code/sequential_traversal/line_intersections/creation.py

"""Line Intersections (turtle-based, anchored endpoints).

Each curve has two preset endpoints placed on the perimeter of the canvas.
A straight "leader" segment connects each endpoint to an interior point
(~150px inward), keeping the perimeter band free of crossings. The middle
body of the curve is a turtle-style walk through waypoints distributed
across a generous interior zone — tangled, but not concentrated at the
very center.

Only one of the two endpoints of each curve is labeled (A, B, C, ...).
The model starts tracing from the labeled endpoint and follows the
queried curve through the interior tangle. At every crossing it passes
through, it records the label of the OTHER curve involved (for a
self-crossing, that label is the queried curve's own letter). The
answer is the ordered sequence of labels.
"""
from __future__ import annotations

import argparse
import json
import math
import os
import random
import string
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 tqdm import tqdm

LINE_COLOR = "#2f2f2f"
LABEL_COLORS = [
    "#c23030",
    "#1a6dba",
    "#2d8e2d",
    "#c47a18",
    "#7a35a0",
]


# ── Perimeter anchors ──────────────────────────────────────────────

def _perimeter_point(s: float, width: int, height: int, margin: int
                     ) -> Tuple[np.ndarray, np.ndarray]:
    """Map s ∈ [0, 4) to (position, inward_unit_vector) on rect perimeter."""
    side = int(s) % 4
    t = s - int(s)
    if side == 0:     # top edge, left -> right
        x = margin + (width - 2 * margin) * t
        y = margin
        inward = np.array([0.0, 1.0])
    elif side == 1:   # right edge, top -> bottom
        x = width - margin
        y = margin + (height - 2 * margin) * t
        inward = np.array([-1.0, 0.0])
    elif side == 2:   # bottom edge, right -> left
        x = width - margin - (width - 2 * margin) * t
        y = height - margin
        inward = np.array([0.0, -1.0])
    else:             # left edge, bottom -> top
        x = margin
        y = height - margin - (height - 2 * margin) * t
        inward = np.array([1.0, 0.0])
    return np.array([x, y]), inward


def sample_perimeter_anchors(
    rng: random.Random,
    num_anchors: int,
    width: int,
    height: int,
    margin: int,
    min_gap: float | None = None,
    jitter_deg: float = 10.0,
    max_attempts: int = 300,
) -> List[Tuple[np.ndarray, np.ndarray]]:
    """Sample `num_anchors` positions around the canvas perimeter, enforcing
    a minimum gap (in perimeter units, 1 unit = one side)."""
    if min_gap is None:
        # 50% of perfectly even spacing
        min_gap = (4.0 / num_anchors) * 0.5
    for _ in range(max_attempts):
        positions = sorted(rng.uniform(0.0, 4.0) for _ in range(num_anchors))
        ok = True
        for i in range(num_anchors):
            gap = (positions[(i + 1) % num_anchors] - positions[i]) % 4.0
            if gap < min_gap:
                ok = False
                break
        if ok:
            anchors = []
            for s in positions:
                pt, inward = _perimeter_point(s, width, height, margin)
                # small angular jitter of the inward direction
                ang = math.atan2(inward[1], inward[0])
                ang += math.radians(rng.uniform(-jitter_deg, jitter_deg))
                inward = np.array([math.cos(ang), math.sin(ang)])
                anchors.append((pt, inward))
            return anchors
    return None


# ── Turtle body with anchored start/end ────────────────────────────

def _angle_diff(current: float, target: float) -> float:
    d = target - current
    return (d + math.pi) % (2 * math.pi) - math.pi


def build_anchored_curve(
    rng: random.Random,
    width: int,
    height: int,
    start_pos: np.ndarray,
    start_inward: np.ndarray,
    end_pos: np.ndarray,
    end_inward: np.ndarray,
    leader_length: float = 150.0,
    step_size: float = 3.3,
    max_turn: float = 0.028,
    drift_rate: float = 0.007,
    num_waypoints: int = 2,
    interior_margin: int = 260,
    max_steps: int = 1800,
) -> np.ndarray:
    """Single-turtle curve from start_pos to a point near end_pos.

