504 lines
38 KiB
HTML
504 lines
38 KiB
HTML
<!DOCTYPE html>
|
||
<html lang="zh-CN">
|
||
<head prefix="og: http://ogp.me/ns# article: http://ogp.me/ns/article#">
|
||
<meta charset="UTF-8" />
|
||
|
||
<meta name="generator" content="Hugo 0.113.0"><meta name="theme-color" content="#fff" />
|
||
<meta name="color-scheme" content="light dark">
|
||
|
||
|
||
<meta name="viewport" content="width=device-width, initial-scale=1.0" />
|
||
|
||
<meta name="format-detection" content="telephone=no, date=no, address=no, email=no" />
|
||
|
||
<meta http-equiv="Cache-Control" content="no-transform" />
|
||
|
||
<meta http-equiv="Cache-Control" content="no-siteapp" />
|
||
|
||
<title>常用光照模型 | 飞鸿踏雪</title>
|
||
|
||
<link rel="stylesheet" href="/css/meme.min.12a3541920a798d49c1bca858f15c53090f14ce9367a34faa2bb51dd38299730.css"/>
|
||
|
||
|
||
|
||
<script src="/js/meme.min.ac2b48f322cff6a9a8036be3baf3e59e300cd9e4191997a8c3765f79de02bf8d.js"></script>
|
||
|
||
|
||
|
||
<link rel="preconnect" href="https://fonts.gstatic.com" crossorigin />
|
||
|
||
<link rel="stylesheet" href="https://fonts.googleapis.com/css2?family=EB+Garamond:ital,wght@0,400;0,500;0,700;1,400;1,700&family=Noto+Serif+SC:wght@400;500;700&family=Source+Code+Pro:ital,wght@0,400;0,700;1,400;1,700&display=swap" media="print" onload="this.media='all'" />
|
||
<noscript><link rel="stylesheet" href="https://fonts.googleapis.com/css2?family=EB+Garamond:ital,wght@0,400;0,500;0,700;1,400;1,700&family=Noto+Serif+SC:wght@400;500;700&family=Source+Code+Pro:ital,wght@0,400;0,700;1,400;1,700&display=swap" /></noscript>
|
||
|
||
<meta name="author" content="InkSoul" /><meta name="description" content="着色(shading) 着色往往是指向模型物体上色或添加材质特性的流程(不包含阴影的计……" />
|
||
|
||
<link rel="shortcut icon" href="/favicon.ico" type="image/x-icon" />
|
||
<link rel="mask-icon" href="/icons/safari-pinned-tab.svg" color="#2a6df4" />
|
||
<link rel="apple-touch-icon" sizes="180x180" href="/icons/apple-touch-icon.png" />
|
||
<meta name="apple-mobile-web-app-capable" content="yes" />
|
||
<meta name="apple-mobile-web-app-title" content="飞鸿踏雪" />
|
||
<meta name="apple-mobile-web-app-status-bar-style" content="black" />
|
||
<meta name="mobile-web-app-capable" content="yes" />
|
||
<meta name="application-name" content="飞鸿踏雪" />
|
||
<meta name="msapplication-starturl" content="../../" />
|
||
<meta name="msapplication-TileColor" content="#fff" />
|
||
<meta name="msapplication-TileImage" content="../../icons/mstile-150x150.png" />
|
||
<link rel="manifest" href="/manifest.json" />
|
||
|
||
|
||
|
||
|
||
|
||
<link rel="canonical" href="http://www.inksoul.top/computergraphic/%E5%B8%B8%E7%94%A8%E5%85%89%E7%85%A7%E6%A8%A1%E5%9E%8B/" />
|
||
|
||
|
||
<script type="application/ld+json">
|
||
{
|
||
"@context": "https://schema.org",
|
||
"@type": "BlogPosting",
|
||
"datePublished": "2022-05-19T11:55:15+08:00",
|
||
"dateModified": "2023-06-18T21:19:01+08:00",
|
||
"url": "http://www.inksoul.top/computergraphic/%E5%B8%B8%E7%94%A8%E5%85%89%E7%85%A7%E6%A8%A1%E5%9E%8B/",
|
||
"headline": "常用光照模型",
|
||
"description": "着色(shading) 着色往往是指向模型物体上色或添加材质特性的流程(不包含阴影的计……",
|
||
"inLanguage" : "zh-CN",
|
||
"articleSection": "computergraphic",
|
||
"wordCount": 1176 ,
|
||
"image": ["http://www.inksoul.top/../../images/shading_light_caculate.png","http://www.inksoul.top/../../images/light_separete.png","http://www.inksoul.top/../../images/lambert%27scosine_low.png","http://www.inksoul.top/../../images/Specular_show.png","http://www.inksoul.top/../../images/specular_cacular.png","http://www.inksoul.top/../../images/specular_value_change_show.png","http://www.inksoul.top/../../images/blinn-phong_model_cacu.png","http://www.inksoul.top/../../images/flat_shading.png","http://www.inksoul.top/../../images/Gourand_shading.png","http://www.inksoul.top/../../images/average_normal.png","http://www.inksoul.top/../../images/phong_shading.png"],
|
||
"author": {
|
||
"@type": "Person",
|
||
"email": "qingci30@163.com",
|
||
"image": "http://www.inksoul.top/icons/apple-touch-icon.png",
|
||
"url": "http://www.inksoul.top",
|
||
"name": "InkSoul"
|
||
},
|
||
"license": "[CC BY-NC-SA 4.0](https://creativecommons.org/licenses/by-nc-sa/4.0/deed.zh)",
|
||
"publisher": {
|
||
"@type": "Organization",
|
||
"name": "飞鸿踏雪",
|
||
"logo": {
|
||
"@type": "ImageObject",
|
||
"url": "http://www.inksoul.top/icons/apple-touch-icon.png"
|
||
},
|
||
"url": "http://www.inksoul.top/"
