Merge pull request 'Update dependency hexo-ai-summary-liushen to v2' (#7) from renovate/hexo-ai-summary-liushen-2.x into master

Reviewed-on: #7

_config.butterfly.yml

@@ -401,7 +401,7 @@ darkmode:
   end:
 
 # Show scroll percent in scroll-to-top button
-rightside_scroll_percent: false
+rightside_scroll_percent: true
 
 # Don't modify the following settings unless you know how they work
 # Choose: readmode,translate,darkmode,hideAside,toc,chat,comment

package-lock.json

@@ -463,9 +463,9 @@
       "license": "MIT"
     },
     "node_modules/axios": {
-      "version": "1.14.0",
+      "version": "1.15.0",
-      "resolved": "https://registry.npmjs.org/axios/-/axios-1.14.0.tgz",
+      "resolved": "https://registry.npmjs.org/axios/-/axios-1.15.0.tgz",
-      "integrity": "sha512-3Y8yrqLSwjuzpXuZ0oIYZ/XGgLwUIBU3uLvbcpb0pidD9ctpShJd43KSlEEkVQg6DS0G9NKyzOvBfUtDKEyHvQ==",
+      "integrity": "sha512-wWyJDlAatxk30ZJer+GeCWS209sA42X+N5jU2jy6oHTp7ufw8uzUTVFBX9+wTfAlhiJXGS0Bq7X6efruWjuK9Q==",
       "license": "MIT",
       "dependencies": {
         "follow-redirects": "^1.15.11",
@@ -654,27 +654,18 @@
       }
     },
     "node_modules/chokidar": {
-      "version": "3.6.0",
+      "version": "4.0.3",
-      "resolved": "https://registry.npmjs.org/chokidar/-/chokidar-3.6.0.tgz",
+      "resolved": "https://registry.npmjs.org/chokidar/-/chokidar-4.0.3.tgz",
-      "integrity": "sha512-7VT13fmjotKpGipCW9JEQAusEPE+Ei8nl6/g4FBAmIm0GOOLMua9NDDo/DWp0ZAxCr3cPq5ZpBqmPAQgDda2Pw==",
+      "integrity": "sha512-Qgzu8kfBvo+cA4962jnP1KkS6Dop5NS6g7R5LFYJr4b8Ub94PPQXUksCw9PvXoeXPRRddRNC5C1JQUR2SMGtnA==",
       "license": "MIT",
       "dependencies": {
-        "anymatch": "~3.1.2",
+        "readdirp": "^4.0.1"
-        "braces": "~3.0.2",
-        "glob-parent": "~5.1.2",
-        "is-binary-path": "~2.1.0",
-        "is-glob": "~4.0.1",
-        "normalize-path": "~3.0.0",
-        "readdirp": "~3.6.0"
       },
       "engines": {
-        "node": ">= 8.10.0"
+        "node": ">= 14.16.0"
       },
       "funding": {
         "url": "https://paulmillr.com/funding/"
-      },
-      "optionalDependencies": {
-        "fsevents": "~2.3.2"
       }
     },
     "node_modules/combined-stream": {
@@ -1173,9 +1164,9 @@
       }
     },
     "node_modules/fast-xml-parser": {
-      "version": "5.5.10",
+      "version": "5.5.11",
-      "resolved": "https://registry.npmjs.org/fast-xml-parser/-/fast-xml-parser-5.5.10.tgz",
+      "resolved": "https://registry.npmjs.org/fast-xml-parser/-/fast-xml-parser-5.5.11.tgz",
-      "integrity": "sha512-go2J2xODMc32hT+4Xr/bBGXMaIoiCwrwp2mMtAvKyvEFW6S/v5Gn2pBmE4nvbwNjGhpcAiOwEv7R6/GZ6XRa9w==",
+      "integrity": "sha512-QL0eb0YbSTVWF6tTf1+LEMSgtCEjBYPpnAjoLC8SscESlAjXEIRJ7cHtLG0pLeDFaZLa4VKZLArtA/60ZS7vyA==",
       "funding": [
         {
           "type": "github",
@@ -1185,8 +1176,8 @@
       "license": "MIT",
       "dependencies": {
         "fast-xml-builder": "^1.1.4",
-        "path-expression-matcher": "^1.2.1",
+        "path-expression-matcher": "^1.4.0",
-        "strnum": "^2.2.2"
+        "strnum": "^2.2.3"
       },
       "bin": {
         "fxparser": "src/cli/cli.js"
@@ -1571,6 +1562,30 @@
         "sprintf-js": "~1.0.2"
       }
     },
