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+# 接口 2：C 端生发 — 技术实现方案（第一步：发际线遮罩渲染）
+
+> 在 **高性能 worker（GPU 机）** 上实现，与接口 1 同机。对外接口经网关代理（见 [`系统架构-网关与高性能后端.md`](系统架构-网关与高性能后端.md)）。
+> 发际线检测算法移植自 **head3d** 项目（已实现 502 点 mesh + UV 贴图方案）。
+
+---
+
+## 0. 本期范围（第一步）
+
+接口 2 输入用户正面照 + **性别**，按性别对应的发际线类型贴图，**逐张把发际线曲线渲染到照片上**，输出多张「叠加了建议发际线的预览图」，按固定顺序返回。
+
+- **本期只做「渲染遮罩/预览图」**，不做真正的文生图生发（那是后续步骤）。当前 `image_url` 返回的是「原照片 + 发际线曲线叠加图」。
+- 排序 `order` 本期不计算，按贴图顺序 `1..N`。
+
+---
+
+## 1. 与现接口文档的差异（接口 2 需同步更新 `接口文档.md`）
+
+| 项 | 现状 | 本期改为 |
+|----|------|----------|
+| 输入参数 | `beauty_enabled` | **新增必填 `gender`（`male`/`female`）**；`beauty_enabled` 保留但本期不生效 |
+| 输出 `results[]` 数量 | Mock 2 个 | = 该性别的贴图数量（**female 5 张 / male 4 张**） |
+| `results[].image_url` | 生发后图片 | **本期 = 发际线曲线叠加在原照片上的预览图** |
+| `results[].hairline_type` | 中文（花瓣形…） | **英文 key**（`flower`/`wave`/`heart`/`ellipse`/`straight`/`m`/`inverse_arc`） |
+| `results[].order` | 排序 | 本期固定 `1..N`（不排序） |
+| 错误码 1004（性别判断异常） | 待确认 | `gender` 改为必填入参 → **不再自动判别性别**；1004 仅在 `gender` 非法值时使用（或弃用） |
+
+> ⚠️ 这是接口 2 的**有意契约变更**（加入参 + 改输出语义），需在 `接口文档.md` 接口 2 章节同步。其余 4 个接口契约不变。
+
+### gender → 贴图集合
+
+`hairline_texture/` 目录下贴图（512×512 RGBA，白色发际线曲线在顶部 UV 条带）：
+
+| gender | 贴图文件 | hairline_type (key) |
+|--------|----------|---------------------|
+| female | `girl_ellipse.png` | `ellipse` |
+| female | `girl_flower.png` | `flower` |
+| female | `girl_heart.png` | `heart` |
+| female | `girl_straight.png` | `straight` |
+| female | `girl_wave.png` | `wave` |
+| male | `man_ellipse.png` | `ellipse` |
+| male | `man_m.png` | `m` |
+| male | `man_straight.png` | `straight` |
+| male | `man_ inverse_arc.png` | `inverse_arc` |
+
+> 注意 `man_ inverse_arc.png` 文件名里有个空格，代码里按 `gender + '_' + key` 生成文件名时需保留/清洗一致。建议**启动时扫描目录**建立 `{gender: [(key, path)]}` 映射，而不是硬编码文件名，并把文件名规范化（去空格）。
+
+---
+
+## 2. 已从 head3d 复制到本项目的文件
+
+全部放在 `hairline/` 包下（已复制，agent 直接用）：
+
+```
+hairline/
+├── __init__.py
+├── constants.py            # 17 锚点、UV 偏移、分割类别、矢状-arc 常量、HF 模型 id
+├── obj_io.py               # OBJ 读写
+├── face_landmarks.py       # MediaPipe Tasks FaceLandmarker 封装（用 face_landmarker.task）
+├── face_parsing.py         # SegFormer 人脸分割封装
+├── hairline_2d.py          # 射线检测发际线 2D + 平滑 + 回退
+├── lift_3d.py              # 2D→3D 矢状-arc 提升 + 中间行 + assemble 502 点
+├── extract_hairline.py     # 主管线（image → 502 点），可复用 run()
+├── _index_map_data.py      # 468→OBJ indexMap（build_extended_obj 用，本期渲染不需要）
+├── _mediapipe_subprocess.py# WSL 下子进程跑 MediaPipe 的兜底（可选）
+├── models/
+│   ├── face_landmarker.task       # MediaPipe 模型（3.7MB，已复制）
+│   └── face-parsing/              # SegFormer 权重（离线，已下载，见 OFFLINE_ASSETS.md）
+│       ├── config.json
+│       ├── preprocessor_config.json
+│       └── model.safetensors
+├── mesh/
+│   ├── face_ext.obj        # 502 点扩展 mesh + UV + 三角面（渲染器读这个）
+│   └── face.obj            # 原始 468 点 mesh（参考/重生成用）
+└── reference/
+    ├── texture0.png        # head3d 原 5 弧线贴图（核对 UV 用）
+    └── uv_template.png     # UV 布局参考
+```
+
+发际线类型贴图在仓库根目录 `hairline_texture/`（用户提供，9 张）。
+
+### 2.1 移植后需要修改的集成点
+
+1. **`face_landmarks.py` 的 `DEFAULT_MODEL_PATH`**：原逻辑是 `dirname(dirname(__file__))/models/...`（head3d 里模块在 `python/` 子目录）。现在模块在 `hairline/` 根，该路径会指向 `hair/models/`，而模型在 `hairline/models/`。**改为** `os.path.join(os.path.dirname(__file__), "models", "face_landmarker.task")`。
+2. **`face_parsing.py` 离线加载**：`C.HF_FACE_PARSER_MODEL` 当前是 HF 在线 id `"jonathandinu/face-parsing"`。内网/离线改为本地目录：把 `constants.py` 的 `HF_FACE_PARSER_MODEL` 指向 `hairline/models/face-parsing` 的绝对路径（`from_pretrained` 支持本地目录）；或设 `HF_HUB_OFFLINE=1`。
+3. **相对导入**：模块用 `from . import constants`，已加 `hairline/__init__.py`，作为包导入即可（`from hairline.extract_hairline import run`）。
+4. **GPU**：`FaceParser(device="cuda")`，worker 有 GPU。
+
+---
+
+## 3. 算法管线（整体）
+
+```
+输入: 用户正面照 + gender
+   │
+   ▼
+[A] head3d 管线（复用 hairline.extract_hairline 的步骤）
+   - MediaPipe 468 点（face_landmarker.task）
+   - SegFormer 人脸分割 → parse_map
+   - 17 锚点射线检测发际线 → 17 个 2D 点 → 平滑
+   - 矢状-arc 提升 → 502 点（归一化 x,y,z）
+   │  失败处理：无人脸→1001
+   ▼
+[B] 投影到图像像素
+   - 502 点的 (x,y) × (W,H) → 502 个 2D 图像坐标
+   - 读 face_ext.obj：UV(502) + 扩展三角面（涉及顶点 ≥468 的 64 个三角形）
+   ▼
+[C] 逐张贴图渲染（新写的服务端渲染器，本方案核心）
+   for 每个该性别的发际线贴图 t:
+     - 对每个扩展三角形：src=UV→贴图像素, dst=投影 2D 坐标 → cv2 仿射 warp
+     - 累积成一张 RGBA 曲线层（贴图 alpha 控制曲线/透明）
+     - 把曲线层 alpha 合成到原照片上 → 预览图
+   ▼
+[D] 输出
+   results[] = N 个 {image(预览图), hairline_type(key), order=1..N}
+   worker 侧每张图以 base64 返回（见 §6）
+```
+
+---
+
+## 4. 渲染器（新代码，本期重点）★
+
+head3d 把贴图渲染到照片是**浏览器 Three.js** 做的（`/preview` ortho overlay），**没有服务端实现**。本期新写一个 **OpenCV 逐三角形仿射 warp** 渲染器，无需 OpenGL 离屏上下文，确定性好、部署简单。
+
+### 4.1 原理
+
+face_ext.obj 的 502 顶点里：
+- `[0..467]` MediaPipe 点，其中 17 个 `MP_TOP_ANCHORS` 是发际线 ribbon 的**下边沿**；
+- `[468..484]` 中间行、`[485..501]` 发际线行，是 ribbon 的中、上两行。
+
+这 34 个新点 + 17 个锚点之间连成 64 个三角形（ribbon），它们的 UV 落在贴图**顶部条带**（V_raw≈0.67..0.94，正是发际线曲线所在）。所以只要把**这 64 个三角形**按 UV→图像坐标 warp，就能把贴图里的发际线曲线贴到照片的额头/发际线区域。
+
+### 4.2 步骤
+
+```python
+# 伪代码
+def render_hairline_overlay(photo_bgr, points502_norm, ext_faces, uv502, texture_rgba):
+    H, W = photo_bgr.shape[:2]
+    # 502 点投影到图像像素
+    img_xy = points502_norm[:, :2] * [W, H]            # (502, 2)
+    TW, TH = texture_rgba.shape[1], texture_rgba.shape[0]  # 512, 512
+
+    overlay = np.zeros((H, W, 4), np.float32)           # 累积曲线层 RGBA
+    for (i, j, k) in ext_faces:                         # 仅扩展三角形（顶点含 ≥468）
+        dst = img_xy[[i, j, k]].astype(np.float32)      # 图像坐标
+        # UV → 贴图像素。注意 flipY：贴图 y = (1 - v_raw) * TH
+        src = np.array([[uv502[v][0]*TW, (1-uv502[v][1])*TH] for v in (i,j,k)], np.float32)
+        M = cv2.getAffineTransform(src, dst)
+        warped = cv2.warpAffine(texture_rgba, M, (W, H), flags=cv2.INTER_LINEAR,
+                                borderMode=cv2.BORDER_CONSTANT, borderValue=(0,0,0,0))
+        # 三角形掩码，避免覆盖整张 warp 结果
+        tri_mask = np.zeros((H, W), np.uint8)
+        cv2.fillConvexPoly(tri_mask, dst.astype(np.int32), 255)
+        sel = tri_mask > 0
+        overlay[sel] = warped[sel]                      # 逐三角形写入（相邻共享边，覆盖等价）
+
+    # alpha 合成到原照片
+    a = overlay[:, :, 3:4] / 255.0
+    out = photo_bgr.astype(np.float32)
+    out = out * (1 - a) + overlay[:, :, :3][..., ::-1] * a   # RGBA→BGR 注意通道序
+    return out.astype(np.uint8)
+```
+
+### 4.3 注意点
+
+- **通道序**：贴图是 RGBA，照片 OpenCV 是 BGR，合成时注意 R/B 调换。
+- **flipY**：face_ext.obj 的 UV 是 V_raw（V=1 对应贴图顶部），转贴图像素 y 要 `(1 - v)`，与 head3d Three.js `texture.flipY=true` 一致。
+- **只 warp 扩展三角形**：从 face_ext.obj 筛出顶点索引含 ≥468 的面（约 64 个）。不要 warp 整脸。
+- **抗锯齿/接缝**：逐三角形 `fillConvexPoly` 掩码可能在共享边留 1px 缝。可对 `tri_mask` 略膨胀，或最后对 overlay alpha 做轻微羽化。先跑通看效果再优化。
+- **裁剪到额头**：曲线层只在 ribbon 区域有内容（贴图其余透明），天然不会画到脸下半部。
+
+---
+
+## 5. 依赖
+
+worker 已有（接口 1）：`opencv-python`、`numpy`、`Pillow`、torch(CUDA)。接口 2 **新增**：
+
+```
+mediapipe>=0.10            # Tasks Vision FaceLandmarker（注意与接口1的 solutions API 可共存）
+transformers>=4.40         # SegFormer 人脸分割
+# torch/torchvision 已由接口1引入（worker CUDA 版）
+```
+
+> ⚠️ **两套人脸分割模型**：接口 1 用 BiSeNet（`79999_iter.pth`），接口 2 用 head3d 的 SegFormer（`jonathandinu/face-parsing`）。两者并存，显存/内存够（worker 32G+GPU）。后续可评估是否统一为一个分割模型，本期先各用各的，**不强行合并**。
+>
+> ⚠️ **MediaPipe API 差异**：接口 1 用 `mp.solutions.face_mesh`（468 点 + 虹膜 refine），接口 2 用 `mp.tasks.vision.FaceLandmarker`（读 `.task` 文件）。同一个 mediapipe 包都支持，但版本需兼容两者（建议先用一个版本把两接口都跑通）。
+
+---
+
+## 6. worker 集成（接口 2 handler）
+
+在 `app.py` 替换 `/api/v1/hair/grow` 的 Mock：
+
+```
+1. 解析图片（三选一）+ 读 gender（必填，male/female；非法→1004 或 1008 参数错误）
+2. 校验（大小/解码/分辨率，同接口1）
+3. 跑 hairline.extract_hairline 的步骤拿 502 点（无人脸→1001）
+4. 按 gender 取贴图集合（启动时扫描 hairline_texture/ 建映射）
+5. for 每张贴图: render_hairline_overlay → PNG
+6. results[] = [{image_base64, hairline_type, order}], 逐张 base64
+7. return ok({"results": results})
+```
+
+- **拆分架构**：worker 返回 `results[].image_base64`，**不落盘不拼 URL**。网关把每个 `image_base64` 落盘改写成 `image_url`（架构文档 §9 的映射表需支持**数组里的图片字段** `results[].image`）。
+- 模型单例：`FaceLandmarker` 和 `FaceParser` 在模块加载时初始化一次，避免每请求重建。face_ext.obj 的 UV/faces 也只解析一次缓存。
+
+---
+
+## 7. 离线资产（内网部署）
+
+接口 2 新增需要随项目带入内网的模型（已下载，登记到 `OFFLINE_ASSETS.md`）：
+- `hairline/models/face_landmarker.task`（MediaPipe，~3.7MB）
+- `hairline/models/face-parsing/`（SegFormer：config + preprocessor + model.safetensors）
+
+> SegFormer 加载方式改本地路径后，内网无需联网（见 §2.1）。
+
+---
+
+## 8. 开发步骤与验证（agent 执行）
+
+| 阶段 | 内容 | 验证 |
+|------|------|------|
+| **M0 跑通管线** | 修好集成点（§2.1），用一张人像跑 `hairline.extract_hairline.run()` 得 502 点 JSON | 502 点、valid_hairline 有 true |
+| **M1 解析 mesh** | 读 face_ext.obj 拿 UV + 扩展三角面（顶点≥468 的面），缓存 | 打印扩展面数（~64）、502 个 UV |
+| **M2 渲染器** | 实现 `render_hairline_overlay`，对 1 张贴图渲染 | 输出预览图，**目视**：发际线曲线贴在额头正确位置、跟随脸 |
+| **M3 全量 + 性别** | 扫描 `hairline_texture/` 建 gender→贴图映射，按性别渲染 N 张 | female 出 5 张、male 出 4 张，hairline_type 对 |
+| **M4 接 app.py** | handler + gender 必填 + base64 返回 | curl 验证 results 数量/字段；无人脸→1001；缺 gender→报错 |
+| **M5 网关映射** | 网关支持 `results[].image_base64`→`image_url`（网关任务书侧） | 端到端经网关返回 image_url，公网可访问 |
+
+**M2 是关键里程碑**：渲染器对齐效果好不好，决定整个接口可用性，先用几张测试人像目视确认贴合。
+
+---
+
+## 9. 风险与待办
+
+1. **新贴图 UV 是否与 texture0 完全一致**：本方案假设 9 张贴图沿用 head3d 的顶部条带 UV 布局（已肉眼确认曲线在顶部）。M2 渲染若位置偏移，核对贴图内容所在的 V 区间与 `UV_MIDDLE_DV/UV_HAIRLINE_DV`。
+2. **接缝/锯齿**：逐三角形 warp 的共享边接缝，M2 跑通后按 §4.3 优化。
+3. **歪头/非正面**：head3d 矢状-arc 假设近正脸，大角度发际线贴合差。可复用接口 1 的 solvePnP 做前置姿态校验（可选）。
+4. **秃头/高发际线/刘海**：SegFormer 找不到头发时射线回退几何外推，曲线可能偏高；valid_hairline 标记可用于提示。
+5. **排序**：本期 order=1..N。后续排序需定义依据（脸型/额型匹配度）。
+6. **真正的生发（文生图）**：本期只出遮罩/预览。下一步把预览图/曲线作为 ControlNet/inpaint 输入接文生图模型，再替换 `image_url` 为真实生发图。
+
+---
+
