""" Programmatic path tracing data generation. Generates images with curved lines that connect start/end icons. The model must trace the line using visual primitives (points). """ import argparse import json import random import math from pathlib import Path from typing import List, Tuple import numpy as np from PIL import Image, ImageDraw def _de_casteljau(control_points: List[Tuple[float, float]], t: float) -> Tuple[float, float]: """Evaluate a Bézier curve at parameter t using De Casteljau's algorithm.""" pts = list(control_points) while len(pts) > 1: pts = [ ((1 - t) * pts[i][0] + t * pts[i + 1][0], (1 - t) * pts[i][1] + t * pts[i + 1][1]) for i in range(len(pts) - 1) ] return pts[0] def generate_curve( start: Tuple[int, int], end: Tuple[int, int], num_control_points: int = 3, curvature: float = 1.0, ) -> List[Tuple[int, int]]: """Generate a smooth curved path from start to end using Bézier curves. Per the paper: "We generate images which consist of multiple Bézier curves." Uses De Casteljau's algorithm for evaluation. """ # Build control points: start, random intermediates, end control_pts = [start] for _ in range(num_control_points): # Interpolate between start and end, then add random offset for curvature frac = random.random() base_x = start[0] + frac * (end[0] - start[0]) base_y = start[1] + frac * (end[1] - start[1]) offset_x = (random.random() - 0.5) * curvature * 200 offset_y = (random.random() - 0.5) * curvature * 200 x = max(0, min(999, int(base_x + offset_x))) y = max(0, min(999, int(base_y + offset_y))) control_pts.append((x, y)) control_pts.append(end) # Sort intermediate control points by their projection onto start->end axis # to avoid self-intersecting curves if len(control_pts) > 2: dx = end[0] - start[0] dy = end[1] - start[1] length_sq = dx * dx + dy * dy if length_sq > 0: intermediates = control_pts[1:-1] intermediates.sort(key=lambda p: ((p[0] - start[0]) * dx + (p[1] - start[1]) * dy) / length_sq) control_pts = [start] + intermediates + [end] # Evaluate Bézier curve at uniform parameter values n_segments = 50 path = [] for i in range(n_segments + 1): t = i / n_segments x, y = _de_casteljau(control_pts, t) path.append((int(x), int(y))) return path def generate_crossing_lines( img_size: int = 800, num_lines: int = 3, uniform_style: bool = False, ) -> Tuple[Image.Image, List[Tuple[int, int]], str, str]: """ Generate an image with multiple curved Bézier lines crossing each other. Args: uniform_style: If True, all lines share the same color and stroke width, stripping away color-based shortcuts and forcing the model to rely solely on curvature continuity at crossings (per paper). Returns: image, target_path_points, start_label, end_label """ img = Image.new("RGB", (img_size, img_size), "white") draw = ImageDraw.Draw(img) # Generate background noise for _ in range(100): x, y = random.randint(0, img_size - 1), random.randint(0, img_size - 1) draw.point((x, y), fill=(240, 240, 240)) lines = [] labels_pool = ["crown", "octopus", "star", "heart", "diamond", "club", "spade", "moon", "sun", "cloud", "tree", "flower", "fish", "bird"] chosen_labels = random.sample(labels_pool, num_lines + 1) # Uniform style: same color and width for all lines if uniform_style: uniform_color = "black" uniform_width = 3 else: uniform_color = None uniform_width = None for i in range(num_lines): start = (random.randint(50, img_size - 50), random.randint(50, img_size - 50)) end = (random.randint(50, img_size - 50), random.randint(50, img_size - 50)) path = generate_curve(start, end, num_control_points=random.randint(2, 5)) color = uniform_color if uniform_style else random.choice( ["red", "blue", "green", "purple", "orange", "black"]) width = uniform_width if uniform_style else random.randint(2, 4) lines.append({ "path": path, "color": color, "width": width, "start": chosen_labels[i], "end": chosen_labels[i + 1], }) # Draw all lines for line in lines: pts = line["path"] # Scale to image size img_pts = [(int(x / 999 * img_size), int(y / 999 * img_size)) for x, y in pts] draw.line(img_pts, fill=line["color"], width=line["width"]) # Pick one line as target target = random.choice(lines) # Draw start/end icons as simple text markers sx, sy = target["path"][0] ex, ey = target["path"][-1] sx_img = int(sx / 999 * img_size) sy_img = int(sy / 999 * img_size) ex_img = int(ex / 999 * img_size) ey_img = int(ey / 999 * img_size) draw.text((sx_img - 10, sy_img - 10), target["start"][:2].upper(), fill="black") draw.text((ex_img - 10, ey_img - 10), target["end"][:2].upper(), fill="black") return img, target["path"], target["start"], target["end"] def generate_path_thinking(path: List[Tuple[int, int]], start_label: str, end_label: str) -> str: """Generate thinking content with point visual primitives tracing the path.""" lines = [] sx, sy = path[0] ex, ey = path[-1] lines.append(f"I find the starting point you mentioned, it's located here: <|point|>[[{sx},{sy}]]<|/point|>.") lines.append("Following this line, the visual path I observe is:") # Sample points adaptively: fewer for straight segments, more for curves sampled = [path[0]] for i in range(1, len(path)): prev = sampled[-1] curr = path[i] dist = math.hypot(curr[0] - prev[0], curr[1] - prev[1]) # Adaptive sampling: if distance > threshold, add point if dist > 20 or i == len(path) - 1: sampled.append(curr) pt_str = ",".join(f"[{x},{y}]" for x, y in sampled) lines.append(f"<|point|>[{pt_str}]<|/point|>") lines.append(f"Following this path, it connects to: <|point|>[[{ex},{ey}]]<|/point|>.") return "\n".join(lines) def main(): parser = argparse.ArgumentParser() parser.add_argument("--output_dir", type=str, default="data/sft/path") parser.add_argument("--num_samples", type=int, default=1000) parser.add_argument("--min_lines", type=int, default=2) parser.add_argument("--max_lines", type=int, default=5) parser.add_argument("--seed", type=int, default=42) args = parser.parse_args() random.seed(args.seed) np.random.seed(args.seed) out_dir = Path(args.output_dir) out_dir.mkdir(parents=True, exist_ok=True) img_dir = out_dir / "images" img_dir.mkdir(exist_ok=True) records = [] for i in range(args.num_samples): num_lines = random.randint(args.min_lines, args.max_lines) # 30% of samples use uniform style (per paper: forces curvature-based reasoning) use_uniform = random.random() < 0.3 img, path, start_label, end_label = generate_crossing_lines( num_lines=num_lines, uniform_style=use_uniform) img_path = img_dir / f"path_{i:06d}.png" img.save(img_path) thinking = generate_path_thinking(path, start_label, end_label) question = f"Where does the {start_label} icon connect to? Put the destination icon name in \\boxed{{}}." answer = f"\\boxed{{{end_label}}}" records.append({ "image": str(img_path.relative_to(out_dir)), "question": question, "thinking": thinking, "start_label": start_label, "end_label": end_label, "answer": answer, }) with open(out_dir / "path_data.jsonl", "w") as f: for rec in records: f.write(json.dumps(rec, ensure_ascii=False) + "\n") print(f"Generated {args.num_samples} path tracing samples in {out_dir}") if __name__ == "__main__": main()