|
||
},
|
||
"mainEntityOfPage": {
|
||
"@type": "WebSite",
|
||
"@id": "http://www.inksoul.top/"
|
||
}
|
||
}
|
||
</script>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<meta property="og:title" content="常用光照模型" />
|
||
<meta property="og:description" content="着色(shading) 着色往往是指向模型物体上色或添加材质特性的流程(不包含阴影的计……" />
|
||
<meta property="og:url" content="http://www.inksoul.top/computergraphic/%E5%B8%B8%E7%94%A8%E5%85%89%E7%85%A7%E6%A8%A1%E5%9E%8B/" />
|
||
<meta property="og:site_name" content="飞鸿踏雪" />
|
||
<meta property="og:locale" content="zh" /><meta property="og:image" content="http://www.inksoul.top/../../images/shading_light_caculate.png" />
|
||
<meta property="og:type" content="article" />
|
||
<meta property="article:published_time" content="2022-05-19T11:55:15+08:00" />
|
||
<meta property="article:modified_time" content="2023-06-18T21:19:01+08:00" />
|
||
|
||
<meta property="article:section" content="computergraphic" />
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
</head>
|
||
|
||
<body>
|
||
<div class="container">
|
||
|
||
<header class="header">
|
||
|
||
<div class="header-wrapper">
|
||
<div class="header-inner single">
|
||
|
||
<div class="site-brand">
|
||
|
||
<a href="/" class="brand">飞鸿踏雪</a>
|
||
|
||
</div>
|
||
|
||
<nav class="nav">
|
||
<ul class="menu" id="menu">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="menu-item active"><a href="/computergraphic/"><svg class="icon computergraphic" fill="none" stroke="currentColor" viewBox="0 0 24 24" xmlns="http://www.w3.org/2000/svg"><path stroke-linecap="round" stroke-linejoin="round" stroke-width="2" d="M20 7l-8-4-8 4m16 0l-8 4m8-4v10l-8 4m0-10L4 7m8 4v10M4 7v10l8 4"></path></svg><span class="menu-item-name">图形学</span></a>
|
||
</li>
|
||
|
||
|
||
|
||
<li class="menu-item"><a href="/algorithm/"><svg class="icon algorithm" fill="none" stroke="currentColor" viewBox="0 0 24 24" xmlns="http://www.w3.org/2000/svg"><path stroke-linecap="round" stroke-linejoin="round" stroke-width="2" d="M9.663 17h4.673M12 3v1m6.364 1.636l-.707.707M21 12h-1M4 12H3m3.343-5.657l-.707-.707m2.828 9.9a5 5 0 117.072 0l-.548.547A3.374 3.374 0 0014 18.469V19a2 2 0 11-4 0v-.531c0-.895-.356-1.754-.988-2.386l-.548-.547z"></path></svg><span class="menu-item-name">算法</span></a>
|
||
</li>
|
||
|
||
|
||
|
||
<li class="menu-item"><a href="/mathematics/"><svg class="icon mathematics" fill="none" stroke="currentColor" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 576 512"><path stroker-linecap="round" stroke-linejoin="round" stroker-width="2" d="M576 32.01c0-17.69-14.33-31.1-32-31.1l-224-.0049c-14.69 0-27.48 10-31.05 24.25L197.9 388.3L124.6 241.7C119.2 230.9 108.1 224 96 224L32 224c-17.67 0-32 14.31-32 31.1s14.33 32 32 32h44.22l103.2 206.3c5.469 10.91 16.6 17.68 28.61 17.68c1.172 0 2.323-.0576 3.495-.1826c13.31-1.469 24.31-11.06 27.56-24.06l105.9-423.8H544C561.7 64.01 576 49.7 576 32.01zM566.6 233.4c-12.5-12.5-32.75-12.5-45.25 0L480 274.8l-41.38-41.37c-12.5-12.5-32.75-12.5-45.25 0s-12.5 32.75 0 45.25l41.38 41.38l-41.38 41.38c-12.5 12.5-12.5 32.75 0 45.25C399.6 412.9 407.8 416 416 416s16.38-3.125 22.62-9.375L480 365.3l41.38 41.38C527.6 412.9 535.8 416 544 416s16.38-3.125 22.62-9.375c12.5-12.5 12.5-32.75 0-45.25l-41.38-41.38L566.6 278.6C579.1 266.1 579.1 245.9 566.6 233.4z"/></svg><span class="menu-item-name">数学</span></a>
|
||
</li>
|
||
|
||
|
||
|
||
<li class="menu-item"><a href="/408/"><svg class="icon 408" fill="none" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 576 512"><!--! Font Awesome Pro 6.1.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license (Commercial License) Copyright 2022 Fonticon 408s, Inc. --><path d="M172.1 40.16L268.1 3.76C280.9-1.089 295.1-1.089 307.9 3.76L403.9 40.16C425.6 48.41 440 69.25 440 92.52V204.7C441.3 205.1 442.6 205.5 443.9 205.1L539.9 242.4C561.6 250.6 576 271.5 576 294.7V413.9C576 436.1 562.9 456.2 542.5 465.1L446.5 507.3C432.2 513.7 415.8 513.7 401.5 507.3L288 457.5L174.5 507.3C160.2 513.7 143.8 513.7 129.5 507.3L33.46 465.1C13.13 456.2 0 436.1 0 413.9V294.7C0 271.5 14.39 250.6 36.15 242.4L132.1 205.1C133.4 205.5 134.7 205.1 136 204.7V92.52C136 69.25 150.4 48.41 172.1 40.16V40.16zM290.8 48.64C289 47.95 286.1 47.95 285.2 48.64L206.8 78.35L287.1 109.5L369.2 78.35L290.8 48.64zM392 210.6V121L309.6 152.6V241.8L392 210.6zM154.8 250.9C153 250.2 150.1 250.2 149.2 250.9L70.81 280.6L152 311.7L233.2 280.6L154.8 250.9zM173.6 455.3L256 419.1V323.2L173.6 354.8V455.3zM342.8 280.6L424 311.7L505.2 280.6L426.8 250.9C425 250.2 422.1 250.2 421.2 250.9L342.8 280.6zM528 413.9V323.2L445.6 354.8V455.3L523.2 421.2C526.1 419.9 528 417.1 528 413.9V413.9z"/></svg><span class="menu-item-name">408</span></a>