    Phase-dependent turning:
      - Entry leader (first `leader_length` of path): max_turn = 0 (straight).
      - Body (interior): waypoint steering within max_turn clamp.
      - Exit leader (within `leader_length` of end_pos perimeter plane):
        head-alignment only (no waypoint steering), rotating toward
        -end_inward at up to max_turn/step. Then drives straight.

    Because the entire curve is a single turtle walk, there are no splice
    discontinuities. The curve terminates when it crosses the perimeter plane
    at end_pos; the final point is wherever it actually crosses (close to
    end_pos when head-alignment locks in time).
    """
    pts: List[np.ndarray] = [start_pos.copy()]
    x, y = float(start_pos[0]), float(start_pos[1])
    theta = math.atan2(start_inward[1], start_inward[0])

    # Waypoints in interior, ordered by progress from start→end.
    raw_wps: List[np.ndarray] = []
    for _ in range(num_waypoints):
        wx = rng.uniform(interior_margin, width - interior_margin)
        wy = rng.uniform(interior_margin, height - interior_margin)
        raw_wps.append(np.array([wx, wy]))
    direction = end_pos - start_pos
    dir_norm = direction / (np.linalg.norm(direction) + 1e-9)
    raw_wps.sort(key=lambda p: float(np.dot(p - start_pos, dir_norm)))

    # Funnel waypoint deep on the exit axis pulls the turtle onto the axis
    # before the exit leader. Virtual lookahead past the exit then keeps
    # heading aligned with -end_inward as we approach end_pos.
    funnel = end_pos + end_inward * 400.0
    lookahead = end_pos + (-end_inward) * 240.0
    waypoints: List[np.ndarray] = raw_wps + [funnel, lookahead]

    exit_theta = math.atan2(-end_inward[1], -end_inward[0])
    entry_steps = max(2, int(leader_length / step_size))

    wp_idx = 0
    drift = 0.0

    # Perp to end_inward (for lateral-offset measurement along perimeter edge).
    perp = np.array([-end_inward[1], end_inward[0]])

    for step_count in range(max_steps):
        # Signed perpendicular distance from turtle to end_pos perimeter plane.
        # end_inward points from perimeter INTO canvas, so on interior side
        # dot(pos - end_pos, end_inward) > 0; crossing the plane → <= 0.
        sd = ((x - end_pos[0]) * end_inward[0]
              + (y - end_pos[1]) * end_inward[1])
        # Lateral offset along the perimeter edge from end_pos.
        lat = abs((x - end_pos[0]) * perp[0] + (y - end_pos[1]) * perp[1])

        # Termination: turtle has reached/crossed the perimeter.
        if sd <= 0.0:
            break

        if step_count < entry_steps:
            # Entry leader: no turn (straight).
            turn = 0.0
        elif sd < leader_length and lat < 40.0:
            # Exit leader: pure head-alignment, no positional steering.
            head_err = _angle_diff(theta, exit_theta)
            turn = max(-max_turn, min(max_turn, head_err))
        else:
            # Body: waypoint steering.
            is_final = (wp_idx == len(waypoints) - 1)
            if is_final:
                wx, wy = waypoints[-1]
                pull = 0.18
            else:
                wx, wy = waypoints[wp_idx]
                steer_dist = math.hypot(wx - x, wy - y)
                # reach must exceed turning diameter (2 * step / max_turn)
                if steer_dist < 140.0:
                    wp_idx += 1
                    continue
                pull = 0.09

            drift += rng.gauss(0, drift_rate)
            drift = max(-max_turn * 0.7, min(max_turn * 0.7, drift))
            turn = drift + rng.gauss(0, max_turn * 0.12)
            target_ang = math.atan2(wy - y, wx - x)
            steer = _angle_diff(theta, target_ang)
            turn += steer * pull
            turn = max(-max_turn, min(max_turn, turn))

        theta += turn
        x += step_size * math.cos(theta)
        y += step_size * math.sin(theta)
        pts.append(np.array([x, y]))

    return np.array(pts)