+> **文档版本**: v1.0 ｜ **创建日期**: 2026-06-14 ｜ 算法来源: head3d（502 点 mesh + UV）｜ 运行位置: worker(GPU)
+> **本期产出**: 发际线曲线叠加预览图（非最终生发图）
diff --git a/docs/接口文档.md b/docs/接口文档.md
index fbcd9d9..27b2dab 100644
--- a/docs/接口文档.md
+++ b/docs/接口文档.md
@@ -177,7 +177,9 @@
 
 ## 接口 2：C 端生发接口
 
-**说明**：输入用户正面照，输出生发后的图片，以及推荐的发际线（可能多张），并按合适度排序。
+**说明**：输入用户正面照 + 性别，按性别对应的发际线类型，逐张把建议发际线渲染到照片上，输出多张方案。
+
+> **当前阶段（第一步）**：`image_url` 返回的是「**原照片 + 发际线曲线叠加的预览图**」，尚未做真正的文生图生发；后续会替换为生发后图片。实现见 [`接口2-C端生发-技术实现方案.md`](接口2-C端生发-技术实现方案.md)。
 
 **请求**：`POST /api/v1/hair/grow`
 
@@ -187,19 +189,20 @@
 
 | 参数 | 类型 | 必填 | 说明 |
 |------|------|------|------|
-| beauty_enabled | bool | 否 | 生发图是否带美颜效果，默认 false。提供该开关 |
+| gender | string | **是** | 性别：`male` / `female`。决定使用的发际线贴图集合 |
+| beauty_enabled | bool | 否 | 生发图是否带美颜效果，默认 false（当前阶段不生效） |
 
 ### 输出（data）
 
-`results`：发际线方案数组（可能多张），每个元素：
+`results`：发际线方案数组，**数量 = 该性别的发际线类型数**（`female` 5 个 / `male` 4 个）。每个元素：
 
 | 字段 | 类型 | 说明 |
 |------|------|------|
-| image_url | string | 生发后图片 URL |
-| hairline_type | string | 图片对应的发际线形（如：花瓣形、波浪形） |
-| order | int | 排序序号（1 = 最优，2 次之 …） |
+| image_url | string | 方案预览图 URL（当前 = 发际线叠加图） |
+| hairline_type | string | 发际线类型 key：`ellipse`/`flower`/`heart`/`straight`/`wave`（female），`ellipse`/`m`/`straight`/`inverse_arc`（male） |
+| order | int | 排序序号（当前阶段固定 `1..N`，按贴图顺序，暂不计算合适度） |
 
-### 响应示例（当前 Mock 返回值）
+### 响应示例
 
 ```json
 {
@@ -208,14 +211,14 @@
   "request_id": "mock-request-id",
   "data": {
     "results": [
-      { "image_url": "https://hair.xiangsilian.com/static/sample.jpg", "hairline_type": "花瓣形", "order": 1 },
-      { "image_url": "https://hair.xiangsilian.com/static/sample.jpg", "hairline_type": "波浪形", "order": 2 }
+      { "image_url": "https://hair.xiangsilian.com/static/annotations/uuid1.png", "hairline_type": "ellipse", "order": 1 },
+      { "image_url": "https://hair.xiangsilian.com/static/annotations/uuid2.png", "hairline_type": "flower", "order": 2 }
     ]
   }
 }
 ```
 
-> 识别失败时返回通用错误码（1001 / 1002 / 1003 等）。
+> 识别失败时返回通用错误码（1001 / 1002 / 1003 等）。`gender` 缺失或非法值返回参数错误（1008）；本接口已改为必填入参，不再自动判别性别（1004 不再使用）。
 
 ---
 
diff --git a/hairline/__init__.py b/hairline/__init__.py
new file mode 100644
index 0000000..f0a2232
--- /dev/null
+++ b/hairline/__init__.py
@@ -0,0 +1,7 @@
+"""接口 2（C 端生发）发际线渲染管线。
+
+从 head3d 项目移植：MediaPipe 468 点 + SegFormer 人脸分割 + 17 锚点射线检测发际线
+→ 502 点 3D mesh（face_ext.obj）+ UV → 把发际线类型贴图渲染到照片对应位置。
+
+模块来源见 docs/接口2-C端生发-技术实现方案.md。
+"""
diff --git a/hairline/_index_map_data.py b/hairline/_index_map_data.py
new file mode 100644
index 0000000..a9e23d6
--- /dev/null
+++ b/hairline/_index_map_data.py
@@ -0,0 +1,55 @@
+"""Auto-extracted indexMap[468] from the SDK's hardcode_data.h.
+
+Each entry: OBJ-vertex-index i -> MediaPipe canonical landmark index.
+Do not edit by hand; regenerate from the C++ source.
+"""
+
+INDEX_MAP_468 = [
+    127,  34, 139,  11,   0,  37, 232, 231, 120,  72,
+     39, 128, 121,  47, 104,  69,  67, 175, 171, 148,
+    118,  50, 101,  73,  40,   9, 151, 108,  48, 115,
+    131, 194, 204, 211,  74, 185,  80,  42, 183,  92,
+    186, 230, 229, 202, 212, 214,  83,  18,  17,  76,
+     61, 146, 160,  29,  30,  56, 157, 173, 106, 135,
+    192, 203, 165,  98,  21,  71,  68,  51,  45,   4,
+    144,  24,  23,  77,  91, 205, 187, 201, 200, 182,
+     90, 181,  85,  84, 206,  36, 140, 193, 189, 244,
+    159, 158,  28, 247, 246, 161, 236,   3, 196,  54,
+    168,   8, 117, 228,  31,  55,  97,  99, 126, 100,
+    166,  79, 218, 155, 154,  26, 209,  49, 136, 150,
+    217, 223,  52,  53, 134, 170,  43, 119, 226, 130,
+     63, 238,  20, 242,  46,  70, 156,  78,  62,  96,
+    143, 227, 123, 111,  44, 125,  19, 216, 153,  22,
+    167, 208, 142,  57,  60,  35, 113,  27, 210, 225,
+    137, 116,  41,  38, 129,  64, 240, 102, 207, 184,
+    169, 149, 176, 105,  66, 122,   6, 147,  65, 107,
+     89, 180,  93,  15,  86,  14,  87, 145,  88, 179,
+     95, 138, 172, 215,  58, 219,  81, 195, 199,  82,
+    163, 110, 234, 109, 235, 191, 222, 141, 221, 197,
+     25,   7,  33, 220, 237, 245, 162, 188, 174,   2,
+    241, 164,  12,  13, 198, 133, 112, 243, 239, 190,
+     32, 178, 132, 177,   1, 213,  59,  94,  75, 224,
+    233, 114, 124, 356, 389, 368, 302, 267, 452, 350,
+    349, 303, 269, 357, 343, 277, 453, 333, 332, 297,
+    152, 377, 347, 348, 330, 304, 270, 336, 337, 278,
+    279, 360, 418, 262, 431, 408, 409, 310, 415, 407,
+    410, 450, 422, 430, 434, 313, 314, 306, 307, 375,
+    387, 388, 260, 286, 414, 398, 335, 406, 364, 367,
+    416, 423, 358, 327, 251, 284, 298, 281,   5, 373,
+    374, 253, 320, 321, 425, 427, 411, 421, 405, 404,
+    315,  16, 426, 266, 400, 369, 322, 391, 417, 465,
+    464, 386, 257, 258, 466, 456, 399, 419, 285, 346,
+    340, 261, 413, 441, 460, 328, 355, 371, 329, 392,
+    439, 438, 382, 341, 256, 429, 420, 394, 379, 437,
+    443, 444, 283, 275, 440, 363, 338, 273, 451, 446,
+    342, 467, 293, 334, 282, 458, 461, 462, 276, 353,
+    383, 308, 324, 325, 300, 372, 345, 447, 352, 274,
+    248, 436, 381, 252, 393, 428, 287, 250, 384, 265,
+    259, 424, 292, 366, 271, 294, 455, 272, 432, 395,
+    299, 351, 280, 319, 295, 296, 403, 323, 454, 316,
+    380, 318, 402, 365, 435, 397, 344, 311, 291, 396,
+    268, 445, 254, 339, 449, 264,  10, 442, 370, 263,
+    255, 359, 412, 301, 378, 326, 457, 362, 459, 463,
+    354, 401, 361, 309, 376, 433, 289, 305, 448, 290,
+    288, 249, 103, 385, 331, 317, 312, 390,
+]
diff --git a/hairline/_mediapipe_subprocess.py b/hairline/_mediapipe_subprocess.py
new file mode 100644
index 0000000..0e952cc
--- /dev/null
+++ b/hairline/_mediapipe_subprocess.py
@@ -0,0 +1,67 @@
+"""Standalone MediaPipe FaceLandmarker runner used by web_service.py.
+
+Running MediaPipe Tasks in the same process as the Flask dev server can
+segfault under WSL (D3D12 EGL backend). Spawning a fresh subprocess per
+request keeps the web server alive and lets us inject WSL-friendly env
+vars before any mediapipe import.
+
+Usage:
+    python -m python._mediapipe_subprocess <image_path> <output_npy>
+"""
+from __future__ import annotations
+
+import os
+import sys
+
+os.environ.setdefault("LIBGL_ALWAYS_SOFTWARE", "1")
+os.environ.setdefault("MESA_LOADER_DRIVER_OVERRIDE", "llvmpipe")
+os.environ.setdefault("GALLIUM_DRIVER", "llvmpipe")
+os.environ.setdefault("MEDIAPIPE_DISABLE_GPU", "1")
+os.environ.setdefault("EGL_PLATFORM", "surfaceless")
+
+import numpy as np  # noqa: E402
+
+THIS_DIR = os.path.dirname(os.path.abspath(__file__))
+PROJECT_DIR = os.path.dirname(THIS_DIR)
+if PROJECT_DIR not in sys.path:
+    sys.path.insert(0, PROJECT_DIR)
+
+from python.face_landmarks import FaceLandmarker  # noqa: E402
+
+
+def main() -> int:
+    if len(sys.argv) != 3:
+        print(
+            "usage: python -m python._mediapipe_subprocess <image_path> <output_npy>",
+            file=sys.stderr,
+        )
+        return 2
+
+    image_path, output_path = sys.argv[1], sys.argv[2]
+
+    import cv2
+
+    bgr = cv2.imread(image_path)
+    if bgr is None:
+        print(f"could not read image: {image_path}", file=sys.stderr)
+        return 3
+
+    rgb = cv2.cvtColor(bgr, cv2.COLOR_BGR2RGB)
+    rgb = np.ascontiguousarray(rgb, dtype=np.uint8)
+
+    landmarker = FaceLandmarker(static_image_mode=True)
+    try:
+        landmarks = landmarker.detect(rgb)
+    finally:
+        landmarker.close()
+
+    if landmarks is None:
+        print("no face detected", file=sys.stderr)
+        return 4
+
+    np.save(output_path, landmarks.astype(np.float32))
+    return 0
+
+
+if __name__ == "__main__":
+    sys.exit(main())
diff --git a/hairline/constants.py b/hairline/constants.py
new file mode 100644
index 0000000..ecafb05
--- /dev/null
+++ b/hairline/constants.py
@@ -0,0 +1,165 @@
+"""Shared constants for the hairline-extension pipeline.
+
+These define the topology of the extended mesh and must stay in sync with
+the C++ side (see sdk/ExtensionConstants.h). If you change anything here,
+regenerate face_ext.obj and update the C++ header.
+"""
+from __future__ import annotations
+
+# Number of MediaPipe FaceMesh landmarks (no iris refinement).
+N_MP = 468
+
+# Anchors along the upper boundary of the MediaPipe face mesh,
+# ordered left-to-right when viewing the face frontally.
+# Each anchor will get a paired hairline sample directly "above" it.
+#
+# Verify visually with scripts/show_anchors.py before locking these in.
+MP_TOP_ANCHORS: list[int] = [
+    127, 234, 162,  21,  54, 103,  67, 109,  10,
+    338, 297, 332, 284, 251, 389, 356, 454,
+]
+N_ANCHORS = len(MP_TOP_ANCHORS)  # 17
+
+# Vertex ID layout in the extended array of length 468 + 2*N_ANCHORS.
+#   [0       .. 468)         : MediaPipe canonical landmarks
+#   [468     .. 468+N)       : middle row (between MP boundary and hairline)
+#   [468+N   .. 468+2N)      : hairline row
+N_EXT = 2 * N_ANCHORS  # 34
+N_TOTAL = N_MP + N_EXT  # 502
+
+MIDDLE_START   = N_MP             # 468
+HAIRLINE_START = N_MP + N_ANCHORS # 485
+
+# Saggital head-curvature radius (in MediaPipe normalized-Y units),
+# expressed as a fraction of face height. The head's mid-line cross
+# section is treated locally as a circular arc; for a hairline / middle
+# vertex located dy=(y_hair - y_anchor) above an MP top anchor (dy < 0
+# since hairline y < anchor y) we compute its Z by
+#
+#     z_hair = z_anchor + dy² / (2 R),     R = HEAD_ARC_RADIUS_FRAC × face_h
+#
+# This always pushes the added vertex BACKWARD (toward +z in MP / face.obj
+# convention, i.e. toward the back of the head), matching the actual
+# anatomy. See README for the derivation.