+    "node_modules/hexo-abbrlink/node_modules/chokidar": {
+      "version": "3.6.0",
+      "resolved": "https://registry.npmjs.org/chokidar/-/chokidar-3.6.0.tgz",
+      "integrity": "sha512-7VT13fmjotKpGipCW9JEQAusEPE+Ei8nl6/g4FBAmIm0GOOLMua9NDDo/DWp0ZAxCr3cPq5ZpBqmPAQgDda2Pw==",
+      "license": "MIT",
+      "dependencies": {
+        "anymatch": "~3.1.2",
+        "braces": "~3.0.2",
+        "glob-parent": "~5.1.2",
+        "is-binary-path": "~2.1.0",
+        "is-glob": "~4.0.1",
+        "normalize-path": "~3.0.0",
+        "readdirp": "~3.6.0"
+      },
+      "engines": {
+        "node": ">= 8.10.0"
+      },
+      "funding": {
+        "url": "https://paulmillr.com/funding/"
+      },
+      "optionalDependencies": {
+        "fsevents": "~2.3.2"
+      }
+    },
     "node_modules/hexo-abbrlink/node_modules/dom-serializer": {
       "version": "1.4.1",
       "resolved": "https://registry.npmjs.org/dom-serializer/-/dom-serializer-1.4.1.tgz",
@@ -1713,6 +1728,18 @@
         "js-yaml": "bin/js-yaml.js"
       }
     },
+    "node_modules/hexo-abbrlink/node_modules/readdirp": {
+      "version": "3.6.0",
+      "resolved": "https://registry.npmjs.org/readdirp/-/readdirp-3.6.0.tgz",
+      "integrity": "sha512-hOS089on8RduqdbhvQ5Z37A0ESjsqz6qnRcffsMU3495FuTdqSm+7bhJ29JvIOsBDEEnan5DPu9t3To9VRlMzA==",
+      "license": "MIT",
+      "dependencies": {
+        "picomatch": "^2.2.1"
+      },
+      "engines": {
+        "node": ">=8.10.0"
+      }
+    },
     "node_modules/hexo-abbrlink/node_modules/sprintf-js": {
       "version": "1.0.3",
       "resolved": "https://registry.npmjs.org/sprintf-js/-/sprintf-js-1.0.3.tgz",
@@ -1826,6 +1853,30 @@
         "node": "^14.17.0 || ^16.13.0 || >=18.0.0"
       }
     },
+    "node_modules/hexo-cli/node_modules/chokidar": {
+      "version": "3.6.0",
+      "resolved": "https://registry.npmjs.org/chokidar/-/chokidar-3.6.0.tgz",
+      "integrity": "sha512-7VT13fmjotKpGipCW9JEQAusEPE+Ei8nl6/g4FBAmIm0GOOLMua9NDDo/DWp0ZAxCr3cPq5ZpBqmPAQgDda2Pw==",
+      "license": "MIT",
+      "dependencies": {
+        "anymatch": "~3.1.2",
+        "braces": "~3.0.2",
+        "glob-parent": "~5.1.2",
+        "is-binary-path": "~2.1.0",
+        "is-glob": "~4.0.1",
+        "normalize-path": "~3.0.0",
+        "readdirp": "~3.6.0"
+      },
+      "engines": {
+        "node": ">= 8.10.0"
+      },
+      "funding": {
+        "url": "https://paulmillr.com/funding/"
+      },
+      "optionalDependencies": {
+        "fsevents": "~2.3.2"
+      }
+    },
     "node_modules/hexo-cli/node_modules/hexo-fs": {
       "version": "4.1.3",
       "resolved": "https://registry.npmjs.org/hexo-fs/-/hexo-fs-4.1.3.tgz",
@@ -1879,6 +1930,18 @@
         "entities": "^4.5.0"
       }
     },
+    "node_modules/hexo-cli/node_modules/readdirp": {
+      "version": "3.6.0",
+      "resolved": "https://registry.npmjs.org/readdirp/-/readdirp-3.6.0.tgz",
+      "integrity": "sha512-hOS089on8RduqdbhvQ5Z37A0ESjsqz6qnRcffsMU3495FuTdqSm+7bhJ29JvIOsBDEEnan5DPu9t3To9VRlMzA==",
+      "license": "MIT",
+      "dependencies": {
+        "picomatch": "^2.2.1"
+      },
+      "engines": {
+        "node": ">=8.10.0"
+      }
+    },
     "node_modules/hexo-deployer-git": {
       "version": "4.0.0",
