Add presentation slides for OU process and Mehler formula

research/math/podcast/build_video.py

@@ -0,0 +1,124 @@
+#!/usr/bin/env python3
+"""把 Hermite 幻灯片 + 已有播客音频合成为 MP4 视频（无需重新调 TTS）。
+
+流程：
+  1) 读已有完整音频时长；按每句文本字符数占比，把总时长分配到 11 页
+     （字符数是中文 TTS 时长的良好代理；总时长严格等于真实音频）。
+  2) 用 Chrome headless 把 11 页各截一张 1920x1080 PNG（?page=N&clean=1）。
+  3) ffmpeg：每页图片按对应时长生成视频轨，叠加音频，输出 MP4。
+
+用法：python3 build_video.py
+"""
+import json
+import os
+import subprocess
+import sys
+
+HERE = os.path.dirname(os.path.abspath(__file__))
+SCRIPT_JSON = os.path.join(HERE, "hermite_polynomials-script.json")
+SLIDE_HTML = os.path.join(HERE, "slides", "Hermite 多项式.html")
+OUT_DIR = os.path.join(HERE, "output")
+SHOT_DIR = os.path.join(OUT_DIR, "shots")
+AUDIO_IN = os.path.join(OUT_DIR, "hermite_polynomials-podcast.mp3")
+VIDEO_OUT = os.path.join(OUT_DIR, "hermite_polynomials-video.mp4")
+
+CHROME = "/Applications/Google Chrome.app/Contents/MacOS/Google Chrome"
+
+# 句(1-based) -> 页(1-based) 映射。共 43 句、11 页。
+LINE_TO_PAGE = {
+    1: 1, 2: 1,
+    3: 2, 4: 2, 5: 2, 6: 2,
+    7: 3, 8: 3,
+    9: 4, 10: 4, 11: 4, 12: 4,
+    13: 5, 14: 5, 15: 5, 16: 5, 17: 5,
+    18: 6, 19: 6, 20: 6,
+    21: 7, 22: 7, 23: 7, 24: 7, 25: 7, 26: 7,
+    27: 8, 28: 8, 29: 8,
+    30: 9, 31: 9, 32: 9, 33: 9,
+    34: 10, 35: 10, 36: 10, 37: 10, 38: 10, 39: 10,
+    40: 11, 41: 11, 42: 11, 43: 11,
+}
+NUM_PAGES = 11
+
+
+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)
+    with open(SCRIPT_JSON, encoding="utf-8") as f:
+        lines = json.load(f)["lines"]
+    # 每句字符数（去空白）作为时长权重
+    page_chars = {p: 0 for p in range(1, NUM_PAGES + 1)}
+    for i, line in enumerate(lines, 1):
+        n = len(line["paragraph"].strip())
+        page_chars[LINE_TO_PAGE.get(i, NUM_PAGES)] += n
+    grand = sum(page_chars.values())
+    page_dur = {p: total * page_chars[p] / grand for p in page_chars}
+    # 修正累计误差，使最后一页吸收余量
+    assigned = sum(page_dur.values())
+    page_dur[NUM_PAGES] += (total - assigned)
+    print(f"音频总时长 {total:.2f}s，按字符占比分配到 {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, total
+
+
+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")
+        url = f"{file_url}?page={p}&clean=1"
+        run([CHROME, "--headless=new", "--disable-gpu", "--hide-scrollbars",
+             "--force-device-scale-factor=1", "--window-size=1920,1080",
+             f"--screenshot={out}", "--virtual-time-budget=2800", url])
+        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)
+    os.makedirs(OUT_DIR, exist_ok=True)
+    print("=== 步骤 1/3：按字符占比分配每页时长 ===")
+    page_dur, _ = step1_page_durations()
+    print("\n=== 步骤 2/3：截取 11 页幻灯片 ===")
+    step2_screenshots()
+    print("\n=== 步骤 3/3：ffmpeg 合成视频 ===")
+    step3_video(page_dur)
+
+
+if __name__ == "__main__":
+    main()