+#
+# Smaller fraction = more pronounced backward bulge. 0.30 produces a
+# moderate offset (~0.024 in normalized z for a 0.08-y hairline lift on
+# a typical face).
+HEAD_ARC_RADIUS_FRAC = 0.30
+
+
+# Extra lift applied to the detected hairline along the face-up direction,
+# expressed as a fraction of the MP face height. The 2D hairline detector
+# stops at the hair-skin boundary (start of the visible hair); the mesh
+# ribbon's top row should sit at the crown of the head instead, so the
+# texture-overlay band can cover the whole forehead → crown region.
+#
+# 0.06 ≈ moves the hairline row up by 6% of face height, which on the
+# reference photos lands the top row just above the visible hairline and
+# below the crown — empirically tuned with the /preview slider and locked
+# in as the project default. Bump to 0.10..0.15 for taller foreheads /
+# higher crowns; drop to 0.03 to keep the ribbon hugging the hair-skin
+# boundary.
+HAIRLINE_CROWN_LIFT_FRAC = 0.06
+
+
+# Pure-geometry hairline offset for the /preview 502-point pipeline.
+#
+# When placing the hairline row WITHOUT hair detection (works for bald /
+# with-hair / hat — all head types), each anchor is offset upward along
+# face-up by  GEOMETRIC_HAIRLINE_OFFSET_FRAC × face_h  in normalised
+# image space. The sagittal-arc model then derives Z.
+#
+# 0.25 × face_h ≈ 0.12 normalised on a typical face (face_h ≈ 0.48),
+# giving  dz ≈ 0.05  — matches the real hairline distance observed on
+# reference photos where hair detection succeeds.
+GEOMETRIC_HAIRLINE_OFFSET_FRAC = 0.25
+
+
+# UV layout for the 34 forehead-extension vertices.
+#
+# The texture (imgs/texture0.png, 512×512) is laid out with the original
+# MediaPipe face skin in V_raw ≈ 0.00..0.77 (image y ≈ 117..511) and a
+# horizontal stack of 5 hairline-design arcs at the TOP of the image
+# (image y ≈ 30..170, i.e. V_raw ≈ 0.67..0.94). Those 5 arcs are the
+# content that the extension strip is supposed to display: hairline row
+# samples the topmost arc (blue), middle row samples the bottom arc
+# (orange), and the 3 arcs in between fall out automatically because the
+# ribbon triangle interpolates V linearly between the two rows.
+#
+# V conventions
+# -------------
+# uv_template.py / Three.js (with texture.flipY=true) treat V_raw=1 as
+# the TOP of the image (image y=0) and V_raw=0 as the BOTTOM.
+#
+# U conventions — IMPORTANT
+# -------------------------
+# The 17 MP_TOP_ANCHORS in face.obj have NON-uniform u (≈ 0.00 at the
+# temples, ≈ 0.50 at the forehead center, ≈ 1.00 at the other temple).
+# Each ribbon triangle (anchor[i] → middle[i] → anchor[i+1] etc.) is a
+# vertical column in UV space ONLY when the middle/hairline vertex
+# inherits its U from the corresponding anchor. If we used a uniform
+# 0.05..0.95 U for the strip the columns would slant relative to the
+# anchor U values, warping the texture's 5 horizontal arcs into
+# zig-zags. So `extension_uv_for` takes `anchor_u` and copies it.
+UV_MIDDLE_DV   = 0.110   # middle 行 V_raw 相对该列 anchor V_raw 上移这么多
+UV_HAIRLINE_DV = 0.220   # hairline 行 V_raw 相对该列 anchor V_raw 上移这么多
+# 为什么是"相对 anchor 平行偏移"而不是固定常数:
+#
+# face.obj 中 17 个 MP_TOP_ANCHORS 的 V_raw 是**非均匀弧形** (额头中央 MP 10
+# = 0.7724, 太阳穴 MP 127 = 0.4668, 横跨 0.30 V 单位)。 如果 middle/hairline
+# 用固定常数 V_raw (例如 0.82 / 0.998), 那每个 ribbon quad 的 V 跨度
+# (= middle.V − anchor[i].V) 在 17 列之间差异巨大 (中央列 0.05, 两端列 0.35,
+# 差了 7 倍)。 贴图最底部的弧线 (V_raw ≈ 0.76) 正好落在 V 跨度大的列上 →
+# 被拉伸成粗大色块, 而顶部弧线 (V_raw ≈ 0.93) 落在 V 跨度小的列上 → 被压
+# 缩成细线。 这就是"最下面那条线特别粗、上面 4 根都细"的根因。
+#
+# 把 middle/hairline 的 V 也设成"anchor V + 固定 Δ", 每列的 V 跨度变成恒定
+# 的 Δm / (Δh − Δm), ribbon 在贴图上是上下都跟随 anchor 弧度的弯月形带,
+# 贴图 5 条弧线在 mesh 上粗细均匀。
+#
+# 硬约束:
+#   1. Δm > 0 且 Δm < Δh (顺序保持 anchor < middle < hairline, 防 V 反向)
+#   2. anchor.V_max + Δh ≤ 1.0  (即 Δh ≤ 1 − 0.7724 = 0.2276)
+#      否则中央列 hairline V 溢出, 采到贴图边缘的抗锯齿像素。
+# 当前 Δh = 0.220 留 ≈ 0.008 V 单位 buffer; Δm = Δh / 2 让上下两段等宽。
+
+
+def extension_uv_for(row: int, anchor_u: float, anchor_v: float) -> tuple[float, float]:
+    """Return (u, v_raw) UV for an extension vertex.
+
+    row:       0 = middle, 1 = hairline.
+    anchor_u:  U of the corresponding MP anchor (copy verbatim → ribbon column
+               is vertical in UV space).
+    anchor_v:  V_raw of the corresponding MP anchor (we add a constant Δ to
+               it → ribbon row stays parallel to anchor row in UV space, so
+               each quad has the same V span and texture arcs render at the
+               same thickness across all 17 columns).
+    """
+    dv = UV_MIDDLE_DV if row == 0 else UV_HAIRLINE_DV
+    return (anchor_u, anchor_v + dv)
+
+
+# Face-parsing class indices for the jonathandinu/face-parsing
+# SegFormer model (matches CelebAMask-HQ labels):
+PARSE_BG       = 0
+PARSE_SKIN     = 1
+PARSE_NOSE     = 2
+PARSE_EYE_G    = 3
+PARSE_L_EYE    = 4
+PARSE_R_EYE    = 5
+PARSE_L_BROW   = 6
+PARSE_R_BROW   = 7
+PARSE_L_EAR    = 8
+PARSE_R_EAR    = 9
+PARSE_MOUTH    = 10
+PARSE_U_LIP    = 11
+PARSE_L_LIP    = 12
+PARSE_HAIR     = 13
+PARSE_HAT      = 14
+PARSE_EAR_R    = 15
+PARSE_NECK_L   = 16
+PARSE_NECK     = 17
+PARSE_CLOTH    = 18
+
+HF_FACE_PARSER_MODEL = "jonathandinu/face-parsing"
diff --git a/hairline/extract_hairline.py b/hairline/extract_hairline.py
new file mode 100644
index 0000000..6f3f1cd
--- /dev/null
+++ b/hairline/extract_hairline.py
@@ -0,0 +1,115 @@
+"""Main CLI: image -> JSON of 502 3D points consumable by the SDK.
+
+Pipeline:
+  1. MediaPipe FaceMesh -> 468 normalized landmarks
+  2. Face parsing (HF SegFormer) -> per-pixel class map
+  3. Hairline curve detection + per-anchor ray casting -> 17 hairline 2D points
+  4. Lift 2D hairline points to 3D using anchor Z + curvature offset
+  5. Interpolate 17 middle-row 3D points
+  6. Concatenate into (502, 3) and emit JSON
+
+Output JSON schema:
+  {
+    "image": {"width": W, "height": H, "path": "..."},
+    "n_total": 502,
+    "n_mp": 468,
+    "n_extension": 34,
+    "layout": ["mp[0..468)", "middle[468..485)", "hairline[485..502)"],
+    "points": [[x_norm, y_norm, z_relative], ...]   # length 502
+    "valid_hairline": [true/false, ...]              # length 17
+  }
+
+Usage:
+  py -3 python/extract_hairline.py path/to/image.jpg
+  py -3 python/extract_hairline.py path/to/image.jpg --out data/out.json
+"""
+from __future__ import annotations
+import argparse
+import json
+import os
+import sys
+import time
+
+import numpy as np
+
+if __package__ is None or __package__ == "":
+    sys.path.insert(0, os.path.dirname(os.path.dirname(os.path.abspath(__file__))))
+    from python import constants as C
+    from python.face_landmarks import FaceLandmarker
+    from python.face_parsing  import FaceParser
+    from python.hairline_2d   import sample_hairline, smooth_hairline
+    from python.lift_3d       import lift_hairline_to_3d, build_middle_row, assemble_full
+else:
+    from . import constants as C
+    from .face_landmarks import FaceLandmarker
+    from .face_parsing  import FaceParser
+    from .hairline_2d   import sample_hairline, smooth_hairline
+    from .lift_3d       import lift_hairline_to_3d, build_middle_row, assemble_full
+
+
+def run(image_path: str, out_path: str | None = None, device: str | None = None) -> dict:
+    import cv2
+    bgr = cv2.imread(image_path)
+    if bgr is None:
+        raise FileNotFoundError(f"could not read image: {image_path}")
+    rgb = cv2.cvtColor(bgr, cv2.COLOR_BGR2RGB)
+    H, W = rgb.shape[:2]
+
+    t0 = time.perf_counter()
+    lmk = FaceLandmarker(static_image_mode=True)
+    landmarks = lmk.detect(rgb)
+    lmk.close()
+    if landmarks is None:
+        raise RuntimeError("no face detected")
+    t1 = time.perf_counter()
+    print(f"  [time] mediapipe: {(t1 - t0)*1000:.0f} ms")
+
+    parser = FaceParser(device=device)
+    parse_map = parser.parse(rgb)
+    t2 = time.perf_counter()
+    print(f"  [time] parsing:   {(t2 - t1)*1000:.0f} ms")
+
+    hairline_2d, valid = sample_hairline(landmarks, parse_map)
+    hairline_2d = smooth_hairline(hairline_2d, valid)
+    hairline_3d = lift_hairline_to_3d(landmarks, hairline_2d)
+    middle_3d   = build_middle_row(landmarks, hairline_3d)
+    points_full = assemble_full(landmarks, middle_3d, hairline_3d)
+    t3 = time.perf_counter()
+    print(f"  [time] hairline:  {(t3 - t2)*1000:.0f} ms")
+
+    record = {
+        "image": {"width": int(W), "height": int(H), "path": image_path},
+        "n_total": C.N_TOTAL,
+        "n_mp": C.N_MP,
+        "n_extension": C.N_EXT,
+        "layout": [
+            f"mp[0..{C.N_MP})",
+            f"middle[{C.MIDDLE_START}..{C.HAIRLINE_START})",
+            f"hairline[{C.HAIRLINE_START}..{C.N_TOTAL})",
+        ],
+        "points": points_full.tolist(),
+        "valid_hairline": valid.tolist(),
+    }
+
+    if out_path is None:
+        base = os.path.splitext(os.path.basename(image_path))[0]
+        out_path = os.path.join("data", base + ".json")
+
+    os.makedirs(os.path.dirname(out_path) or ".", exist_ok=True)
+    with open(out_path, "w", encoding="utf-8") as f:
+        json.dump(record, f, ensure_ascii=False, indent=2)
+    print(f"  wrote {out_path}")
+    return record
+
+
+def main() -> None:
+    ap = argparse.ArgumentParser(description="Extract MediaPipe + hairline points from one image.")
+    ap.add_argument("image", help="path to input image (jpg/png)")
+    ap.add_argument("--out", default=None, help="output JSON path")
+    ap.add_argument("--device", default=None, help="torch device (cpu/cuda); auto if omitted")
+    args = ap.parse_args()
+    run(args.image, args.out, args.device)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/hairline/face_landmarks.py b/hairline/face_landmarks.py
new file mode 100644
index 0000000..77fe3b7
--- /dev/null
+++ b/hairline/face_landmarks.py
@@ -0,0 +1,103 @@
+"""MediaPipe FaceMesh wrappers returning 468 3D landmarks in [0,1] x/y space.
+
+`FaceLandmarker` uses the modern mediapipe.tasks.vision API and requires
+models/face_landmarker.task.
+
+`SolutionsFaceLandmarker` uses the older mediapipe.solutions.face_mesh API.
+It is useful as a CPU fallback in WSL environments where the Tasks API may
+segfault while initializing EGL/OpenGL.
+"""
+from __future__ import annotations
+import os
+import numpy as np
+
+DEFAULT_MODEL_PATH = os.path.join(
+    os.path.dirname(os.path.dirname(os.path.abspath(__file__))),
+    "models", "face_landmarker.task",
+)
+
+
+class FaceLandmarker:
+    def __init__(self, static_image_mode: bool = True, model_path: str | None = None):
+        import mediapipe as mp
+        from mediapipe.tasks import python as mp_python
+        from mediapipe.tasks.python import vision
+
+        path = model_path or DEFAULT_MODEL_PATH
+        if not os.path.isfile(path):
+            raise FileNotFoundError(
+                f"face_landmarker.task not found at {path}. "
+                "Download it from "
+                "https://storage.googleapis.com/mediapipe-models/face_landmarker/"
+                "face_landmarker/float16/1/face_landmarker.task"
+            )
+
+        running_mode = vision.RunningMode.IMAGE if static_image_mode else vision.RunningMode.VIDEO
+        options = vision.FaceLandmarkerOptions(
+            base_options=mp_python.BaseOptions(model_asset_path=path),
+            running_mode=running_mode,
+            num_faces=1,
+            output_face_blendshapes=False,
+            output_facial_transformation_matrixes=False,
+        )
+        self._detector = vision.FaceLandmarker.create_from_options(options)
+        self._mp = mp
+
+    def detect(self, image_rgb: np.ndarray) -> np.ndarray | None:
+        """Returns (468, 3) float32 of normalized x, y and relative z, or None.
+
+        The task model produces 478 landmarks (468 face + 10 iris); we return
+        only the first 468 to match the canonical FaceMesh topology used by
+        the SDK's OBJ file.