# ── Intersection detection ─────────────────────────────────────────

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 _crossing_angle(p0, p1, q0, q1) -> float:
    d1 = p1 - p0
    d2 = q1 - q0
    cos_a = np.dot(d1, d2) / (np.linalg.norm(d1) * np.linalg.norm(d2) + 1e-12)
    return math.degrees(math.acos(min(1.0, abs(cos_a))))


def _find_crossings(
    poly_a: np.ndarray,
    poly_b: np.ndarray,
    same_curve: bool = False,
    min_seg_gap: int = 10,
):
    """Returns (count, worst_angle, details).

    `details` is a list of dicts, one per crossing, with keys:
      i, j        — segment indices on poly_a and poly_b
      ti, tj      — crossing parameters ∈ (0, 1) along each segment
      px, py      — exact crossing point
      angle       — crossing angle in degrees
    For same_curve=True, i < j is enforced so each crossing appears once.
    """
    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])

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

    grid_a = defaultdict(list)
    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):
                grid_a[(gx, gy)].append(i)

    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()
    worst_angle = 180.0
    details: List[Dict] = []
    for cell_key in grid_a:
        if cell_key not in grid_b:
            continue
        for i in grid_a[cell_key]:
            for j in grid_b[cell_key]:
                if same_curve:
                    ii, jj = min(i, j), max(i, j)
                    if jj - ii < min_seg_gap:
                        continue
                    key = (ii, jj)
                else:
                    key = (i, j)
                if key in checked:
                    continue
                checked.add(key)

                if a_max_x[i] < b_min_x[j] or b_max_x[j] < a_min_x[i] or \
                   a_max_y[i] < b_min_y[j] or b_max_y[j] < a_min_y[i]:
                    continue

                if same_curve:
                    si, sj = key  # enforce i < j for self-crossings
                    p0, p1 = poly_a[si], poly_a[si + 1]
                    q0, q1 = poly_b[sj], poly_b[sj + 1]
                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
                tj = ((q0[0] - p0[0]) * d1[1] - (q0[1] - p0[1]) * d1[0]) / denom
                px = float(p0[0] + ti * d1[0])
                py = float(p0[1] + ti * d1[1])
                angle = _crossing_angle(p0, p1, q0, q1)
                worst_angle = min(worst_angle, angle)
                details.append({
                    "i": int(si), "j": int(sj),
                    "ti": float(ti), "tj": float(tj),
                    "px": px, "py": py, "angle": float(angle),
                })
    return len(details), worst_angle, 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 = 50,
    known_crossings: np.ndarray | None = None,
    crossing_exclude_radius: float = 30.0,
) -> bool:
    """Flag if ANY sample point on A comes within `min_dist` of B without
    being attributable to a real crossing. Samples within
    `crossing_exclude_radius` of any point in `known_crossings` are ignored
    (that's the crossing region itself, where near-zero distance is expected).
    """
    nb = len(poly_b) - 1
    if nb <= 0 or len(poly_a) == 0:
        return False
    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:
            mask = np.abs(np.arange(nb) - idx) < 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  # close approach explained by a real crossing
            return True
    return False


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

def sample_instance(
    rng: random.Random,
    width: int,
    height: int,
    min_lines: int = 4,
    max_lines: int = 4,
    min_total_crossings: int = 12,
    max_total_crossings: int = 60,
    perimeter_margin: int = 70,
    leader_length: float = 150.0,
    interior_margin: int = 260,
    max_attempts: int = 2500,
) -> Dict | None:
    labels = list(string.ascii_uppercase)

    for _ in range(max_attempts):
        num_lines = rng.randint(min_lines, max_lines)

        anchors = sample_perimeter_anchors(
            rng, num_lines * 2, width, height,
            margin=perimeter_margin,
        )
        if anchors is None:
            continue

