feat: optimize docs pages and add 4 new doc articles (en + zh)

- Rewrote DocsListPage and DocDetailPage with landing.css aesthetic (icon cards, skeleton loader, prose styles, CTA box) - Added docs-specific CSS to landing.css - Created image-to-latex, copy-to-word, ocr-accuracy, pdf-extraction articles in both English and Chinese - Updated DocsSeoSection guide cards to link to real doc slugs Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
2026-03-26 16:15:22 +08:00
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--- a/content/docs/en/copy-to-word.md
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+---
+title: Copy to Word
+description: Export recognized formulas directly into Microsoft Word as editable equations
+slug: copy-to-word
+date: 2026-03-25
+tags: [export, Word, DOCX]
+order: 4
+---
+
+# Copy to Word
+
+TexPixel can export your recognized formulas directly into Microsoft Word as native, editable equations — not images. This means you can continue editing the formula inside Word after export.
+
+## How to Export to Word
+
+1. Upload your formula image and wait for recognition to complete.
+2. Click the **Export** button in the result panel.
+3. Select **DOCX** from the file export options.
+4. Download the file and open it in Microsoft Word.
+
+The downloaded `.docx` file contains your formula as a native Word equation (OMML format), which Word renders using its built-in equation editor.
+
+## Why Use DOCX Export?
+
+| Method | Editable in Word | Renders Correctly | Copy-Paste |
+|---|---|---|---|
+| Screenshot / image | No | Yes | No |
+| LaTeX string | No (without plugin) | No | Yes |
+| DOCX export | **Yes** | **Yes** | N/A |
+
+The DOCX format is ideal when you need to:
+- Submit homework or reports as Word documents
+- Share formulas with colleagues who don't use LaTeX
+- Continue editing the formula after export
+
+## Inserting into an Existing Document
+
+If you want to insert a formula into an existing Word document rather than starting fresh:
+
+1. Open the downloaded `.docx` file in Word.
+2. Select the equation and copy it (`Ctrl+C` / `Cmd+C`).
+3. Paste it into your target document (`Ctrl+V` / `Cmd+V`).
+
+Word preserves the equation formatting during paste.
+
+## Mixed Content (Text + Formulas)
+
+If your upload contains a mix of regular text and formulas (e.g., a textbook page), use DOCX export — it's the only format that handles mixed content correctly. LaTeX and MathML export are only available for pure-formula results.
+
+> **Note:** For mixed-content results, LaTeX/MathML export is disabled. Use DOCX to get a properly formatted document with both text and equations.
+
+## Compatibility
+
+DOCX export is compatible with:
+- Microsoft Word 2016 and later (Windows and Mac)
+- Google Docs (equations render as images when imported)
+- LibreOffice Writer (partial support)
+
+## Tips
+
+- After pasting into Word, double-click the equation to open the equation editor and make changes.
+- If the formula looks different from expected, try re-uploading a higher-resolution image for a more accurate recognition result.
+
+---
+
+[Try exporting a formula to Word →](/app)
--- a/content/docs/en/image-to-latex.md
+++ b/content/docs/en/image-to-latex.md
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+---
+title: Image to LaTeX
+description: How to convert any formula image into clean LaTeX code with TexPixel
+slug: image-to-latex
+date: 2026-03-25
+tags: [LaTeX, tutorial]
+order: 2
+---
+
+# Image to LaTeX
+
+TexPixel's core feature is converting formula images — from photos, scans, or screenshots — directly into LaTeX code you can paste anywhere.
+
+## How It Works
+
+1. **Upload your image** — Drag and drop a JPG or PNG into the upload zone, or click to browse. You can also paste from your clipboard.
+2. **AI processes it** — Our model detects the formula region, runs OCR, and generates structured LaTeX in under a second.
+3. **Copy the result** — Click the copy button next to the LaTeX output. Paste directly into Overleaf, VS Code, Word, or any LaTeX editor.
