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<!DOCTYPE html>
<html lang="zh-CN">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<!-- ============================================
SEO Meta 标签
============================================ -->
<title>MathMate 技术详解 | Flutter + AI | 几何可视化引擎</title>
<meta name="description" content="深入剖析 MathMate 的技术架构：Flutter 跨平台、多 AI 模型协作（DeepSeek、火山引擎、Qwen）、自研几何可视化引擎、GeoGebra 集成、60fps Canvas 渲染。">
<meta name="keywords" content="MathMate技术,Flutter,DeepSeek,AI数学,几何引擎,Canvas渲染,技术架构,开源项目">
<meta name="author" content="AK完全队">
<meta name="robots" content="index, follow">
<!-- Open Graph -->
<meta property="og:type" content="article">
<meta property="og:url" content="https://mathmate.top/tech.html">
<meta property="og:title" content="MathMate 技术详解">
<meta property="og:description" content="Flutter + AI 驱动的智能数学学习应用技术架构">
<meta property="og:image" content="https://mathmate.top/images/architecture.png">
<!-- Canonical URL -->
<link rel="canonical" href="https://mathmate.top/tech.html">
<!-- Favicon -->
<link rel="icon" type="image/png" href="/icon.png">
<link rel="apple-touch-icon" href="/icon.png">
<link rel="icon" type="image/svg+xml" href="/favicon.svg">
<style>
@import url('https://fonts.googleapis.com/css2?family=JetBrains+Mono:wght@400;500;600;700&display=swap');
:root {
--primary: #6C5CE7;
--primary-light: #A29BFE;
--primary-dark: #5A4BD1;
--accent: #00CEC9;
--accent-light: #81ECEC;
--gradient-1: linear-gradient(135deg, #6C5CE7 0%, #A29BFE 50%, #00CEC9 100%);
--gradient-2: linear-gradient(135deg, #667eea 0%, #764ba2 100%);
--gradient-3: linear-gradient(135deg, #00CEC9 0%, #6C5CE7 100%);
--bg: #0F0F1A;
--bg-card: #1A1A2E;
--bg-card-hover: #222240;
--text: #E8E8F0;
--text-secondary: #A0A0C0;
--border: rgba(108, 92, 231, 0.2);
--shadow: 0 8px 32px rgba(0, 0, 0, 0.3);
--radius: 16px;
--font-mono: 'JetBrains Mono', 'Cascadia Code', 'Fira Code', monospace;
}
* { margin: 0; padding: 0; box-sizing: border-box; }
html { scroll-behavior: smooth; }
body {
font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, 'PingFang SC', 'Microsoft YaHei', sans-serif;
background: var(--bg); color: var(--text); line-height: 1.7; overflow-x: hidden;
}
/* ===== Reading Progress Bar ===== */
.reading-progress {
position: fixed; top: 0; left: 0; height: 3px; z-index: 200;
background: var(--gradient-1); width: 0%; transition: width 0.1s linear;
}
/* ===== Matrix Grid Background ===== */
.matrix-bg {
position: fixed; inset: 0; pointer-events: none; z-index: 0; opacity: 0.03;
background-image:
linear-gradient(rgba(108,92,231,0.4) 1px, transparent 1px),
linear-gradient(90deg, rgba(108,92,231,0.4) 1px, transparent 1px);
background-size: 60px 60px;
}
/* ===== Floating Symbols ===== */
.floating-symbols {
position: fixed; inset: 0; pointer-events: none; z-index: 0; overflow: hidden;
}
.float-sym {
position: absolute; font-family: var(--font-mono); color: rgba(108,92,231,0.07);
animation: symbolDrift linear infinite; font-size: 14px; user-select: none;
}
@keyframes symbolDrift {
0% { transform: translateY(100vh) rotate(0deg); opacity: 0; }
10% { opacity: 1; }
90% { opacity: 1; }
100% { transform: translateY(-100px) rotate(360deg); opacity: 0; }
}
/* ===== Cursor Glow ===== */
.cursor-glow {
position: fixed; pointer-events: none; z-index: 998;
width: 300px; height: 300px; border-radius: 50%;
background: radial-gradient(circle, rgba(108,92,231,0.06) 0%, rgba(0,206,201,0.03) 40%, transparent 70%);
transform: translate(-50%, -50%);
transition: left 0.08s ease-out, top 0.08s ease-out;
}
/* ===== Nav ===== */
nav {
position: fixed; top: 0; left: 0; right: 0; z-index: 100;
padding: 0.8rem 2rem; display: flex; justify-content: space-between; align-items: center;
backdrop-filter: blur(20px); background: rgba(15,15,26,0.85);
border-bottom: 1px solid var(--border); transition: all 0.3s;
}
nav.scrolled { padding: 0.5rem 2rem; background: rgba(15,15,26,0.95); }
.nav-logo {
display: flex; align-items: center; gap: 0.75rem; font-size: 1.3rem; font-weight: 700;
background: var(--gradient-1); -webkit-background-clip: text; -webkit-text-fill-color: transparent; text-decoration: none;
}
.nav-logo svg { width: 30px; height: 30px; }
.nav-links { display: flex; gap: 1.5rem; list-style: none; flex-wrap: wrap; }
.nav-links a {
color: var(--text-secondary); text-decoration: none; font-size: 0.88rem; transition: color 0.3s; position: relative;
}
.nav-links a:hover { color: var(--primary-light); }
.nav-links a::after {
content: ''; position: absolute; bottom: -4px; left: 0; width: 0; height: 2px;
background: var(--gradient-1); transition: width 0.3s; border-radius: 1px;
}
.nav-links a:hover::after { width: 100%; }
.nav-back {
display: flex; align-items: center; gap: 0.5rem; padding: 0.45rem 1rem;
background: var(--bg-card); border: 1px solid var(--border); border-radius: 8px;
color: var(--text); text-decoration: none; font-size: 0.85rem; transition: all 0.3s;
}
.nav-back:hover { border-color: var(--primary); background: var(--bg-card-hover); }
/* ===== Section Common ===== */
.section { padding: 5rem 2rem; position: relative; }
.section-bg-glow {
position: absolute; inset: 0;
background: linear-gradient(180deg, transparent, rgba(108,92,231,0.03), transparent);
pointer-events: none;
}
.container { max-width: 1100px; margin: 0 auto; position: relative; }
