From f537db975877d80c126a62ef78d34630160b4fec Mon Sep 17 00:00:00 2001 From: didericis Date: Mon, 15 Jun 2026 14:11:27 -0400 Subject: [PATCH] Draw random medial tire decompositions --- .../draw_random_medial_tire_decompositions.py | 480 ++++++++++++++++++ ...ndom_c5_n30_medial_tire_decomposition_1.md | 18 + ...dom_c5_n30_medial_tire_decomposition_1.pdf | Bin 0 -> 34659 bytes ...dom_c5_n30_medial_tire_decomposition_1.png | Bin 0 -> 367904 bytes ...ndom_c5_n30_medial_tire_decomposition_2.md | 17 + ...dom_c5_n30_medial_tire_decomposition_2.pdf | Bin 0 -> 34117 bytes ...dom_c5_n30_medial_tire_decomposition_2.png | Bin 0 -> 346202 bytes 7 files changed, 515 insertions(+) create mode 100644 papers/medial_tire_decompositions_of_plane_triangulations/experiments/draw_random_medial_tire_decompositions.py create mode 100644 papers/medial_tire_decompositions_of_plane_triangulations/experiments/random_medial_tire_decompositions/random_c5_n30_medial_tire_decomposition_1.md create mode 100644 papers/medial_tire_decompositions_of_plane_triangulations/experiments/random_medial_tire_decompositions/random_c5_n30_medial_tire_decomposition_1.pdf create mode 100644 papers/medial_tire_decompositions_of_plane_triangulations/experiments/random_medial_tire_decompositions/random_c5_n30_medial_tire_decomposition_1.png create mode 100644 papers/medial_tire_decompositions_of_plane_triangulations/experiments/random_medial_tire_decompositions/random_c5_n30_medial_tire_decomposition_2.md create mode 100644 papers/medial_tire_decompositions_of_plane_triangulations/experiments/random_medial_tire_decompositions/random_c5_n30_medial_tire_decomposition_2.pdf create mode 100644 papers/medial_tire_decompositions_of_plane_triangulations/experiments/random_medial_tire_decompositions/random_c5_n30_medial_tire_decomposition_2.png diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/draw_random_medial_tire_decompositions.py b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/draw_random_medial_tire_decompositions.py new file mode 100644 index 0000000..6a170a0 --- /dev/null +++ b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/draw_random_medial_tire_decompositions.py @@ -0,0 +1,480 @@ +"""Draw medial tire decompositions of random 5-connected triangulations. + +The source graphs come from ``plantri -c5`` in graph6 format. For each sampled +30-vertex triangulation, this script chooses a random source vertex, builds the +BFS depth-component tire tree, recognizes every full medial tire graph in the +decomposition, and draws both the tire tree and the realized full medial tire +graphs. +""" + +from __future__ import annotations + +import argparse +import math +import os +import random +import subprocess +import sys +from collections import defaultdict +from dataclasses import dataclass +from pathlib import Path + +PAPER_DIR = Path(__file__).resolve().parents[1] +REPO_ROOT = PAPER_DIR.parents[1] +os.environ.setdefault( + "MPLCONFIGDIR", str(PAPER_DIR / "experiments" / ".matplotlib-cache") +) +os.environ.setdefault("XDG_CACHE_HOME", str(PAPER_DIR / "experiments" / ".cache")) + +import matplotlib + +matplotlib.use("Agg") +import matplotlib.pyplot as plt +from matplotlib.lines import Line2D +import networkx as nx + +if str(PAPER_DIR) not in sys.path: + sys.path.insert(0, str(PAPER_DIR)) + +from lib.medial_tire_decomposition import ekey, medial_tire_facemodel, recognise +from lib.full_medial_tire_generator import FullMedialTireGraph + + +@dataclass(frozen=True) +class TreadNode: + idx: int + depth: int + face_indices: tuple[int, ...] + annular: frozenset + up: frozenset + down: frozenset + bites: frozenset + tires: tuple[tuple[FullMedialTireGraph, dict], ...] + + +def sample_plantri_graphs(n: int, count: int, seed: int, scan_limit: int) -> list[nx.Graph]: + cmd = [str(REPO_ROOT / "plantri" / "plantri"), "-g", "-c5", str(n)] + rng = random.Random(seed) + sample: list[tuple[int, nx.Graph]] = [] + seen = 0 + with subprocess.Popen(cmd, stdout=subprocess.PIPE, stderr=subprocess.PIPE) as proc: + assert proc.stdout is not None + for raw in proc.stdout: + line = raw.strip() + if not line or line.startswith(b">>"): + continue + graph = nx.from_graph6_bytes(line) + if nx.node_connectivity(graph) < 5: + continue + seen += 1 + if len(sample) < count: + sample.append((seen, graph)) + else: + j = rng.randrange(seen) + if j < count: + sample[j] = (seen, graph) + if seen >= scan_limit: + proc.terminate() + break + proc.wait(timeout=10) + if len(sample) < count: + raise RuntimeError(f"only found {len(sample)} graphs after scanning {seen}") + return [graph for _ordinal, graph in sample] + + +def triangular_faces(g: nx.Graph): + ok, emb = nx.check_planarity(g) + if not ok: + raise ValueError("not planar") + seen = set() + faces = [] + for u, v in list(emb.edges()): + if (u, v) in seen: + continue + face = tuple(emb.traverse_face(u, v, mark_half_edges=seen)) + faces.append(face) + return faces + + +def edge_face_data(faces): + face_edges = [] + edge_faces: dict[tuple, list[int]] = defaultdict(list) + for i, face in enumerate(faces): + edges = { + ekey(face[0], face[1]), + ekey(face[1], face[2]), + ekey(face[2], face[0]), + } + face_edges.append(edges) + for edge in edges: + edge_faces[edge].append(i) + return face_edges, edge_faces + + +def depth_components(faces, face_edges, edge_faces, levels): + depths = [min(levels[v] for v in face) for face in faces] + dual_adj: dict[int, set[int]] = defaultdict(set) + for incident in edge_faces.values(): + for a in range(len(incident)): + for b in range(a + 1, len(incident)): + dual_adj[incident[a]].add(incident[b]) + dual_adj[incident[b]].add(incident[a]) + + comps = [] + seen = [False] * len(faces) + for start in range(len(faces)): + if seen[start]: + continue + depth = depths[start] + stack = [start] + comp = [] + seen[start] = True + while stack: + face = stack.pop() + comp.append(face) + for other in dual_adj[face]: + if not seen[other] and depths[other] == depth: + seen[other] = True + stack.append(other) + comps.append((depth, tuple(sorted(comp)))) + return comps, depths, dual_adj + + +def tread_from_component(faces, levels, face_indices): + tread_faces = [faces[i] for i in face_indices] + if not tread_faces: + return None + depth = min(min(levels[v] for v in face) for face in tread_faces) + annular, up, down = set(), set(), set() + face_of_down = defaultdict(int) + for face in tread_faces: + for x, y in ((face[0], face[1]), (face[1], face[2]), (face[2], face[0])): + e = ekey(x, y) + lx, ly = levels[x], levels[y] + if {lx, ly} == {depth, depth + 1}: + annular.add(e) + elif lx == ly == depth: + up.add(e) + elif lx == ly == depth + 1: + down.add(e) + face_of_down[e] += 1 + if len(annular) < 3: + return None + return { + "tread_faces": tread_faces, + "annular": annular, + "up": up, + "down": down, + "bites": {e for e in down if face_of_down[e] == 2}, + } + + +def build_tire_tree(g: nx.Graph, source: int): + faces = triangular_faces(g) + face_edges, edge_faces = edge_face_data(faces) + levels = nx.single_source_shortest_path_length(g, source) + comps, depths, dual_adj = depth_components(faces, face_edges, edge_faces, levels) + comp_of_face = {} + for comp_idx, (_depth, face_indices) in enumerate(comps): + for face in face_indices: + comp_of_face[face] = comp_idx + + nodes: list[TreadNode] = [] + comp_to_node = {} + for comp_idx, (depth, face_indices) in enumerate(comps): + tread = tread_from_component(faces, levels, face_indices) + if tread is None or len(tread["up"]) < 3: + continue + mt = medial_tire_facemodel(tread["tread_faces"]) + tires = tuple(recognise(mt, tread)) + if not tires: + continue + node = TreadNode( + idx=len(nodes), + depth=depth, + face_indices=face_indices, + annular=frozenset(tread["annular"]), + up=frozenset(tread["up"]), + down=frozenset(tread["down"]), + bites=frozenset(tread["bites"]), + tires=tires, + ) + comp_to_node[comp_idx] = node.idx + nodes.append(node) + + tree_edges = set() + for comp_idx, (depth, face_indices) in enumerate(comps): + if comp_idx not in comp_to_node: + continue + child = comp_to_node[comp_idx] + parent_candidates = set() + for face in face_indices: + for other in dual_adj[face]: + other_comp = comp_of_face[other] + if depths[other] == depth - 1 and other_comp in comp_to_node: + parent_candidates.add(comp_to_node[other_comp]) + for parent in parent_candidates: + tree_edges.add((parent, child)) + return faces, levels, nodes, sorted(tree_edges) + + +def graph_layout(g: nx.Graph): + try: + return nx.planar_layout(g) + except nx.NetworkXException: + return nx.spring_layout(g, seed=0) + + +def draw_base_graph(ax, g, levels, source): + pos = graph_layout(g) + max_level = max(levels.values()) + cmap = plt.get_cmap("viridis", max_level + 1) + node_colors = [cmap(levels[v]) for v in g.nodes()] + nx.draw_networkx_edges(g, pos, ax=ax, edge_color="#cbd5e1", width=0.8) + nx.draw_networkx_nodes( + g, + pos, + ax=ax, + node_color=node_colors, + node_size=[150 if v == source else 72 for v in g.nodes()], + edgecolors=["#dc2626" if v == source else "#111827" for v in g.nodes()], + linewidths=[1.8 if v == source else 0.45 for v in g.nodes()], + ) + labels = {v: str(v) for v in g.nodes()} + nx.draw_networkx_labels(g, pos, labels=labels, ax=ax, font_size=5) + ax.set_title(f"G, source {source}; vertex levels 0..{max_level}", fontsize=10) + ax.set_aspect("equal") + ax.axis("off") + + +def tree_positions(nodes: list[TreadNode], tree_edges): + children: dict[int, list[int]] = defaultdict(list) + has_parent = set() + for parent, child in tree_edges: + children[parent].append(child) + has_parent.add(child) + roots = [node.idx for node in nodes if node.idx not in has_parent] + for child_list in children.values(): + child_list.sort(key=lambda idx: (nodes[idx].depth, idx)) + + x_counter = 0 + pos = {} + + def place(idx, depth): + nonlocal x_counter + if not children[idx]: + pos[idx] = (x_counter, -depth) + x_counter += 1 + return pos[idx][0] + xs = [place(child, depth + 1) for child in children[idx]] + x = sum(xs) / len(xs) + pos[idx] = (x, -depth) + return x + + for root in sorted(roots, key=lambda idx: (nodes[idx].depth, idx)): + place(root, 0) + x_counter += 1 + return pos + + +def draw_tire_tree(ax, nodes: list[TreadNode], tree_edges): + pos = tree_positions(nodes, tree_edges) + for parent, child in tree_edges: + x0, y0 = pos[parent] + x1, y1 = pos[child] + ax.plot([x0, x1], [y0, y1], color="#374151", lw=1.0, zorder=1) + for node in nodes: + x, y = pos[node.idx] + ax.text( + x, + y, + f"T{node.idx}\nd={node.depth}\n{len(node.tires)} tire(s)", + ha="center", + va="center", + fontsize=8, + bbox={ + "boxstyle": "round,pad=0.32", + "facecolor": "#fef3c7", + "edgecolor": "#111827", + "linewidth": 0.9, + }, + zorder=3, + ) + ax.set_title("Depth-component tire tree", fontsize=10) + if pos: + xs = [p[0] for p in pos.values()] + ys = [p[1] for p in pos.values()] + ax.set_xlim(min(xs) - 1.0, max(xs) + 1.0) + ax.set_ylim(min(ys) - 0.7, max(ys) + 