code/distributed_scanning/tangled_loops/creation.py

"""Tangled Closed-Loop Counting.

Each string is a smooth **closed curve** living entirely in the interior
of the canvas. Loops are generated by sampling interior waypoints on a
jittered ring around a random centre and fitting a periodic cubic
B-spline through them — the resulting curve has no endpoints at all,
which plugs the "skeletonize → count degree-1 pixels → divide by 2"
shortcut that beat the previous perimeter-anchored design.

All loops render in the same dark colour. Loops may cross other loops
or themselves, but long parallel runs are rejected so every loop stays
individually traceable.

The model is asked to count the total number of distinct closed loops.
"""
from __future__ import annotations

import argparse
import json
import math
import os
import random
import sys
from collections import defaultdict
from pathlib import Path
from typing import Dict, List, Tuple

import matplotlib
matplotlib.use("Agg")
import matplotlib.pyplot as plt
import numpy as np
from scipy.interpolate import splev, splprep
from tqdm import tqdm


LINE_COLOR = "#2f2f2f"


# ── Closed-loop construction ───────────────────────────────────────

def build_closed_loop(
    rng: random.Random,
    width: int,
    height: int,
    interior_margin: int = 55,
    num_waypoints_range: Tuple[int, int] = (6, 10),
    radius_range: Tuple[float, float] = (130.0, 215.0),
    radius_jitter: float = 0.30,
    angle_jitter: float = 0.42,
    num_samples: int = 520,
    existing_centers: List[Tuple[float, float]] | None = None,
    min_center_gap: float = 190.0,
    center_placement_attempts: int = 80,
) -> Tuple[np.ndarray, Tuple[float, float]] | None:
    """Build one smooth closed curve through jittered ring waypoints.

    Returns ``(polyline, (cx, cy))`` where the polyline's last point
    equals its first, or ``None`` if no valid placement was found.
    """
    num_wp = rng.randint(*num_waypoints_range)
    r_mean = rng.uniform(*radius_range)
    max_r = r_mean * (1 + radius_jitter)

    low_x = interior_margin + max_r
    high_x = width - interior_margin - max_r
    low_y = interior_margin + max_r
    high_y = height - interior_margin - max_r
    if low_x >= high_x or low_y >= high_y:
        return None

    cx = cy = None
    centers = existing_centers or []
    for _ in range(center_placement_attempts):
        cand_x = rng.uniform(low_x, high_x)
        cand_y = rng.uniform(low_y, high_y)
        ok = True
        for ex_x, ex_y in centers:
            if (cand_x - ex_x) ** 2 + (cand_y - ex_y) ** 2 < min_center_gap ** 2:
                ok = False
                break
        if ok:
            cx, cy = cand_x, cand_y
            break
    if cx is None:
        return None

    base_angles = np.linspace(0.0, 2 * math.pi, num_wp, endpoint=False)
    phase = rng.uniform(0.0, 2 * math.pi)

    xs: List[float] = []
    ys: List[float] = []
    for base in base_angles:
        ang = base + phase + rng.uniform(-angle_jitter, angle_jitter)
        r = r_mean * (1.0 + rng.uniform(-radius_jitter, radius_jitter))
        xs.append(cx + r * math.cos(ang))
        ys.append(cy + r * math.sin(ang))

    # splprep with per=True expects the input to already be closed.
    xs.append(xs[0])
    ys.append(ys[0])

    try:
        tck, _ = splprep([xs, ys], s=0.0, per=True, k=3)
    except (TypeError, ValueError):
        return None

    u_dense = np.linspace(0.0, 1.0, num_samples)
    x_dense, y_dense = splev(u_dense, tck)
    poly = np.column_stack([np.asarray(x_dense), np.asarray(y_dense)])

    if (poly[:, 0].min() < interior_margin - 5
            or poly[:, 0].max() > width - interior_margin + 5
            or poly[:, 1].min() < interior_margin - 5
            or poly[:, 1].max() > height - interior_margin + 5):
        return None

    poly[-1] = poly[0]
    return poly, (cx, cy)