       "resolved": "https://registry.npmjs.org/hexo-deployer-git/-/hexo-deployer-git-4.0.0.tgz",
@@ -1896,6 +1959,30 @@
         "node": ">=14"
       }
     },
+    "node_modules/hexo-deployer-git/node_modules/chokidar": {
+      "version": "3.6.0",
+      "resolved": "https://registry.npmjs.org/chokidar/-/chokidar-3.6.0.tgz",
+      "integrity": "sha512-7VT13fmjotKpGipCW9JEQAusEPE+Ei8nl6/g4FBAmIm0GOOLMua9NDDo/DWp0ZAxCr3cPq5ZpBqmPAQgDda2Pw==",
+      "license": "MIT",
+      "dependencies": {
+        "anymatch": "~3.1.2",
+        "braces": "~3.0.2",
+        "glob-parent": "~5.1.2",
+        "is-binary-path": "~2.1.0",
+        "is-glob": "~4.0.1",
+        "normalize-path": "~3.0.0",
+        "readdirp": "~3.6.0"
+      },
+      "engines": {
+        "node": ">= 8.10.0"
+      },
+      "funding": {
+        "url": "https://paulmillr.com/funding/"
+      },
+      "optionalDependencies": {
+        "fsevents": "~2.3.2"
+      }
+    },
     "node_modules/hexo-deployer-git/node_modules/dom-serializer": {
       "version": "1.4.1",
       "resolved": "https://registry.npmjs.org/dom-serializer/-/dom-serializer-1.4.1.tgz",
@@ -2106,6 +2193,18 @@
         "entities": "^3.0.1"
       }
     },
+    "node_modules/hexo-deployer-git/node_modules/readdirp": {
+      "version": "3.6.0",
+      "resolved": "https://registry.npmjs.org/readdirp/-/readdirp-3.6.0.tgz",
+      "integrity": "sha512-hOS089on8RduqdbhvQ5Z37A0ESjsqz6qnRcffsMU3495FuTdqSm+7bhJ29JvIOsBDEEnan5DPu9t3To9VRlMzA==",
+      "license": "MIT",
+      "dependencies": {
+        "picomatch": "^2.2.1"
+      },
+      "engines": {
+        "node": ">=8.10.0"
+      }
+    },
     "node_modules/hexo-douban": {
       "version": "2.3.6",
       "resolved": "https://registry.npmjs.org/hexo-douban/-/hexo-douban-2.3.6.tgz",
@@ -2120,6 +2219,30 @@
         "node": ">= 18"
       }
     },
+    "node_modules/hexo-douban/node_modules/chokidar": {
+      "version": "3.6.0",
+      "resolved": "https://registry.npmjs.org/chokidar/-/chokidar-3.6.0.tgz",
+      "integrity": "sha512-7VT13fmjotKpGipCW9JEQAusEPE+Ei8nl6/g4FBAmIm0GOOLMua9NDDo/DWp0ZAxCr3cPq5ZpBqmPAQgDda2Pw==",
+      "license": "MIT",
+      "dependencies": {
+        "anymatch": "~3.1.2",
+        "braces": "~3.0.2",
+        "glob-parent": "~5.1.2",
+        "is-binary-path": "~2.1.0",
+        "is-glob": "~4.0.1",
+        "normalize-path": "~3.0.0",
+        "readdirp": "~3.6.0"
+      },
+      "engines": {
+        "node": ">= 8.10.0"
+      },
+      "funding": {
+        "url": "https://paulmillr.com/funding/"
+      },
+      "optionalDependencies": {
+        "fsevents": "~2.3.2"
+      }
+    },
     "node_modules/hexo-douban/node_modules/dom-serializer": {
       "version": "1.4.1",
       "resolved": "https://registry.npmjs.org/dom-serializer/-/dom-serializer-1.4.1.tgz",
@@ -2249,6 +2372,18 @@
         "entities": "^3.0.1"
       }
     },
+    "node_modules/hexo-douban/node_modules/readdirp": {
+      "version": "3.6.0",
+      "resolved": "https://registry.npmjs.org/readdirp/-/readdirp-3.6.0.tgz",
+      "integrity": "sha512-hOS089on8RduqdbhvQ5Z37A0ESjsqz6qnRcffsMU3495FuTdqSm+7bhJ29JvIOsBDEEnan5DPu9t3To9VRlMzA==",
+      "license": "MIT",
+      "dependencies": {