+        """
+        mp_image = self._mp.Image(image_format=self._mp.ImageFormat.SRGB, data=image_rgb)
+        result = self._detector.detect(mp_image)
+        if not result.face_landmarks:
+            return None
+        lm = result.face_landmarks[0][:468]
+        arr = np.array([[p.x, p.y, p.z] for p in lm], dtype=np.float32)
+        return arr
+
+    def close(self):
+        try:
+            self._detector.close()
+        except Exception:
+            pass
+
+
+class SolutionsFaceLandmarker:
+    """CPU-oriented fallback using mediapipe.solutions.face_mesh."""
+
+    def __init__(self, static_image_mode: bool = True):
+        import mediapipe as mp
+
+        try:
+            face_mesh_module = mp.solutions.face_mesh
+        except AttributeError as exc:
+            raise RuntimeError(
+                "当前 mediapipe 包不包含 mediapipe.solutions.face_mesh。"
+                "请使用 web_service.py 的默认 parsing backend，或安装包含 solutions API 的 mediapipe 版本。"
+            ) from exc
+
+        self._face_mesh = face_mesh_module.FaceMesh(
+            static_image_mode=static_image_mode,
+            max_num_faces=1,
+            refine_landmarks=False,
+            min_detection_confidence=0.5,
+        )
+
+    def detect(self, image_rgb: np.ndarray) -> np.ndarray | None:
+        """Returns (468, 3) float32 of normalized x, y and relative z, or None."""
+        image_rgb.flags.writeable = False
+        result = self._face_mesh.process(image_rgb)
+        image_rgb.flags.writeable = True
+        if not result.multi_face_landmarks:
+            return None
+        lm = result.multi_face_landmarks[0].landmark[:468]
+        return np.array([[p.x, p.y, p.z] for p in lm], dtype=np.float32)
+
+    def close(self):
+        try:
+            self._face_mesh.close()
+        except Exception:
+            pass
diff --git a/hairline/face_parsing.py b/hairline/face_parsing.py
new file mode 100644
index 0000000..e20ce4f
--- /dev/null
+++ b/hairline/face_parsing.py
@@ -0,0 +1,42 @@
+"""Face parsing via HuggingFace SegFormer (jonathandinu/face-parsing).
+
+First call downloads ~150 MB of weights into the HF cache.
+"""
+from __future__ import annotations
+import numpy as np
+from typing import TYPE_CHECKING
+
+from . import constants as C
+
+if TYPE_CHECKING:  # avoid hard import at module load
+    pass
+
+
+class FaceParser:
+    """Wraps a SegFormer face-parsing model and returns a (H, W) int label map."""
+
+    def __init__(self, device: str | None = None):
+        import torch
+        from transformers import SegformerImageProcessor, SegformerForSemanticSegmentation
+
+        self.device = device or ("cuda" if torch.cuda.is_available() else "cpu")
+        self.processor = SegformerImageProcessor.from_pretrained(C.HF_FACE_PARSER_MODEL)
+        self.model = SegformerForSemanticSegmentation.from_pretrained(C.HF_FACE_PARSER_MODEL)
+        self.model.to(self.device).eval()
+        self._torch = torch
+
+    def parse(self, image_rgb: np.ndarray) -> np.ndarray:
+        """image_rgb: (H, W, 3) uint8. Returns (H, W) int64 of class indices."""
+        from PIL import Image
+
+        H, W = image_rgb.shape[:2]
+        pil = Image.fromarray(image_rgb)
+        inputs = self.processor(images=pil, return_tensors="pt").to(self.device)
+        with self._torch.no_grad():
+            logits = self.model(**inputs).logits  # (1, C, h, w)
+        # Upsample to original resolution
+        up = self._torch.nn.functional.interpolate(
+            logits, size=(H, W), mode="bilinear", align_corners=False
+        )
+        labels = up.argmax(dim=1).squeeze(0).to("cpu").numpy().astype(np.int32)
+        return labels
diff --git a/hairline/hairline_2d.py b/hairline/hairline_2d.py
new file mode 100644
index 0000000..758e076
--- /dev/null
+++ b/hairline/hairline_2d.py
@@ -0,0 +1,1029 @@
+"""2D hairline detection from a face-parsing label map.
+
+Given the parser output, find the boundary curve between hair-above and
+skin-below in the upper face region, then sample one point per anchor
+along the face's local "up" direction.
+
+This module also exposes several alternative strategies (see
+``sample_hairline_*`` functions) that the Web service runs side-by-side
+for visual comparison.
+"""
+from __future__ import annotations
+from typing import Callable
+import numpy as np
+
+from . import constants as C
+
+
+def face_up_vector(landmarks_norm: np.ndarray) -> np.ndarray:
+    """Return a unit 2D vector pointing "up" in image space.
+
+    landmarks_norm: (468, 3) MediaPipe output (normalized x,y in [0,1]).
+    Uses chin (152) → forehead-top (10).
+    """
+    chin = landmarks_norm[152, :2]
+    top  = landmarks_norm[10,  :2]
+    v = top - chin   # in normalized image space
+    n = np.linalg.norm(v) + 1e-9
+    return v / n
+
+
+def build_hair_mask(parse_map: np.ndarray) -> np.ndarray:
+    """Boolean (H, W) mask of pixels strictly classified as hair (or hat)."""
+    return np.isin(parse_map, [C.PARSE_HAIR, C.PARSE_HAT])
+
+
+def build_skin_mask(parse_map: np.ndarray) -> np.ndarray:
+    """Boolean (H, W) mask of pixels classified as facial skin / ears / brows / nose / lips.
+
+    Used to validate that a ray actually travels through the face before
+    hitting hair — guards against the case where the ray exits laterally
+    into background (e.g. from a temple anchor next to white background)
+    and would otherwise stop at the first non-skin pixel.
+    """
+    face_classes = [
+        C.PARSE_SKIN, C.PARSE_NOSE, C.PARSE_L_BROW, C.PARSE_R_BROW,
+        C.PARSE_L_EYE, C.PARSE_R_EYE, C.PARSE_EYE_G,
+        C.PARSE_L_EAR, C.PARSE_R_EAR, C.PARSE_EAR_R,
+        C.PARSE_MOUTH, C.PARSE_U_LIP, C.PARSE_L_LIP,
+    ]
+    return np.isin(parse_map, face_classes)
+
+
+def ray_first_hair_hit(
+    origin_xy: np.ndarray,
+    direction_xy: np.ndarray,
+    hair_mask: np.ndarray,
+    max_steps: int = 800,
+    step_px: float = 1.0,
+) -> np.ndarray | None:
+    """March a ray until it hits a hair pixel. Returns float (x, y) or None.
+
+    Unlike a generic boundary tracer, we explicitly target the HAIR class so
+    a ray that drifts into background while traversing a temple anchor will
+    continue searching rather than stopping at the face/background edge.
+    """
+    H, W = hair_mask.shape
+    pos = origin_xy.astype(np.float64).copy()
+    for _ in range(max_steps):
+        pos += direction_xy * step_px
+        ix, iy = int(round(pos[0])), int(round(pos[1]))
+        if ix < 0 or iy < 0 or ix >= W or iy >= H:
+            return None
+        if hair_mask[iy, ix]:
+            return pos.copy()
+    return None
+
+
+def sample_hairline(
+    landmarks_norm: np.ndarray,
+    parse_map: np.ndarray,
+    fallback_extrapolation: float = 0.18,
+) -> tuple[np.ndarray, np.ndarray]:
+    """Find one hairline point per MP_TOP_ANCHORS, in normalized [0,1] image space.
+
+    Returns:
+        hairline_norm: (N_ANCHORS, 2) float — hairline points (x_norm, y_norm)
+        valid_mask:    (N_ANCHORS,)  bool  — True where a hair-pixel was hit
+
+    Algorithm:
+      For each anchor, march a ray along the face's up-vector and return the
+      first hair-classified pixel encountered. If the ray exits the image
+      without ever finding hair (bald, hat, or hairline outside the frame),
+      fall back to extrapolating along the up-vector by `fallback_extrapolation`.
+
+      For lateral anchors (temples, ears) the ray may leave the face into
+      background skin-less area before encountering hair on top of the
+      head — that is OK because we only stop on hair, not background.
+    """
+    H, W = parse_map.shape
+    hair_mask = build_hair_mask(parse_map)
+
+    up_norm = face_up_vector(landmarks_norm)
+    up_px = up_norm * np.array([W, H], dtype=np.float64)
+    up_px = up_px / (np.linalg.norm(up_px) + 1e-9)
+
+    hairline = np.zeros((C.N_ANCHORS, 2), dtype=np.float32)
+    valid = np.zeros((C.N_ANCHORS,), dtype=bool)
+
+    for i, mp_idx in enumerate(C.MP_TOP_ANCHORS):
+        anchor_norm = landmarks_norm[mp_idx, :2]
+        anchor_px = anchor_norm * np.array([W, H], dtype=np.float64)
+        hit_px = ray_first_hair_hit(anchor_px, up_px, hair_mask)
+        if hit_px is not None:
+            hairline[i] = (hit_px / np.array([W, H])).astype(np.float32)
+            valid[i] = True
+        else:
+            hairline[i] = (anchor_norm + up_norm * fallback_extrapolation).astype(np.float32)
+            valid[i] = False
+    return hairline, valid
+
+
+# Backwards-compat alias for callers from the previous API.
+def build_hairline_mask(parse_map: np.ndarray) -> np.ndarray:
+    return build_hair_mask(parse_map)
+
+
+def smooth_hairline(
+    hairline_norm: np.ndarray,
+    valid: np.ndarray,
+    iterations: int = 2,
+) -> np.ndarray:
+    """Light smoothing along the curve to absorb segmentation jitter.
+
+    Uses a 1-2-1 binomial filter over neighbors with the same validity.
+    Note: this also rounds off real corners. For data with sharp corners
+    (e.g. M-shaped hairlines), use :func:`smooth_hairline_corner_aware` instead.
+    """
+    out = hairline_norm.copy()
+    n = len(out)
+    for _ in range(iterations):
+        new = out.copy()
+        for i in range(1, n - 1):
+            if not valid[i]:
+                continue
+            new[i] = 0.25 * out[i - 1] + 0.5 * out[i] + 0.25 * out[i + 1]
+        out = new
+    return out
+
+
+def smooth_hairline_corner_aware(
+    hairline_norm: np.ndarray,
+    valid: np.ndarray,
+    iterations: int = 2,
+    corner_cos_threshold: float = 0.6,
+) -> np.ndarray:
+    """1-2-1 smoothing, but skip points that look like corners.
+
+    A "corner" is detected by the cosine of the angle between (P[i] - P[i-1])
+    and (P[i+1] - P[i]): smaller cosine = sharper bend. If
+    ``cos(angle) < corner_cos_threshold`` (i.e. bend > ~53°), point i keeps
+    its raw position; otherwise the binomial filter is applied.
+
+    This preserves the user's expected M-shape / trapezoidal hairline whose
+    "shoulders" are sharp corners.
+    """
+    out = hairline_norm.copy()
+    n = len(out)
+    for _ in range(iterations):
+        new = out.copy()
+        for i in range(1, n - 1):
+            if not valid[i]:
+                continue
+            v1 = out[i] - out[i - 1]
+            v2 = out[i + 1] - out[i]
+            n1 = float(np.linalg.norm(v1))
+            n2 = float(np.linalg.norm(v2))
+            if n1 < 1e-9 or n2 < 1e-9:
+                new[i] = 0.25 * out[i - 1] + 0.5 * out[i] + 0.25 * out[i + 1]
+                continue
+            cos_a = float(np.dot(v1, v2)) / (n1 * n2)
+            if cos_a >= corner_cos_threshold:
+                # smooth: not a corner
+                new[i] = 0.25 * out[i - 1] + 0.5 * out[i] + 0.25 * out[i + 1]
+            # else: keep raw (preserve corner)
+        out = new
+    return out
+
+
+# ---------------------------------------------------------------------------
+# Alternative hairline sampling strategies.
+#
+# All functions share the signature ``(landmarks_norm, parse_map) -> (hairline,
+# valid)`` so the caller can switch strategies uniformly. ``landmarks_norm``
+# may be ``None`` for parsing-only strategies (e.g. ``sample_hairline_top_arc``).
+# ---------------------------------------------------------------------------
+
+
+def head_top_target(landmarks_norm: np.ndarray, scale: float = 0.6) -> np.ndarray:
+    """Return a 2D point above the forehead used as a ray convergence target.
+
+    The point is placed `scale * face_height` above the forehead-top landmark
+    (10), measured along the chin->forehead axis. ``scale = 0.6`` roughly
+    matches the human "crown" position relative to the chin->forehead line.
+    """
+    chin = landmarks_norm[152, :2]
+    top = landmarks_norm[10, :2]
+    face_height = float(np.linalg.norm(top - chin)) + 1e-9
+    face_up_unit = (top - chin) / face_height
+    return top + face_up_unit * face_height * scale
+
+
+def build_face_adjacent_hair_mask(
+    parse_map: np.ndarray,
+    dilate_radius: int | None = None,
+) -> np.ndarray:
+    """Hair pixels that lie within ``dilate_radius`` px of any face-skin pixel.
+
+    Used to filter out background blobs that the parser mis-classified as
+    hair (chairs, dark walls, etc.) which would otherwise stop a ray prematurely.
+    """
+    import cv2
+
+    hair = np.isin(parse_map, [C.PARSE_HAIR, C.PARSE_HAT]).astype(np.uint8)
+    face = build_skin_mask(parse_map).astype(np.uint8)
+
+    if dilate_radius is None:
+        face_area = int(face.sum())
+        dilate_radius = max(6, int(np.sqrt(max(face_area, 1)) * 0.05))
+
+    k = 2 * dilate_radius + 1
+    kernel = cv2.getStructuringElement(cv2.MORPH_ELLIPSE, (k, k))
+    face_dil = cv2.dilate(face, kernel)
+    return (hair > 0) & (face_dil > 0)
+
+
+def ray_first_mask_hit(
+    origin_xy: np.ndarray,
+    direction_xy: np.ndarray,
+    mask: np.ndarray,
+    max_steps: int = 1500,
+    step_px: float = 1.0,
+) -> np.ndarray | None:
+    """Generic version of :func:`ray_first_hair_hit` that targets any boolean mask."""
+    H, W = mask.shape
+    pos = origin_xy.astype(np.float64).copy()
+    for _ in range(max_steps):
+        pos += direction_xy * step_px
+        ix, iy = int(round(pos[0])), int(round(pos[1]))
+        if ix < 0 or iy < 0 or ix >= W or iy >= H:
+            return None
+        if mask[iy, ix]:
+            return pos.copy()
+    return None
+
+
+def ray_first_dense_hit(
+    origin_xy: np.ndarray,
+    direction_xy: np.ndarray,
+    mask: np.ndarray,
+    run_length: int,
+    max_steps: int = 2000,
+) -> np.ndarray | None:
+    """Density-based stopping: stop only after `run_length` consecutive hit pixels.