.section-header { text-align: center; margin-bottom: 1rem; }
.section-label {
display: inline-block; font-size: 0.78rem; font-weight: 600; color: var(--accent);
text-transform: uppercase; letter-spacing: 0.1em; margin-bottom: 0.6rem;
}
.section-header h2 { font-size: clamp(1.7rem, 3.5vw, 2.3rem); font-weight: 700; margin-bottom: 0.8rem; }
.section-header p { color: var(--text-secondary); max-width: 620px; margin: 0 auto; font-size: 0.95rem; }
/* ===== Hero ===== */
.tech-hero {
min-height: 55vh; display: flex; align-items: center; justify-content: center;
text-align: center; padding: 7rem 2rem 3rem; position: relative; overflow: hidden;
}
.tech-hero::before {
content: ''; position: absolute; top: -50%; left: -50%; width: 200%; height: 200%;
background:
radial-gradient(circle at 25% 40%, rgba(108,92,231,0.1) 0%, transparent 40%),
radial-gradient(circle at 75% 60%, rgba(0,206,201,0.08) 0%, transparent 40%),
radial-gradient(circle at 50% 50%, rgba(108,92,231,0.04) 0%, transparent 60%);
animation: heroFloat 20s ease-in-out infinite;
}
.tech-hero::after {
content: ''; position: absolute; inset: 0;
background: repeating-linear-gradient(
0deg, transparent, transparent 2px, rgba(108,92,231,0.015) 2px, rgba(108,92,231,0.015) 4px
);
pointer-events: none; animation: scanlines 8s linear infinite;
}
@keyframes scanlines { 0%{transform:translateY(0)} 100%{transform:translateY(4px)} }
@keyframes heroFloat { 0%,100%{transform:translate(0,0)} 50%{transform:translate(-2%,-2%)} }
.tech-hero-content { position: relative; z-index: 1; max-width: 750px; }
.tech-hero h1 { font-size: clamp(2rem, 5vw, 3.2rem); font-weight: 800; line-height: 1.15; margin-bottom: 1rem; }
.tech-hero h1 .gradient-text { background: var(--gradient-1); -webkit-background-clip: text; -webkit-text-fill-color: transparent; background-clip: text; }
.tech-hero p { font-size: 1.1rem; color: var(--text-secondary); max-width: 600px; margin: 0 auto 1.5rem; line-height: 1.8; }
.tech-hero-links { display: flex; gap: 1rem; justify-content: center; flex-wrap: wrap; margin-top: 1.5rem; }
.btn-primary {
display: inline-flex; align-items: center; gap: 0.5rem; padding: 0.85rem 1.8rem;
background: var(--gradient-2); color: white; border: none; border-radius: 12px;
font-size: 0.95rem; font-weight: 600; cursor: pointer; transition: all 0.3s;
text-decoration: none; box-shadow: 0 4px 20px rgba(108,92,231,0.4);
}
.btn-primary:hover { transform: translateY(-2px); box-shadow: 0 6px 30px rgba(108,92,231,0.5); }
.btn-secondary {
display: inline-flex; align-items: center; gap: 0.5rem; padding: 0.85rem 1.8rem;
background: transparent; color: var(--text); border: 1px solid var(--border);
border-radius: 12px; font-size: 0.95rem; font-weight: 500; cursor: pointer;
transition: all 0.3s; text-decoration: none;
}
.btn-secondary:hover { border-color: var(--primary); background: rgba(108,92,231,0.1); transform: translateY(-2px); }
/* ===== Quick Nav ===== */
.quick-nav {
display: flex; flex-wrap: wrap; gap: 0.8rem; justify-content: center;
margin-top: 2.5rem; padding-top: 1.5rem; border-top: 1px solid var(--border);
}
.quick-nav a {
padding: 0.4rem 1rem; background: var(--bg-card); border: 1px solid var(--border);
border-radius: 8px; color: var(--text-secondary); text-decoration: none; font-size: 0.82rem;
transition: all 0.3s;
}
.quick-nav a:hover { border-color: var(--primary); color: var(--primary-light); transform: translateY(-2px); box-shadow: 0 4px 16px rgba(108,92,231,0.2); }
/* ===== Philosophy Cards ===== */
.philosophy-grid {
display: grid; grid-template-columns: repeat(auto-fit, minmax(300px, 1fr));
gap: 1.5rem; margin-top: 2rem;
}
.philosophy-card {
padding: 2rem; background: var(--bg-card); border: 1px solid var(--border);
border-radius: var(--radius); position: relative; overflow: hidden; transition: all 0.4s;
}
.philosophy-card::before {
content: ''; position: absolute; top: 0; left: 0; right: 0; height: 3px;
opacity: 0; transition: opacity 0.3s;
}
.philosophy-card:nth-child(1)::before { background: #6C5CE7; }
.philosophy-card:nth-child(2)::before { background: #00CEC9; }
.philosophy-card:nth-child(3)::before { background: #FF6B6B; }
.philosophy-card:nth-child(4)::before { background: #FDCB6E; }
.philosophy-card:nth-child(5)::before { background: #A29BFE; }
.philosophy-card:hover { transform: translateY(-4px); border-color: rgba(108,92,231,0.4); box-shadow: var(--shadow); }
.philosophy-card:hover::before { opacity: 1; }
.philosophy-card h3 { font-size: 1.1rem; margin-bottom: 0.8rem; display: flex; align-items: center; gap: 0.5rem; }
.philosophy-card p { color: var(--text-secondary); font-size: 0.88rem; line-height: 1.8; }
.philosophy-icon { font-size: 1.4rem; }
/* ===== Pipeline Deep Dive ===== */
.pipeline-detail {
display: grid; grid-template-columns: 1fr; gap: 0; margin-top: 2rem; position: relative;
}
.pipeline-detail::before {
content: ''; position: absolute; left: 28px; top: 70px; bottom: 20px; width: 2px;
background: linear-gradient(180deg, var(--primary) 0%, var(--accent) 50%, #FF6B6B 100%); opacity: 0.2;
}
.pipeline-stage {
padding: 2rem; background: var(--bg-card); border: 1px solid var(--border);
border-radius: var(--radius); display: grid; grid-template-columns: auto 1fr; gap: 1.5rem; transition: all 0.3s;
margin-bottom: 1.5rem; position: relative;