|
||
</li>
|
||
|
||
|
||
|
||
<li class="menu-item"><a href="/stuff/"><svg class="icon stuff" fill="none" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Pro 6.1.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license (Commercial License) Copyright 2022 Fonticon stuffs, Inc. --><path d="M216 104C202.8 104 192 114.8 192 128s10.75 24 24 24c79.41 0 144 64.59 144 144C360 309.3 370.8 320 384 320s24-10.75 24-24C408 190.1 321.9 104 216 104zM224 0C206.3 0 192 14.31 192 32s14.33 32 32 32c123.5 0 224 100.5 224 224c0 17.69 14.33 32 32 32s32-14.31 32-32C512 129.2 382.8 0 224 0zM188.9 346l27.37-27.37c2.625 .625 5.059 1.506 7.809 1.506c17.75 0 31.99-14.26 31.99-32c0-17.62-14.24-32.01-31.99-32.01c-17.62 0-31.99 14.38-31.99 32.01c0 2.875 .8099 5.25 1.56 7.875L166.2 323.4L49.37 206.5c-7.25-7.25-20.12-6-24.1 3c-41.75 77.88-29.88 176.7 35.75 242.4c65.62 65.62 164.6 77.5 242.4 35.75c9.125-5 10.38-17.75 3-25L188.9 346z"/></svg><span class="menu-item-name">杂物</span></a>
|
||
</li>
|
||
|
||
|
||
|
||
<li class="menu-item"><a href="/about/"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 496 512" class="icon user-circle"><path d="M248 8C111 8 0 119 0 256s111 248 248 248 248-111 248-248S385 8 248 8zm0 96c48.6 0 88 39.4 88 88s-39.4 88-88 88-88-39.4-88-88 39.4-88 88-88zm0 344c-58.7 0-111.3-26.6-146.5-68.2 18.8-35.4 55.6-59.8 98.5-59.8 2.4 0 4.8.4 7.1 1.1 13 4.2 26.6 6.9 40.9 6.9 14.3 0 28-2.7 40.9-6.9 2.3-.7 4.7-1.1 7.1-1.1 42.9 0 79.7 24.4 98.5 59.8C359.3 421.4 306.7 448 248 448z"/></svg><span class="menu-item-name">关于</span></a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="menu-item">
|
||
<a id="theme-switcher" href="#"><span class="icon theme-icon-light">🌞</span><span class="icon theme-icon-dark">🌙</span></a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
|
||
</div>
|
||
</div>
|
||
|
||
<input type="checkbox" id="nav-toggle" aria-hidden="true" />
|
||
<label for="nav-toggle" class="nav-toggle"></label>
|
||
<label for="nav-toggle" class="nav-curtain"></label>
|
||
|
||
|
||
|
||
</header>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<main class="main single" id="main">
|
||
<div class="main-inner">
|
||
|
||
|
||
|
||
<article class="content post h-entry" data-align="justify" data-type="computergraphic" data-toc-num="true">
|
||
|
||
<h1 class="post-title p-name">常用光照模型</h1>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<div class="post-body e-content">
|
||
<h4 id="着色shading"><a href="#着色shading" class="anchor-link"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon anchor-icon"><path d="M326.612 185.391c59.747 59.809 58.927 155.698.36 214.59-.11.12-.24.25-.36.37l-67.2 67.2c-59.27 59.27-155.699 59.262-214.96 0-59.27-59.26-59.27-155.7 0-214.96l37.106-37.106c9.84-9.84 26.786-3.3 27.294 10.606.648 17.722 3.826 35.527 9.69 52.721 1.986 5.822.567 12.262-3.783 16.612l-13.087 13.087c-28.026 28.026-28.905 73.66-1.155 101.96 28.024 28.579 74.086 28.749 102.325.51l67.2-67.19c28.191-28.191 28.073-73.757 0-101.83-3.701-3.694-7.429-6.564-10.341-8.569a16.037 16.037 0 0 1-6.947-12.606c-.396-10.567 3.348-21.456 11.698-29.806l21.054-21.055c5.521-5.521 14.182-6.199 20.584-1.731a152.482 152.482 0 0 1 20.522 17.197zM467.547 44.449c-59.261-59.262-155.69-59.27-214.96 0l-67.2 67.2c-.12.12-.25.25-.36.37-58.566 58.892-59.387 154.781.36 214.59a152.454 152.454 0 0 0 20.521 17.196c6.402 4.468 15.064 3.789 20.584-1.731l21.054-21.055c8.35-8.35 12.094-19.239 11.698-29.806a16.037 16.037 0 0 0-6.947-12.606c-2.912-2.005-6.64-4.875-10.341-8.569-28.073-28.073-28.191-73.639 0-101.83l67.2-67.19c28.239-28.239 74.3-28.069 102.325.51 27.75 28.3 26.872 73.934-1.155 101.96l-13.087 13.087c-4.35 4.35-5.769 10.79-3.783 16.612 5.864 17.194 9.042 34.999 9.69 52.721.509 13.906 17.454 20.446 27.294 10.606l37.106-37.106c59.271-59.259 59.271-155.699.001-214.959z"/></svg></a>着色(shading)</h4>
|
||
<p>着色往往是指向模型物体上色或添加材质特性的流程(不包含阴影的计算)</p>
|
||
<p>对于计算以某个点为反射点的反射向摄像机的光照，我们需要四个主要数据</p>
|
||
<ol>
|
||
<li>视线方向，v</li>
|
||
<li>模型表面法线，n</li>
|
||
<li>光线方向(许多光线中的一条)，l</li>
|
||
<li>模型表面性质(如，颜色，粗糙度等)</li>
|
||
</ol>
|
||
<p><img src="../../images/shading_light_caculate.png" alt=""></p>
|
||