+
+    Returns the position of the FIRST pixel of the qualifying run (i.e., the
+    edge where the dense region begins). This filters out single-pixel
+    classification noise and isolated wisps.
+
+    The ray is allowed to start outside the image and walk in until it enters
+    the image bounds (used by the "from-above" strategies). Once inside, if the
+    ray exits the image again, the search stops.
+    """
+    H, W = mask.shape
+    pos = np.asarray(origin_xy, dtype=np.float64).copy()
+    direction = np.asarray(direction_xy, dtype=np.float64)
+    consecutive = 0
+    run_start: np.ndarray | None = None
+    entered_image = False
+
+    for _ in range(max_steps):
+        pos += direction
+        ix, iy = int(round(pos[0])), int(round(pos[1]))
+        in_image = (0 <= ix < W) and (0 <= iy < H)
+        if not in_image:
+            if entered_image:
+                return None
+            continue
+        entered_image = True
+        if mask[iy, ix]:
+            if consecutive == 0:
+                run_start = pos.copy()
+            consecutive += 1
+            if consecutive >= run_length:
+                return run_start
+        else:
+            consecutive = 0
+            run_start = None
+    return None
+
+
+def _face_height_px(landmarks_norm: np.ndarray, W: int, H: int) -> float:
+    chin = landmarks_norm[152, :2] * np.array([W, H], dtype=np.float64)
+    top = landmarks_norm[10, :2] * np.array([W, H], dtype=np.float64)
+    return float(np.linalg.norm(top - chin))
+
+
+def density_run_length(landmarks_norm: np.ndarray, W: int, H: int, ratio: float = 0.06) -> int:
+    """Adaptive density threshold proportional to face size.
+
+    Default ratio = 0.06 of the chin-to-forehead distance: for a 200 px face
+    height that gives a 12-pixel run requirement; for 400 px → 24 pixels.
+    """
+    fh = _face_height_px(landmarks_norm, W, H)
+    return max(6, int(round(fh * ratio)))
+
+
+def _ray_sample_with_direction(
+    landmarks_norm: np.ndarray,
+    parse_map: np.ndarray,
+    mask: np.ndarray,
+    direction_factory: Callable[[np.ndarray, np.ndarray, int, int], np.ndarray],
+    fallback_extrapolation: float = 0.18,
+) -> tuple[np.ndarray, np.ndarray]:
+    """Common ray-marching loop. ``direction_factory`` returns a unit pixel-space
+    direction for a given anchor (passed `(landmarks, anchor_px, W, H)`)."""
+    H, W = parse_map.shape
+    up_norm_fallback = face_up_vector(landmarks_norm)
+
+    hairline = np.zeros((C.N_ANCHORS, 2), dtype=np.float32)
+    valid = np.zeros((C.N_ANCHORS,), dtype=bool)
+
+    for i, mp_idx in enumerate(C.MP_TOP_ANCHORS):
+        anchor_norm = landmarks_norm[mp_idx, :2]
+        anchor_px = anchor_norm * np.array([W, H], dtype=np.float64)
+        direction_px = direction_factory(landmarks_norm, anchor_px, W, H)
+        hit_px = ray_first_mask_hit(anchor_px, direction_px, mask)
+        if hit_px is not None:
+            hairline[i] = (hit_px / np.array([W, H])).astype(np.float32)
+            valid[i] = True
+        else:
+            hairline[i] = (anchor_norm + up_norm_fallback * fallback_extrapolation).astype(np.float32)
+            valid[i] = False
+    return hairline, valid
+
+
+def _direction_face_up(landmarks_norm, anchor_px, W, H) -> np.ndarray:
+    up_norm = face_up_vector(landmarks_norm)
+    up_px = up_norm * np.array([W, H], dtype=np.float64)
+    return up_px / (np.linalg.norm(up_px) + 1e-9)
+
+
+def _direction_converging(landmarks_norm, anchor_px, W, H, scale: float = 0.6) -> np.ndarray:
+    target_norm = head_top_target(landmarks_norm, scale=scale)
+    target_px = target_norm * np.array([W, H], dtype=np.float64)
+    d = target_px - anchor_px
+    return d / (np.linalg.norm(d) + 1e-9)
+
+
+def sample_hairline_baseline(landmarks_norm: np.ndarray, parse_map: np.ndarray) -> tuple[np.ndarray, np.ndarray]:
+    """策略 1: 当前算法 - 沿 face-up 直上, 命中首个 hair/hat 像素。"""
+    mask = build_hair_mask(parse_map)
+    return _ray_sample_with_direction(landmarks_norm, parse_map, mask, _direction_face_up)
+
+
+def sample_hairline_adjacent(landmarks_norm: np.ndarray, parse_map: np.ndarray) -> tuple[np.ndarray, np.ndarray]:
+    """策略 2: baseline + hair 必须邻接 face skin, 过滤背景误分。"""
+    mask = build_face_adjacent_hair_mask(parse_map)
+    return _ray_sample_with_direction(landmarks_norm, parse_map, mask, _direction_face_up)
+
+
+def _topmost_hair_y_per_col(mask: np.ndarray) -> np.ndarray:
+    """For each column return the smallest y where ``mask[y, x]`` is True, or -1."""
+    H, W = mask.shape
+    cols_has = mask.any(axis=0)
+    out = np.full(W, -1, dtype=np.int32)
+    cols = np.where(cols_has)[0]
+    for x in cols:
+        out[x] = int(np.argmax(mask[:, x]))
+    return out
+
+
+def sample_hairline_window(
+    landmarks_norm: np.ndarray,
+    parse_map: np.ndarray,
+    window_lateral_ratio: float = 0.05,
+    window_central_ratio: float = 0.015,
+    use_adjacent: bool = False,
+    fallback_extrapolation: float = 0.18,
+) -> tuple[np.ndarray, np.ndarray]:
+    """For each anchor, search a horizontal window biased OUTWARD and snap to
+    the topmost hair pixel column inside it.
+
+    Why this helps the 6/12-point problem:
+      The lateral-middle anchors (MP 54/103 on the left, MP 332/284 on the
+      right) sit on the forehead skin. A pure straight-up ray finds the top
+      of the hair plateau at the anchor's x — but the real "shoulder corner"
+      of the hairline is several pixels OUTWARD from the anchor. By widening
+      the search to a window that extends further toward the image edge,
+      these anchors can slide LATERALLY onto the actual shoulder.
+
+    Per-anchor window:
+      [anchor_x - lateral_w, anchor_x + central_w]   for LEFT anchors
+      [anchor_x - central_w, anchor_x + lateral_w]   for RIGHT anchors
+    Center anchor (anchor.x ≈ face center) uses symmetric window.
+
+    Both ``x`` and ``y`` of each output point are FREELY chosen inside the
+    window — the function returns the (col, top_y) of the topmost hair pixel.
+    """
+    H, W = parse_map.shape
+    hair = (
+        build_face_adjacent_hair_mask(parse_map)
+        if use_adjacent
+        else build_hair_mask(parse_map)
+    )
+    top_y = _topmost_hair_y_per_col(hair)
+    up_norm = face_up_vector(landmarks_norm)
+    face_center_x = float(landmarks_norm[10, 0])  # MP 10 = forehead top
+
+    w_lat = max(1, int(round(W * window_lateral_ratio)))
+    w_cen = max(1, int(round(W * window_central_ratio)))
+
+    hairline = np.zeros((C.N_ANCHORS, 2), dtype=np.float32)
+    valid = np.zeros((C.N_ANCHORS,), dtype=bool)
+
+    for i, mp_idx in enumerate(C.MP_TOP_ANCHORS):
+        anchor_norm = landmarks_norm[mp_idx, :2]
+        ax = int(round(np.clip(anchor_norm[0] * W, 0, W - 1)))
+
+        side = 1 if anchor_norm[0] > face_center_x else (-1 if anchor_norm[0] < face_center_x else 0)
+        if side > 0:
+            x_lo = max(0, ax - w_cen)
+            x_hi = min(W, ax + w_lat + 1)
+        elif side < 0:
+            x_lo = max(0, ax - w_lat)
+            x_hi = min(W, ax + w_cen + 1)
+        else:
+            x_lo = max(0, ax - w_cen)
+            x_hi = min(W, ax + w_cen + 1)
+
+        sub = top_y[x_lo:x_hi]
+        valid_cols = sub >= 0
+        if not valid_cols.any():
+            hairline[i] = (anchor_norm + up_norm * fallback_extrapolation).astype(np.float32)
+            continue
+
+        sub_masked = np.where(valid_cols, sub, H + 1)
+        best_off = int(np.argmin(sub_masked))
+        best_x = x_lo + best_off
+        best_y = int(sub[best_off])
+        hairline[i, 0] = best_x / W
+        hairline[i, 1] = best_y / H
+        valid[i] = True
+
+    return hairline, valid
+
+
+def sample_hairline_window_adjacent(landmarks_norm: np.ndarray, parse_map: np.ndarray) -> tuple[np.ndarray, np.ndarray]:
+    """window 策略的 adjacent 变体: 候选 hair 必须邻接 face skin。"""
+    return sample_hairline_window(landmarks_norm, parse_map, use_adjacent=True)
+
+
+def sample_hairline_lateral_extend(
+    landmarks_norm: np.ndarray,
+    parse_map: np.ndarray,
+    use_adjacent: bool = True,
+    outer_anchors_per_side: int = 3,
+    max_walk_ratio: float = 0.015,
+) -> tuple[np.ndarray, np.ndarray]:
+    """baseline (+adjacent) 之后, 把最外侧 ``outer_anchors_per_side`` 个锚点
+    沿 hit 所在的横行向外侧推到真实的 hair 视觉边缘。
+
+    动机
+    ----
+    1, 2, 3 号 / 15, 16, 17 号锚点 (MP 127/234/162 和 389/356/454) 本来就长在
+    眉外角和耳前的皮肤上, 射线垂直向上停在 parser 给出的 hair 边界 —— 而
+    parser 对侧鬓的边界比视觉上的 hair 边缘保守几个像素, 所以这些点看起来
+    比红线略微偏向脸内。
+
+    这一步仅修改 X 坐标 (Y 保持 baseline hit 不变): 从 hit 像素出发, 沿同一
+    行向外 (远离脸部中心) 一步一步走, 只要下一像素还是 hair 就更新 X, 否则
+    停止。走距上限为 ``max_walk_ratio * W`` (默认 1.5%, ~11 px@734 宽); 太大
+    容易跑出可见 hair 之外 —— parser 会把侧鬓 / 头侧轮廓后面几像素也判成 hair,
+    所以 1.5% 是相对保守的值。
+
+    只对最外 ``outer_anchors_per_side`` 个锚点应用; 中间锚点保持 baseline。
+    """
+    if use_adjacent:
+        raw, valid = sample_hairline_adjacent(landmarks_norm, parse_map)
+        hair = build_face_adjacent_hair_mask(parse_map)
+    else:
+        raw, valid = sample_hairline_baseline(landmarks_norm, parse_map)
+        hair = build_hair_mask(parse_map)
+
+    H, W = parse_map.shape
+    max_walk_px = max(2, int(round(W * max_walk_ratio)))
+    n = C.N_ANCHORS
+
+    targets = (
+        [(i, -1) for i in range(0, outer_anchors_per_side)]
+        + [(i, +1) for i in range(n - outer_anchors_per_side, n)]
+    )
+
+    for i, side in targets:
+        if not valid[i]:
+            continue
+        x_px = int(round(raw[i, 0] * W))
+        y_px = int(round(raw[i, 1] * H))
+        if y_px < 0 or y_px >= H:
+            continue
+
+        x_outer = x_px
+        for step in range(1, max_walk_px + 1):
+            nx = x_px + step * side
+            if nx < 0 or nx >= W:
+                break
+            if hair[y_px, nx]:
+                x_outer = nx
+            else:
+                break
+
+        raw[i, 0] = x_outer / W
+
+    return raw, valid
+
+
+def sample_hairline_lateral_extend_dense(
+    landmarks_norm: np.ndarray,
+    parse_map: np.ndarray,
+    intermediates: int = 1,
+    use_adjacent: bool = True,
+    max_walk_ratio: float = 0.015,
+    outer_per_side: int | None = None,
+    density_run_length: int = 0,
+    fallback_extrapolation: float = 0.18,
+) -> tuple[np.ndarray, np.ndarray]:
+    """`lateral_extend` 的加密版本: 每对相邻 MP 锚点之间插入 ``intermediates`` 个
+    中间采样列, 再各自射线 + 横向延伸。
+
+    总点数 = ``N_ANCHORS + (N_ANCHORS - 1) * intermediates``
+    默认 17 + 16 = **33 点**, 是原始 17 点密度的 ~2 倍。
+
+    做法
+    ----
+    1. 把 17 个 MP_TOP_ANCHORS 的归一化坐标按顺序线性插值, 在每对之间塞入
+       ``intermediates`` 个等距中间种子。种子点 (x, y) 都在原 MP 锚点的连线上。
+    2. 每个种子点沿 face-up 方向直上, 命中首个 hair 像素 (用 adjacent hair
+       过滤背景误分)。中间点的 y 来自其相邻两个原锚点的 y 内插, 起射高度
+       与真实锚点一致, 所以命中位置自然落在 hair 平台上。
+    3. 对最外侧 ``(intermediates + 1) * 3`` 个点 (覆盖原始 1-3 号 / 15-17 号
+       周围的加密点), 沿 hit 横行向外侧走最多 1.5% 图宽, 推到可见 hair 边缘。
+    4. 配合 corner-aware 平滑使用, 转角自动被保留。
+
+    加密带来的两个直接收益
+    ----
+    * **6 号点和 12 号点之间的几个新点** (原始 5-6 / 12-13 之间) 会落在
+      hair 平台的左上 / 右上转角处, 让发际线在角落处不再被两个稀疏的 MP
+      点跨过。
+    * 整条发际线更平滑, 同时 corner-aware 还能定位出新的转角。
+    """
+    if use_adjacent:
+        hair = build_face_adjacent_hair_mask(parse_map)
+    else:
+        hair = build_hair_mask(parse_map)
+
+    H, W = parse_map.shape
+    up_norm = face_up_vector(landmarks_norm)
+    up_px = up_norm * np.array([W, H], dtype=np.float64)
+    up_px /= np.linalg.norm(up_px) + 1e-9
+
+    seeds: list[np.ndarray] = []