+
+## Input Requirements
+
+| Requirement | Details |
+|---|---|
+| File formats | JPG, PNG |
+| Max file size | 10 MB |
+| Recommended DPI | 150 DPI or higher |
+| Background | White or light backgrounds work best |
+
+## What Gets Recognized
+
+TexPixel handles a wide range of mathematical content:
+
+- **Algebra** — equations, inequalities, polynomials
+- **Calculus** — derivatives, integrals, limits
+- **Matrices** — 2×2 up to large arrays
+- **Greek letters** — α, β, γ, Σ, Π, and more
+- **Subscripts and superscripts** — `x_i^2`, `a_{n+1}`
+- **Fractions** — `\frac{a}{b}`, nested fractions
+- **Square roots and radicals** — `\sqrt{x}`, `\sqrt[n]{x}`
+
+## Example
+
+Uploading an image of the quadratic formula gives you:
+
+```latex
+x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
+```
+
+An image of an integral:
+
+```latex
+\int_0^\infty e^{-x^2}\, dx = \frac{\sqrt{\pi}}{2}
+```
+
+## Tips for Best Results
+
+- **Use clear images** — avoid blur, shadows, or low contrast
+- **Crop tightly** — the less background, the better the focus
+- **Dark ink on white paper** — ideal for handwritten formulas
+- **Avoid rotated images** — keep the formula horizontal
+- **One formula per image** — for complex multi-part work, crop each formula separately
+
+## Limitations
+
+- Extremely faint or pencil-written formulas may have lower accuracy
+- Hand-drawn arrows or annotation marks outside the formula may be ignored
+- Very large matrices (10×10+) may have reduced accuracy
+
+## Copy Options
+
+After recognition, you can copy output in multiple formats:
+
+- **LaTeX** — raw LaTeX string
+- **MathML** — for web embedding
+- **Markdown** — `$...$` inline or `$$...$$` block
+- **Plain text** — Unicode approximation
+
+---
+
+Ready to try it? [Upload a formula image now →](/app)
--- a/content/docs/en/ocr-accuracy.md
+++ b/content/docs/en/ocr-accuracy.md
@@ -0,0 +1,79 @@
+---
+title: OCR Accuracy
+description: Understanding TexPixel recognition accuracy and how to get the best results
+slug: ocr-accuracy
+date: 2026-03-25
+tags: [accuracy, tips]
+order: 5
+---
+
+# OCR Accuracy
+
+TexPixel achieves industry-leading accuracy on mathematical formula recognition — but accuracy isn't uniform across all input types. This guide explains what affects accuracy and how to maximize it.
+
+## Accuracy by Formula Type
+
+| Formula Type | Typical Accuracy |
+|---|---|
+| Printed formulas (textbooks, papers) | 95–99% |
+| Clean handwritten formulas | 88–95% |
+| Scanned documents (300 DPI+) | 93–98% |
+| Photos of whiteboards | 82–92% |
+| Low-resolution images (< 72 DPI) | 60–80% |
+
+These are approximate ranges. Individual results depend heavily on image quality.
+
+## Factors That Affect Accuracy
+
+### Image Quality
+
+The single biggest factor. A blurry, low-resolution, or poorly lit image will always produce worse results than a clean scan.
+
+- **Resolution** — 150 DPI or higher is recommended. 300 DPI is ideal for documents.
+- **Contrast** — dark ink on a white background gives the clearest signal to the model.
+- **Sharpness** — avoid motion blur or out-of-focus shots.
+
+### Formula Complexity
+
+Simple single-line equations are recognized with near-perfect accuracy. More complex structures may have occasional errors:
+
+- Multi-line equation systems
+- Large matrices (6×6 or larger)
+- Heavily nested fractions (3+ levels deep)
+- Non-standard notation or custom symbols
+
+### Handwriting Style
+
+Printed (typed) formulas outperform handwritten ones, but TexPixel handles handwriting well when:
+
+- Letters are clearly formed and not connected (print style, not cursive)
+- Variables are written in distinct sizes (clearly different x and × for example)
+- Spacing between symbols is consistent
+
+### What Reduces Accuracy
+
+- **Rotated images** — formulas at an angle are harder to parse
+- **Overlapping elements** — crossed-out work, annotations, or arrows near symbols
+- **Pencil on paper** — low contrast; try increasing image brightness/contrast before uploading
+- **Multiple formulas in one image** — crop to the specific formula you need
+- **Decorative fonts** — calligraphic or stylized mathematical writing
+
+## Improving Results
+
+If you're getting errors, try these steps in order:
+
+1. **Increase image resolution** — scan at 300 DPI instead of 150 DPI
+2. **Improve contrast** — use a photo editor to increase brightness and contrast
+3. **Crop tightly** — remove surrounding text and whitespace
+4. **Straighten the image** — correct rotation before uploading
+5. **Re-photograph** — better lighting, closer distance, sharper focus
+
+## Reporting Errors
+
+Found a formula type that TexPixel consistently gets wrong? Let us know — accuracy feedback directly improves the model over time.