+        "picomatch": "^2.2.1"
+      },
+      "engines": {
+        "node": ">=8.10.0"
+      }
+    },
     "node_modules/hexo-filter-mathjax": {
       "version": "0.9.1",
       "resolved": "https://registry.npmjs.org/hexo-filter-mathjax/-/hexo-filter-mathjax-0.9.1.tgz",
@@ -2285,21 +2420,6 @@
         "node": ">=18"
       }
     },
-    "node_modules/hexo-fs/node_modules/chokidar": {
-      "version": "4.0.3",
-      "resolved": "https://registry.npmjs.org/chokidar/-/chokidar-4.0.3.tgz",
-      "integrity": "sha512-Qgzu8kfBvo+cA4962jnP1KkS6Dop5NS6g7R5LFYJr4b8Ub94PPQXUksCw9PvXoeXPRRddRNC5C1JQUR2SMGtnA==",
-      "license": "MIT",
-      "dependencies": {
-        "readdirp": "^4.0.1"
-      },
-      "engines": {
-        "node": ">= 14.16.0"
-      },
-      "funding": {
-        "url": "https://paulmillr.com/funding/"
-      }
-    },
     "node_modules/hexo-fs/node_modules/hexo-util": {
       "version": "3.3.0",
       "resolved": "https://registry.npmjs.org/hexo-util/-/hexo-util-3.3.0.tgz",
@@ -2338,19 +2458,6 @@
         "entities": "^4.5.0"
       }
     },
-    "node_modules/hexo-fs/node_modules/readdirp": {
-      "version": "4.1.2",
-      "resolved": "https://registry.npmjs.org/readdirp/-/readdirp-4.1.2.tgz",
-      "integrity": "sha512-GDhwkLfywWL2s6vEjyhri+eXmfH6j1L7JE27WhqLeYzoh/A3DBaYGEj2H/HFZCn/kMfim73FXxEJTw06WtxQwg==",
-      "license": "MIT",
-      "engines": {
-        "node": ">= 14.18.0"
-      },
-      "funding": {
-        "type": "individual",
-        "url": "https://paulmillr.com/funding/"
-      }
-    },
     "node_modules/hexo-generator-archive": {
       "version": "2.0.0",
       "resolved": "https://registry.npmjs.org/hexo-generator-archive/-/hexo-generator-archive-2.0.0.tgz",
@@ -3760,9 +3867,9 @@
       }
     },
     "node_modules/path-expression-matcher": {
-      "version": "1.4.0",
+      "version": "1.5.0",
-      "resolved": "https://registry.npmjs.org/path-expression-matcher/-/path-expression-matcher-1.4.0.tgz",
+      "resolved": "https://registry.npmjs.org/path-expression-matcher/-/path-expression-matcher-1.5.0.tgz",
-      "integrity": "sha512-s4DQMxIdhj3jLFWd9LxHOplj4p9yQ4ffMGowFf3cpEgrrJjEhN0V5nxw4Ye1EViAGDoL4/1AeO6qHpqYPOzE4Q==",
+      "integrity": "sha512-cbrerZV+6rvdQrrD+iGMcZFEiiSrbv9Tfdkvnusy6y0x0GKBXREFg/Y65GhIfm0tnLntThhzCnfKwp1WRjeCyQ==",
       "funding": [
         {
           "type": "github",
@@ -4034,15 +4141,16 @@
       }
     },
     "node_modules/readdirp": {
-      "version": "3.6.0",
+      "version": "4.1.2",
-      "resolved": "https://registry.npmjs.org/readdirp/-/readdirp-3.6.0.tgz",
+      "resolved": "https://registry.npmjs.org/readdirp/-/readdirp-4.1.2.tgz",
-      "integrity": "sha512-hOS089on8RduqdbhvQ5Z37A0ESjsqz6qnRcffsMU3495FuTdqSm+7bhJ29JvIOsBDEEnan5DPu9t3To9VRlMzA==",
+      "integrity": "sha512-GDhwkLfywWL2s6vEjyhri+eXmfH6j1L7JE27WhqLeYzoh/A3DBaYGEj2H/HFZCn/kMfim73FXxEJTw06WtxQwg==",
       "license": "MIT",
-      "dependencies": {
-        "picomatch": "^2.2.1"
-      },
       "engines": {
-        "node": ">=8.10.0"
+        "node": ">= 14.18.0"
+      },
+      "funding": {
+        "type": "individual",
+        "url": "https://paulmillr.com/funding/"
       }
     },
     "node_modules/resolve": {