}
.pipeline-stage:last-child { margin-bottom: 0; }
.pipeline-stage:hover { border-color: rgba(108,92,231,0.4); }
.stage-num {
width: 56px; height: 56px; border-radius: 14px; display: flex; align-items: center;
justify-content: center; font-weight: 800; font-size: 1.3rem; color: white; flex-shrink: 0;
}
.stage-num.s1 { background: linear-gradient(135deg, #6C5CE7, #A29BFE); }
.stage-num.s2 { background: linear-gradient(135deg, #00CEC9, #81ECEC); }
.stage-num.s3 { background: linear-gradient(135deg, #FF6B6B, #FDCB6E); }
.stage-content h3 { font-size: 1.1rem; margin-bottom: 0.5rem; }
.stage-content p { color: var(--text-secondary); font-size: 0.88rem; line-height: 1.7; margin-bottom: 0.6rem; }
.stage-tech { display: flex; flex-wrap: wrap; gap: 0.4rem; }
.stage-tech span {
padding: 0.2rem 0.6rem; background: rgba(108,92,231,0.1); border: 1px solid rgba(108,92,231,0.2);
border-radius: 6px; font-size: 0.75rem; color: var(--primary-light);
}
/* ===== Code Block ===== */
.code-block {
background: #0c0c18; border: 1px solid var(--border); border-radius: 12px;
padding: 1.5rem; margin-top: 1rem; overflow-x: auto; font-family: var(--font-mono);
font-size: 0.78rem; line-height: 1.8; color: var(--text-secondary); position: relative;
box-shadow: inset 0 0 30px rgba(0,0,0,0.3);
}
.code-block::before {
content: ''; position: absolute; top: 0; left: 0; right: 0; height: 1px;
background: linear-gradient(90deg, transparent, var(--primary), transparent); opacity: 0.4;
}
.code-block .code-label {
font-size: 0.72rem; color: var(--accent); margin-bottom: 0.8rem; font-weight: 600;
display: flex; align-items: center; gap: 0.5rem;
}
.code-block .code-label::before {
content: ''; display: inline-flex; gap: 3px;
width: 8px; height: 8px; border-radius: 50%; background: #FF6B6B;
box-shadow: 14px 0 0 #FDCB6E, 28px 0 0 #00CEC9;
}
.code-key { color: #A29BFE; }
.code-str { color: #00CEC9; }
.code-comment { color: #555580; font-style: italic; }
.code-num { color: #FDCB6E; }
/* ===== Library Table ===== */
.lib-table {
width: 100%; border-collapse: collapse; margin-top: 2rem; font-size: 0.85rem;
background: var(--bg-card); border-radius: var(--radius); overflow: hidden;
}
.lib-table th {
text-align: left; padding: 1rem; background: rgba(108,92,231,0.1);
border-bottom: 2px solid var(--primary); font-size: 0.82rem; color: var(--primary-light);
}
.lib-table td {
padding: 0.75rem 1rem; border-bottom: 1px solid var(--border); color: var(--text-secondary); vertical-align: top;
}
.lib-table tr:last-child td { border-bottom: none; }
.lib-table tr:hover td { background: rgba(108,92,231,0.03); }
.lib-name { color: var(--text); font-weight: 500; font-family: var(--font-mono); font-size: 0.82rem; }
.lib-version { color: var(--accent); font-size: 0.78rem; font-family: var(--font-mono); }
/* ===== Timeline ===== */
.timeline { max-width: 800px; margin: 2rem auto 0; position: relative; padding-left: 2rem; }
.timeline::before {
content: ''; position: absolute; left: 8px; top: 0; bottom: 0; width: 2px;
background: linear-gradient(180deg, var(--primary), var(--accent)); opacity: 0.3;
}
.timeline-item { position: relative; padding: 0 0 2.5rem 2.2rem; }
.timeline-item:last-child { padding-bottom: 0; }
.timeline-dot {
position: absolute; left: -2px; top: 4px; width: 18px; height: 18px;
border-radius: 50%; background: var(--bg); border: 3px solid var(--primary); z-index: 1;
}
.timeline-item:first-child .timeline-dot { background: var(--primary); box-shadow: 0 0 12px rgba(108,92,231,0.5); }
.timeline-version { font-size: 0.78rem; font-weight: 700; color: var(--primary-light); margin-bottom: 0.2rem; }
.timeline-date { font-size: 0.72rem; color: var(--text-secondary); opacity: 0.7; margin-bottom: 0.2rem; }
.timeline-title { font-size: 1rem; font-weight: 600; margin-bottom: 0.3rem; }
.timeline-desc { font-size: 0.85rem; color: var(--text-secondary); line-height: 1.7; }
.timeline-tags { display: flex; flex-wrap: wrap; gap: 0.3rem; margin-top: 0.4rem; }
.timeline-tag {
padding: 0.15rem 0.5rem; border-radius: 4px; font-size: 0.7rem; font-weight: 500;
}
.timeline-tag.new { background: rgba(0,206,201,0.15); color: #00CEC9; }
.timeline-tag.fix { background: rgba(255,107,107,0.15); color: #FF6B6B; }
.timeline-tag.refactor { background: rgba(253,203,110,0.15); color: #FDCB6E; }
.timeline-tag.perf { background: rgba(108,92,231,0.15); color: #A29BFE; }
/* ===== Test Data Grid ===== */
.test-grid {
display: grid; grid-template-columns: repeat(auto-fit, minmax(200px, 1fr));
gap: 1.2rem; margin-top: 2rem;
}
.test-card {
padding: 1.8rem; background: var(--bg-card); border: 1px solid var(--border);
border-radius: var(--radius); text-align: center; transition: all 0.3s; position: relative; overflow: hidden;
}
.test-card::after {
content: ''; position: absolute; bottom: 0; left: 0; right: 0; height: 3px;
background: var(--gradient-1); opacity: 0; transition: opacity 0.3s;
}
.test-card:hover { transform: translateY(-3px); border-color: var(--primary); }
.test-card:hover::after { opacity: 1; }
.test-value { font-size: 2.2rem; font-weight: 800; background: var(--gradient-1); -webkit-background-clip: text; -webkit-text-fill-color: transparent; background-clip: text; }
.test-label { font-size: 0.85rem; color: var(--text-secondary); margin-top: 0.3rem; }
