math-research/papers/medial_tire_cuts/experiments/draw_medial_tire_cut.py

"""Draw the walk-depth labelling and cut of a medial tire decomposition.

Paper-graphics companion to ``run_medial_tire_cut_experiment.py``: it imports
``run_experiment`` from there, runs the pipeline on a random maximal planar
graph, and emits TikZ.  By default it draws one ``tikzpicture`` (walk-depth
labels + cut slits) per recognised full medial tire graph, using ``to_tikz``
from ``medial_tire_cut_labelling``.  With ``--whole`` it instead draws the whole
medial graph M(G) with every tire's cuts applied, on a Kamada--Kawai layout, the
recognised tires highlighted and the rest of M(G) in grey.

This script only renders; the experiment itself draws nothing.  Run with the
repo venv (networkx): ``.venv/bin/python``.

Examples:
    .venv/bin/python draw_medial_tire_cut.py -n 20 --seed 72 > panels.tex
    .venv/bin/python draw_medial_tire_cut.py -n 20 --seed 72 --whole > whole.tex
"""

from __future__ import annotations

import argparse
import math
import os
import sys

import networkx as nx

_HERE = os.path.dirname(os.path.abspath(__file__))
sys.path.insert(0, _HERE)

from run_medial_tire_cut_experiment import run_experiment  # noqa: E402
from medial_tire_cut_labelling import to_tikz  # noqa: E402


def tikz_panels(n: int, seed: int, scale: float = 1.6) -> tuple[dict, list[str]]:
    """Run the experiment and return ``(result, panels)``, one TikZ panel per
    recognised tread, each showing that tread's walk-depth labelling and cut."""
    result = run_experiment(n=n, seed=seed)
    panels = []
    for d in sorted(result["results"]):
        rec = result["results"][d]
        panels.append(to_tikz(rec["g"], depth=rec["depth"], cuts=rec["cuts"],
                              entry_edge=rec["entry_edge"], scale=scale))
    return result, panels


# --------------------------------------------------------------------------- #
# The whole medial graph: M(G) with all tire cuts applied.
# --------------------------------------------------------------------------- #

def _is_split(node) -> bool:
    return isinstance(node, tuple) and len(node) == 3 and node[1] in ("A", "B")


def _medial_layout(H: nx.Graph) -> dict:
    """A Kamada--Kawai layout of the (planar) cut graph, normalised to the unit
    box.  The two copies of a cut vertex have different neighbours, so the layout
    separates them automatically, showing the slit."""
    pos = nx.kamada_kawai_layout(H)
    xs = [p[0] for p in pos.values()]
    ys = [p[1] for p in pos.values()]
    cx, cy = 0.5 * (max(xs) + min(xs)), 0.5 * (max(ys) + min(ys))
    span = max(max(xs) - min(xs), max(ys) - min(ys)) or 1.0
    return {v: ((p[0] - cx) / span, (p[1] - cy) / span) for v, p in pos.items()}


def medial_tikz(result: dict, scale: float = 9.0) -> str:
    """A TikZ ``tikzpicture`` of the whole medial graph M(G) with every tire's
    cuts applied.  Tire teeth are coloured and carry their walk depth; annular
    medial vertices are black; medial vertices outside any recognised tire are
    grey; cut (split) vertices are drawn as separated copies."""
    H = result["cut_graph"]
    pos = _medial_layout(H)

    # role of each medial vertex: annular / up / down / bite, and walk depth.
    annular = set()
    for d in sorted(result["results"]):
        g, bij = result["results"][d]["g"], result["results"][d]["bij"]
        annular.update(bij[f"a{k}"] for k in range(g.n))
    apex = {r["apex"]: (r["role"], r["walk"]) for r in result["labels"]}

    def edge_of(node):
        return node[0] if _is_split(node) else node

    L = []
    A = L.append
    A(f"\\begin{{tikzpicture}}[scale={scale},")
    A("    med/.style={black!30, line width=0.3pt},")
    A("    grey/.style={circle, draw=black!45, fill=black!8, inner sep=0.9pt},")
    A("    ann/.style={circle, fill=black, inner sep=1.0pt},")
    A("    cutv/.style={circle, draw=red!75!black, fill=red!12, inner sep=1.0pt},")
    A("    upv/.style={circle, draw=blue!70!black, fill=blue!15, inner sep=1.3pt},")
    A("    downv/.style={circle, draw=red!70!black, fill=red!15, inner sep=1.3pt},")
    A("    bitev/.style={circle, draw=red!70!black, fill=red!35, inner sep=1.6pt},")
    A("    dlbl/.style={font=\\tiny\\bfseries, text=black, inner sep=0.5pt}]")

    def pt(node):
        x, y = pos[node]
        return f"({x:.3f},{y:.3f})"

    for u, v in H.edges():
        A(f"\\draw[med] {pt(u)}--{pt(v)};")
    for node in H.nodes():
        mv = edge_of(node)
        if mv in apex:
            role, _ = apex[mv]
            style = {"up": "upv", "down": "downv", "bite": "bitev"}[role]
        elif mv in annular:
            style = "cutv" if _is_split(node) else "ann"
        else:
            style = "grey"
        A(f"\\node[{style}] at {pt(node)} {{}};")
    for node in H.nodes():
        mv = edge_of(node)
        if _is_split(node) or mv not in apex:
            continue
        x, y = pos[node]
        A(f"\\node[dlbl] at ({x:.3f},{y:.3f}) [yshift=4.5pt] {{{apex[mv][1]}}};")
    A("\\end{tikzpicture}")
    return "\n".join(L)


def main() -> None:
    parser = argparse.ArgumentParser(description=__doc__,
                                     formatter_class=argparse.RawDescriptionHelpFormatter)
    parser.add_argument("-n", type=int, default=20)
    parser.add_argument("--seed", type=int, default=72)
    parser.add_argument("--scale", type=float, default=1.6)
    parser.add_argument("--whole", action="store_true",
                        help="draw the whole medial graph M(G) with all cuts, "
                             "instead of one panel per tread")
    args = parser.parse_args()

    if args.whole:
        result = run_experiment(n=args.n, seed=args.seed)
        treads = sorted(result["results"])
        print(f"% whole medial graph: n={args.n} seed={args.seed} "
              f"source={result['source']} recognised treads={treads} "
              f"|M(G)|={result['M'].number_of_nodes()}")
        print(medial_tikz(result, scale=args.scale if args.scale != 1.6 else 9.0))
        return

    result, panels = tikz_panels(args.n, args.seed, scale=args.scale)
    treads = sorted(result["results"])
    print(f"% medial tire cut: n={args.n} seed={args.seed} "
          f"source={result['source']} recognised treads={treads}")
    if not panels:
        print("% (no recognised full medial tire graphs for this graph)")
    for d, panel in zip(treads, panels):
        g = result["results"][d]["g"]
        print(f"% --- tread {d}: |A(T)|={g.n} word={g.tooth_word} "
              f"bites={sorted(g.bites)} ---")
        print(panel)


if __name__ == "__main__":
    main()