package.json

@@ -12,11 +12,11 @@
     "version": "8.1.1"
   },
   "dependencies": {
-    "axios": "^1.14.0",
+    "axios": "^1.15.0",
     "cheerio": "^1.2.0",
     "hexo": "^8.1.1",
     "hexo-abbrlink": "^2.2.1",
-    "hexo-ai-summary-liushen": "^1.4.0",
+    "hexo-ai-summary-liushen": "^2.0.0",
     "hexo-butterfly-swiper-lyx": "^1.0.2",
     "hexo-deployer-git": "^4.0.0",
     "hexo-douban": "^2.3.6",

source/_posts/2026/2026.4/opengl-1.md

@@ -0,0 +1,131 @@
+---
+title: OpenGL-基础程序
+cover: https://pic.biss.click/image/2fcb9566-f7f6-4132-81cb-4cd646967519.webp
+categories:
+  - 技术
+  - 学习
+series: OpenGL
+tags: OpenGL
+abbrlink: 437a5198
+summary: >-
+  这篇文章详细介绍了OpenGL的基础程序，包括代码展示和代码解释两部分。代码展示部分呈现了一个简单的OpenGL程序，涵盖了初始化与窗口管理、状态设置与缓冲区操作、矩阵与坐标变换以及几何图形绘制等关键步骤。代码解释则将这些步骤按照功能类别进行了归纳，帮助读者更好地理解OpenGL的渲染流程。通过这个示例，读者可以初步掌握OpenGL的基本操作和概念。
+date: 2026-04-11 18:20:34
+---
+
+# 代码展示
+
+我们先从基本的OpenGL程序开始吧，这是一个简单的OpenGL程序：
+
+```cpp
+#include<GL/glut.h>
+using namespace std;
+
+// 回调函数
+void myDisplay()
+{
+	// 清除缓冲区
+	glClearColor(0.0, 0.0, 0.0, 0.0);
+	glClear(GL_COLOR_BUFFER_BIT);
+	// 正交模式
+	glMatrixMode(GL_PROJECTION);
+	gluOrtho2D(0.0, 500.0, 0.0, 500.0);
+	glColor4f(0.0, 1.0, 0.0, 0.0);
+	glRectf(50.0, 50.0, 400.0, 400.0);
+
+	// 划线
+	glColor3f(1.0, 1.0, 0.0);
+	glBegin(GL_LINES);
+	glVertex2f(50.0, 50.0);
+	glVertex2f(400.0, 400.0);
+	glVertex2f(400.0, 50.0);
+	glVertex2f(50.0, 400.0);
+	glEnd();
+
+	// 画点
+	glColor3f(1.0, 0.0,  0.0);
+	glPointSize(20.0);
+	glBegin(GL_POINTS);
+	glVertex2f(15.0, 15.0);
+	glEnd();
+
+	// 画三角形
+	glBegin(GL_TRIANGLES);
+	glColor3f(0.0, 0.0, 1.0);
+	glVertex2i(200, 300);
+	glVertex2i(100, 100);
+	glVertex2i(300, 100);
+	glEnd();
+
+
+	glFlush();
+
+}
+int main(int argc, char* argv[])
+{
+	glutInit(&argc, argv);
+	glutInitDisplayMode(GLUT_RGB | GLUT_SINGLE);
+	glutInitWindowPosition(100, 100);
+	glutInitWindowSize(500, 500);
+	glutCreateWindow("");
+	glutDisplayFunc(&myDisplay);
+	glutMainLoop();
+	return 0;
+}
+```
+这是运行结果图：
+![第一个OpenGL程序](https://pic.biss.click/image/0ef5fbe7-0338-4cd0-94c7-1874273461f7.png)
+
+# 代码解释
+这段代码展示了经典的 OpenGL (GLUT) 固定渲染管线基本操作。为了方便理解，我将这些函数按照 **初始化与窗口管理**、**状态设置**、**坐标变换** 以及 **图形绘制** 四个类别进行了整理。
+
+## 1. 窗口管理与初始化 (GLUT 库)
+这类函数主要用于配置窗口系统和处理程序的运行流程。
+
+| 函数名称 | 功能描述 | 核心参数说明 |
+| :--- | :--- | :--- |
+| `glutInit` | 初始化 GLUT 库 | 接收 `main` 函数的命令行参数 |
+| `glutInitDisplayMode` | 设置显示模式 | `GLUT_RGB` (使用颜色模式), `GLUT_SINGLE` (单缓冲区) |
+| `glutInitWindowPosition` | 设置窗口在屏幕上的初始位置 | 窗口左上角坐标 $(x, y)$ |
+| `glutInitWindowSize` | 设置窗口的宽度和高度 | 像素值 (Width, Height) |
+| `glutCreateWindow` | 创建窗口 | 字符串参数作为窗口标题 |
+| `glutDisplayFunc` | 注册显示回调函数 | 传入负责绘图的函数指针 |
+| `glutMainLoop` | 进入 GLUT 事件处理循环 | 让程序持续运行，等待重绘或交互 |
+
+---
+
+## 2. 状态设置与缓冲区操作
+这些函数用于配置 OpenGL 的全局状态（如颜色、点大小）或清理画布。
+
+| 函数名称 | 功能描述 | 核心参数说明 |
+| :--- | :--- | :--- |
+| `glClearColor` | 设置清除颜色（背景色） | RGBA 值 (0.0~1.0)，此处设为黑色 |
+| `glClear` | 清除指定的缓冲区 | `GL_COLOR_BUFFER_BIT` 表示清除颜色缓存 |
+| `glColor4f` | 设置当前的绘制颜色 (带透明度) | RGBA 分量 |
+| `glColor3f` | 设置当前的绘制颜色 (不带透明度) | RGB 分量 |
+| `glPointSize` | 设置点的像素大小 | 浮点数，数值越大点越粗 |
+| `glFlush` | 强制刷新缓冲区 | 确保绘图命令立即执行并输出到显示设备 |
+
+---
+
+## 3. 矩阵与坐标变换
+用于定义物体是如何投影到屏幕上的。
+
+| 函数名称 | 功能描述 | 核心参数说明 |
+| :--- | :--- | :--- |
+| `glMatrixMode` | 设置当前矩阵模式 | `GL_PROJECTION` 切换到投影矩阵堆栈 |
+| `gluOrtho2D` | 定义二维正交投影裁剪区域 | 定义视野的左、右、下、上边界范围 |
+
+---
+
+## 4. 几何图形绘制
+OpenGL 的核心绘图逻辑，通过指定顶点来构建形状。
+
+| 函数名称 | 功能描述 | 核心参数说明 |
+| :--- | :--- | :--- |
+| `glRectf` | 绘制一个实心矩形 | 传入左下角坐标和右上角坐标 $(x1, y1, x2, y2)$ |
+| `glBegin` | 标记图元绘制的开始 | `GL_LINES` (线), `GL_POINTS` (点), `GL_TRIANGLES` (三角形) |
+| `glVertex2f` | 指定一个二维顶点 (浮点型) | 坐标 $(x, y)$ |
+| `glVertex2i` | 指定一个二维顶点 (整型) | 坐标 $(x, y)$ |
+| `glEnd` | 标记图元绘制的结束 | 必须与 `glBegin` 成对出现 |
+
+---