.test-desc { font-size: 0.75rem; color: var(--text-secondary); opacity: 0.7; margin-top: 0.2rem; }
/* ===== Open Source Cards ===== */
.oss-grid {
display: grid; grid-template-columns: repeat(auto-fit, minmax(280px, 1fr));
gap: 1.2rem; margin-top: 2rem;
}
.oss-card {
padding: 1.5rem; background: var(--bg-card); border: 1px solid var(--border);
border-radius: var(--radius); transition: all 0.3s; display: block; text-decoration: none; color: var(--text);
}
.oss-card:hover { transform: translateY(-3px); border-color: var(--primary); box-shadow: var(--shadow); }
.oss-card h4 { font-size: 0.95rem; margin-bottom: 0.3rem; display: flex; align-items: center; gap: 0.4rem; }
.oss-source { font-size: 0.75rem; color: var(--accent); margin-bottom: 0.5rem; }
.oss-card p { font-size: 0.82rem; color: var(--text-secondary); line-height: 1.7; }
/* ===== Video Section ===== */
.video-container {
max-width: 800px; margin: 2rem auto 0; background: var(--bg-card);
border: 1px solid var(--border); border-radius: var(--radius); overflow: hidden;
}
.video-embed { position: relative; padding-bottom: 56.25%; height: 0; }
.video-embed iframe { position: absolute; top: 0; left: 0; width: 100%; height: 100%; border: none; }
.video-info { padding: 1.5rem 2rem; }
.video-info h3 { font-size: 1.1rem; margin-bottom: 0.4rem; }
.video-info p { color: var(--text-secondary); font-size: 0.88rem; }
/* ===== Link Cards ===== */
.link-grid {
display: grid; grid-template-columns: repeat(auto-fit, minmax(260px, 1fr));
gap: 1.2rem; margin-top: 2rem;
}
.link-card {
padding: 1.8rem; background: var(--bg-card); border: 1px solid var(--border);
border-radius: var(--radius); text-align: center; transition: all 0.4s;
text-decoration: none; color: var(--text); display: block; position: relative; overflow: hidden;
}
.link-card::before {
content: ''; position: absolute; top: 0; left: 0; right: 0; height: 3px;
opacity: 0; transition: opacity 0.3s;
}
.link-card:nth-child(1)::before { background: #FF6B6B; }
.link-card:nth-child(2)::before { background: #00CEC9; }
.link-card:nth-child(3)::before { background: #6C5CE7; }
.link-card:nth-child(4)::before { background: #FDCB6E; }
.link-card:hover { transform: translateY(-4px); border-color: rgba(108,92,231,0.4); box-shadow: var(--shadow); }
.link-card:hover::before { opacity: 1; }
.link-icon { font-size: 2.5rem; margin-bottom: 0.8rem; display: block; }
.link-card h3 { font-size: 1.05rem; margin-bottom: 0.3rem; }
.link-card p { color: var(--text-secondary); font-size: 0.82rem; }
.link-url { font-size: 0.78rem; color: var(--accent); margin-top: 0.5rem; font-family: monospace; }
/* ===== AI Model Cards ===== */
.compare-grid {
display: grid; grid-template-columns: repeat(auto-fit, minmax(320px, 1fr));
gap: 1.8rem; margin-top: 2rem;
}
.compare-card {
padding: 0; background: rgba(26,26,46,0.6);
backdrop-filter: blur(10px);
border: 1px solid rgba(108,92,231,0.15);
border-radius: var(--radius); transition: all 0.4s cubic-bezier(0.4,0,0.2,1);
overflow: hidden; position: relative;
}
.compare-card:hover {
border-color: rgba(108,92,231,0.4);
transform: translateY(-4px);
box-shadow: 0 12px 40px rgba(108,92,231,0.12);
}
.compare-card .card-header {
padding: 1.2rem 1.5rem;
border-bottom: 1px solid rgba(108,92,231,0.1);
display: flex; align-items: center; gap: 0.8rem;
}
.compare-card .card-header .icon-wrap {
width: 38px; height: 38px; border-radius: 10px;
display: flex; align-items: center; justify-content: center;
font-size: 1.2rem; flex-shrink: 0;
}
.compare-card:nth-child(1) .icon-wrap { background: rgba(108,92,231,0.15); }
.compare-card:nth-child(2) .icon-wrap { background: rgba(0,206,201,0.15); }
.compare-card:nth-child(3) .icon-wrap { background: rgba(253,203,110,0.15); }
.compare-card .card-header .title-group h4 {
font-size: 1rem; font-weight: 700; margin: 0;
background: linear-gradient(135deg, #E8E8F0, #A29BFE);
-webkit-background-clip: text; -webkit-text-fill-color: transparent; background-clip: text;
}
.compare-card .card-header .title-group .subtitle {
font-size: 0.75rem; color: var(--accent); font-weight: 600; margin-top: 0.15rem;
}
.compare-card .card-body {
padding: 1.2rem 1.5rem 1.5rem;
}
.compare-card .field {
margin-bottom: 0.9rem;
}
.compare-card .field:last-child { margin-bottom: 0; }
.compare-card .field-label {
font-size: 0.72rem; font-weight: 700; color: var(--primary-light);
text-transform: uppercase; letter-spacing: 0.08em; margin-bottom: 0.3rem;
}
.compare-card .field-value {
font-size: 0.85rem; color: var(--text-secondary); line-height: 1.65;
}
.compare-card .field-value code {
font-family: var(--font-mono); font-size: 0.78em;
background: rgba(108,92,231,0.1); padding: 0.15rem 0.4rem;
border-radius: 4px; color: var(--accent);
}
.compare-card .tag-row {
display: flex; flex-wrap: wrap; gap: 0.4rem; margin-top: 0.3rem;
}
.compare-card .tag {
padding: 0.2rem 0.55rem; background: rgba(108,92,231,0.1);
border: 1px solid rgba(108,92,231,0.15); border-radius: 6px;
font-size: 0.72rem; color: var(--primary-light);
}
.compare-card:nth-child(2) .tag {
background: rgba(0,206,201,0.08); border-color: rgba(0,206,201,0.15); color: var(--accent);
}
.compare-card:nth-child(3) .tag {
background: rgba(253,203,110,0.08); border-color: rgba(253,203,110,0.15); color: #FDCB6E;
}
/* ===== Divider ===== */
.section-divider {
max-width: 120px; height: 1px; margin: 0 auto; padding: 3rem 0;