<h4 id="blinn-phong"><a href="#blinn-phong" class="anchor-link"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon anchor-icon"><path d="M326.612 185.391c59.747 59.809 58.927 155.698.36 214.59-.11.12-.24.25-.36.37l-67.2 67.2c-59.27 59.27-155.699 59.262-214.96 0-59.27-59.26-59.27-155.7 0-214.96l37.106-37.106c9.84-9.84 26.786-3.3 27.294 10.606.648 17.722 3.826 35.527 9.69 52.721 1.986 5.822.567 12.262-3.783 16.612l-13.087 13.087c-28.026 28.026-28.905 73.66-1.155 101.96 28.024 28.579 74.086 28.749 102.325.51l67.2-67.19c28.191-28.191 28.073-73.757 0-101.83-3.701-3.694-7.429-6.564-10.341-8.569a16.037 16.037 0 0 1-6.947-12.606c-.396-10.567 3.348-21.456 11.698-29.806l21.054-21.055c5.521-5.521 14.182-6.199 20.584-1.731a152.482 152.482 0 0 1 20.522 17.197zM467.547 44.449c-59.261-59.262-155.69-59.27-214.96 0l-67.2 67.2c-.12.12-.25.25-.36.37-58.566 58.892-59.387 154.781.36 214.59a152.454 152.454 0 0 0 20.521 17.196c6.402 4.468 15.064 3.789 20.584-1.731l21.054-21.055c8.35-8.35 12.094-19.239 11.698-29.806a16.037 16.037 0 0 0-6.947-12.606c-2.912-2.005-6.64-4.875-10.341-8.569-28.073-28.073-28.191-73.639 0-101.83l67.2-67.19c28.239-28.239 74.3-28.069 102.325.51 27.75 28.3 26.872 73.934-1.155 101.96l-13.087 13.087c-4.35 4.35-5.769 10.79-3.783 16.612 5.864 17.194 9.042 34.999 9.69 52.721.509 13.906 17.454 20.446 27.294 10.606l37.106-37.106c59.271-59.259 59.271-155.699.001-214.959z"/></svg></a>blinn-phong</h4>
|
||
<p>在进一步计算时，我们先对效果进行分析，将效果拆分如下图为3个部分</p>
|
||
<p>分别为</p>
|
||
<ol>
|
||
<li>镜面反射高光（Specular highlights）：对于绝缘体而言其与高光对应，对于金属而言其与它本身的光对应</li>
|
||
<li>漫反射(diffuse reflection):来自于光在物体表面的散射现象</li>
|
||
<li>环境光(ambient lighting)：光在物体之间弹射，最终在整个环境中形成的一个基本光</li>
|
||
</ol>
|
||
<p><img src="../../images/light_separete.png" alt=""></p>
|
||
<p>由此可见，一个物体在渲染后体现的颜色是这三种光的总和，即每个位置的颜色就是specular+diffuse+ambient</p>
|
||
<h5 id="diffuse-reflection"><a href="#diffuse-reflection" class="anchor-link"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon anchor-icon"><path d="M326.612 185.391c59.747 59.809 58.927 155.698.36 214.59-.11.12-.24.25-.36.37l-67.2 67.2c-59.27 59.27-155.699 59.262-214.96 0-59.27-59.26-59.27-155.7 0-214.96l37.106-37.106c9.84-9.84 26.786-3.3 27.294 10.606.648 17.722 3.826 35.527 9.69 52.721 1.986 5.822.567 12.262-3.783 16.612l-13.087 13.087c-28.026 28.026-28.905 73.66-1.155 101.96 28.024 28.579 74.086 28.749 102.325.51l67.2-67.19c28.191-28.191 28.073-73.757 0-101.83-3.701-3.694-7.429-6.564-10.341-8.569a16.037 16.037 0 0 1-6.947-12.606c-.396-10.567 3.348-21.456 11.698-29.806l21.054-21.055c5.521-5.521 14.182-6.199 20.584-1.731a152.482 152.482 0 0 1 20.522 17.197zM467.547 44.449c-59.261-59.262-155.69-59.27-214.96 0l-67.2 67.2c-.12.12-.25.25-.36.37-58.566 58.892-59.387 154.781.36 214.59a152.454 152.454 0 0 0 20.521 17.196c6.402 4.468 15.064 3.789 20.584-1.731l21.054-21.055c8.35-8.35 12.094-19.239 11.698-29.806a16.037 16.037 0 0 0-6.947-12.606c-2.912-2.005-6.64-4.875-10.341-8.569-28.073-28.073-28.191-73.639 0-101.83l67.2-67.19c28.239-28.239 74.3-28.069 102.325.51 27.75 28.3 26.872 73.934-1.155 101.96l-13.087 13.087c-4.35 4.35-5.769 10.79-3.783 16.612 5.864 17.194 9.042 34.999 9.69 52.721.509 13.906 17.454 20.446 27.294 10.606l37.106-37.106c59.271-59.259 59.271-155.699.001-214.959z"/></svg></a>Diffuse Reflection</h5>
|
||
<p>在计算漫反射时我们要考虑反射点接收了多少能量从而判断高光的亮度大小</p>
|
||
<p>根据lambert's cosine law,反射点吸收能量的多少与反射点法线和光线的夹角有关,即如图中表现的$\cos{\theta}=l\cdot n$</p>
|
||
<p><img src="../../images/lambert'scosine_low.png" alt=""></p>
|
||
<p>由此我们可以将漫反射总结为如下公式(lambertian Shading)</p>
|
||
<p>$L_d=k_d(I/r^2)max(0,n\cdot l)$</p>
|
||
<ol>
|
||
<li>$L_d$ : 我们想要的反射光线</li>
|
||
<li>$k_d$ : 漫反射系数</li>
|
||
<li>$(I/r^2)$ :到达反射点的能量值</li>
|
||
<li>$max(0,n\cdot l)$ : 反射点接收的能量值</li>
|
||
</ol>
|
||
<h5 id="specular-term高光"><a href="#specular-term高光" class="anchor-link"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon anchor-icon"><path d="M326.612 185.391c59.747 59.809 58.927 155.698.36 214.59-.11.12-.24.25-.36.37l-67.2 67.2c-59.27 59.27-155.699 59.262-214.96 0-59.27-59.26-59.27-155.7 0-214.96l37.106-37.106c9.84-9.84 26.786-3.3 27.294 10.606.648 17.722 3.826 35.527 9.69 52.721 1.986 5.822.567 12.262-3.783 16.612l-13.087 13.087c-28.026 28.026-28.905 73.66-1.155 101.96 28.024 28.579 74.086 28.749 102.325.51l67.2-67.19c28.191-28.191 28.073-73.757 0-101.83-3.701-3.694-7.429-6.564-10.341-8.569a16.037 16.037 0 0 1-6.947-12.606c-.396-10.567 3.348-21.456 11.698-29.806l21.054-21.055c5.521-5.521 14.182-6.199 