source/_posts/2026/2026.4/opengl-2.md

@@ -0,0 +1,279 @@
+---
+title: OpenGL-直线的扫描转换
+cover: https://pic.biss.click/image/c5457adc-214c-4a18-9aa6-43fbc0bfc2f4.webp
+categories:
+  - 技术
+  - 学习
+series: OpenGL
+tags: OpenGL
+abbrlink: 7207243b
+summary: >-
+  这篇文章介绍了三种直线扫描转换算法：DDA算法、中点画线算法和Bresenham算法。
+  DDA算法通过计算直线起点和终点的坐标差值来确定步数和增量，依次绘制直线上的点。算法实现简单，适用于任意直线，但精度较低。
+  中点画线算法仅适用于斜率为0或1的直线，通过计算中点和斜率来确定直线上的像素点，效率较高。
+  Bresenham算法根据直线的斜率和误差项来确定像素点的位置，适用于任意直线，且精度高，但实现稍复杂。
+date: 2026-04-11 19:01:02
+---
+
+这篇文章来介绍直线扫描转换算法
+# DDA数值微分线段算法
+## 算法简介
+数值微分法即DDA法(Digital Differential Analyzer)，是一种基于微分方程来生成直线的方法。在计算机图形学中，并没有线段的概念，而是一个个像素点组成了线段。
+
+DDA法生成线段的步骤一般如下：
+
+1. 有了起始点（$x_1，y_1$）和终点（$x_n，y_n$）；
+2. $$\Delta x =|x_n-x_1|, \Delta y=|y_n-y_1|$$
+3. 比较$\Delta x$和$\Delta y$的大小；
+    steps=$\Delta x$和$\Delta y$中较大者；
+4. $$step_x=\frac{\Delta x}{steps}，step_y=\frac{\Delta y}{steps}$$
+## 算法实现
+DDA算法实现如下：
+```cpp
+#include <cmath>
+#include <iostream>
+#include <GL/glut.h>
+
+// 窗口宽度和高度
+const int WIDTH = 640;
+const int HEIGHT = 480;
+
+void drawDDALine(int x1, int y1, int x2, int y2) {
+    float x = x1;
+    float y = y1;
+
+    // 计算差值
+    int dx = x2 - x1;
+    int dy = y2 - y1;
+
+    // 确定步数，取 dx 和 dy 中绝对值较大的那个
+    int steps = std::abs(dx) > std::abs(dy) ? std::abs(dx) : std::abs(dy);  //三元表达式
+
+    // 计算每一步的增量
+    float xIncrement = (float)dx / steps;
+    float yIncrement = (float)dy / steps;
+
+    // 开始绘制点
+    glBegin(GL_POINTS);
+    glVertex2i((int)round(x), (int)round(y)); // 绘制起点
+
+    for (int k = 0; k < steps; k++) {
+        x += xIncrement;
+        y += yIncrement;
+        // 将浮点坐标四舍五入取整转换为整数像素坐标
+		std::cout << (int)round(x) << ", " << (int)round(y)<<"\n";
+        glVertex2i((int)round(x), (int)round(y));
+    }
+    glEnd();
+}
+
+// 显示回调函数
+void display() {
+    drawDDALine(0, 0, 50, 20);
+    glFlush();
+}
+
+// 初始化 OpenGL 设置
+void init() {
+    // 设置背景颜色为白色
+    glClearColor(1.0f, 1.0f, 1.0f, 1.0f);
+
+    // 设置投影矩阵为 2D 正交投影
+    glMatrixMode(GL_PROJECTION);
+    glLoadIdentity();
+    // 定义可视区域，左下角(0,0)，右上角(WIDTH, HEIGHT)
+    gluOrtho2D(0.0, WIDTH, 0.0, HEIGHT);
+}
+
+int main(int argc, char** argv) {
+    // 初始化 GLUT
+    glutInit(&argc, argv);
+
+    // 设置显示模式：单缓冲、RGB 颜色模式
+    glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB);
+
+    // 设置窗口大小和位置
+    glutInitWindowSize(WIDTH, HEIGHT);
+    glutInitWindowPosition(100, 100);
+
+    // 创建窗口
+    glutCreateWindow("DDA算法");
+
+    // 注册回调函数
+    glutDisplayFunc(display);
+
+    // 初始化设置
+    init();
+
+    // 进入主循环
+    glutMainLoop();
+
+    return 0;
+}
+```
+
+# 中点画线算法
+## 算法简介
+只考虑当直线的斜率$|k|< 1$时的情况，假设现在有一条直线$(x_1,y_1,x_2,y_2)$,那么第一个点一定是$(x_1,y_1)$无疑，下一个点的$x$坐标为$x_1+1$,$y$坐标要么为$y1$要么为$y1+1$。关键在于每次取下一个点时，是取前一个的$y1$呢，还是$y1+1$,这时一定是取直线上点最靠近的那个了，而判断取哪个点就用到了中点，我们将中点代入直线中 $d=F(x_1+1,y_1+0.5)=a \cdot (x_1+1)+b \cdot (y_1+0.5)+c$。
+
+1. 如果直线$d>=0$，则取下边的点也就是$(x_1+1,y_1)$。
+2. 如果直线$d<0$,则取上边的点也就是$(x_1+1,y_1+1)$。
+
+它的实际过程就是这样每次根据前边的点判断下一个点在哪，然后进行打亮，但这样每次判断的时候都得代入直线方程计算太麻烦了，我们将这俩种情况分别代入直线方程中可以找出规律：
+
+1. 当直线$d>=0$时，经过化解得$d_1=d+a$;
+2. 当直线$d<0$时，经过化解得$d_2=d+a+b$;
+3. 初始值$d_0=a+0.5b$。
+
+也就是说每次的增量要么为$a$,要么为$a+b$,那么这样判断的时候就简单多了，因为我们每次只是判断它的正负。所以给等式同时乘2，将其中浮点数0.5化为整数，这样硬件操作时无疑更快了。
+
+## 算法实现
+```cpp
+#include <GL/freeglut.h>
+#include <iostream>
+#include <cmath>
+
+// 中点画线算法函数 (仅针对斜率 0 <= k <= 1 的情况进行演示，其它象限需类比处理)
+void drawLineMidpoint(int x0, int y0, int x1, int y1) {
+    int a = y0 - y1;
+    int b = x1 - x0;
+    int d = 2 * a + b;
+    int d1 = 2 * a;
+    int d2 = 2 * (a + b);
+
+    int x = x0, y = y0;
+