+    for k in range(C.N_ANCHORS):
+        p_anchor = landmarks_norm[C.MP_TOP_ANCHORS[k], :2].astype(np.float64).copy()
+        seeds.append(p_anchor)
+        if k + 1 < C.N_ANCHORS:
+            p_next = landmarks_norm[C.MP_TOP_ANCHORS[k + 1], :2].astype(np.float64)
+            for j in range(1, intermediates + 1):
+                t = j / (intermediates + 1)
+                seeds.append((1.0 - t) * p_anchor + t * p_next)
+
+    n_dense = len(seeds)
+    hairline = np.zeros((n_dense, 2), dtype=np.float32)
+    valid = np.zeros(n_dense, dtype=bool)
+
+    for i, sn in enumerate(seeds):
+        anchor_px = sn * np.array([W, H], dtype=np.float64)
+        if density_run_length > 0:
+            hit_px = ray_first_dense_hit(anchor_px, up_px, hair, density_run_length)
+        else:
+            hit_px = ray_first_mask_hit(anchor_px, up_px, hair)
+        if hit_px is not None:
+            hairline[i] = (hit_px / np.array([W, H])).astype(np.float32)
+            valid[i] = True
+        else:
+            hairline[i] = (sn + up_norm * fallback_extrapolation).astype(np.float32)
+
+    if outer_per_side is None:
+        outer = (intermediates + 1) * 3
+    else:
+        outer = max(0, min(outer_per_side, n_dense // 2))
+    targets = (
+        [(i, -1) for i in range(0, outer)]
+        + [(i, +1) for i in range(n_dense - outer, n_dense)]
+    )
+    max_walk_px = max(2, int(round(W * max_walk_ratio))) if max_walk_ratio > 0 else 0
+
+    if max_walk_px > 0:
+        for i, side in targets:
+            if not valid[i]:
+                continue
+            x_px = int(round(hairline[i, 0] * W))
+            y_px = int(round(hairline[i, 1] * H))
+            if y_px < 0 or y_px >= H:
+                continue
+
+            x_outer = x_px
+            for step in range(1, max_walk_px + 1):
+                nx = x_px + step * side
+                if nx < 0 or nx >= W:
+                    break
+                if hair[y_px, nx]:
+                    x_outer = nx
+                else:
+                    break
+
+            hairline[i, 0] = x_outer / W
+
+    return hairline, valid
+
+
+def sample_hairline_converging(landmarks_norm: np.ndarray, parse_map: np.ndarray) -> tuple[np.ndarray, np.ndarray]:
+    """策略 3: 每个锚点的射线方向都收敛到头顶上方目标点。"""
+    mask = build_hair_mask(parse_map)
+    return _ray_sample_with_direction(landmarks_norm, parse_map, mask, _direction_converging)
+
+
+def sample_hairline_converging_adjacent(landmarks_norm: np.ndarray, parse_map: np.ndarray) -> tuple[np.ndarray, np.ndarray]:
+    """策略 4: 收敛方向 + 邻接约束。"""
+    mask = build_face_adjacent_hair_mask(parse_map)
+    return _ray_sample_with_direction(landmarks_norm, parse_map, mask, _direction_converging)
+
+
+def sample_hairline_boundary_proj(landmarks_norm: np.ndarray, parse_map: np.ndarray) -> tuple[np.ndarray, np.ndarray]:
+    """策略 5: 计算 hair-skin 边界曲线, 每个锚点投影到带方向约束的最近边界点。
+
+    "方向约束" 指: 候选边界点必须位于锚点的 face-up 方向之上 (cos(angle) >= 0),
+    并且对横向偏移加额外惩罚, 避免吸到锚点正侧的边界。
+    """
+    import cv2
+
+    H, W = parse_map.shape
+    hair = np.isin(parse_map, [C.PARSE_HAIR, C.PARSE_HAT]).astype(np.uint8)
+    face = build_skin_mask(parse_map).astype(np.uint8)
+    face_dil = cv2.dilate(face, cv2.getStructuringElement(cv2.MORPH_RECT, (3, 3)))
+    boundary = (hair > 0) & (face_dil > 0)
+
+    bys, bxs = np.where(boundary)
+    hairline = np.zeros((C.N_ANCHORS, 2), dtype=np.float32)
+    valid = np.zeros((C.N_ANCHORS,), dtype=bool)
+
+    up_norm = face_up_vector(landmarks_norm)
+    up_px = up_norm * np.array([W, H], dtype=np.float64)
+    up_px /= np.linalg.norm(up_px) + 1e-9
+    perp_px = np.array([-up_px[1], up_px[0]], dtype=np.float64)
+
+    if bxs.size == 0:
+        for i, mp_idx in enumerate(C.MP_TOP_ANCHORS):
+            anchor_norm = landmarks_norm[mp_idx, :2]
+            hairline[i] = (anchor_norm + up_norm * 0.18).astype(np.float32)
+        return hairline, valid
+
+    for i, mp_idx in enumerate(C.MP_TOP_ANCHORS):
+        anchor_norm = landmarks_norm[mp_idx, :2]
+        anchor_px = anchor_norm * np.array([W, H], dtype=np.float64)
+        dx = bxs - anchor_px[0]
+        dy = bys - anchor_px[1]
+        proj_up = dx * up_px[0] + dy * up_px[1]
+        keep = proj_up > 1.0
+        if not keep.any():
+            hairline[i] = (anchor_norm + up_norm * 0.18).astype(np.float32)
+            continue
+        d_up = proj_up[keep]
+        d_perp = np.abs(dx[keep] * perp_px[0] + dy[keep] * perp_px[1])
+        cost = d_up + 2.5 * d_perp
+        local_best = int(np.argmin(cost))
+        chosen = np.where(keep)[0][local_best]
+        hairline[i, 0] = bxs[chosen] / W
+        hairline[i, 1] = bys[chosen] / H
+        valid[i] = True
+
+    return hairline, valid
+
+
+def _ray_dense_sample(
+    landmarks_norm: np.ndarray,
+    parse_map: np.ndarray,
+    mask: np.ndarray,
+    direction_factory: Callable[[np.ndarray, np.ndarray, int, int], np.ndarray],
+    fallback_extrapolation: float = 0.18,
+    run_ratio: float = 0.06,
+) -> tuple[np.ndarray, np.ndarray]:
+    """Density-stopping variant of :func:`_ray_sample_with_direction`."""
+    H, W = parse_map.shape
+    run_length = density_run_length(landmarks_norm, W, H, run_ratio)
+    up_norm_fallback = face_up_vector(landmarks_norm)
+
+    hairline = np.zeros((C.N_ANCHORS, 2), dtype=np.float32)
+    valid = np.zeros((C.N_ANCHORS,), dtype=bool)
+
+    for i, mp_idx in enumerate(C.MP_TOP_ANCHORS):
+        anchor_norm = landmarks_norm[mp_idx, :2]
+        anchor_px = anchor_norm * np.array([W, H], dtype=np.float64)
+        direction_px = direction_factory(landmarks_norm, anchor_px, W, H)
+        hit_px = ray_first_dense_hit(anchor_px, direction_px, mask, run_length)
+        if hit_px is not None:
+            hairline[i] = (hit_px / np.array([W, H])).astype(np.float32)
+            valid[i] = True
+        else:
+            hairline[i] = (anchor_norm + up_norm_fallback * fallback_extrapolation).astype(np.float32)
+            valid[i] = False
+    return hairline, valid
+
+
+def sample_hairline_density(landmarks_norm: np.ndarray, parse_map: np.ndarray) -> tuple[np.ndarray, np.ndarray]:
+    """密度策略 1: 沿 face-up 直上, 但要求连续 `density_run_length` 个 hair 像素才停。"""
+    mask = build_hair_mask(parse_map)
+    return _ray_dense_sample(landmarks_norm, parse_map, mask, _direction_face_up)
+
+
+def sample_hairline_density_adjacent(landmarks_norm: np.ndarray, parse_map: np.ndarray) -> tuple[np.ndarray, np.ndarray]:
+    """密度策略 2: face-up + density + 邻接约束。"""
+    mask = build_face_adjacent_hair_mask(parse_map)
+    return _ray_dense_sample(landmarks_norm, parse_map, mask, _direction_face_up)
+
+
+def sample_hairline_density_converging(landmarks_norm: np.ndarray, parse_map: np.ndarray) -> tuple[np.ndarray, np.ndarray]:
+    """密度策略 3: 收敛方向 + density。"""
+    mask = build_hair_mask(parse_map)
+    return _ray_dense_sample(landmarks_norm, parse_map, mask, _direction_converging)
+
+
+def _ray_dense_inverse_sample(
+    landmarks_norm: np.ndarray,
+    parse_map: np.ndarray,
+    mask: np.ndarray,
+    target_scale: float = 1.5,
+    run_ratio: float = 0.06,
+    fallback_extrapolation: float = 0.18,
+) -> tuple[np.ndarray, np.ndarray]:
+    """For each anchor, march FROM a target above the head DOWN toward the anchor.
+
+    Density-based stopping returns the first dense hair pixel encountered. Since
+    the ray comes from outside/above the head, the first dense hair = top edge
+    of the head silhouette = actual hairline crown. This bypasses the side-hair
+    interception problem entirely for lateral anchors.
+    """
+    H, W = parse_map.shape
+    run_length = density_run_length(landmarks_norm, W, H, run_ratio)
+    up_norm_fallback = face_up_vector(landmarks_norm)
+
+    target_norm = head_top_target(landmarks_norm, scale=target_scale)
+    target_px = target_norm * np.array([W, H], dtype=np.float64)
+
+    hairline = np.zeros((C.N_ANCHORS, 2), dtype=np.float32)
+    valid = np.zeros((C.N_ANCHORS,), dtype=bool)
+
+    for i, mp_idx in enumerate(C.MP_TOP_ANCHORS):
+        anchor_norm = landmarks_norm[mp_idx, :2]
+        anchor_px = anchor_norm * np.array([W, H], dtype=np.float64)
+        direction = anchor_px - target_px
+        norm = float(np.linalg.norm(direction)) + 1e-9
+        direction_unit = direction / norm
+        max_steps = int(norm) + 200
+        hit_px = ray_first_dense_hit(target_px, direction_unit, mask, run_length, max_steps=max_steps)
+        accepted = False
+        if hit_px is not None:
+            t_along = float(np.dot(hit_px - target_px, direction_unit))
+            if 0.0 < t_along < norm:
+                hairline[i] = (hit_px / np.array([W, H])).astype(np.float32)
+                valid[i] = True
+                accepted = True
+        if not accepted:
+            hairline[i] = (anchor_norm + up_norm_fallback * fallback_extrapolation).astype(np.float32)
+    return hairline, valid
+
+
+def sample_hairline_density_inverse(landmarks_norm: np.ndarray, parse_map: np.ndarray) -> tuple[np.ndarray, np.ndarray]:
+    """密度策略 4: 反向射线 - 从头顶上方目标点向锚点扫, density stop。
+
+    完全绕开 baseline 的核心痛点: 不再从锚点向上找头发, 而是从头部上方"找下来",
+    第一段 dense hair 自然就是头部的上边缘 (冠状发际线)。
+    """
+    mask = build_hair_mask(parse_map)
+    return _ray_dense_inverse_sample(landmarks_norm, parse_map, mask)
+
+
+def sample_hairline_density_inverse_adj(landmarks_norm: np.ndarray, parse_map: np.ndarray) -> tuple[np.ndarray, np.ndarray]:
+    """密度策略 5: 反向射线 + adjacent + density。"""
+    mask = build_face_adjacent_hair_mask(parse_map)
+    return _ray_dense_inverse_sample(landmarks_norm, parse_map, mask)
+
+
+def sample_hairline_silhouette_at_anchor_x(
+    landmarks_norm: np.ndarray,
+    parse_map: np.ndarray,
+    window_radius_ratio: float = 0.01,
+) -> tuple[np.ndarray, np.ndarray]:
+    """密度策略 6 (head silhouette 锚点对齐): 对每个 MP 锚点, 取它 x 列附近的头部上沿 y。
+
+    与 ``top_arc`` 相比, 17 个点的 x 仍然跟 MediaPipe 锚点的 x 一一对应,
+    但 y 直接来自 (face ∪ adjacent_hair) 在该 x 列的最高点 (最小 y),
+    所以点会自然贴到头顶轮廓上, 形成冠状弧, 而不是被侧鬓拽下来。
+
+    window_radius_ratio: 用 anchor x 周围一小段窗口 (W·ratio) 取最小 y 做平滑。
+    """
+    H, W = parse_map.shape
+    head = build_skin_mask(parse_map) | build_face_adjacent_hair_mask(parse_map)
+    up_norm_fallback = face_up_vector(landmarks_norm)
+
+    hairline = np.zeros((C.N_ANCHORS, 2), dtype=np.float32)
+    valid = np.zeros((C.N_ANCHORS,), dtype=bool)
+
+    radius = max(1, int(round(W * window_radius_ratio)))
+    for i, mp_idx in enumerate(C.MP_TOP_ANCHORS):
+        anchor_norm = landmarks_norm[mp_idx, :2]
+        cx = int(round(np.clip(anchor_norm[0] * W, 0, W - 1)))
+        x0 = max(0, cx - radius)
+        x1 = min(W, cx + radius + 1)
+        sub = head[:, x0:x1]
+        col_has = sub.any(axis=1)
+        if not col_has.any():
+            hairline[i] = (anchor_norm + up_norm_fallback * 0.18).astype(np.float32)
+            continue
+        top_y = int(np.argmax(col_has))
+        hairline[i, 0] = anchor_norm[0]
+        hairline[i, 1] = top_y / H
+        valid[i] = True
+    return hairline, valid
+
+
+def _head_top_y_per_column(
+    parse_map: np.ndarray,
+    use_full_hair: bool = True,
+) -> tuple[np.ndarray, np.ndarray]:
+    """Return (cols_with_head, top_y) where top_y[k] is the smallest y for which
+    ``head_mask[top_y[k], cols_with_head[k]]`` is True.
+
+    ``use_full_hair=True`` uses the FULL hair mask (proper head silhouette);
+    pass ``False`` to fall back to the face-adjacent strip only.