20.584-1.731a152.482 152.482 0 0 1 20.522 17.197zM467.547 44.449c-59.261-59.262-155.69-59.27-214.96 0l-67.2 67.2c-.12.12-.25.25-.36.37-58.566 58.892-59.387 154.781.36 214.59a152.454 152.454 0 0 0 20.521 17.196c6.402 4.468 15.064 3.789 20.584-1.731l21.054-21.055c8.35-8.35 12.094-19.239 11.698-29.806a16.037 16.037 0 0 0-6.947-12.606c-2.912-2.005-6.64-4.875-10.341-8.569-28.073-28.073-28.191-73.639 0-101.83l67.2-67.19c28.239-28.239 74.3-28.069 102.325.51 27.75 28.3 26.872 73.934-1.155 101.96l-13.087 13.087c-4.35 4.35-5.769 10.79-3.783 16.612 5.864 17.194 9.042 34.999 9.69 52.721.509 13.906 17.454 20.446 27.294 10.606l37.106-37.106c59.271-59.259 59.271-155.699.001-214.959z"/></svg></a>Specular Term(高光)</h5>
|
||
<p>高光(Specular)指的是视线在一定的角度区域观看模型表面时会产生一个类似镜面反射的效果</p>
|
||
<p><img src="../../images/Specular_show.png" alt=""></p>
|
||
<p>如图中黄色区域为可见高光的视线范围</p>
|
||
<p>计算过程中需要引入一个半程向量(光线与视线夹角一半方向上的一个单位向量，半程向量与法线向量越接近，镜面反射强度越高)</p>
|
||
<p>$$ h=bisector(v,l) = \frac{v+l}{ || v+l || } $$</p>
|
||
<p>$$L_s=k_s(I/r^2)max(0,\cos \alpha)^p$$
|
||
$$\quad =k_s(I/r^2)max(0,n \cdot h)^p$$</p>
|
||
<p><img src="../../images/specular_cacular.png" alt=""></p>
|
||
<p>$ k_s $ : 镜面反射系数
|
||
$ p $ : 高光的面积，P越大高光面积越小
|
||
$ L_s $ : 计算的高光效果光线</p>
|
||
<p>高光的效果和范围大小与$k_s$和p有关，下图展示了变化效果</p>
|
||
<p><img src="../../images/specular_value_change_show.png" alt=""></p>
|
||
<h5 id="ambient-term-环境光"><a href="#ambient-term-环境光" class="anchor-link"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon anchor-icon"><path d="M326.612 185.391c59.747 59.809 58.927 155.698.36 214.59-.11.12-.24.25-.36.37l-67.2 67.2c-59.27 59.27-155.699 59.262-214.96 0-59.27-59.26-59.27-155.7 0-214.96l37.106-37.106c9.84-9.84 26.786-3.3 27.294 10.606.648 17.722 3.826 35.527 9.69 52.721 1.986 5.822.567 12.262-3.783 16.612l-13.087 13.087c-28.026 28.026-28.905 73.66-1.155 101.96 28.024 28.579 74.086 28.749 102.325.51l67.2-67.19c28.191-28.191 28.073-73.757 0-101.83-3.701-3.694-7.429-6.564-10.341-8.569a16.037 16.037 0 0 1-6.947-12.606c-.396-10.567 3.348-21.456 11.698-29.806l21.054-21.055c5.521-5.521 14.182-6.199 20.584-1.731a152.482 152.482 0 0 1 20.522 17.197zM467.547 44.449c-59.261-59.262-155.69-59.27-214.96 0l-67.2 67.2c-.12.12-.25.25-.36.37-58.566 58.892-59.387 154.781.36 214.59a152.454 152.454 0 0 0 20.521 17.196c6.402 4.468 15.064 3.789 20.584-1.731l21.054-21.055c8.35-8.35 12.094-19.239 11.698-29.806a16.037 16.037 0 0 0-6.947-12.606c-2.912-2.005-6.64-4.875-10.341-8.569-28.073-28.073-28.191-73.639 0-101.83l67.2-67.19c28.239-28.239 74.3-28.069 102.325.51 27.75 28.3 26.872 73.934-1.155 101.96l-13.087 13.087c-4.35 4.35-5.769 10.79-3.783 16.612 5.864 17.194 9.042 34.999 9.69 52.721.509 13.906 17.454 20.446 27.294 10.606l37.106-37.106c59.271-59.259 59.271-155.699.001-214.959z"/></svg></a>ambient Term (环境光)</h5>
|
||
<p>任何物体都可以反射光，这使得光在多个物体间弹射，最终会在环境中形成一个最基本的光，通常会被视为常量</p>
|
||
<p>！这是一个近似的效果(不符合物理)</p>
|
||
<p>$$L_a=k_a I_a$$</p>
|
||
<p>$k_a$ : 环境光系数，确定当前环境的底色</p>
|
||
<h5 id="blinn-phong-reflection-model"><a href="#blinn-phong-reflection-model" class="anchor-link"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon anchor-icon"><path d="M326.612 185.391c59.747 59.809 58.927 155.698.36 214.59-.11.12-.24.25-.36.37l-67.2 67.2c-59.27 59.27-155.699 59.262-214.96 0-59.27-59.26-59.27-155.7 0-214.96l37.106-37.106c9.84-9.84 26.786-3.3 27.294 10.606.648 17.722 3.826 35.527 9.69 52.721 1.986 5.822.567 12.262-3.783 16.612l-13.087 13.087c-28.026 28.026-28.905 73.66-1.155 101.96 28.024 28.579 74.086 28.749 102.325.51l67.2-67.19c28.191-28.191 28.073-73.757 0-101.83-3.701-3.694-7.429-6.564-10.341-8.569a16.037 16.037 0 0 1-6.947-12.606c-.396-10.567 3.348-21.456 11.698-29.806l21.054-21.055c5.521-5.521 14.182-6.199 20.584-1.731a152.482 152.482 0 0 1 20.522 17.197zM467.547 44.449c-59.261-59.262-155.69-59.27-214.96 0l-67.2 67.2c-.12.12-.25.25-.36.37-58.566 58.892-59.387 154.781.36 214.59a152.454 152.454 0 0 0 20.521 17.196c6.402 4.468 15.064 3.789 20.584-1.731l21.054-21.055c8.35-8.35 12.094-19.239 11.698-29.806a16.037 16.037 0 0 0-6.947-12.606c-2.912-2.005-6.64-4.875-10.341-8.569-28.073-28.073-28.191-73.639 0-101.83l67.2-67.19c28.239-28.239 74.3-28.069 102.325.51 27.75 28.3 26.872 73.934-1.155 101.96l-13.087 13.087c-4.35 4.35-5.769 10.79-3.783 16.612 5.864 17.194 9.042 34.999 9.69 52.721.509 13.906 17.454 20.446 27.294 10.606l37.106-37.106c59.271-59.259 59.271-155.699.001-214.959z"/></svg></a>Blinn-phong Reflection Model</h5>