+    glBegin(GL_POINTS);
+    glVertex2i(x, y); // 画起点
+
+    while (x < x1) {
+        if (d < 0) {
+            x++;
+            y++;
+            d += d2;
+        } else {
+            x++;
+            d += d1;
+        }
+        glVertex2i(x, y);
+    }
+    glEnd();
+}
+
+// 渲染回调函数
+void display() {
+    glClear(GL_COLOR_BUFFER_BIT);
+    glColor3f(1.0, 1.0, 1.0); // 设置画笔颜色为白色
+
+    // 调用算法画一条直线 (x0, y0) 到 (x1, y1)
+    // 注意：此处的坐标对应屏幕像素坐标
+    drawLineMidpoint(50, 50, 450, 300);
+
+    glFlush();
+}
+
+// 初始化设置
+void init() {
+    glClearColor(0.0, 0.0, 0.0, 1.0); // 背景设为黑色
+    glMatrixMode(GL_PROJECTION);
+    glLoadIdentity();
+    // 设置正交投影矩阵，使坐标系与窗口像素对应
+    gluOrtho2D(0, 500, 0, 500); 
+}
+
+int main(int argc, char** argv) {
+    glutInit(&argc, argv);
+    glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB);
+    glutInitWindowSize(500, 500);
+    glutInitWindowPosition(100, 100);
+    glutCreateWindow("Midpoint Line Algorithm - FreeGLUT");
+
+    init();
+    glutDisplayFunc(display);
+    glutMainLoop();
+
+    return 0;
+}
+```
+
+#  Bresenham算法
+## 算法简介
+假设我们需要由$(x_0, y_0)$这一点，绘画一直线至右下角的另一点$(x_1, y_1)$，x,y分别代表其水平及垂直坐标，并且$x_1 - x_0 > y_1 - y_0$。在此我们使用电脑系统常用的坐标系，即$x$坐标值沿$x$轴向右增长，$y$坐标值沿$y$轴向下增长。
+
+因此x及y之值分别向右及向下增加，而两点之水平距离为$x_{1}-x_{0}$且垂直距离为$y_{1}-y_{0}$。由此得之，该线的斜率必定介乎于$0$至$1$之间。而此算法之目的，就是找出在$x_{0}$与$x_{1}$之间，第$x$行相对应的第$y$列，从而得出一像素点，使得该像素点的位置最接近原本的线。
+
+对于由$(x_0, y_0)$及$(x_1, y_1)$两点所组成之直线，公式如下：
+$$y-y_{0}={\frac {y_{1}-y_{0}}{x_{1}-x_{0}}}(x-x_{0})$$
+因此，对于每一点的x，其y的值是
+$${\frac {y_{1}-y_{0}}{x_{1}-x_{0}}}(x-x_{0})+y_{0}$$
+因为$x$及$y$皆为整数，但并非每一点$x$所对应的$y$皆为整数，故此没有必要去计算每一点x所对应之$y$值。反之由于此线之斜率介乎于$1$至$0$之间，故此我们只需要找出当$x$到达那一个数值时，会使$y$上升$1$，若$x$尚未到此值，则$y$不变。至于如何找出相关的$x$值，则需依靠斜率。斜率之计算方法为$m=(y_{1}-y_{0})/(x_{1}-x_{0})$。由于此值不变，故可于运算前预先计算，减少运算次数。
+
+要实行此算法，我们需计算每一像素点与该线之间的误差。于上述例子中，误差应为每一点$x$中，其相对的像素点之$y$值与该线实际之$y$值的差距。每当$y$的值增加$1$，误差的值就会增加$m$。每当误差的值超出$0.5$，线就会比较靠近下一个映像点，因此$y$的值便会加$1$，且误差减$1$。
+
+## 算法实现
+```cpp
+#include <GL/freeglut.h>
+#include <iostream>
+#include <cmath>
+
+// 通用 Bresenham 画线算法
+void drawLineBresenham(int x0, int y0, int x1, int y1) {
+    int dx = abs(x1 - x0);
+    int dy = abs(y1 - y0);
+    int sx = (x0 < x1) ? 1 : -1; // X 方向步进
+    int sy = (y0 < y1) ? 1 : -1; // Y 方向步进
+    int err = dx - dy;           // 初始误差项
+
+    glBegin(GL_POINTS);
+    while (true) {
+        glVertex2i(x0, y0); // 绘制当前点
+
+        if (x0 == x1 && y0 == y1) break; // 到达终点
+
+        int e2 = 2 * err;
+        // 判断是否在 X 方向步进
+        if (e2 > -dy) {
+            err -= dy;
+            x0 += sx;
+        }
+        // 判断是否在 Y 方向步进
+        if (e2 < dx) {
+            err += dx;
+            y0 += sy;
+        }
+    }
+    glEnd();
+}
+
+// 渲染回调
+void display() {
+    glClear(GL_COLOR_BUFFER_BIT);
+    glColor3f(0.0f, 0.8f, 0.4f); // 设置一个好看的绿色（类似你图中的图标颜色）
+
+    // 绘制几条不同方向的线来测试算法的健壮性
+    drawLineBresenham(50, 50, 450, 400);  // 第一象限
+    drawLineBresenham(50, 400, 450, 50);  // 第四象限
+    drawLineBresenham(250, 50, 250, 450); // 垂直线
+    drawLineBresenham(50, 250, 450, 250); // 水平线
+
+    glFlush();
+}
+
+void init() {
+    glClearColor(0.1f, 0.1f, 0.1f, 1.0f); // 深色背景
+    glMatrixMode(GL_PROJECTION);
+    glLoadIdentity();
+    gluOrtho2D(0, 500, 0, 500); // 建立 500x500 的直角坐标系
+}
+
+int main(int argc, char** argv) {
+    glutInit(&argc, argv);
+    glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB);
+    glutInitWindowSize(600, 600);
+    glutCreateWindow("Bresenham Line Algorithm");
+    init();
+    glutDisplayFunc(display);
+    glutMainLoop();
+    return 0;
+}
+```