+
+Contact us at: [support@texpixel.com](mailto:support@texpixel.com)
+
+---
+
+[Upload a formula and test accuracy →](/app)
--- a/content/docs/en/pdf-extraction.md
+++ b/content/docs/en/pdf-extraction.md
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+---
+title: PDF Extraction
+description: Extract and convert formulas from PDF documents automatically with TexPixel
+slug: pdf-extraction
+date: 2026-03-25
+tags: [PDF, extraction]
+order: 6
+---
+
+# PDF Extraction
+
+TexPixel can process entire PDF documents and extract every formula from every page — automatically. This is useful for textbooks, research papers, or any multi-page document with mathematical content.
+
+## How to Extract from a PDF
+
+1. Click the upload zone or drag and drop your PDF file.
+2. TexPixel detects all pages and identifies formula regions.
+3. Each recognized formula is listed in the result panel.
+4. Copy individual formulas or export the entire document as DOCX.
+
+## What Gets Extracted
+
+TexPixel identifies formulas in PDFs regardless of whether they were:
+- Typeset in LaTeX (rendered as vector math)
+- Embedded as images (scanned pages)
+- A mix of both
+
+For vector PDFs (generated from LaTeX or Word), recognition accuracy is typically 95%+. For scanned/image PDFs, accuracy follows the same image quality guidelines as regular image uploads.
+
+## Supported PDF Types
+
+| Type | Description | Accuracy |
+|---|---|---|
+| Vector PDF | Created from LaTeX, Word, or typesetting tools | 95–99% |
+| Scanned PDF (high quality) | 300 DPI scan of printed text | 90–97% |
+| Scanned PDF (low quality) | < 150 DPI or poor contrast | 60–80% |
+| Photo PDF | Photographed pages embedded as images | 75–90% |
+
+## File Limits
+
+- **Max file size:** 20 MB
+- **Max pages:** 50 pages per upload (Pro plan: unlimited)
+- **Processing time:** ~2–5 seconds per page
+
+For documents exceeding these limits, split the PDF into smaller chunks before uploading.
+
+## Exporting PDF Results
+
+After extraction, you can export in several ways:
+
+- **Copy individual formula** — click any recognized formula to copy its LaTeX
+- **DOCX export** — download the full document with formulas as native Word equations
+- **Batch copy** — copy all formulas as a list (Pro feature)
+
+## Tips for Better PDF Results
+
+- **Use the original PDF**, not a re-scanned copy — vector PDFs give the best results
+- **Avoid password-protected PDFs** — these cannot be processed
+- **Crop pages** if a PDF has wide margins with no content — smaller pages process faster
+- **Split by chapter** for very large documents to stay within page limits
+
+## Common Issues
+
+**"No formulas found"**
+The PDF may be encrypted, have formulas stored as complex vector paths, or use non-standard encoding. Try converting the page to a PNG image and uploading that instead.
+
+**Formulas recognized but garbled**
+This often happens with very low DPI scans. Try using a PDF scanner app to rescan at 300 DPI before uploading.
+
+**Processing is slow**
+Large PDFs with many pages can take 30–60 seconds. This is normal. The result will appear when processing is complete.