|
||
<p><img src="../../images/blinn-phong_model_cacu.png" alt=""></p>
|
||
<p>$$L = L_a + L_d + L_s $$
|
||
$$\quad = k_aI_a+k_d(I/r^2)max(0,n\cdot l)+k_s(I/r^2)max(0,n\cdot h)^p$$</p>
|
||
<p>当然这种方式会产生严重的塑料感，这种感觉可以通过调整参数来减少或避免，下次再述(挖坑)</p>
|
||
<hr>
|
||
<h4 id="渲染序列"><a href="#渲染序列" class="anchor-link"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon anchor-icon"><path d="M326.612 185.391c59.747 59.809 58.927 155.698.36 214.59-.11.12-.24.25-.36.37l-67.2 67.2c-59.27 59.27-155.699 59.262-214.96 0-59.27-59.26-59.27-155.7 0-214.96l37.106-37.106c9.84-9.84 26.786-3.3 27.294 10.606.648 17.722 3.826 35.527 9.69 52.721 1.986 5.822.567 12.262-3.783 16.612l-13.087 13.087c-28.026 28.026-28.905 73.66-1.155 101.96 28.024 28.579 74.086 28.749 102.325.51l67.2-67.19c28.191-28.191 28.073-73.757 0-101.83-3.701-3.694-7.429-6.564-10.341-8.569a16.037 16.037 0 0 1-6.947-12.606c-.396-10.567 3.348-21.456 11.698-29.806l21.054-21.055c5.521-5.521 14.182-6.199 20.584-1.731a152.482 152.482 0 0 1 20.522 17.197zM467.547 44.449c-59.261-59.262-155.69-59.27-214.96 0l-67.2 67.2c-.12.12-.25.25-.36.37-58.566 58.892-59.387 154.781.36 214.59a152.454 152.454 0 0 0 20.521 17.196c6.402 4.468 15.064 3.789 20.584-1.731l21.054-21.055c8.35-8.35 12.094-19.239 11.698-29.806a16.037 16.037 0 0 0-6.947-12.606c-2.912-2.005-6.64-4.875-10.341-8.569-28.073-28.073-28.191-73.639 0-101.83l67.2-67.19c28.239-28.239 74.3-28.069 102.325.51 27.75 28.3 26.872 73.934-1.155 101.96l-13.087 13.087c-4.35 4.35-5.769 10.79-3.783 16.612 5.864 17.194 9.042 34.999 9.69 52.721.509 13.906 17.454 20.446 27.294 10.606l37.106-37.106c59.271-59.259 59.271-155.699.001-214.959z"/></svg></a>渲染序列</h4>
|
||
<p>渲染序列可以分为三种：</p>
|
||
<p>逐三角渲染（flat shading）</p>
|
||
<ol>
|
||
<li>三角形面或一个法线向量视为是一个平面</li>
|
||
<li>对平滑表面的表现力不友好</li>
|
||
</ol>
|
||
<p><img src="../../images/flat_shading.png" alt=""></p>
|
||
<p>逐顶点渲染（Gouraud shading）</p>
|
||
<ol>
|
||
<li>根据三角形顶点对颜色进行插值计算</li>
|
||
<li>每一个顶点都有一个法线向量</li>
|
||
</ol>
|
||
<p><img src="../../images/Gourand_shading.png" alt=""></p>
|
||
<ol>
|
||
<li>如何获取逐顶点的法线向量
|
||
<ol>
|
||
<li>对于标准的几何图形：顶点的法线向量就在顶点位置</li>
|
||
<li>对于非标准的几何图形：包含该顶点的周围几个表面的法线取平均值,可由计算公式$$ N_v=\frac{\sum_{i}N_i}{\lVert \sum_{i}N_i \rVert}$$ 得到</li>
|
||
</ol>
|
||
</li>
|
||
</ol>
|
||
<p><img src="../../images/average_normal.png" alt=""></p>
|
||
<p>逐像素渲染（phong shading）</p>
|
||
<ol>
|
||
<li>对每一个三角形的法线向量插值(Barycentric interpolation)</li>
|
||
<li>对每一个像素计算完整的渲染模型</li>
|
||
<li>注意：非Blinn-Phong反射模型</li>
|
||
</ol>
|
||
<p><img src="../../images/phong_shading.png" alt=""></p>
|
||
<hr>
|
||
|
||
</div>
|
||
|
||
|
||
|
||
|
||
</article>
|
||
|
||
|
||
|
||
|
||
<div class="updated-badge-container">
|
||
<span title="Updated @ 2023-06-18 21:19:01 CST" style="cursor:help">
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" width="130" height="20" class="updated-badge"><linearGradient id="b" x2="0" y2="100%"><stop offset="0" stop-color="#bbb" stop-opacity=".1"/><stop offset="1" stop-opacity=".1"/></linearGradient><clipPath id="a"><rect width="130" height="20" rx="3" fill="#fff"/></clipPath><g clip-path="url(#a)"><path class="updated-badge-left" d="M0 0h55v20H0z"/><path class="updated-badge-right" d="M55 0h75v20H55z"/><path fill="url(#b)" d="M0 0h130v20H0z"/></g><g fill="#fff" text-anchor="middle" font-size="110"><text x="285" y="150" fill="#010101" fill-opacity=".3" textLength="450" transform="scale(.1)">updated</text><text x="285" y="140" textLength="450" transform="scale(.1)">updated</text><text x="915" y="150" fill="#010101" fill-opacity=".3" textLength="650" transform="scale(.1)">2023-06-18</text><text x="915" y="140" textLength="650" transform="scale(.1)">2023-06-18</text></g></svg>
|
||
</span></div>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<ul class="post-nav">
|
||
|
||
<li class="post-nav-prev">
|
||
<a href="/computergraphic/%E7%BA%B9%E7%90%86/" rel="prev">< 纹理</a>
|
||
</li>
|
||
|
||
|
||
<li class="post-nav-next">
|
||
<a href="/computergraphic/z-buffer_%E6%B7%B1%E5%BA%A6%E7%BC%93%E5%AD%98/" rel="next">Z-Buffer 深度缓存 ></a>
|
||
</li>
|
||
|
||
</ul>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
</div>
|
||
</main>
|
||
|
||
|
||
|
||
<div id="back-to-top" class="back-to-top">
|
||
<a href="#"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 448 512" class="icon arrow-up"><path d="M34.9 289.5l-22.2-22.2c-9.4-9.4-9.4-24.6 0-33.9L207 39c9.4-9.4 24.6-9.4 33.9 0l194.3 194.3c9.4 9.4 9.4 24.6 0 33.9L413 289.4c-9.5 9.5-25 9.3-34.3-.4L264 168.6V456c0 13.3-10.7 24-24 24h-32c-13.3 0-24-10.7-24-24V168.6L69.2 289.1c-9.3 9.8-24.8 10-34.3.4z"/></svg></a>