background: linear-gradient(90deg, transparent, var(--primary), var(--accent), transparent);
opacity: 0.4; position: relative;
}
.section-divider::before {
content: ''; position: absolute; top: 50%; left: 50%; transform: translate(-50%, -50%);
width: 6px; height: 6px; background: var(--primary); border-radius: 50%;
box-shadow: 0 0 12px rgba(108,92,231,0.5);
}
/* ===== Footer ===== */
footer {
padding: 2rem; text-align: center; border-top: 1px solid var(--border);
color: var(--text-secondary); font-size: 0.82rem;
}
footer a { color: var(--primary-light); text-decoration: none; }
footer a:hover { text-decoration: underline; }
/* ===== Animations ===== */
.fade-in { opacity: 0; transform: translateY(25px); transition: opacity 0.6s ease, transform 0.6s ease; }
.fade-in.visible { opacity: 1; transform: translateY(0); }
/* ===== Inline Code ===== */
code {
font-family: var(--font-mono); font-size: 0.82em;
padding: 0.15rem 0.45rem; background: rgba(108,92,231,0.12);
border: 1px solid rgba(108,92,231,0.15); border-radius: 4px;
color: var(--primary-light);
}
.compare-card li code { font-size: 0.78em; }
/* ===== HERO Neural Network SVG ===== */
.hero-neural-net {
position: absolute; inset: 0; pointer-events: none; z-index: 0; overflow: hidden;
}
.hero-neural-net svg { width: 100%; height: 100%; }
.neural-node { animation: neuralPulse 3s ease-in-out infinite; }
.neural-node:nth-child(odd) { animation-delay: 0.5s; }
.neural-node:nth-child(3n) { animation-delay: 1.2s; }
@keyframes neuralPulse {
0%,100% { opacity: 0.15; r: 3; }
50% { opacity: 0.5; r: 4.5; }
}
.neural-edge { animation: edgeGlow 4s ease-in-out infinite; }
.neural-edge:nth-child(even) { animation-delay: 1s; }
@keyframes edgeGlow {
0%,100% { stroke-opacity: 0.04; }
50% { stroke-opacity: 0.12; }
}
/* ===== Holographic shimmer on hero h1 ===== */
.tech-hero h1 {
position: relative; display: inline-block;
}
.tech-hero h1 .gradient-text {
background: linear-gradient(
90deg,
#6C5CE7 0%, #A29BFE 20%, #00CEC9 40%,
#81ECEC 50%, #00CEC9 60%, #A29BFE 80%, #6C5CE7 100%
);
background-size: 200% 100%;
-webkit-background-clip: text; background-clip: text;
-webkit-text-fill-color: transparent;
animation: holoShift 4s linear infinite;
}
@keyframes holoShift {
0% { background-position: 0% 50%; }
100% { background-position: 200% 50%; }
}
/* ===== Section header glow particles ===== */
.section-header { position: relative; }
.header-glow {
position: absolute; width: 6px; height: 6px; border-radius: 50%;
background: var(--primary); box-shadow: 0 0 10px var(--primary), 0 0 20px rgba(108,92,231,0.3);
animation: glowFloat 6s ease-in-out infinite;
pointer-events: none;
}
.header-glow:nth-child(1) { top: -8px; left: 30%; animation-delay: 0s; background: var(--primary); box-shadow: 0 0 10px var(--primary), 0 0 20px rgba(108,92,231,0.3); }
.header-glow:nth-child(2) { top: 50%; right: 25%; animation-delay: 2s; background: var(--accent); box-shadow: 0 0 10px var(--accent), 0 0 20px rgba(0,206,201,0.3); }
.header-glow:nth-child(3) { bottom: -5px; left: 50%; animation-delay: 4s; background: #A29BFE; box-shadow: 0 0 10px #A29BFE, 0 0 20px rgba(162,155,254,0.3); }
@keyframes glowFloat {
0%,100% { transform: translate(0, 0) scale(1); opacity: 0.6; }
25% { transform: translate(8px, -6px) scale(1.3); opacity: 1; }
50% { transform: translate(-4px, 4px) scale(0.8); opacity: 0.4; }
75% { transform: translate(6px, 2px) scale(1.1); opacity: 0.8; }
}
/* ===== Animated gradient border on pipeline stages ===== */
.pipeline-stage {
position: relative;
background: linear-gradient(var(--bg-card), var(--bg-card)) padding-box,
linear-gradient(135deg, rgba(108,92,231,0.3), rgba(0,206,201,0.1), rgba(108,92,231,0.3)) border-box;
border: 1px solid transparent;
}
.pipeline-stage::after {
content: ''; position: absolute; inset: -1px; border-radius: var(--radius); padding: 1px;
background: linear-gradient(135deg, var(--primary), var(--accent), var(--primary));
background-size: 300% 300%;
-webkit-mask: linear-gradient(#fff 0 0) content-box, linear-gradient(#fff 0 0);
-webkit-mask-composite: xor; mask-composite: exclude;
animation: borderShift 6s linear infinite;
pointer-events: none; opacity: 0.35;
}
.pipeline-stage:hover::after { opacity: 0.7; }
@keyframes borderShift {
0% { background-position: 0% 50%; }
50% { background-position: 100% 50%; }
100% { background-position: 0% 50%; }
}
/* ===== Circuit board code block ===== */
.code-block {
position: relative;
border: 1px solid transparent;
background:
linear-gradient(var(--bg-card), var(--bg-card)) padding-box,
linear-gradient(135deg, var(--primary), rgba(0,206,201,0.5), var(--primary)) border-box;
border-radius: 12px;
}
.code-block::after {
content: ''; position: absolute; top: -8px; right: -8px; bottom: -8px; width: 40px;
border-right: 2px dashed rgba(108,92,231,0.15);
border-top: 2px dashed rgba(108,92,231,0.15);
border-radius: 0 12px 0 0;
pointer-events: none;
}
/* ===== Math formula section background ===== */
.section-formula-bg {
position: absolute; inset: 0; pointer-events: none; overflow: hidden; z-index: 0;
}
.formula-watermark {
position: absolute; font-family: var(--font-mono); color: rgba(108,92,231,0.025);
font-size: clamp(10px, 1.5vw, 16px); white-space: nowrap; user-select: none;
animation: formulaSlide 40s linear infinite;