themes/butterfly/source/css/style.css

@@ -697,3 +697,90 @@
 [data-theme='dark'] .my-footer-social-amoeba-path {
     fill: #2b3f49;
 }
+
+/* 仿照 Liushen & Butterfly 逻辑的高级表格美化 */
+
+/* 1. 表格容器处理 - 关键响应式滚动层 */
+#article-container .table-wrap,
+#article-container > table {
+    background: var(--liushen-card-bg);
+    border: var(--liushen-card-border);
+    border-radius: 12px;
+    box-shadow: var(--card-box-shadow);
+    margin: 20px 0;
+    backdrop-filter: blur(10px);
+    
+    /* 开启横向滚动逻辑 */
+    width: 100%;
+    overflow-x: auto; /* 小屏幕自动开启滚动 */
+    display: block;   /* 必须设为 block 滚动才生效 */
+}
+
+/* 2. 针对数据表格的结构重置（排除代码块 .highlight） */
+#article-container :not(.highlight) > table {
+    display: table; /* 容器内部恢复为 table 模式 */
+    border-collapse: separate;
+    border-spacing: 0;
+    border: none !important; 
+    width: 100%;
+    min-width: 500px; /* 强制表格在窄屏下不收缩过猛，从而触发容器滚动 */
+}
+
+/* 3. 表头美化 - 渐变风格 */
+#article-container :not(.highlight) > table thead {
+    background: linear-gradient(-45deg, #3eb8be, #6ecad0);
+}
+
+#article-container :not(.highlight) > table th {
+    color: #fff !important;
+    font-weight: 700;
+    padding: 12px 16px;
+    border: none !important;
+    text-align: left;
+}
+
+/* 4. 单元格美化 */
+#article-container :not(.highlight) > table td {
+    padding: 10px 16px;
+    color: var(--liushen-text);
+    /* 仅保留底部细线，模仿 Liushen 的极简风格 */
+    border-bottom: 1px solid rgba(128, 128, 128, 0.1) !important;
+    border-right: none !important; 
+    border-top: none !important;
+    border-left: none !important;
+    transition: background 0.3s;
+}
+
+/* 5. 隔行变色 */
+#article-container :not(.highlight) > table tbody tr:nth-child(even) {
+    background: rgba(153, 169, 191, 0.05);
+}
+
+/* 6. 悬停高亮 */
+#article-container :not(.highlight) > table tbody tr:hover td {
+    background: rgba(62, 184, 190, 0.1);
+}
+
+/* 7. 滚动条美化 (仿照你代码中的蓝色滚动条) */
+#article-container .table-wrap::-webkit-scrollbar {
+    height: 4px; /* 横向滚动条高度 */
+}
+#article-container .table-wrap::-webkit-scrollbar-thumb {
+    background: var(--scrollbar-color, #2679cc);
+    border-radius: 10px;
+}
+
+/* 8. 黑夜模式适配 */
+[data-theme='dark'] #article-container .table-wrap,
+[data-theme='dark'] #article-container > table {
+    background: var(--liushen-card-secondbg);
+}
+
+[data-theme='dark'] #article-container :not(.highlight) > table thead {
+    background: linear-gradient(-45deg, #1f4a4d, #3eb8be);
+}
+
+[data-theme='dark'] #article-container :not(.highlight) > table td {
+    border-bottom: 1px solid rgba(255, 255, 255, 0.05) !important;
+    color: rgba(255, 255, 255, 0.7);
+}