        # Pair anchor i with anchor i+num_lines: opposite-side pairing to
        # force curves through the interior.
        pairs = [(anchors[i], anchors[i + num_lines]) for i in range(num_lines)]
        rng.shuffle(pairs)

        polylines = []
        for (sp, sd), (ep, ed) in pairs:
            poly = build_anchored_curve(
                rng, width, height,
                start_pos=sp, start_inward=sd,
                end_pos=ep, end_inward=ed,
                leader_length=leader_length,
                step_size=rng.uniform(3.0, 3.8),
                max_turn=rng.uniform(0.034, 0.044),
                drift_rate=rng.uniform(0.010, 0.016),
                num_waypoints=rng.randint(4, 6),
                interior_margin=interior_margin,
            )
            polylines.append(poly)

        total = 0
        global_min_angle = 180.0
        self_details: Dict[int, List[Dict]] = {}
        pair_details: Dict[Tuple[int, int], List[Dict]] = {}

        for a in range(num_lines):
            sc, ang, det = _find_crossings(polylines[a], polylines[a],
                                           same_curve=True)
            self_details[a] = det
            total += sc
            global_min_angle = min(global_min_angle, ang)
            for b in range(a + 1, num_lines):
                cc, ang, det = _find_crossings(polylines[a], polylines[b])
                pair_details[(a, b)] = det
                total += cc
                global_min_angle = min(global_min_angle, ang)

        if total < min_total_crossings or total > max_total_crossings:
            continue
        if global_min_angle < 45.0:
            continue

        # 1% of the canvas's short side keeps curves visibly separated
        # at any resolution while still letting the sampler converge at
        # higher difficulties.
        min_dist_px = 0.01 * float(min(width, height))
        too_close = False
        for a in range(num_lines):
            if _curves_too_close(polylines[a], polylines[a], same_curve=True,
                                 min_dist=min_dist_px,
                                 known_crossings=_details_to_points(self_details[a])):
                too_close = True; break
            for b in range(a + 1, num_lines):
                if _curves_too_close(polylines[a], polylines[b],
                                     min_dist=min_dist_px,
                                     known_crossings=_details_to_points(pair_details[(a, b)])):
                    too_close = True; break
            if too_close:
                break
        if too_close:
            continue

        # Reject if any two crossing points are too close to each other —
        # that would let multiple intersections be mistaken for one.
        all_cross_pts = []
        for a in range(num_lines):
            pts = _details_to_points(self_details[a])
            if len(pts) > 0:
                all_cross_pts.append(pts)
            for b in range(a + 1, num_lines):
                pts = _details_to_points(pair_details[(a, b)])
                if len(pts) > 0:
                    all_cross_pts.append(pts)
        if all_cross_pts:
            stacked = np.concatenate(all_cross_pts, axis=0)
            if len(stacked) >= 2:
                diffs = stacked[:, None, :] - stacked[None, :, :]
                dmat = np.sqrt((diffs ** 2).sum(axis=-1))
                np.fill_diagonal(dmat, np.inf)
                if dmat.min() < 20.0:
                    continue

        # Pick label positions: one of the two endpoints per curve.
        # "label_at_start" picks the first endpoint (index 0) when True.
        label_starts = [rng.random() < 0.5 for _ in range(num_lines)]

        # Per-curve sequence length: each self-crossing is hit twice during
        # the trace (entering + leaving), each pair-crossing once.
        seq_lens = []
        for q in range(num_lines):
            sl = 2 * len(self_details[q])
            for b in range(num_lines):
                if b == q:
                    continue
                key = (min(q, b), max(q, b))
                sl += len(pair_details[key])
            seq_lens.append(sl)

        # Prefer a query line whose sequence length is near ~10.
        TARGET = 10
        candidates = sorted(
            range(num_lines), key=lambda i: abs(seq_lens[i] - TARGET)
        )
        query_line = candidates[0]
        seq_len = seq_lens[query_line]
        if seq_len < 8 or seq_len > 13:
            continue

        query_label = labels[query_line]
        line_labels = labels[:num_lines]