# ── Crossing detection (used for the close-approach validation) ────

def _segments_cross(p0, p1, q0, q1) -> bool:
    eps = 1e-8
    o1 = (p1[0]-p0[0])*(q0[1]-p0[1]) - (p1[1]-p0[1])*(q0[0]-p0[0])
    o2 = (p1[0]-p0[0])*(q1[1]-p0[1]) - (p1[1]-p0[1])*(q1[0]-p0[0])
    o3 = (q1[0]-q0[0])*(p0[1]-q0[1]) - (q1[1]-q0[1])*(p0[0]-q0[0])
    o4 = (q1[0]-q0[0])*(p1[1]-q0[1]) - (q1[1]-q0[1])*(p1[0]-q0[0])
    return ((o1 > eps and o2 < -eps) or (o1 < -eps and o2 > eps)) and \
           ((o3 > eps and o4 < -eps) or (o3 < -eps and o4 > eps))


def _circular_seg_gap(i: int, j: int, n: int) -> int:
    d = abs(i - j)
    return min(d, n - d)


def _find_crossings(
    poly_a: np.ndarray,
    poly_b: np.ndarray,
    same_curve: bool = False,
    min_seg_gap: int = 10,
) -> List[Dict]:
    na = len(poly_a) - 1
    nb = len(poly_b) - 1

    a_min_x = np.minimum(poly_a[:-1, 0], poly_a[1:, 0])
    a_max_x = np.maximum(poly_a[:-1, 0], poly_a[1:, 0])
    a_min_y = np.minimum(poly_a[:-1, 1], poly_a[1:, 1])
    a_max_y = np.maximum(poly_a[:-1, 1], poly_a[1:, 1])

    b_min_x = np.minimum(poly_b[:-1, 0], poly_b[1:, 0])
    b_max_x = np.maximum(poly_b[:-1, 0], poly_b[1:, 0])
    b_min_y = np.minimum(poly_b[:-1, 1], poly_b[1:, 1])
    b_max_y = np.maximum(poly_b[:-1, 1], poly_b[1:, 1])

    cell_size = max(np.median(np.concatenate([a_max_x - a_min_x,
                                              b_max_x - b_min_x])), 1.0) * 3

    grid_b = defaultdict(list)
    for j in range(nb):
        cx0 = int(b_min_x[j] / cell_size); cx1 = int(b_max_x[j] / cell_size)
        cy0 = int(b_min_y[j] / cell_size); cy1 = int(b_max_y[j] / cell_size)
        for gx in range(cx0, cx1 + 1):
            for gy in range(cy0, cy1 + 1):
                grid_b[(gx, gy)].append(j)

    checked = set()
    details: List[Dict] = []
    for i in range(na):
        cx0 = int(a_min_x[i] / cell_size); cx1 = int(a_max_x[i] / cell_size)
        cy0 = int(a_min_y[i] / cell_size); cy1 = int(a_max_y[i] / cell_size)
        for gx in range(cx0, cx1 + 1):
            for gy in range(cy0, cy1 + 1):
                if (gx, gy) not in grid_b:
                    continue
                for j in grid_b[(gx, gy)]:
                    if same_curve:
                        ii, jj = min(i, j), max(i, j)
                        # Closed curve: neighbours wrap around.
                        if _circular_seg_gap(ii, jj, na) < min_seg_gap:
                            continue
                        key = (ii, jj)
                    else:
                        key = (i, j)
                    if key in checked:
                        continue
                    checked.add(key)
                    if same_curve:
                        si, sj = key
                    else:
                        si, sj = i, j
                    p0, p1 = poly_a[si], poly_a[si + 1]
                    q0, q1 = poly_b[sj], poly_b[sj + 1]
                    if not _segments_cross(p0, p1, q0, q1):
                        continue
                    d1 = p1 - p0
                    d2 = q1 - q0
                    denom = d1[0] * d2[1] - d1[1] * d2[0]
                    if abs(denom) < 1e-12:
                        continue
                    ti = ((q0[0] - p0[0]) * d2[1] - (q0[1] - p0[1]) * d2[0]) / denom
                    px = float(p0[0] + ti * d1[0])
                    py = float(p0[1] + ti * d1[1])
                    details.append({"px": px, "py": py})
    return details