0.7) + ax.axis("off") + + +def vertex_xy(k: int, n: int, radius: float) -> tuple[float, float]: + angle = math.pi / 2 - 2 * math.pi * k / n + return radius * math.cos(angle), radius * math.sin(angle) + + +def edge_midpoint_angle(i: int, n: int) -> float: + return math.pi / 2 - 2 * math.pi * (i + 0.5) / n + + +def draw_full_medial_tire(ax, graph: FullMedialTireGraph, title: str): + n = graph.n + ann = [vertex_xy(k, n, 1.0) for k in range(n)] + matched = graph.bite_edges + cyc_x = [p[0] for p in ann] + [ann[0][0]] + cyc_y = [p[1] for p in ann] + [ann[0][1]] + ax.plot(cyc_x, cyc_y, color="black", lw=1.3, zorder=2) + for i, tooth in enumerate(graph.tooth_word): + if tooth == "U": + r, color = 1.42, "#2563eb" + elif i not in matched: + r, color = 0.58, "#dc2626" + else: + continue + ang = edge_midpoint_angle(i, n) + apex = (r * math.cos(ang), r * math.sin(ang)) + for corner in (ann[i], ann[(i + 1) % n]): + ax.plot([apex[0], corner[0]], [apex[1], corner[1]], color="#9ca3af", lw=0.5) + ax.scatter([apex[0]], [apex[1]], s=12, color=color, zorder=3) + for i, j in sorted(graph.bites): + corners = [ann[i], ann[(i + 1) % n], ann[j], ann[(j + 1) % n]] + apex = (0.82 * sum(p[0] for p in corners) / 4, 0.82 * sum(p[1] for p in corners) / 4) + for corner in corners: + ax.plot([apex[0], corner[0]], [apex[1], corner[1]], color="#9ca3af", lw=0.5) + ax.scatter([apex[0]], [apex[1]], s=22, color="#7f1d1d", edgecolors="black", lw=0.4) + ax.scatter([p[0] for p in ann], [p[1] for p in ann], s=9, color="black", zorder=4) + bites = ",".join(f"{i}{j}" for i, j in sorted(graph.bites)) or "-" + ax.set_title(f"{title}\n{graph.tooth_word} b:{bites}", fontsize=5.8, pad=1.5) + ax.set_xlim(-1.6, 1.6) + ax.set_ylim(-1.6, 1.6) + ax.set_aspect("equal") + ax.axis("off") + + +def draw_medial_tire_grid(fig, outer_spec, nodes): + tires = [] + for node in nodes: + for comp_idx, (graph, _bij) in enumerate(node.tires): + tires.append((node.idx, comp_idx, graph)) + if not tires: + ax = fig.add_subplot(outer_spec) + ax.text(0.5, 0.5, "No full medial tire graphs recognized", ha="center") + ax.axis("off") + return + cols = min(5, max(1, math.ceil(math.sqrt(len(tires))))) + rows = math.ceil(len(tires) / cols) + sub = outer_spec.subgridspec(rows, cols, wspace=0.08, hspace=0.35) + for i in range(rows * cols): + ax = fig.add_subplot(sub[i // cols, i % cols]) + if i < len(tires): + node_idx, comp_idx, graph = tires[i] + draw_full_medial_tire(ax, graph, f"T{node_idx}.{comp_idx} n={graph.n}") + else: + ax.axis("off") + + +def write_index(path: Path, graph_idx: int, source: int, g: nx.Graph, nodes, tree_edges): + lines = [ + f"# Random medial tire decomposition {graph_idx}", + "", + f"- vertices: {g.number_of_nodes()}", + f"- edges: {g.number_of_edges()}", + f"- node connectivity: {nx.node_connectivity(g)}", + f"- source vertex: {source}", + f"- tire-tree nodes: {len(nodes)}", + f"- tire-tree edges: {len(tree_edges)}", + "", + "| node | depth | faces | annular | up | down | bites | full medial tires |", + "|--:|--:|--:|--:|--:|--:|--:|--:|", + ] + for node in nodes: + lines.append( + f"| T{node.idx} | {node.depth} | {len(node.face_indices)} | " + f"{len(node.annular)} | {len(node.up)} | {len(node.down)} | " + f"{len(node.bites)} | {len(node.tires)} |" + ) + for comp_idx, (tire, _bij) in enumerate(node.tires): + bites = ",".join(f"({i},{j})" for i, j in sorted(tire.bites)) or "-" + lines.append( + f"| T{node.idx}.