Add presentation slides for OU process and Mehler formula

research/math/podcast2/build_video2.py

@@ -0,0 +1,114 @@
+#!/usr/bin/env python3
+"""把 OU/Mehler 幻灯片 + 已有播客音频合成为 MP4（复用第一篇流程）。
+
+流程：读已有音频时长 → 按每句字符占比分配到 12 页 → Chrome 截 12 页 → ffmpeg 合成。
+用法：python3 build_video2.py
+"""
+import json
+import os
+import subprocess
+import sys
+
+HERE = os.path.dirname(os.path.abspath(__file__))
+SCRIPT_JSON = os.path.join(HERE, "ou_mehler-script.json")
+SLIDE_HTML = os.path.join(HERE, "slides", "OU 过程与 Mehler 公式.html")
+OUT_DIR = os.path.join(HERE, "output")
+SHOT_DIR = os.path.join(OUT_DIR, "shots")
+AUDIO_IN = os.path.join(OUT_DIR, "ou_mehler-podcast.mp3")
+VIDEO_OUT = os.path.join(OUT_DIR, "ou_mehler-video.mp4")
+CHROME = "/Applications/Google Chrome.app/Contents/MacOS/Google Chrome"
+
+NUM_PAGES = 12
+# 句(1-based) -> 页(1-based)。共 44 句、12 页。
+# 1 封面 / 2 核心问题 / 3 OU直觉 / 4 离散定义 / 5 三性质 / 6 Mehler / 7 核心推论
+# 8 数值例子 / 9 对齐损失 / 10 衰减图 / 11 小结 / 12 尾页
+LINE_TO_PAGE = {
+    1: 1, 2: 1,                          # 封面
+    3: 2,                                # 核心问题
+    4: 3, 5: 3, 6: 3,                    # OU 物理直觉
+    7: 4, 8: 4, 9: 4,                    # 离散定义
+    10: 5, 11: 5, 12: 5, 13: 5, 14: 5, 15: 5,  # 三性质
+    16: 6, 17: 6, 18: 6, 19: 6, 20: 6,   # Mehler 公式
+    21: 7, 22: 7, 23: 7,                 # 核心推论
+    24: 8, 25: 8, 26: 8, 27: 8, 28: 8, 29: 8,  # 数值例子
+    30: 9, 31: 9, 32: 9, 33: 9, 34: 9,   # 对齐损失
+    35: 10, 36: 10,                      # 衰减图示
+    37: 11, 38: 11, 39: 11, 40: 11, 41: 11,    # 小结
+    42: 12, 43: 12, 44: 12,              # 尾页
+}
+
+
+def run(cmd):
+    subprocess.run(cmd, check=True, stdout=subprocess.DEVNULL, stderr=subprocess.DEVNULL)
+
+
+def ffprobe_dur(path):
+    out = subprocess.check_output(
+        ["ffprobe", "-v", "error", "-show_entries", "format=duration",
+         "-of", "default=noprint_wrappers=1:nokey=1", path])
+    return float(out.strip())
+
+
+def step1_page_durations():
+    total = ffprobe_dur(AUDIO_IN)
+    lines = json.load(open(SCRIPT_JSON, encoding="utf-8"))["lines"]
+    page_chars = {p: 0 for p in range(1, NUM_PAGES + 1)}
+    for i, line in enumerate(lines, 1):
+        page_chars[LINE_TO_PAGE.get(i, NUM_PAGES)] += len(line["paragraph"].strip())
+    grand = sum(page_chars.values())
+    page_dur = {p: total * page_chars[p] / grand for p in page_chars}
+    page_dur[NUM_PAGES] += (total - sum(page_dur.values()))
+    print(f"音频总时长 {total:.2f}s，分配到 {NUM_PAGES} 页：")
+    for p in range(1, NUM_PAGES + 1):
+        print(f"  page {p:>2}: {page_dur[p]:6.2f}s  ({page_chars[p]} 字)")
+    return page_dur
+
+
+def step2_screenshots():
+    os.makedirs(SHOT_DIR, exist_ok=True)
+    file_url = "file://" + SLIDE_HTML.replace(" ", "%20")
+    for p in range(1, NUM_PAGES + 1):
+        out = os.path.join(SHOT_DIR, f"page_{p:02d}.png")
+        run([CHROME, "--headless=new", "--disable-gpu", "--hide-scrollbars",
+             "--force-device-scale-factor=1", "--window-size=1920,1080",
+             f"--screenshot={out}", "--virtual-time-budget=2800",
+             f"{file_url}?page={p}&clean=1"])
+        if not os.path.exists(out):
+            raise RuntimeError(f"截图失败 page {p}")
+        print(f"截图 page {p:02d} ✓")
+
+
+def step3_video(page_dur):
+    tmp_list = os.path.join(SHOT_DIR, "vlist.txt")
+    with open(tmp_list, "w") as lf:
+        for p in range(1, NUM_PAGES + 1):
+            img = os.path.join(SHOT_DIR, f"page_{p:02d}.png")
+            dur = max(page_dur[p], 0.8)
+            vid = os.path.join(SHOT_DIR, f"v_{p:02d}.mp4")
+            run(["ffmpeg", "-y", "-loop", "1", "-i", img, "-t", f"{dur:.3f}",
+                 "-r", "30", "-pix_fmt", "yuv420p",
+                 "-vf", "scale=1920:1080:force_original_aspect_ratio=decrease,"
+                        "pad=1920:1080:(ow-iw)/2:(oh-ih)/2",
+                 "-c:v", "libx264", "-preset", "medium", "-crf", "20", vid])
+            lf.write(f"file '{vid}'\n")
+            print(f"页视频 {p:02d}  {dur:.2f}s ✓")
+    silent = os.path.join(SHOT_DIR, "silent.mp4")
+    run(["ffmpeg", "-y", "-f", "concat", "-safe", "0", "-i", tmp_list, "-c", "copy", silent])
+    run(["ffmpeg", "-y", "-i", silent, "-i", AUDIO_IN,
+         "-c:v", "copy", "-c:a", "aac", "-b:a", "192k", "-shortest", VIDEO_OUT])
+    print(f"\n✅ 视频已输出：{VIDEO_OUT}  ({ffprobe_dur(VIDEO_OUT):.1f}s)")
+
+
+def main():
+    if not os.path.exists(AUDIO_IN):
+        print(f"ERROR: 找不到音频 {AUDIO_IN}", file=sys.stderr); sys.exit(1)
+    print("=== 步骤 1/3：分配每页时长 ===")
+    page_dur = step1_page_durations()
+    print("\n=== 步骤 2/3：截取 12 页 ===")
+    step2_screenshots()
+    print("\n=== 步骤 3/3：ffmpeg 合成 ===")
+    step3_video(page_dur)
+
+
+if __name__ == "__main__":
+    main()