def _details_to_points(details: List[Dict]) -> np.ndarray:
    if not details:
        return np.zeros((0, 2))
    return np.array([[d["px"], d["py"]] for d in details])


def _curves_too_close(
    poly_a: np.ndarray,
    poly_b: np.ndarray,
    same_curve: bool = False,
    min_dist: float = 7.0,
    sample_step: int = 3,
    self_index_gap: int = 30,
    known_crossings: np.ndarray | None = None,
    crossing_exclude_radius: float = 55.0,
) -> bool:
    nb = len(poly_b) - 1
    b_pts = poly_b[:-1]
    b_vecs = poly_b[1:] - poly_b[:-1]
    b_lens_sq = np.maximum((b_vecs ** 2).sum(axis=1), 1e-12)

    has_crossings = known_crossings is not None and len(known_crossings) > 0

    for idx in range(0, len(poly_a), sample_step):
        px, py = poly_a[idx]
        p = np.array([px, py])
        dp = p - b_pts
        t = (dp * b_vecs).sum(axis=1) / b_lens_sq
        t = np.clip(t, 0.0, 1.0)
        proj = b_pts + t[:, None] * b_vecs
        dists = np.sqrt(((p - proj) ** 2).sum(axis=1))
        if same_curve:
            # Closed curve: mask neighbours with wraparound distance.
            seg_idx = np.arange(nb)
            lin = np.abs(seg_idx - idx)
            circ = np.minimum(lin, nb - lin)
            mask = circ < self_index_gap
            dists[mask] = 9999.0
        if dists.min() < min_dist:
            if has_crossings:
                cross_dists = np.sqrt(((p - known_crossings) ** 2).sum(axis=1))
                if cross_dists.min() < crossing_exclude_radius:
                    continue
            return True
    return False


# ── Instance sampling ──────────────────────────────────────────────

QUESTION = (
    "How many distinct closed loops are tangled together in this image? "
    "Each loop is a single continuous curve that closes back on itself — "
    "there are no loose endpoints anywhere. All loops are drawn in the "
    "same colour and may cross other loops or themselves freely. Count "
    "the total number of distinct closed loops and report the count as "
    "a positive integer. "
    "Provide your final answer enclosed in <answer>...</answer> tags."
)


def _min_crossing_angle_deg(poly_a: np.ndarray, poly_b: np.ndarray,
                             details: List[Dict], same_curve: bool = False) -> float:
    """Return the smallest crossing angle (deg) across all crossings, or
    180.0 if there are no crossings."""
    if not details:
        return 180.0
    # Re-detect with segment indices for angle computation.
    na = len(poly_a) - 1
    nb = len(poly_b) - 1
    min_angle = 180.0
    for i in range(na):
        p0, p1 = poly_a[i], poly_a[i + 1]
        for j in range(nb):
            if same_curve:
                ii, jj = min(i, j), max(i, j)
                if _circular_seg_gap(ii, jj, na) < 10:
                    continue
            q0, q1 = poly_b[j], poly_b[j + 1]
            if not _segments_cross(p0, p1, q0, q1):
                continue
            d1 = p1 - p0
            d2 = q1 - q0
            n1 = math.hypot(d1[0], d1[1])
            n2 = math.hypot(d2[0], d2[1])
            if n1 < 1e-9 or n2 < 1e-9:
                continue
            cos_a = (d1[0] * d2[0] + d1[1] * d2[1]) / (n1 * n2)
            cos_a = max(-1.0, min(1.0, cos_a))
            ang = math.degrees(math.acos(abs(cos_a)))
            if ang < min_angle:
                min_angle = ang
    return min_angle