+    """
+    if use_full_hair:
+        head = build_skin_mask(parse_map) | build_hair_mask(parse_map)
+    else:
+        head = build_skin_mask(parse_map) | build_face_adjacent_hair_mask(parse_map)
+    cols_with_head = np.where(head.any(axis=0))[0]
+    if cols_with_head.size == 0:
+        return cols_with_head, np.array([], dtype=np.int32)
+    top_y = np.empty(cols_with_head.size, dtype=np.int32)
+    for j, x in enumerate(cols_with_head):
+        top_y[j] = int(np.argmax(head[:, x]))
+    return cols_with_head, top_y
+
+
+def sample_hairline_arch(
+    landmarks_norm: np.ndarray,
+    parse_map: np.ndarray,
+    central_drop: int = 3,
+    require_lift_px_ratio: float = 0.02,
+    density_ratio: float = 0.03,
+    use_adjacent_for_central: bool = False,
+) -> tuple[np.ndarray, np.ndarray]:
+    """冠状弧 (coronal arch) 策略 — 从一只耳朵上方画到另一只耳朵上方。
+
+    流程
+    ----
+      1. 中间 ``N_ANCHORS - 2*central_drop`` 个锚点（默认丢掉颧骨/太阳穴附近的 6 个），
+         沿 face-up 做密度门限射线，命中 ``run_length`` 个连续 hair 像素的入口作为
+         真实发际线点。``run_length = face_height * density_ratio``。
+      2. 拒掉那些 hit 离锚点向上不到 ``face_height * require_lift_px_ratio``
+         的，它们多半是侧鬓或假阳性。
+      3. 取整个头部 (face ∪ 全部 hair) 的 silhouette：在最左 / 最右极限列上，
+         记录 silhouette 上沿点。这两个点是耳朵上方的曲线终点。
+      4. 控制点 = [左极限 silhouette] + [中间锚点真实 hit] + [右极限 silhouette]，
+         按 x 排序，线性插值到 17 个等距输出 x。
+      5. 钳位：任何输出 y 都不能比该 x 处头部 silhouette 上沿还小，避免曲线
+         跑到头顶上方的虚空里去。
+      6. 上层 web_service 会再调用 ``smooth_hairline`` 平滑一遍。
+
+    生成的 17 个点 x 均匀覆盖整个头部宽度（从左耳上方到右耳上方），中间 y 贴近
+    真实发际线、两侧 y 自然抬升到头部 silhouette 上沿，形成冠状弧。它们的 x
+    不再与对应 MP_TOP_ANCHORS 一一对应，但顺序保持一致。
+    """
+    H, W = parse_map.shape
+    hair_for_rays = (
+        build_face_adjacent_hair_mask(parse_map)
+        if use_adjacent_for_central
+        else build_hair_mask(parse_map)
+    )
+    run_length = max(4, int(round(_face_height_px(landmarks_norm, W, H) * density_ratio)))
+    up_norm = face_up_vector(landmarks_norm)
+    up_px = up_norm * np.array([W, H], dtype=np.float64)
+    up_px /= np.linalg.norm(up_px) + 1e-9
+
+    face_h_px = _face_height_px(landmarks_norm, W, H)
+    min_lift = face_h_px * require_lift_px_ratio
+
+    # Step 1: central density-ray hits
+    central_indices = range(central_drop, C.N_ANCHORS - central_drop)
+    central_hits: list[tuple[float, float]] = []
+    for i in central_indices:
+        mp_idx = C.MP_TOP_ANCHORS[i]
+        anchor_px = landmarks_norm[mp_idx, :2] * np.array([W, H], dtype=np.float64)
+        hit = ray_first_dense_hit(anchor_px, up_px, hair_for_rays, run_length)
+        if hit is None:
+            continue
+        # signed distance "up" from anchor to hit (positive when hit is above anchor)
+        delta_up = float(np.dot(hit - anchor_px, up_px))
+        if delta_up < min_lift:
+            continue
+        central_hits.append((float(hit[0]), float(hit[1])))
+
+    # Step 2: head silhouette
+    cols_with_head, top_y = _head_top_y_per_column(parse_map, use_full_hair=True)
+    if cols_with_head.size < 2:
+        return sample_hairline_baseline(landmarks_norm, parse_map)
+
+    left_x = float(cols_with_head[0])
+    right_x = float(cols_with_head[-1])
+
+    def silhouette_y_at(x_px: float) -> float:
+        idx = int(round(np.clip(x_px, left_x, right_x)))
+        k = int(np.searchsorted(cols_with_head, idx))
+        k = min(k, cols_with_head.size - 1)
+        return float(top_y[k])
+
+    if not central_hits:
+        # No reliable central hits — fall back to silhouette top across the head
+        # (still a coronal arc, just less precise on the forehead)
+        output_xs = np.linspace(left_x, right_x, C.N_ANCHORS)
+        output_ys = np.array([silhouette_y_at(float(x)) for x in output_xs], dtype=np.float64)
+        hairline = np.column_stack([output_xs / W, output_ys / H]).astype(np.float32)
+        return hairline, np.ones(C.N_ANCHORS, dtype=bool)
+
+    # Step 3: control points = [left endpoint] + central hits + [right endpoint]
+    control_pts: list[tuple[float, float]] = list(central_hits)
+    control_pts.append((left_x, silhouette_y_at(left_x)))
+    control_pts.append((right_x, silhouette_y_at(right_x)))
+
+    # Step 4: sort + dedupe by x, then linear-interp 17 evenly-spaced output xs
+    cps = sorted(control_pts, key=lambda p: p[0])
+    cxs = [cps[0][0]]
+    cys = [cps[0][1]]
+    for x, y in cps[1:]:
+        if x - cxs[-1] < 0.5:
+            # collision: prefer the LARGER y (the actual hairline, not silhouette)
+            cys[-1] = max(cys[-1], y)
+        else:
+            cxs.append(x)
+            cys.append(y)
+    cxs_arr = np.asarray(cxs, dtype=np.float64)
+    cys_arr = np.asarray(cys, dtype=np.float64)
+    output_xs = np.linspace(left_x, right_x, C.N_ANCHORS)
+    output_ys = np.interp(output_xs, cxs_arr, cys_arr)
+
+    # Step 5: hairline cannot be above the head silhouette top
+    for k, x in enumerate(output_xs):
+        sil_y = silhouette_y_at(float(x))
+        if output_ys[k] < sil_y:
+            output_ys[k] = sil_y
+
+    hairline = np.column_stack([output_xs / W, output_ys / H]).astype(np.float32)
+    valid = np.ones(C.N_ANCHORS, dtype=bool)
+    return hairline, valid
+
+
+def sample_hairline_arch_strict(landmarks_norm: np.ndarray, parse_map: np.ndarray) -> tuple[np.ndarray, np.ndarray]:
+    """冠状弧策略 (严格版): 只用中间 5 个最可靠的额头锚点; 同时要求 hit 离锚点更远。
+
+    适合中间锚点也容易被刘海/眉毛干扰的场景，曲线更"瘦高"。
+    """
+    return sample_hairline_arch(
+        landmarks_norm,
+        parse_map,
+        central_drop=6,                    # 只保留中间 5 个锚点
+        require_lift_px_ratio=0.04,
+        density_ratio=0.04,
+    )
+
+
+def sample_hairline_arch_adj(landmarks_norm: np.ndarray, parse_map: np.ndarray) -> tuple[np.ndarray, np.ndarray]:
+    """冠状弧策略 (邻接版): 中间锚点的射线只命中"贴脸"的 hair 像素。
+
+    更不容易被远离脸部的背景或后脑勺误命中，但要求 face-adjacent hair 必须
+    形成连续 ``run_length`` 像素 (默认 ratio=0.025) 的密度。
+    """
+    return sample_hairline_arch(
+        landmarks_norm,
+        parse_map,
+        central_drop=3,
+        require_lift_px_ratio=0.015,
+        density_ratio=0.025,
+        use_adjacent_for_central=True,
+    )
+
+
+def sample_hairline_top_arc(landmarks_norm, parse_map: np.ndarray) -> tuple[np.ndarray, np.ndarray]:
+    """策略 6: 不用锚点, 取 (face ∪ adjacent_hair) 的上沿, 按 x 等距 17 点。
+
+    ``landmarks_norm`` 仅用于 fallback 并允许传 None。
+    """
+    H, W = parse_map.shape
+    head = build_skin_mask(parse_map) | build_face_adjacent_hair_mask(parse_map)
+    hairline = np.zeros((C.N_ANCHORS, 2), dtype=np.float32)
+    valid = np.zeros((C.N_ANCHORS,), dtype=bool)
+
+    cols_with_head = np.where(head.any(axis=0))[0]
+    if cols_with_head.size < 2:
+        return hairline, valid
+
+    top_y = np.empty(cols_with_head.size, dtype=np.int32)
+    for j, x in enumerate(cols_with_head):
+        top_y[j] = int(np.argmax(head[:, x]))
+
+    left, right = int(cols_with_head[0]), int(cols_with_head[-1])
+    xs = np.linspace(left, right, C.N_ANCHORS)
+    ys = np.interp(xs, cols_with_head.astype(np.float64), top_y.astype(np.float64))
+    hairline[:, 0] = xs / W
+    hairline[:, 1] = ys / H
+    valid[:] = True
+    return hairline, valid
diff --git a/hairline/lift_3d.py b/hairline/lift_3d.py
new file mode 100644
index 0000000..17c68d2
--- /dev/null
+++ b/hairline/lift_3d.py
@@ -0,0 +1,133 @@
+"""Lift 2D hairline samples to 3D in MediaPipe's normalized space.
+
+Saggital-arc Z model
+--------------------
+MediaPipe / face.obj use ``-z = front of face`` (nose tip is the most
+negative z), ``+z = back of head``. The frontal head surface curves
+backward as you move up from the forehead to the crown, so any vertex
+**above** an MP top anchor (smaller y in image coords) must have a
+**larger** z than that anchor.
+
+For each new hairline / middle vertex (x_h, y_h) attached to MP anchor a
+located at (x_a, y_a, z_a), we model the local sagittal cross-section
+of the head as a circular arc of radius ``R = HEAD_ARC_RADIUS_FRAC × face_h``
+and derive
+
+    z_new = z_a + (y_h - y_a)² / (2 R)
+
+The squared dy term guarantees ``z_new ≥ z_a`` (the surface always
+bulges backward as you walk up the head, never forward). x is taken
+directly from the 2D hairline detection (we don't project x onto the
+arc — the parsing tells us exactly where the hairline sits in x).
+"""
+from __future__ import annotations
+import numpy as np
+
+from . import constants as C
+from .hairline_2d import face_up_vector
+
+
+def _face_height(landmarks_norm: np.ndarray) -> float:
+    """Range of MP y for the visible face (used for the arc radius)."""
+    y = landmarks_norm[:, 1]
+    return float(y.max() - y.min())
+
+
+def _arc_dz(dy: float, R: float) -> float:
+    """Backward (positive) z offset along a circular arc of radius R for
+    a vertical displacement dy. Always non-negative."""
+    return (dy * dy) / (2.0 * max(R, 1e-6))
+
+
+def lift_hairline_to_3d(
+    landmarks_norm: np.ndarray,
+    hairline_norm_xy: np.ndarray,
+    crown_lift_frac: float | None = None,
+) -> np.ndarray:
+    """Combine 2D hairline samples with a sagittal-arc Z, after lifting
+    the (x, y) along the face-up direction by ``crown_lift_frac × face_h``
+    so the ribbon's top row sits at the crown of the head rather than at
+    the detected hair-skin boundary.
+
+    landmarks_norm:    (468, 3) MediaPipe normalized landmarks.
+    hairline_norm_xy:  (N_ANCHORS, 2) 2D hairline samples in [0,1] image space.
+    crown_lift_frac:   how far above the detected hairline (in fractions of
+                       face height) the mesh row should sit. ``None`` uses
+                       ``C.HAIRLINE_CROWN_LIFT_FRAC``.
+    Returns:           (N_ANCHORS, 3) — (x_norm_lifted, y_norm_lifted, z).
+    """
+    face_h = _face_height(landmarks_norm)
+    R = C.HEAD_ARC_RADIUS_FRAC * face_h
+    if crown_lift_frac is None:
+        crown_lift_frac = C.HAIRLINE_CROWN_LIFT_FRAC
+    up = face_up_vector(landmarks_norm)
+    lift = up * (crown_lift_frac * face_h)        # 2D offset, face-up direction
+
+    out = np.zeros((C.N_ANCHORS, 3), dtype=np.float32)
+    for i, mp_idx in enumerate(C.MP_TOP_ANCHORS):
+        z_a = float(landmarks_norm[mp_idx, 2])
+        y_a = float(landmarks_norm[mp_idx, 1])
+        x_h = float(hairline_norm_xy[i, 0]) + float(lift[0])
+        y_h = float(hairline_norm_xy[i, 1]) + float(lift[1])
+        dy = y_h - y_a                              # < 0 (上移更多 → dz 更大)
+        out[i, 0] = x_h
+        out[i, 1] = y_h
+        out[i, 2] = z_a + _arc_dz(dy, R)
+    return out
+
+
+def build_middle_row(
+    landmarks_norm: np.ndarray,
+    hairline_3d: np.ndarray,
+    bias: float = 0.5,
+) -> np.ndarray:
+    """Place the middle row at the arc-length midpoint between each MP
+    anchor and its hairline point.
+
+    The old approach used bias=0.5 linear interpolation in XY and then
+    independently recomputed Z via the arc formula.  Because dz ∝ dy²,
+    the middle row only received 25 % of the hairline Z offset, creating
+    a visible dent where the extension met the face mesh.
+
+    New approach: for each anchor→hairline pair, parameterise the
+    sagittal circular arc by the angle θ and place the middle vertex at
+    θ_mid = bias × θ_hair.  This distributes both the Y displacement
+    **and** the Z displacement smoothly along the arc, so the surface
+    transitions from the face mesh through middle to hairline without
+    any concavity.
+    """
+    R = C.HEAD_ARC_RADIUS_FRAC * _face_height(landmarks_norm)
+    out = np.zeros((C.N_ANCHORS, 3), dtype=np.float32)
+    for i, mp_idx in enumerate(C.MP_TOP_ANCHORS):
+        a = landmarks_norm[mp_idx]
+        h = hairline_3d[i]
+        # X: simple linear interpolation (no arc model in the coronal plane)
+        out[i, 0] = (1 - bias) * float(a[0]) + bias * float(h[0])
+        # Y, Z: interpolate along the circular arc in the sagittal plane.
+        # The arc angle for the hairline point:
+        #   θ_h = |dy_h| / R   (small-angle: arc-length ≈ R θ)
+        # Middle sits at θ_m = bias × θ_h, giving:
+        #   dy_m = R sin(θ_m) ≈ R θ_m   for small θ
+        #   dz_m = R (1 − cos(θ_m))
+        # For the parabolic regime (θ < 0.8 rad ≈ 46°) these simplify to
+        # the same formula but we use the full trig for correctness.
+        dy_h = float(h[1]) - float(a[1])          # negative (upward)
+        sign = -1.0 if dy_h < 0 else 1.0
+        theta_h = abs(dy_h) / max(R, 1e-9)
+        theta_m = bias * theta_h
+        dy_m = sign * R * np.sin(theta_m)          # same sign as dy_h
+        dz_m = R * (1.0 - np.cos(theta_m))         # always ≥ 0
+        out[i, 1] = float(a[1]) + dy_m
+        out[i, 2] = float(a[2]) + dz_m
+    return out
+
+
+def assemble_full(landmarks_norm: np.ndarray,
+                  middle_3d: np.ndarray,
+                  hairline_3d: np.ndarray) -> np.ndarray:
+    """Concatenate to a (N_TOTAL, 3) array in the SDK's expected order:
+    [0..468) MediaPipe / [468..485) middle / [485..502) hairline."""