|
||
</div>
|
||
|
||
|
||
|
||
<footer id="footer" class="footer">
|
||
<div class="footer-inner">
|
||
<div class="site-info">© 2022–2023 <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon footer-icon"><path d="M462.3 62.6C407.5 15.9 326 24.3 275.7 76.2L256 96.5l-19.7-20.3C186.1 24.3 104.5 15.9 49.7 62.6c-62.8 53.6-66.1 149.8-9.9 207.9l193.5 199.8c12.5 12.9 32.8 12.9 45.3 0l193.5-199.8c56.3-58.1 53-154.3-9.8-207.9z"/></svg> InkSoul</div><div class="powered-by">Powered by <a href="https://github.com/gohugoio/hugo" target="_blank" rel="noopener">Hugo</a> | Theme is <a href="https://github.com/reuixiy/hugo-theme-meme" target="_blank" rel="noopener">MemE</a></div><div class="site-copyright"><a href="https://creativecommons.org/licenses/by-nc-sa/4.0/deed.zh" target="_blank" rel="noopener">CC BY-NC-SA 4.0</a></div><div class="custom-footer"><a href="https://beian.miit.gov.cn" target="_blank" rel="noopener">闽ICP备2022009452号-1</a></div>
|
||
|
||
|
||
|
||
<ul class="socials"><li class="socials-item">
|
||
<a href="mailto:qingci30@163.com" target="_blank" rel="external noopener" title="Email"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon social-icon"><path d="M464 64H48C21.49 64 0 85.49 0 112v288c0 26.51 21.49 48 48 48h416c26.51 0 48-21.49 48-48V112c0-26.51-21.49-48-48-48zm0 48v40.805c-22.422 18.259-58.168 46.651-134.587 106.49-16.841 13.247-50.201 45.072-73.413 44.701-23.208.375-56.579-31.459-73.413-44.701C106.18 199.465 70.425 171.067 48 152.805V112h416zM48 400V214.398c22.914 18.251 55.409 43.862 104.938 82.646 21.857 17.205 60.134 55.186 103.062 54.955 42.717.231 80.509-37.199 103.053-54.947 49.528-38.783 82.032-64.401 104.947-82.653V400H48z"/></svg></a>
|
||
</li><li class="socials-item">
|
||
<a href="https://github.com/ink-soul" target="_blank" rel="external noopener" title="GitHub"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" class="icon social-icon"><path d="M12 .297c-6.63 0-12 5.373-12 12 0 5.303 3.438 9.8 8.205 11.385.6.113.82-.258.82-.577 0-.285-.01-1.04-.015-2.04-3.338.724-4.042-1.61-4.042-1.61C4.422 18.07 3.633 17.7 3.633 17.7c-1.087-.744.084-.729.084-.729 1.205.084 1.838 1.236 1.838 1.236 1.07 1.835 2.809 1.305 3.495.998.108-.776.417-1.305.76-1.605-2.665-.3-5.466-1.332-5.466-5.93 0-1.31.465-2.38 1.235-3.22-.135-.303-.54-1.523.105-3.176 0 0 1.005-.322 3.3 1.23.96-.267 1.98-.399 3-.405 1.02.006 2.04.138 3 .405 2.28-1.552 3.285-1.23 3.285-1.23.645 1.653.24 2.873.12 3.176.765.84 1.23 1.91 1.23 3.22 0 4.61-2.805 5.625-5.475 5.92.42.36.81 1.096.81 2.22 0 1.606-.015 2.896-.015 3.286 0 .315.21.69.825.57C20.565 22.092 24 17.592 24 12.297c0-6.627-5.373-12-12-12"/></svg></a>
|
||
</li><li class="socials-item">
|
||
<a href="http://gitea.inksoul.top/inksoul" target="_blank" rel="external noopener" title="gitea"><svg class="icon social-icon" fill="none" viewBox="0 0 24 24" xmlns="http://www.w3.org/2000/svg"><path d="M4.209 4.603c-.247 0-.525.02-.84.088-.333.07-1.28.283-2.054 1.027C-.403 7.25.035 9.685.089 10.052c.065.446.263 1.687 1.21 2.768 1.749 2.141 5.513 2.092 5.513 2.092s.462 1.103 1.168 2.119c.955 1.263 1.936 2.248 2.89 2.367 2.406 0 7.212-.004 7.212-.004s.458.004 1.08-.394c.535-.324 1.013-.893 1.013-.893s.492-.527 1.18-1.73c.21-.37.385-.729.538-1.068 0 0 2.107-4.471 2.107-8.823-.042-1.318-.367-1.55-.443-1.627-.156-.156-.366-.153-.366-.153s-4.475.252-6.792.306c-.508.011-1.012.023-1.512.027v4.474l-.634-.301c0-1.39-.004-4.17-.004-4.17-1.107.016-3.405-.084-3.405-.084s-5.399-.27-5.987-.324c-.187-.011-.401-.032-.648-.032zm.354 1.832h.111s.271 2.269.6 3.597C5.549 11.147 6.22 13 6.22 13s-.996-.119-1.641-.348c-.99-.324-1.409-.714-1.409-.714s-.73-.511-1.096-1.52C1.444 8.73 2.021 7.7 2.021 7.7s.32-.859 1.47-1.145c.395-.106.863-.12 1.072-.12zm8.33 2.554c.26.003.509.127.509.127l.868.422-.529 1.075a.686.686 0 0 0-.614.359.685.685 0 0 0 .072.756l-.939 1.924a.69.69 0 0 0-.66.527.687.687 0 0 0 .347.763.686.686 0 0 0 .867-.206.688.688 0 0 0-.069-.882l.916-1.874a.667.667 0 0 0 .237-.02.657.657 0 0 0 .271-.137 8.826 8.826 0 0 1 1.016.512.761.761 0 0 1 .286.282c.073.21-.073.569-.073.569-.087.29-.702 1.55-.702 1.55a.692.692 0 0 0-.676.477.681.681 0 1 0 1.157-.252c.073-.141.141-.282.214-.431.19-.397.515-1.16.515-1.16.035-.066.218-.394.103-.814-.095-.435-.48-.638-.48-.638-.467-.301-1.116-.58-1.116-.58s0-.156-.042-.27a.688.688 0 0 0-.148-.241l.516-1.062 2.89 1.401s.48.218.583.619c.073.282-.019.534-.069.657-.24.587-2.1 4.317-2.1 4.317s-.232.554-.748.588a1.065 1.065 0 0 1-.393-.045l-.202-.08-4.31-2.1s-.417-.218-.49-.596c-.083-.31.104-.691.104-.691l2.073-4.272s.183-.37.466-.497a.855.855 0 0 1 .35-.077z" ></path></svg></a>