}
.formula-watermark:nth-child(2) { top: 25%; animation-delay: -10s; color: rgba(0,206,201,0.02); }
.formula-watermark:nth-child(3) { top: 50%; animation-delay: -20s; }
.formula-watermark:nth-child(4) { top: 75%; animation-delay: -30s; color: rgba(0,206,201,0.02); }
@keyframes formulaSlide {
0% { transform: translateX(100vw); }
100% { transform: translateX(-200%); }
}
/* ===== Responsive ===== */
@media (max-width: 768px) {
.nav-links { display: none; }
.philosophy-grid, .compare-grid { grid-template-columns: 1fr; }
.pipeline-stage { grid-template-columns: 1fr; }
.stage-num { width: 48px; height: 48px; font-size: 1.1rem; }
.test-grid { grid-template-columns: repeat(2, 1fr); }
.tech-hero { min-height: 45vh; padding: 6rem 2rem 2rem; }
}
@media (max-width: 480px) {
.test-grid { grid-template-columns: 1fr; }
.link-grid { grid-template-columns: 1fr; }
}
</style>
</head>
<body>
<!-- Reading Progress -->
<div class="reading-progress" id="readingProgress"></div>
<!-- Matrix Grid Background -->
<div class="matrix-bg"></div>
<!-- Floating Math Symbols -->
<div class="floating-symbols" id="floatingSymbols"></div>
<!-- Cursor Glow -->
<div class="cursor-glow" id="cursorGlow"></div>
<!-- Navigation -->
<nav id="navbar">
<a href="index.html" class="nav-logo">
<svg viewBox="0 0 32 32" fill="none"><rect width="32" height="32" rx="8" fill="url(#g1)"/><path d="M8 22L16 10L24 22" stroke="white" stroke-width="2.5" stroke-linecap="round" stroke-linejoin="round"/><circle cx="16" cy="17" r="2" fill="white"/><defs><linearGradient id="g1" x1="0" y1="0" x2="32" y2="32"><stop stop-color="#6C5CE7"/><stop offset="1" stop-color="#00CEC9"/></linearGradient></defs></svg>
MathMate
</a>
<ul class="nav-links">
<li><a href="#philosophy">设计思路</a></li>
<li><a href="#pipeline-deep">技术路径</a></li>
<li><a href="#libraries">外源库</a></li>
<li><a href="#models">AI 模型选型</a></li>
<li><a href="#iteration">迭代过程</a></li>
<li><a href="#testing">测试数据</a></li>
<li><a href="#opensource">开源参考</a></li>
<li><a href="#links">视频与链接</a></li>
</ul>
<a href="index.html" class="nav-back">
<svg width="14" height="14" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2"><path d="M19 12H5M12 19l-7-7 7-7"/></svg>
返回首页
</a>
</nav>
<!-- ====== Hero ====== -->
<section class="tech-hero" id="top">
<!-- Neural Network SVG Decoration -->
<div class="hero-neural-net">
<svg viewBox="0 0 1200 600" preserveAspectRatio="xMidYMid slice" xmlns="http://www.w3.org/2000/svg">
<!-- Layer 1 (left) -->
<circle class="neural-node" cx="120" cy="100" r="3" fill="#6C5CE7"/>
<circle class="neural-node" cx="120" cy="200" r="3" fill="#6C5CE7"/>
<circle class="neural-node" cx="120" cy="300" r="3" fill="#6C5CE7"/>
<circle class="neural-node" cx="120" cy="400" r="3" fill="#6C5CE7"/>
<circle class="neural-node" cx="120" cy="500" r="3" fill="#6C5CE7"/>
<!-- Layer 2 -->
<circle class="neural-node" cx="300" cy="80" r="3" fill="#A29BFE"/>
<circle class="neural-node" cx="300" cy="180" r="3" fill="#A29BFE"/>
<circle class="neural-node" cx="300" cy="300" r="3" fill="#A29BFE"/>
<circle class="neural-node" cx="300" cy="420" r="3" fill="#A29BFE"/>
<circle class="neural-node" cx="300" cy="520" r="3" fill="#A29BFE"/>
<!-- Layer 3 -->
<circle class="neural-node" cx="500" cy="150" r="3" fill="#00CEC9"/>
<circle class="neural-node" cx="500" cy="300" r="3" fill="#00CEC9"/>
<circle class="neural-node" cx="500" cy="450" r="3" fill="#00CEC9"/>
<!-- Layer 4 (right) -->
<circle class="neural-node" cx="720" cy="120" r="3" fill="#81ECEC"/>
<circle class="neural-node" cx="720" cy="250" r="3" fill="#81ECEC"/>
<circle class="neural-node" cx="720" cy="380" r="3" fill="#81ECEC"/>
<circle class="neural-node" cx="720" cy="500" r="3" fill="#81ECEC"/>
<!-- Output -->
<circle class="neural-node" cx="920" cy="200" r="3" fill="#6C5CE7"/>
<circle class="neural-node" cx="920" cy="400" r="3" fill="#00CEC9"/>
<!-- Edges L1→L2 -->
<line class="neural-edge" x1="120" y1="100" x2="300" y2="80" stroke="#6C5CE7" stroke-width="0.5" stroke-opacity="0.06"/>
<line class="neural-edge" x1="120" y1="100" x2="300" y2="180" stroke="#6C5CE7" stroke-width="0.5" stroke-opacity="0.04"/>
<line class="neural-edge" x1="120" y1="200" x2="300" y2="180" stroke="#6C5CE7" stroke-width="0.5" stroke-opacity="0.06"/>
<line class="neural-edge" x1="120" y1="200" x2="300" y2="300" stroke="#6C5CE7" stroke-width="0.5" stroke-opacity="0.04"/>
<line class="neural-edge" x1="120" y1="300" x2="300" y2="300" stroke="#A29BFE" stroke-width="0.5" stroke-opacity="0.06"/>
<line class="neural-edge" x1="120" y1="300" x2="300" y2="420" stroke="#A29BFE" stroke-width="0.5" stroke-opacity="0.04"/>
<line class="neural-edge" x1="120" y1="400" x2="300" y2="420" stroke="#A29BFE" stroke-width="0.5" stroke-opacity="0.06"/>
<line class="neural-edge" x1="120" y1="400" x2="300" y2="520" stroke="#A29BFE" stroke-width="0.5" stroke-opacity="0.04"/>
<line class="neural-edge" x1="120" y1="500" x2="300" y2="520" stroke="#6C5CE7" stroke-width="0.5" stroke-opacity="0.06"/>
<line class="neural-edge" x1="120" y1="100" x2="300" y2="300" stroke="#6C5CE7" stroke-width="0.5" stroke-opacity="0.03"/>
<line class="neural-edge" x1="120" y1="500" x2="300" y2="300" stroke="#6C5CE7" stroke-width="0.5" stroke-opacity="0.03"/>
<!-- Edges L2→L3 -->
<line class="neural-edge" x1="300" y1="80" x2="500" y2="150" stroke="#00CEC9" stroke-width="0.5" stroke-opacity="0.05"/>