        # Build the ordered crossing sequence along the query curve.
        query_poly = polylines[query_line]
        qdiffs = np.diff(query_poly, axis=0)
        qseg_lens = np.sqrt((qdiffs ** 2).sum(axis=1))
        qcum = np.concatenate([[0.0], np.cumsum(qseg_lens)])

        entries: List[Tuple[float, str]] = []
        # Self-crossings contribute two entries (both passes), labeled Q.
        for d in self_details[query_line]:
            pos_a = qcum[d["i"]] + d["ti"] * qseg_lens[d["i"]]
            pos_b = qcum[d["j"]] + d["tj"] * qseg_lens[d["j"]]
            entries.append((pos_a, query_label))
            entries.append((pos_b, query_label))
        # Pair-crossings contribute one entry, labeled with the other curve.
        for other in range(num_lines):
            if other == query_line:
                continue
            if query_line < other:
                dets = pair_details[(query_line, other)]
                for d in dets:
                    pos = qcum[d["i"]] + d["ti"] * qseg_lens[d["i"]]
                    entries.append((pos, labels[other]))
            else:
                dets = pair_details[(other, query_line)]
                for d in dets:
                    # query curve is poly_b in this pair → use j, tj
                    pos = qcum[d["j"]] + d["tj"] * qseg_lens[d["j"]]
                    entries.append((pos, labels[other]))

        # Orientation: labeled endpoint at poly[0] → forward arc order;
        # labeled endpoint at poly[-1] → reverse arc order.
        trace_forward = label_starts[query_line]
        entries.sort(key=lambda e: e[0] if trace_forward else -e[0])
        answer_sequence = [label for _, label in entries]
        answer = ", ".join(answer_sequence)

        question = (
            f"The image shows {num_lines} curves. Each curve has one labeled "
            f"endpoint on the perimeter (labels: {', '.join(line_labels)}). "
            f"Starting from the labeled endpoint of curve {query_label}, follow "
            f"curve {query_label} through the interior tangle. At every "
            f"crossing you pass through, record the label of the OTHER curve "
            f"involved — when curve {query_label} crosses itself, record "
            f"{query_label}. Report the ordered sequence of labels, separated "
            f"by commas (for example: A, C, B, C, A). "
            f"Provide your final answer enclosed in <answer>...</answer> tags."
        )

        return {
            "width": width,
            "height": height,
            "num_lines": num_lines,
            "query_line": query_line,
            "query_label": query_label,
            "line_labels": line_labels,
            "total_crossings": total,
            "sequence_length": seq_len,
            "polylines": polylines,
            "label_starts": label_starts,
            "question": question,
            "answer": answer,
        }
    return None


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

def label_anchor_for_endpoint(
    polyline: np.ndarray,
    at_start: bool,
    width: int,
    height: int,
    offset: float = 46.0,
    tangent_span: int = 10,
) -> Tuple[float, float]:
    """Offset a label perpendicular to the leader direction at a labeled
    curve endpoint. Prefer the side that keeps the label inside the canvas
    and farther from the polyline."""
    if at_start:
        pt = polyline[0]
        tan = polyline[min(tangent_span, len(polyline) - 1)] - polyline[0]
    else:
        pt = polyline[-1]
        tan = polyline[-1] - polyline[max(-tangent_span - 1, -len(polyline))]
    tnorm = math.hypot(float(tan[0]), float(tan[1]))
    if tnorm < 1e-8:
        ux, uy = 0.0, -1.0
    else:
        ux = float(tan[0]) / tnorm
        uy = float(tan[1]) / tnorm
    perps = [(-uy, ux), (uy, -ux)]
    best = None
    best_score = -1e9
    for px, py in perps:
        cx = float(pt[0]) + px * offset
        cy = float(pt[1]) + py * offset
        score = 0.0
        if 30 < cx < width - 30 and 30 < cy < height - 30:
            score += 200.0
        diffs = polyline - np.array([cx, cy])
        dists = np.sqrt((diffs ** 2).sum(axis=1))
        score += float(dists.min())
        if score > best_score:
            best_score = score
            best = (cx, cy)
    cx, cy = best
    return (
        float(np.clip(cx, 28, width - 28)),
        float(np.clip(cy, 28, height - 28)),
    )