|
||
</li><li class="socials-item">
|
||
<a href="https://space.bilibili.com/262369930" target="_blank" rel="external noopener" title="bilibili"><svg class="icon social-icon" viewBox="0 0 24 24" xmlns="http://www.w3.org/2000/svg"><path d="M17.813 4.653h.854c1.51.054 2.769.578 3.773 1.574 1.004.995 1.524 2.249 1.56 3.76v7.36c-.036 1.51-.556 2.769-1.56 3.773s-2.262 1.524-3.773 1.56H5.333c-1.51-.036-2.769-.556-3.773-1.56S.036 18.858 0 17.347v-7.36c.036-1.511.556-2.765 1.56-3.76 1.004-.996 2.262-1.52 3.773-1.574h.774l-1.174-1.12a1.234 1.234 0 0 1-.373-.906c0-.356.124-.658.373-.907l.027-.027c.267-.249.573-.373.92-.373.347 0 .653.124.92.373L9.653 4.44c.071.071.134.142.187.213h4.267a.836.836 0 0 1 .16-.213l2.853-2.747c.267-.249.573-.373.92-.373.347 0 .662.151.929.4.267.249.391.551.391.907 0 .355-.124.657-.373.906zM5.333 7.24c-.746.018-1.373.276-1.88.773-.506.498-.769 1.13-.786 1.894v7.52c.017.764.28 1.395.786 1.893.507.498 1.134.756 1.88.773h13.334c.746-.017 1.373-.275 1.88-.773.506-.498.769-1.129.786-1.893v-7.52c-.017-.765-.28-1.396-.786-1.894-.507-.497-1.134-.755-1.88-.773zM8 11.107c.373 0 .684.124.933.373.25.249.383.569.4.96v1.173c-.017.391-.15.711-.4.96-.249.25-.56.374-.933.374s-.684-.125-.933-.374c-.25-.249-.383-.569-.4-.96V12.44c0-.373.129-.689.386-.947.258-.257.574-.386.947-.386zm8 0c.373 0 .684.124.933.373.25.249.383.569.4.96v1.173c-.017.391-.15.711-.4.96-.249.25-.56.374-.933.374s-.684-.125-.933-.374c-.25-.249-.383-.569-.4-.96V12.44c.017-.391.15-.711.4-.96.249-.249.56-.373.933-.373Z"/></svg></a>
|
||
</li></ul>
|
||
|
||
|
||
|
||
|
||
|
||
</div>
|
||
</footer>
|
||
|
||
|
||
</div>
|
||
<script>
|
||
if ('serviceWorker' in navigator) {
|
||
window.addEventListener('load', function() {
|
||
navigator.serviceWorker.register('\/sw.js');
|
||
});
|
||
}
|
||
</script>
|
||
|
||
|
||
|
||
<link rel="stylesheet" href="https://fastly.jsdelivr.net/npm/katex@0.13.0/dist/katex.min.css" integrity="sha256-gPJfuwTULrEAAcI3X4bALVU/2qBU+QY/TpoD3GO+Exw=" crossorigin="anonymous">
|
||
|
||
<script>
|
||
if (typeof renderMathInElement === 'undefined') {
|
||
var getScript = (options) => {
|
||
var script = document.createElement('script');
|
||
script.defer = true;
|
||
script.crossOrigin = 'anonymous';
|
||
Object.keys(options).forEach((key) => {
|
||
script[key] = options[key];
|
||
});
|
||
document.body.appendChild(script);
|
||
};
|
||
getScript({
|
||
src: 'https:\/\/fastly.jsdelivr.net/npm/katex@0.13.0/dist/katex.min.js',
|
||
integrity: 'sha256-YTW9cMncW/ZQMhY69KaUxIa2cPTxV87Uh627Gf5ODUw=',
|
||
onload: () => {
|
||
getScript({
|
||
src: 'https:\/\/fastly.jsdelivr.net/npm/katex@0.13.0/dist/contrib/mhchem.min.js',
|
||
integrity: 'sha256-yzSfYeVsWJ1x+2g8CYHsB/Mn7PcSp8122k5BM4T3Vxw=',
|
||
onload: () => {
|
||
getScript({
|
||
src: 'https:\/\/fastly.jsdelivr.net/npm/katex@0.13.0/dist/contrib/auto-render.min.js',
|
||
integrity: 'sha256-fxJzNV6hpc8tgW8tF0zVobKa71eTCRGTgxFXt1ZpJNM=',
|
||
onload: () => {
|
||
renderKaTex();
|
||
}
|
||
});
|
||
}
|
||
});
|
||
}
|
||
});
|
||
} else {
|
||
renderKaTex();
|
||
}
|
||
function renderKaTex() {
|
||
renderMathInElement(
|
||
document.body,
|
||
{
|
||
delimiters: [
|
||
{left: "$$", right: "$$", display: true},
|
||
{left: "\\[", right: "\\]", display: true},
|
||
{left: "$", right: "$", display: false},
|
||
{left: "\\(", right: "\\)", display: false}
|
||
]
|
||
}
|
||
);
|
||
}
|
||
</script>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<script src="https://fastly.jsdelivr.net/npm/medium-zoom@latest/dist/medium-zoom.min.js"></script>
|
||
|
||
<script>
|
||
let imgNodes = document.querySelectorAll('div.post-body img');
|
||
imgNodes = Array.from(imgNodes).filter(node => node.parentNode.tagName !== "A");
|
||
|
||
mediumZoom(imgNodes, {
|
||
background: 'hsla(var(--color-bg-h), var(--color-bg-s), var(--color-bg-l), 0.95)'
|
||
})
|
||
</script>
|
||
|
||
|
||
|
||
|
||
<script src="https://fastly.jsdelivr.net/npm/instant.page@5.1.0/instantpage.min.js" type="module" defer></script>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
</body>
|
||
</html>
|