<line class="neural-edge" x1="300" y1="180" x2="500" y2="150" stroke="#00CEC9" stroke-width="0.5" stroke-opacity="0.05"/>
<line class="neural-edge" x1="300" y1="180" x2="500" y2="300" stroke="#00CEC9" stroke-width="0.5" stroke-opacity="0.04"/>
<line class="neural-edge" x1="300" y1="300" x2="500" y2="300" stroke="#00CEC9" stroke-width="0.5" stroke-opacity="0.06"/>
<line class="neural-edge" x1="300" y1="300" x2="500" y2="450" stroke="#00CEC9" stroke-width="0.5" stroke-opacity="0.04"/>
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<text x="60" y="60" fill="rgba(108,92,231,0.08)" font-family="monospace" font-size="11">f(x)=ax²+bx+c</text>
<text x="380" y="50" fill="rgba(0,206,201,0.07)" font-family="monospace" font-size="11">∇×E = -∂B/∂t</text>
<text x="800" y="60" fill="rgba(108,92,231,0.07)" font-family="monospace" font-size="11">∫₀^∞ e^(-x²) dx = √π/2</text>
<text x="100" y="580" fill="rgba(0,206,201,0.06)" font-family="monospace" font-size="10">σ(z) = 1/(1+e^(-z))</text>
<text x="550" y="580" fill="rgba(108,92,231,0.06)" font-family="monospace" font-size="10">∂L/∂w = ∑(ŷ-y)x</text>
<text x="900" y="560" fill="rgba(0,206,201,0.06)" font-family="monospace" font-size="10">P(A|B) = P(B|A)P(A)/P(B)</text>
</svg>
</div>
<div class="tech-hero-content fade-in">
<div class="section-label">Technical Deep Dive</div>
<h1>技术<span class="gradient-text">详解</span></h1>
<p>深入剖析 MathMate 的技术选型、设计思路、核心路径、迭代过程与开源参考。从 Flutter 原生可视化引擎到多模型协作 AI 流水线，完整呈现技术全貌。</p>
<div class="quick-nav">
<a href="#philosophy">设计思路</a>
<a href="#pipeline-deep">技术路径</a>
<a href="#libraries">外源库引用</a>
<a href="#models">AI 模型选型</a>
<a href="#iteration">迭代历程</a>
<a href="#testing">测试数据</a>
<a href="#opensource">开源参考</a>
<a href="#links">视频与链接</a>
</div>
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<span style="padding:0.18rem 0.55rem;background:rgba(0,206,201,0.18);border-radius:6px;color:var(--accent);font-size:0.8rem;font-weight:700;">v2.3.1 Latest</span>
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</div>
</section>
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<!-- ====== Section 1: 设计思路 ====== -->
<section class="section" id="philosophy">
<div class="section-formula-bg">
<div class="formula-watermark">E = mc² ∫ sin(x)dx = -cos(x)+C ∑(n=0→∞) xⁿ/n! = eˣ det(A) = |a₁₁ a₁₂; a₂₁ a₂₂| ∀ε>0 ∃δ>0 lim(n→∞) (1+1/n)ⁿ = e</div>
<div class="formula-watermark">Δ = b²-4ac cos²θ+sin²θ = 1 ∮ F·ds = ∫∫ (∇×F)·dA aⁿ·aᵐ = aⁿ⁺ᵐ log(ab) = log(a)+log(b) ∑(k=1→n) k = n(n+1)/2</div>
<div class="formula-watermark">dy/dx = lim(Δx→0) [f(x+Δx)-f(x)]/Δx |x| = √(x²) C(n,r) = n!/(r!(n-r)!) eⁱᶿ = cosθ+i·sinθ</div>
<div class="formula-watermark">∇f = (∂f/∂x, ∂f/∂y, ∂f/∂z) ∫∫∫ ρ dV = M P(A∪B) = P(A)+P(B)-P(A∩B) λ = h/p S = k·ln(W)</div>
</div>
<div class="container">
<div class="section-header fade-in">
<div class="header-glow"></div><div class="header-glow"></div><div class="header-glow"></div>
<div class="section-label">Design Philosophy</div>
<h2>设计思路与核心决策</h2>
<p>每一个技术选型背后都有明确的取舍逻辑</p>
</div>
<div class="philosophy-grid">
<div class="philosophy-card fade-in">
<h3><span class="philosophy-icon">🎯</span> Flutter 原生优先</h3>
<p>选择 Flutter 作为唯一前端框架，而非 React Native 或原生开发。核心考量：Canvas 绘图能力是几何可视化引擎的基石，Flutter 的 <code>CustomPaint</code> + <code>Canvas</code> API 提供了 60fps 的原生渲染性能，无需 WebView 中间层。一套代码覆盖 Android、iOS、Web、桌面全平台。</p>
</div>
<div class="philosophy-card fade-in">
<h3><span class="philosophy-icon">🧩</span> 无外部状态管理</h3>
<p>不引入 Provider、Riverpod、Bloc 等状态管理框架。全部使用 <code>StatefulWidget</code> + <code>setState</code>。理由：MathMate 的页面间数据流是单向的（拍照 → 识别 → 解题 → 展示），没有复杂的全局状态共享需求。减少依赖、降低复杂度、提升可维护性。</p>
</div>
<div class="philosophy-card fade-in">
<h3><span class="philosophy-icon">🔗</span> 自研可视化引擎</h3>
<p>拒绝使用现成图表库，从零构建 <code>GeometryPainter</code>。原因：通用图表库无法理解数学语义（如"动点在圆上滑动"的约束关系）。自研引擎实现了 <strong>GeometryJSON 协议</strong>——AI 输出结构化 JSON，引擎解析并渲染为交互式几何图形，形成"语义-图形"的完整闭环。</p>
</div>
<div class="philosophy-card fade-in">
<h3><span class="philosophy-icon">🤖</span> 多模型协作流水线</h3>
<p>没有将所有 AI 任务绑定到单一模型，而是根据各模型的优势分配任务：<strong>DeepSeek</strong> 负责数学推理（解题+可视化），<strong>火山引擎</strong> 负责多模态 OCR（手写/印刷识别），<strong>Qwen-PLUS</strong> 负责流式对话。每个模型在各自领域做到最优，整体效果超越单模型方案。</p>
</div>
<div class="philosophy-card fade-in">
<h3><span class="philosophy-icon">💾</span> 纯本地数据架构</h3>
<p>不依赖云数据库或后端服务器。全部数据存储在本地：<strong>Hive</strong> 用于结构化数据（搜题历史、对话记录），<strong>SharedPreferences</strong> 用于键值偏好（主题、年级、用户设置）。优势：零服务器成本、用户数据完全本地化、离线可用、隐私安全。</p>
</div>
</div>
</div>
</section>
<div class="section-divider"></div>
<!-- ====== Section 2: 技术路径 ====== -->
<section class="section" id="pipeline-deep">
<div class="section-bg-glow"></div>
<div class="container">
<div class="section-header fade-in">
<div class="header-glow"></div><div class="header-glow"></div><div class="header-glow"></div>
<div class="section-label">Technical Path</div>
<h2>核心技术路径</h2>
<p>从拍照到交互式可视化的三阶段 AI 流水线</p>
</div>
<div class="pipeline-detail">
<!-- Stage 1 -->
<div class="pipeline-stage fade-in">
<div class="stage-num s1">1</div>
<div class="stage-content">
<h3>多模态 OCR 识别</h3>
<p>用户拍照后，图片经过裁剪与预处理（自动透视校正、自适应锐化、背景二值化），送入火山引擎多模态 API。AI 将手写或印刷的数学公式、文字识别为结构化的 Markdown + LaTeX 文本。<code>SafeJsonParser</code> 容错处理 AI 返回的非标准 JSON（如 <code>Infinity</code>、<code>NaN</code>）。</p>
<div class="stage-tech">