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

    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("#f3efe8")

    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=0.06, extent=(0, width, height, 0),
              interpolation="bilinear")

    for i in range(num_lines):
        poly = polylines[i]
        ax.plot(
            poly[:, 0], poly[:, 1],
            color=LINE_COLOR, linewidth=2.8,
            solid_capstyle="round", solid_joinstyle="round",
            zorder=2.0 + i * 0.05,
        )

    for i in range(num_lines):
        poly = polylines[i]
        labeled_pt = poly[0] if label_starts[i] else poly[-1]
        lc = LABEL_COLORS[i % len(LABEL_COLORS)]
        lx, ly = label_anchor_for_endpoint(
            poly, at_start=label_starts[i], width=width, height=height,
        )
        # Dashed connector from endpoint to offset label
        ax.plot([labeled_pt[0], lx], [labeled_pt[1], ly],
                color="#9b7b56", linewidth=1.0, alpha=0.7,
                linestyle=(0, (2.0, 3.2)), zorder=3.8)
        # Dot at the actual endpoint
        ax.scatter([labeled_pt[0]], [labeled_pt[1]], s=110,
                   facecolors=lc, edgecolors="white", linewidths=1.8, zorder=4.0)
        # Label at offset position
        ax.text(lx, ly, line_labels[i],
                fontsize=17, fontweight="bold", color=lc,
                ha="center", va="center", zorder=5.0,
                bbox=dict(boxstyle="round,pad=0.2", facecolor="#f3efe8",
                          edgecolor=lc, alpha=0.95, linewidth=1.2))

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


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

def main():
    parser = argparse.ArgumentParser()
    parser.add_argument("--output-root", type=Path, required=True)
    parser.add_argument("--count", type=int, default=20)
    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-lines", type=int, default=3)
    parser.add_argument("--max-lines", type=int, default=5)
    parser.add_argument("--min-crossings", type=int, default=3)
    parser.add_argument("--max-crossings", type=int, default=25)
    parser.add_argument("--difficulty", type=int, default=5,
                        help="Integer difficulty >=0; scales line and crossing counts.")
    parser.add_argument("--workers", type=int, default=8)
    args = parser.parse_args()

    d = max(0, int(args.difficulty))
    # num_lines grows as 3 + d//3 (no cap). num_crossings ∈ [3, 5 + 2d].
    # Fixed 45° minimum crossing angle (handled inside sample_instance).
    args.min_lines = 3 + d // 3
    args.max_lines = 3 + d // 3
    args.min_crossings = 10
    args.max_crossings = 10 + 2 * d

    # Canvas scaling: area ∝ N_d / N_0 with N_d = 5 + 2d.
    N_d = 5 + 2 * 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))

    out_root = 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

    def _attempt(rng):
        return sample_instance(
            rng, args.width, args.height,
            min_lines=args.min_lines, max_lines=args.max_lines,
            min_total_crossings=args.min_crossings,
            max_total_crossings=args.max_crossings,
            max_attempts=50,
        )

    records_raw = parallel_sample_records(
        _attempt, count=args.count, workers=args.workers,
        seed_base=args.seed,
    )
    rng_render = random.Random(args.seed ^ 0xA5A5)
    records = []
    for idx, record in enumerate(records_raw):
        name = f"line_intersections_{idx:05d}.png"
        ns = rng_render.randint(0, 10**9)
        render_instance(img_dir / name, record, noise_seed=ns)
        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": "line_intersections",
        "category": "sequential_traversal",
        "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()