{comp_idx} | | | | {len(tire.up_edges)} | " + f"{len(tire.down_edges)} | {bites} | `{tire.tooth_word}` |" + ) + path.write_text("\n".join(lines) + "\n") + + +def draw_case(out_dir: Path, graph_idx: int, g: nx.Graph, source: int): + _faces, levels, nodes, tree_edges = build_tire_tree(g, source) + fig = plt.figure(figsize=(17, 10)) + spec = fig.add_gridspec(2, 2, width_ratios=[1.15, 1.0], height_ratios=[1.0, 1.25]) + ax_graph = fig.add_subplot(spec[0, 0]) + ax_tree = fig.add_subplot(spec[1, 0]) + draw_base_graph(ax_graph, g, levels, source) + draw_tire_tree(ax_tree, nodes, tree_edges) + draw_medial_tire_grid(fig, spec[:, 1], nodes) + fig.suptitle( + f"Random 5-connected maximal planar graph {graph_idx}: " + f"n={g.number_of_nodes()}, source={source}", + fontsize=13, + ) + legend = [ + Line2D([0], [0], marker="o", color="w", label="source", + markerfacecolor="#fde68a", markeredgecolor="#dc2626", markersize=8), + Line2D([0], [0], color="black", lw=1.3, label="annular cycle A(T)"), + Line2D([0], [0], marker="o", color="w", label="up tooth", + markerfacecolor="#2563eb", markersize=6), + Line2D([0], [0], marker="o", color="w", label="down tooth", + markerfacecolor="#dc2626", markersize=6), + Line2D([0], [0], marker="o", color="w", label="bite apex", + markerfacecolor="#7f1d1d", markeredgecolor="black", markersize=6), + ] + fig.legend(handles=legend, loc="lower center", ncol=5, fontsize=9) + fig.subplots_adjust(left=0.03, right=0.99, top=0.92, bottom=0.08, wspace=0.08, hspace=0.16) + + png = out_dir / f"random_c5_n30_medial_tire_decomposition_{graph_idx}.png" + pdf = out_dir / f"random_c5_n30_medial_tire_decomposition_{graph_idx}.pdf" + fig.savefig(png, dpi=180) + fig.savefig(pdf) + plt.close(fig) + write_index( + out_dir / f"random_c5_n30_medial_tire_decomposition_{graph_idx}.md", + graph_idx, + source, + g, + nodes, + tree_edges, + ) + return png, pdf, len(nodes), sum(len(node.tires) for node in nodes) + + +def run(args: argparse.Namespace): + out_dir = Path(args.out_dir) + out_dir.mkdir(parents=True, exist_ok=True) + graphs = sample_plantri_graphs(args.n, args.count, args.seed, args.scan_limit) + rng = random.Random(args.seed + 101) + for i, graph in enumerate(graphs, start=1): + source = rng.choice(list(graph.nodes())) + png, pdf, node_count, tire_count = draw_case(out_dir, i, graph, source) + print( + f"case {i}: source={source}, connectivity={nx.node_connectivity(graph)}, " + f"tire nodes={node_count}, full medial tires={tire_count}" + ) + print(f" wrote {png}") + print(f" wrote {pdf}") + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--n", type=int, default=30) + parser.add_argument("--count", type=int, default=2) + parser.add_argument("--seed", type=int, default=20260615) + parser.add_argument("--scan-limit", type=int, default=500) + parser.add_argument( + "--out-dir", + default=str(PAPER_DIR / "experiments" / "random_medial_tire_decompositions"), + ) + run(parser.parse_args()) + + +if __name__ == "__main__": + main() diff --git a/papers/medial_tire_decompositions_of_plane_triangulations/experiments/random_medial_tire_decompositions/random_c5_n30_medial_tire_decomposition_1.md b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/random_medial_tire_decompositions/random_c5_n30_medial_tire_decomposition_1.md new file mode 100644 index 0000000..2b830ff --- /dev/null +++ b/papers/medial_tire_decompositions_of_plane_triangulations/experiments/random_medial_tire_decompositions/random_c5_n30_medial_tire_decomposition_1.md @@ -0,0 +1,18 @@ +# Random medial tire decomposition 1 + +- vertices: 30 +- edges: 84 +- node connectivity: 5 +- source vertex: 9 +- tire-tree nodes: 3 +- tire-tree edges: 2 + +| node | depth | faces | annular | up | down | bites | full medial tires | +|--:|--:|--:|--:|--:|--:|--:|--:| +| T0 | 1 | 16 | 16 | 6 | 10 | 0 | 1 | +| T0.0 | | | | 6 | 10 | - | 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