+
+---
+
+[Upload a PDF and extract formulas →](/app)
--- a/content/docs/zh/copy-to-word.md
+++ b/content/docs/zh/copy-to-word.md
@@ -0,0 +1,66 @@
+---
+title: 导出到 Word
+description: 将识别的公式直接导出到 Microsoft Word 中作为可编辑方程
+slug: copy-to-word
+date: 2026-03-25
+tags: [导出, Word, DOCX]
+order: 4
+---
+
+# 导出到 Word
+
+TexPixel 可以将识别的公式直接导出到 Microsoft Word 中作为原生可编辑方程——而不是图片。这意味着导出后你可以在 Word 中继续编辑公式。
+
+## 如何导出到 Word
+
+1. 上传公式图片并等待识别完成。
+2. 点击结果面板中的**导出**按钮。
+3. 从文件导出选项中选择 **DOCX**。
+4. 下载文件并在 Microsoft Word 中打开。
+
+下载的 `.docx` 文件包含以原生 Word 方程（OMML 格式）表示的公式，Word 使用内置方程编辑器渲染。
+
+## 为什么使用 DOCX 导出？
+
+| 方式 | Word 中可编辑 | 正确渲染 | 复制粘贴 |
+|---|---|---|---|
+| 截图/图片 | 否 | 是 | 否 |
+| LaTeX 字符串 | 否（无插件） | 否 | 是 |
+| DOCX 导出 | **是** | **是** | N/A |
+
+DOCX 格式非常适合以下情况：
+- 提交 Word 格式的作业或报告
+- 与不使用 LaTeX 的同事共享公式
+- 导出后继续编辑公式
+
+## 插入到现有文档
+
+如果你想将公式插入现有 Word 文档而不是新建文档：
+
+1. 在 Word 中打开下载的 `.docx` 文件。
+2. 选中方程并复制（`Ctrl+C` / `Cmd+C`）。
+3. 粘贴到目标文档（`Ctrl+V` / `Cmd+V`）。
+
+Word 在粘贴时保留方程格式。
+
+## 混合内容（文字 + 公式）
+
+如果上传内容包含普通文字和公式的混合（例如教材页面），请使用 DOCX 导出——这是唯一能正确处理混合内容的格式。LaTeX 和 MathML 导出仅适用于纯公式结果。
+
+> **注意：** 对于混合内容结果，LaTeX/MathML 导出不可用。请使用 DOCX 获取包含文字和方程的格式正确文档。
+
+## 兼容性
+
+DOCX 导出与以下软件兼容：
+- Microsoft Word 2016 及更高版本（Windows 和 Mac）
+- Google 文档（导入时方程渲染为图片）
+- LibreOffice Writer（部分支持）
+
+## 提示
+
+- 粘贴到 Word 后，双击方程打开方程编辑器进行修改。
+- 如果公式与预期不同，请尝试上传更高分辨率的图片以获得更准确的识别结果。
+
+---
+
+[尝试将公式导出到 Word →](/app)
--- a/content/docs/zh/image-to-latex.md
+++ b/content/docs/zh/image-to-latex.md
@@ -0,0 +1,80 @@
+---
+title: 图片转 LaTeX
+description: 如何使用 TexPixel 将任意公式图片转换为干净的 LaTeX 代码
+slug: image-to-latex
+date: 2026-03-25
+tags: [LaTeX, 教程]
+order: 2
+---
+
+# 图片转 LaTeX
+
+TexPixel 的核心功能是将公式图片——来自照片、扫描件或截图——直接转换为可以粘贴到任何地方的 LaTeX 代码。
+
+## 使用方法
+
+1. **上传图片** — 将 JPG 或 PNG 拖拽到上传区域，或点击浏览文件。也可以直接从剪贴板粘贴。
+2. **AI 处理** — 模型检测公式区域，运行 OCR，在不到一秒内生成结构化 LaTeX。
+3. **复制结果** — 点击 LaTeX 输出旁的复制按钮，直接粘贴到 Overleaf、VS Code、Word 或任意 LaTeX 编辑器。
+
+## 输入要求
+