+    assert landmarks_norm.shape == (C.N_MP, 3)
+    assert middle_3d.shape   == (C.N_ANCHORS, 3)
+    assert hairline_3d.shape == (C.N_ANCHORS, 3)
+    return np.concatenate([landmarks_norm, middle_3d, hairline_3d], axis=0).astype(np.float32)
diff --git a/hairline/mesh/face.obj b/hairline/mesh/face.obj
new file mode 100644
index 0000000..a4c9eac
--- /dev/null
+++ b/hairline/mesh/face.obj
@@ -0,0 +1,2279 @@
+# 3ds Max Wavefront OBJ Exporter v0.97b - (c)2007 guruware
+# �������ļ�:02.12.2025 18:33:58
+
+mtllib ��1202.mtl
+
+#
+# object default
+#
+
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+f 97/97/97 225/225/225 125/125/125 
+f 194/194/194 234/234/234 195/195/195 
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+f 250/250/250 249/249/249 254/254/254 
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+f 253/253/253 252/252/252 267/267/267 
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+f 427/427/427 270/270/270 272/272/272 
+f 402/402/402 273/273/273 275/275/275 
+f 267/267/267 266/266/266 277/277/277 
+f 408/408/408 278/278/278 280/280/280 
+f 327/327/327 267/267/267 281/281/281 
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+f 48/48/48 286/286/286 49/49/49 
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+f 285/285/285 299/299/299 301/301/301 
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+f 290/290/290 289/289/289 314/314/314 
+f 413/413/413 315/315/315 317/317/317 
+f 79/79/79 318/318/318 48/48/48 
+f 297/297/297 314/314/314 298/298/298 
+f 314/314/314 313/313/313 319/319/319 
+f 287/287/287 321/321/321 49/49/49 
+f 302/302/302 323/323/323 324/324/324 
+f 430/430/430 262/262/262 326/326/326 
+f 267/267/267 327/327/327 253/253/253 
+f 343/343/343 329/329/329 331/331/331 
+f 464/464/464 332/332/332 334/334/334 
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+f 307/307/307 306/306/306 258/258/258 
+f 101/101/101 329/329/329 102/102/102 
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+f 329/329/329 343/343/343 339/339/339 
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+f 370/370/370 400/400/400 371/371/371 
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+f 283/283/283 368/368/368 402/402/402 
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+f 389/389/389 404/404/404 387/387/387 
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+f 445/445/445 410/410/410 325/325/325 
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+f 313/313/313 414/414/414 320/320/320 
+f 349/349/349 265/265/265 251/251/251 
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+f 420/420/420 184/184/184 321/321/321 
+f 465/465/465 303/303/303 271/271/271 
+f 466/466/466 186/186/186 420/420/420 
+f 102/102/102 339/339/339 26/26/26 
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+f 312/312/312 311/311/311 394/394/394 
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+f 412/412/412 177/177/177 338/338/338 
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+f 426/426/426 300/300/300 424/424/424 
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+f 459/459/459 435/435/435 340/340/340 
+f 244/244/244 436/436/436 419/419/419 
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+f 339/339/339 344/344/344 415/415/415 
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+f 329/329/329 412/412/412 330/330/330 
+f 305/305/305 444/444/444 245/245/245 
+f 358/358/358 410/410/410 359/359/359 
+f 337/337/337 443/443/443 338/338/338 
+f 281/281/281 392/392/392 327/327/327 
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+f 395/395/395 222/222/222 248/248/248 
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+f 467/467/467 431/431/431 224/224/224 
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+f 327/327/327 323/323/323 328/328/328 
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+f 395/395/395 328/328/328 446/446/446 
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+f 299/299/299 285/285/285 358/358/358 
+f 396/396/396 430/430/430 274/274/274 
+f 390/390/390 451/451/451 447/447/447 
+f 466/466/466 420/420/420 423/423/423 
+f 420/420/420 321/321/321 417/417/417 
+f 321/321/321 287/287/287 320/320/320 
+f 287/287/287 286/286/286 319/319/319 
+f 286/286/286 318/318/318 298/298/298 
+f 418/418/418 404/404/404 453/453/453 
+f 403/403/403 288/288/288 280/280/280 
+f 288/288/288 429/429/429 276/276/276 
+f 429/429/429 397/397/397 277/277/277 
+f 397/397/397 409/409/409 281/281/281 
+f 316/316/316 285/285/285 317/317/317 
+f 386/386/386 436/436/436 381/381/381 
+f 449/449/449 454/454/454 447/447/447 
+f 404/404/404 389/389/389 452/452/452 
+f 235/235/235 390/390/390 70/70/70 
+f 273/273/273 318/318/318 274/274/274 
+f 465/465/465 406/406/406 303/303/303 
+f 425/425/425 456/456/456 300/300/300 
+f 350/350/350 457/457/457 351/351/351 
+f 346/346/346 378/378/378 446/446/446 
+f 238/238/238 220/220/220 439/439/439 
+f 457/457/457 458/458/458 407/407/407 
+f 434/434/434 433/433/433 459/459/459 
+f 442/442/442 441/441/441 370/370/370 
+f 433/433/433 312/312/312 435/435/435 
+f 312/312/312 394/394/394 282/282/282 
+f 394/394/394 355/355/355 369/369/369 
+f 355/355/355 354/354/354 249/249/249 
+f 295/295/295 343/343/343 450/450/450 
+f 294/294/294 344/344/344 295/295/295 
+f 294/294/294 334/334/334 344/344/344 
+f 334/334/334 333/333/333 438/438/438 
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+f 254/254/254 257/257/257 330/330/330 
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+f 453/453/453 452/452/452 461/461/461 
+f 400/400/400 386/386/386 380/380/380 
+f 468/468/468 434/434/434 462/462/462 
+f 434/434/434 459/459/459 441/441/441 
+# 852 faces
+
diff --git a/hairline/mesh/face_ext.obj b/hairline/mesh/face_ext.obj
new file mode 100644
index 0000000..9144ff5
--- /dev/null
+++ b/hairline/mesh/face_ext.obj
@@ -0,0 +1,2428 @@
+# head3d extended face mesh
+# vertices=502 texcoords=502 normals=502 faces=916
+
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diff --git a/hairline/models/face-parsing/config.json b/hairline/models/face-parsing/config.json
new file mode 100644
index 0000000..ec0bfdc
--- /dev/null
+++ b/hairline/models/face-parsing/config.json
@@ -0,0 +1,111 @@
+{
+  "_name_or_path": "jonathandinu/face-parsing",
+  "architectures": [
+    "SegformerForSemanticSegmentation"
+  ],
+  "attention_probs_dropout_prob": 0.0,
+  "classifier_dropout_prob": 0.1,
+  "decoder_hidden_size": 768,
+  "depths": [
+    3,
+    6,
+    40,
+    3
+  ],
+  "downsampling_rates": [
+    1,
+    4,
+    8,
+    16
+  ],
+  "drop_path_rate": 0.1,
+  "hidden_act": "gelu",
+  "hidden_dropout_prob": 0.0,
+  "hidden_sizes": [
+    64,
+    128,
+    320,
+    512
+  ],
+  "id2label": {
+    "0": "background",
+    "1": "skin",
+    "2": "nose",
+    "3": "eye_g",
+    "4": "l_eye",
+    "5": "r_eye",
+    "6": "l_brow",
+    "7": "r_brow",
+    "8": "l_ear",
+    "9": "r_ear",
+    "10": "mouth",
+    "11": "u_lip",
+    "12": "l_lip",
+    "13": "hair",
+    "14": "hat",
+    "15": "ear_r",
+    "16": "neck_l",
+    "17": "neck",
+    "18": "cloth"
+  },
+  "image_size": 224,
+  "initializer_range": 0.02,
+  "label2id": {
+    "background": 0,
+    "skin": 1,
+    "nose": 2,
+    "eye_g": 3,
+    "l_eye": 4,
+    "r_eye": 5,
+    "l_brow": 6,
+    "r_brow": 7,
+    "l_ear": 8,
+    "r_ear": 9,
+    "mouth": 10,
+    "u_lip": 11,
+    "l_lip": 12,
+    "hair": 13,
+    "hat": 14,
+    "ear_r": 15,
+    "neck_l": 16,
+    "neck": 17,
+    "cloth": 18
+  },
+  "layer_norm_eps": 1e-06,
+  "mlp_ratios": [
+    4,
+    4,
+    4,
+    4
+  ],
+  "model_type": "segformer",
+  "num_attention_heads": [
+    1,
+    2,
+    5,
+    8
+  ],
+  "num_channels": 3,
+  "num_encoder_blocks": 4,
+  "patch_sizes": [
+    7,
+    3,
+    3,
+    3
+  ],
+  "reshape_last_stage": true,
+  "semantic_loss_ignore_index": 255,
+  "sr_ratios": [
+    8,
+    4,
+    2,
+    1
+  ],
+  "strides": [
+    4,
+    2,
+    2,
+    2
+  ],
+  "transformers_version": "4.37.0.dev0"
+}
diff --git a/hairline/models/face-parsing/preprocessor_config.json b/hairline/models/face-parsing/preprocessor_config.json
new file mode 100644
index 0000000..89faa86
--- /dev/null
+++ b/hairline/models/face-parsing/preprocessor_config.json
@@ -0,0 +1,23 @@
+{
+  "do_normalize": true,
+  "do_reduce_labels": false,
+  "do_rescale": true,
+  "do_resize": true,
+  "image_mean": [
+    0.485,
+    0.456,
+    0.406
+  ],
+  "image_processor_type": "SegformerFeatureExtractor",
+  "image_std": [
+    0.229,
+    0.224,
+    0.225
+  ],
+  "resample": 2,
+  "rescale_factor": 0.00392156862745098,
+  "size": {
+    "height": 512,
+    "width": 512
+  }
+}
diff --git a/hairline/models/face_landmarker.task b/hairline/models/face_landmarker.task
new file mode 100644
index 0000000..c50c845
Binary files /dev/null and b/hairline/models/face_landmarker.task differ
diff --git a/hairline/obj_io.py b/hairline/obj_io.py
new file mode 100644
index 0000000..11d12c2
--- /dev/null
+++ b/hairline/obj_io.py
@@ -0,0 +1,97 @@
+"""Minimal Wavefront OBJ reader/writer.
+
+Tailored to the project's face.obj:
+- Latin-1 / GB-encoded comments allowed (we tolerate undecodable bytes).
+- Vertices written with 4 decimal places (matches existing file).
+- Preserves comment/mtllib/group lines if requested.
+"""
+from __future__ import annotations
+from dataclasses import dataclass, field
+from typing import Sequence
+
+
+@dataclass
+class ObjMesh:
+    """1-indexed in OBJ files; stored 0-indexed internally."""
+    positions: list[tuple[float, float, float]] = field(default_factory=list)
+    texcoords: list[tuple[float, float]]        = field(default_factory=list)
+    normals:   list[tuple[float, float, float]] = field(default_factory=list)
+    # Each face is a list of 3 (pos_idx, uv_idx, normal_idx) tuples, 0-indexed.
+    # -1 means "absent".
+    faces:     list[list[tuple[int, int, int]]] = field(default_factory=list)
+    header_lines: list[str] = field(default_factory=list)  # comments / mtllib
+
+    def n_v(self) -> int:  return len(self.positions)
+    def n_vt(self) -> int: return len(self.texcoords)
+    def n_vn(self) -> int: return len(self.normals)
+    def n_f(self) -> int:  return len(self.faces)
+
+
+def read_obj(path: str) -> ObjMesh:
+    """Read an OBJ file, ignoring undecodable bytes in comments."""
+    with open(path, "rb") as f:
+        raw = f.read()
+    text = raw.decode("latin-1", errors="replace")
+    mesh = ObjMesh()
+
+    for line in text.splitlines():
+        line = line.strip()
+        if not line:
+            continue
+        if line.startswith("#") or line.startswith("mtllib") or line.startswith("o ") or line.startswith("g ") or line.startswith("s "):
+            mesh.header_lines.append(line)
+            continue
+        parts = line.split()
+        kind = parts[0]
+        if kind == "v":
+            mesh.positions.append((float(parts[1]), float(parts[2]), float(parts[3])))
+        elif kind == "vt":
+            mesh.texcoords.append((float(parts[1]), float(parts[2])))
+        elif kind == "vn":
+            mesh.normals.append((float(parts[1]), float(parts[2]), float(parts[3])))
+        elif kind == "f":
+            verts = []
+            for spec in parts[1:]:
+                seg = spec.split("/")
+                pi = int(seg[0]) - 1 if seg[0] else -1
+                ti = int(seg[1]) - 1 if len(seg) > 1 and seg[1] else -1
+                ni = int(seg[2]) - 1 if len(seg) > 2 and seg[2] else -1
+                verts.append((pi, ti, ni))
+            # Triangulate fan if quad/n-gon (shouldn't happen for our mesh)
+            for k in range(1, len(verts) - 1):
+                mesh.faces.append([verts[0], verts[k], verts[k + 1]])
+        # ignore everything else
+    return mesh
+
+
+def write_obj(path: str, mesh: ObjMesh, header: Sequence[str] | None = None) -> None:
+    """Write an OBJ file with the project's conventions (1-indexed, 4dp)."""
+    out: list[str] = []
+    if header is not None:
+        out.extend(header)
+    else:
+        out.append("# head3d extended face mesh")
+        out.append(f"# vertices={mesh.n_v()} texcoords={mesh.n_vt()} normals={mesh.n_vn()} faces={mesh.n_f()}")
+
+    out.append("")
+    for x, y, z in mesh.positions:
+        out.append(f"v  {x:.4f} {y:.4f} {z:.4f}")
+    out.append("")
+    for u, v in mesh.texcoords:
+        out.append(f"vt {u:.4f} {v:.4f} 0.0000")
+    out.append("")
+    for nx, ny, nz in mesh.normals:
+        out.append(f"vn {nx:.4f} {ny:.4f} {nz:.4f}")
+    out.append("")
+    for face in mesh.faces:
+        toks = []
+        for pi, ti, ni in face:
+            a = str(pi + 1)
+            b = str(ti + 1) if ti >= 0 else ""
+            c = str(ni + 1) if ni >= 0 else ""
+            toks.append(f"{a}/{b}/{c}")
+        out.append("f " + " ".join(toks))
+
+    with open(path, "w", encoding="utf-8", newline="\r\n") as f:
+        f.write("\n".join(out))
+        f.write("\n")
diff --git a/hairline/reference/texture0.png b/hairline/reference/texture0.png
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diff --git a/hairline/reference/uv_template.png b/hairline/reference/uv_template.png
new file mode 100644
index 0000000..39a6739
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