def sample_instance(
    rng: random.Random,
    width: int,
    height: int,
    num_loops: int,
    interior_margin: int = 55,
    max_attempts: int = 600,
    min_inter_crossings: int = 0,
    max_self_crossings_per_loop: int = 0,
    min_crossing_angle_deg: float = 30.0,
) -> Dict | None:
    for _ in range(max_attempts):
        polylines: List[np.ndarray] = []
        centers: List[Tuple[float, float]] = []
        build_failed = False
        for _ in range(num_loops):
            result = None
            for _ in range(40):
                result = build_closed_loop(
                    rng, width, height,
                    interior_margin=interior_margin,
                    existing_centers=centers,
                )
                if result is not None:
                    break
            if result is None:
                build_failed = True
                break
            poly, centre = result
            polylines.append(poly)
            centers.append(centre)
        if build_failed:
            continue

        self_details: List[List[Dict]] = []
        pair_details: Dict[Tuple[int, int], List[Dict]] = {}
        for a in range(num_loops):
            self_details.append(_find_crossings(polylines[a], polylines[a],
                                                same_curve=True))
            for b in range(a + 1, num_loops):
                pair_details[(a, b)] = _find_crossings(polylines[a], polylines[b])

        # Enforce: no self-crossings beyond allowed limit.
        if any(len(sd) > max_self_crossings_per_loop for sd in self_details):
            continue

        # Enforce: total inter-loop crossings >= min_inter_crossings.
        total_inter = sum(len(v) for v in pair_details.values())
        if total_inter < min_inter_crossings:
            continue

        # Enforce: every crossing has angle >= min_crossing_angle_deg.
        bad_angle = False
        for a in range(num_loops):
            if _min_crossing_angle_deg(polylines[a], polylines[a],
                                       self_details[a], same_curve=True) < min_crossing_angle_deg:
                bad_angle = True
                break
            for b in range(a + 1, num_loops):
                if _min_crossing_angle_deg(polylines[a], polylines[b],
                                           pair_details[(a, b)]) < min_crossing_angle_deg:
                    bad_angle = True
                    break
            if bad_angle:
                break
        if bad_angle:
            continue

        too_close = False
        for a in range(num_loops):
            if _curves_too_close(polylines[a], polylines[a], same_curve=True,
                                 known_crossings=_details_to_points(self_details[a])):
                too_close = True
                break
            for b in range(a + 1, num_loops):
                if _curves_too_close(polylines[a], polylines[b],
                                     known_crossings=_details_to_points(pair_details[(a, b)])):
                    too_close = True
                    break
            if too_close:
                break
        if too_close:
            continue

        return {
            "width": width,
            "height": height,
            "num_loops": num_loops,
            "polylines": polylines,
            "inter_loop_crossings": int(total_inter),
            "question": QUESTION,
            "answer": num_loops,
        }
    return None


# ── Rendering ──────────────────────────────────────────────────────

def render_instance(out_path: Path, record: Dict, noise_seed: int,
                    thickness: float) -> None:
    width = int(record["width"])
    height = int(record["height"])
    polylines = record["polylines"]

    fig = plt.figure(figsize=(width / 100, height / 100), dpi=100)
    ax = fig.add_axes([0, 0, 1, 1])
    ax.set_xlim(0, width)
    ax.set_ylim(height, 0)
    ax.axis("off")
    ax.set_facecolor("#f8f6f0")

    nrng = np.random.default_rng(noise_seed)
    noise = nrng.normal(0.0, 1.0, size=(height, width))
    noise = (noise - noise.min()) / max(noise.max() - noise.min(), 1e-6)
    ax.imshow(noise, cmap="Greys", alpha=0.05, extent=(0, width, height, 0),
              interpolation="bilinear")

    for poly in polylines:
        ax.plot(poly[:, 0], poly[:, 1],
                color=LINE_COLOR, linewidth=thickness, alpha=0.92,
                solid_capstyle="round", solid_joinstyle="round",
                zorder=2.0)

    fig.savefig(out_path, dpi=100, bbox_inches="tight", pad_inches=0)
    plt.close(fig)