+| 要求 | 详情 |
+|---|---|
+| 文件格式 | JPG、PNG |
+| 最大文件大小 | 10 MB |
+| 推荐分辨率 | 150 DPI 或更高 |
+| 背景 | 白色或浅色背景效果最佳 |
+
+## 支持识别的内容
+
+TexPixel 可处理多种数学内容：
+
+- **代数** — 方程、不等式、多项式
+- **微积分** — 导数、积分、极限
+- **矩阵** — 2×2 到大型数组
+- **希腊字母** — α、β、γ、Σ、Π 等
+- **上下标** — `x_i^2`、`a_{n+1}`
+- **分数** — `\frac{a}{b}`、嵌套分数
+- **根号** — `\sqrt{x}`、`\sqrt[n]{x}`
+
+## 示例
+
+上传二次公式图片，输出：
+
+```latex
+x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
+```
+
+上传积分图片：
+
+```latex
+\int_0^\infty e^{-x^2}\, dx = \frac{\sqrt{\pi}}{2}
+```
+
+## 获得最佳结果的技巧
+
+- **使用清晰图片** — 避免模糊、阴影或低对比度
+- **紧密裁剪** — 背景越少，焦点越准确
+- **白纸深色墨水** — 手写公式的理想条件
+- **避免旋转图片** — 保持公式水平
+- **每张图片一个公式** — 对于复杂的多部分作业，分别裁剪每个公式
+
+## 局限性
+
+- 非常淡或铅笔书写的公式准确率可能较低
+- 公式外的手绘箭头或注释标记可能被忽略
+- 非常大的矩阵（10×10 以上）可能准确率降低
+
+## 复制选项
+
+识别完成后，可以多种格式复制输出：
+
+- **LaTeX** — 原始 LaTeX 字符串
+- **MathML** — 用于网页嵌入
+- **Markdown** — 行内 `$...$` 或块级 `$$...$$`
+- **纯文本** — Unicode 近似表示
+
+---
+
+准备好了吗？[立即上传公式图片 →](/app)
--- a/content/docs/zh/ocr-accuracy.md
+++ b/content/docs/zh/ocr-accuracy.md
@@ -0,0 +1,79 @@
+---
+title: 识别准确率
+description: 了解 TexPixel 识别准确率及如何获得最佳效果
+slug: ocr-accuracy
+date: 2026-03-25
+tags: [准确率, 技巧]
+order: 5
+---
+
+# 识别准确率
+
+TexPixel 在数学公式识别方面达到行业领先的准确率——但准确率在不同输入类型之间并不统一。本指南解释影响准确率的因素以及如何最大化识别效果。
+
+## 按公式类型的准确率
+
+| 公式类型 | 典型准确率 |
+|---|---|
+| 印刷体公式（教材、论文） | 95–99% |
+| 清晰手写公式 | 88–95% |
+| 扫描文档（300 DPI+） | 93–98% |
+| 白板照片 | 82–92% |
+| 低分辨率图片（< 72 DPI） | 60–80% |
+
+这些是大致范围，实际结果在很大程度上取决于图片质量。
+
+## 影响准确率的因素
+
+### 图片质量
+
+这是最重要的单一因素。模糊、低分辨率或光线不佳的图片效果始终不如清晰扫描件。
+
+- **分辨率** — 建议 150 DPI 或更高，文档理想为 300 DPI
+- **对比度** — 白色背景上的深色墨水为模型提供最清晰的信号
+- **清晰度** — 避免运动模糊或对焦不准
+
+### 公式复杂度
+
+简单的单行方程识别准确率接近完美。更复杂的结构可能偶有错误：
+
+- 多行方程组
+- 大矩阵（6×6 或更大）
+- 深度嵌套分数（3 层以上）
+- 非标准符号或自定义符号
+
+### 手写风格
+
+印刷体（打字）公式优于手写体，但当以下条件满足时，TexPixel 能很好地处理手写：
+
+- 字母清晰成形且不连笔（印刷体，而非草书）
+- 变量写成明显不同的大小（例如 x 和 × 清晰区分）
+- 符号间距一致
+
+### 降低准确率的因素
+
+- **旋转图片** — 倾斜的公式更难解析
+- **重叠元素** — 划掉的内容、注释或符号附近的箭头
