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59c5fa6 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 | """
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() |