] = (r * math.cos(a), r * math.sin(a))
-    return pos
 
 
 def _draw_dual_cut_ax(ax, result):
@@ -459,7 +442,7 @@ def _draw_dual_cut_ax(ax, result):
     source = result["source"]
     entry_medial = result.get("entry_medial_vertex")
     dist, root = dual_cut_distances(result)
-    pos_v = _radial_source_layout(G, source, result["levels"])
+    pos_v = _straight_line_source_layout(result)
 
     def centroid(fi):
         xs = [pos_v[u][0] for u in faces[fi]]
@@ -542,13 +525,14 @@ def draw_png(result, path, scale=6.0):
     """Render the source-dual cut: dual nodes at face centroids, dual edges
     drawn light gray where the cut removed them, labelled by missing count.
 
-    The source graph is laid out concentrically around the cap source so the
+    The source graph is drawn on a valid straight-line embedding (see
-    BFS/plane-depth rings read as nested circles."""
+    ``_straight_line_source_layout``) so no primal edges cross and each dual
+    node sits inside its own triangle."""
     import matplotlib
     matplotlib.use("Agg")
     import matplotlib.pyplot as plt
 
-    fig, ax = plt.subplots(figsize=(7.6, 7.6))
+    fig, ax = plt.subplots(figsize=(12.0, 12.0))
     _draw_dual_cut_ax(ax, result)
     fig.tight_layout()
     fig.savefig(path, dpi=150)