# ── Main ───────────────────────────────────────────────────────────

def main() -> None:
    parser = argparse.ArgumentParser()
    parser.add_argument("--output-root", type=Path, required=True)
    parser.add_argument("--count", type=int, default=30)
    parser.add_argument("--seed", type=int, default=42)
    parser.add_argument("--width", type=int, default=1024)
    parser.add_argument("--height", type=int, default=1024)
    parser.add_argument("--min-loops", type=int, default=3)
    parser.add_argument("--max-loops", type=int, default=5)
    parser.add_argument("--thickness", type=float, default=2.0,
                        help="Absolute pixel thickness; never scaled.")
    parser.add_argument("--difficulty", type=int, default=5,
                        help="Integer difficulty >=0; scales loop count.")
    parser.add_argument("--workers", type=int, default=8,
                        help="Parallel worker processes for sampling. 1 = serial.")
    args = parser.parse_args()

    d = max(0, int(args.difficulty))

    # Canvas scaling: N_d = 5 + d, N_0 = 5.
    N_d = 5 + d
    N_0 = 5
    s = math.sqrt(max(1.0, N_d / N_0))
    args.width = int(round(args.width * s))
    args.height = int(round(args.height * s))

    # num_loops ∈ [3, 5 + d]
    args.min_loops = 10
    args.max_loops = 10 + 2 * d

    # Fixed constraints.
    max_self_crossings_per_loop = 0
    min_inter_crossings = 10 + 2 * d
    min_crossing_angle_deg = 30.0
    loop_thickness_px = 4.0  # absolute; do not scale

    out_root: Path = args.output_root
    img_dir = out_root / "images"
    img_dir.mkdir(parents=True, exist_ok=True)

    sys.path.insert(0, str(Path(__file__).resolve().parents[3]))
    from _sample_pool import parallel_sample_records  # noqa: E402

    # Force evenly-spaced answer counts across [min_loops, max_loops].
    if args.count > 1:
        forced_targets = [
            int(round(args.min_loops + i * (args.max_loops - args.min_loops) / (args.count - 1)))
            for i in range(args.count)
        ]
    else:
        forced_targets = [args.min_loops]
    print(f"forced loop counts: {forced_targets}")

    records_raw = []
    for ti, tgt in enumerate(forced_targets):
        def _attempt(rng, _tgt=tgt):
            rec = sample_instance(
                rng, args.width, args.height, num_loops=_tgt,
                min_inter_crossings=min_inter_crossings,
                max_self_crossings_per_loop=max_self_crossings_per_loop,
                min_crossing_angle_deg=min_crossing_angle_deg,
                max_attempts=50,
            )
            return rec
        sub = parallel_sample_records(
            _attempt, count=1, workers=args.workers,
            seed_base=args.seed + ti * 977,
        )
        records_raw.extend(sub)
    rng_render = random.Random(args.seed ^ 0xA5A5)
    records = []
    for idx, record in enumerate(records_raw):
        name = f"tangled_loops_{idx:05d}.png"
        ns = rng_render.randint(0, 10**9)
        render_instance(img_dir / name, record, noise_seed=ns,
                        thickness=loop_thickness_px)
        record.pop("polylines")
        record["image"] = f"images/{name}"
        records.append(record)
    print(f"  {len(records)}/{args.count} valid samples (workers={args.workers})")

    with (out_root / "annotations.jsonl").open("w") as fh:
        for r in records:
            fh.write(json.dumps(r) + "\n")

    data_json = {
        "task": "tangled_loops",
        "category": "distributed_scanning",
        "count": len(records),
        "items": [
            {"image": r["image"], "question": r["question"], "answer": r["answer"]}
            for r in records
        ],
    }
    (out_root / "data.json").write_text(json.dumps(data_json, indent=2))
    print(f"Saved {len(records)} items to {out_root}")


if __name__ == "__main__":
    main()