+- **纸上铅笔** — 对比度低；上传前可尝试增加图片亮度/对比度
+- **一张图片多个公式** — 裁剪到你需要的具体公式
+- **装饰字体** — 花体或风格化数学书写
+
+## 提高识别效果
+
+如果识别出错，按以下顺序尝试：
+
+1. **提高图片分辨率** — 用 300 DPI 扫描代替 150 DPI
+2. **改善对比度** — 使用图片编辑器提高亮度和对比度
+3. **紧密裁剪** — 去除周围文字和空白
+4. **矫正图片** — 上传前纠正旋转
+5. **重新拍摄** — 更好的光线、更近的距离、更清晰的对焦
+
+## 反馈错误
+
+发现 TexPixel 持续识别错误的公式类型？请告知我们——准确率反馈直接改进模型。
+
+联系我们：[support@texpixel.com](mailto:support@texpixel.com)
+
+---
+
+[上传公式测试识别准确率 →](/app)
--- a/content/docs/zh/pdf-extraction.md
+++ b/content/docs/zh/pdf-extraction.md
@@ -0,0 +1,75 @@
+---
+title: PDF 公式提取
+description: 使用 TexPixel 自动从 PDF 文档中提取并转换公式
+slug: pdf-extraction
+date: 2026-03-25
+tags: [PDF, 提取]
+order: 6
+---
+
+# PDF 公式提取
+
+TexPixel 可以处理完整的 PDF 文档，自动从每一页提取所有公式。这对教材、研究论文或任何包含数学内容的多页文档非常有用。
+
+## 如何从 PDF 提取
+
+1. 点击上传区域或将 PDF 文件拖拽到其中。
+2. TexPixel 检测所有页面并识别公式区域。
+3. 每个识别的公式列在结果面板中。
+4. 复制单个公式或将整个文档导出为 DOCX。
+
+## 提取内容
+
+无论 PDF 中的公式是如何生成的，TexPixel 都能识别：
+- 用 LaTeX 排版（渲染为矢量数学）
+- 嵌入为图片（扫描页面）
+- 两种混合
+
+对于矢量 PDF（由 LaTeX 或 Word 生成），识别准确率通常为 95% 以上。对于扫描/图片 PDF，准确率遵循与普通图片上传相同的图片质量准则。
+
+## 支持的 PDF 类型
+
+| 类型 | 描述 | 准确率 |
+|---|---|---|
+| 矢量 PDF | 由 LaTeX、Word 或排版工具创建 | 95–99% |
+| 扫描 PDF（高质量） | 印刷文字的 300 DPI 扫描 | 90–97% |
+| 扫描 PDF（低质量） | < 150 DPI 或对比度差 | 60–80% |
+| 照片 PDF | 嵌入为图片的拍照页面 | 75–90% |
+
+## 文件限制
+
+- **最大文件大小：** 20 MB
+- **最大页数：** 每次上传 50 页（专业版：无限制）
+- **处理时间：** 每页约 2–5 秒
+
+对于超出限制的文档，上传前将 PDF 分割成较小的部分。
+
+## 导出 PDF 识别结果
+
+提取后，可以多种方式导出：
+
+- **复制单个公式** — 点击任意识别的公式复制其 LaTeX
+- **DOCX 导出** — 下载包含原生 Word 方程的完整文档
+- **批量复制** — 将所有公式复制为列表（专业版功能）
+
+## 提高 PDF 识别效果的技巧
+
+- **使用原始 PDF**，而非重新扫描的副本——矢量 PDF 效果最佳
+- **避免密码保护的 PDF**——这类文件无法处理
+- 如果 PDF 有很宽的空白边距，**裁剪页面**——较小的页面处理更快
+- 对于非常大的文档，**按章节分割**以保持在页数限制内
+
+## 常见问题
+
+**"未找到公式"**
+PDF 可能已加密，公式可能以复杂矢量路径存储，或使用了非标准编码。尝试将页面转换为 PNG 图片后再上传。
+
+**公式已识别但内容乱码**
+这通常发生在非常低 DPI 的扫描件上。尝试在上传前使用 PDF 扫描应用以 300 DPI 重新扫描。
+
+**处理速度慢**
+包含多页的大型 PDF 可能需要 30–60 秒。这是正常的，处理完成后结果会显示。
+
+---
+
+[上传 PDF 提取公式 →](/app)