<span>Volc Engine API</span>
<span>OcrService</span>
<span>SafeJsonParser</span>
<span>图像预处理管线</span>
</div>
</div>
</div>
<!-- Stage 2 -->
<div class="pipeline-stage fade-in">
<div class="stage-num s2">2</div>
<div class="stage-content">
<h3>AI 分步解题推理</h3>
<p>OCR 识别的数学文本送入 DeepSeek API，配合专门设计的解题 System Prompt（<code>solve_prompt.dart</code>）。AI 执行分步推理，输出完整的 Markdown 解题过程，包含 LaTeX 公式、步骤说明和最终答案。支持小学到大学各难度层级的数学题。</p>
<div class="stage-tech">
<span>DeepSeek API</span>
<span>SolverService</span>
<span>Chain-of-Thought 推理</span>
<span>专用 Prompt 模板</span>
</div>
</div>
</div>
<!-- Stage 3 -->
<div class="pipeline-stage fade-in">
<div class="stage-num s3">3</div>
<div class="stage-content">
<h3>GeometryJSON 可视化生成与渲染</h3>
<p>这是 MathMate 的技术核心。AI 将题目中的几何语义转化为结构化的 <strong>GeometryJSON</strong> 协议——定义视口（viewport）、几何元素（点、线、圆、椭圆、双曲线、抛物线）、动态约束（动点在曲线上滑动）。<code>GeometryValidator</code> 校验 JSON 合法性，<code>GeometryPainter</code> 使用纯 Dart Canvas 渲染为 60fps 交互式图形，支持手势拖拽动点。</p>
<div class="stage-tech">
<span>GeometryJSON 协议</span>
<span>VisualizationService</span>
<span>GeometryPainter</span>
<span>GeometryValidator</span>
<span>Constraint Solver</span>
<span>GestureDetector</span>
</div>
</div>
</div>
</div>
<!-- GeometryJSON Protocol Example -->
<div class="code-block fade-in" style="margin-top:2rem;">
<div class="code-label">// GeometryJSON 协议示例 — AI 输出的结构化几何描述</div>
<span class="code-key">{</span>
<span class="code-str">"viewport"</span>: { <span class="code-str">"xMin"</span>: <span class="code-num">-5</span>, <span class="code-str">"xMax"</span>: <span class="code-num">5</span>, <span class="code-str">"yMin"</span>: <span class="code-num">-5</span>, <span class="code-str">"yMax"</span>: <span class="code-num">5</span> },
<span class="code-str">"elements"</span>: [
{ <span class="code-str">"type"</span>: <span class="code-str">"point"</span>, <span class="code-str">"id"</span>: <span class="code-str">"A"</span>, <span class="code-str">"x"</span>: <span class="code-num">-3</span>, <span class="code-str">"y"</span>: <span class="code-num">0</span> },
{ <span class="code-str">"type"</span>: <span class="code-str">"point"</span>, <span class="code-str">"id"</span>: <span class="code-str">"B"</span>, <span class="code-str">"x"</span>: <span class="code-num">3</span>, <span class="code-str">"y"</span>: <span class="code-num">0</span> },
{ <span class="code-str">"type"</span>: <span class="code-str">"circle"</span>, <span class="code-str">"id"</span>: <span class="code-str">"c1"</span>, <span class="code-str">"cx"</span>: <span class="code-num">0</span>, <span class="code-str">"cy"</span>: <span class="code-num">0</span>, <span class="code-str">"r"</span>: <span class="code-num">3</span> },
{
<span class="code-str">"type"</span>: <span class="code-str">"dynamic_point"</span>, <span class="code-str">"id"</span>: <span class="code-str">"P"</span>,
<span class="code-str">"constraint"</span>: { <span class="code-str">"target"</span>: <span class="code-str">"c1"</span>, <span class="code-str">"param"</span>: <span class="code-num">0.785</span> }
<span class="code-comment">// 动点P约束在圆c1上，可拖拽交互</span>
}
]
<span class="code-key">}</span>
</div>
<!-- Visualization Engine Architecture -->
<div class="section-header fade-in" style="margin-top:4rem;">
<div class="section-label">Visualization Engine</div>
<h2>自研可视化引擎架构</h2>
<p>纯 Dart + Flutter Canvas，零 WebView 依赖，原生 60fps</p>
</div>
<div class="compare-grid">
<div class="compare-card fade-in">
<h4>📐 数据模型层</h4>
<ul>
<li>抽象 <code>GeoElement</code> 基类</li>
<li><code>GeoPoint</code> — 静态点（固定坐标）</li>
<li><code>GeoCircle</code> — 圆（圆心+半径）</li>
<li><code>DynamicPoint</code> — 动点（含约束目标 ID + 参数化位置）</li>
<li>支持：线、椭圆、双曲线、抛物线</li>
</ul>
</div>
<div class="compare-card accent fade-in">
<h4>🔄 约束求解器</h4>
<ul>
<li>用户拖拽动点时触发约束求解</li>
<li>计算动点在约束目标上的最近合法位置</li>
<li>投影到圆弧 / 线段 / 曲线</li>
<li>纯 Dart 数学计算，无外部依赖</li>
<li>实时 <code>setState</code> 触发重绘</li>
</ul>
</div>
<div class="compare-card fade-in">
<h4>🎨 交互式渲染器</h4>
<ul>
<li><code>CustomPaint</code> + <code>GestureDetector</code></li>
<li>触摸查找最近动点 → 拖拽 → 约束求解 → 重绘</li>
<li>坐标系自动缩放适配 viewport</li>
<li>60fps 原生帧率</li>
<li>支持缩放、平移手势</li>
</ul>
</div>
</div>
<!-- Four-phase implementation -->
<div style="margin-top:3rem;" class="fade-in">
<h3 style="text-align:center;font-size:1.1rem;margin-bottom:1.5rem;">可视化引擎四阶段实现路径</h3>
<div style="display:grid;grid-template-columns:repeat(auto-fit,minmax(220px,1fr));gap:1rem;">
<div style="padding:1.5rem;background:var(--bg-card);border:1px solid var(--border);border-radius:var(--radius);border-top:3px solid #6C5CE7;">
<div style="font-size:0.75rem;color:var(--primary-light);font-weight:700;margin-bottom:0.3rem;">Phase 1</div>
<h4 style="font-size:0.95rem;margin-bottom:0.3rem;">JSON 协议定义</h4>
<p style="font-size:0.82rem;color:var(--text-secondary);">设计 LLM 友好的 GeometryJSON Schema，包含 viewport、elements、constraint 语义</p>
</div>
<div style="padding:1.5rem;background:var(--bg-card);border:1px solid var(--border);border-radius:var(--radius);border-top:3px solid #00CEC9;">
<div style="font-size:0.75rem;color:var(--accent);font-weight:700;margin-bottom:0.3rem;">Phase 2</div>
<h4 style="font-size:0.95rem;margin-bottom:0.3rem;">Prompt 工程</h4>
<p style="font-size:0.82rem;color:var(--text-secondary);">注入"几何翻译家"System Prompt，强制 AI 输出严格格式的 GeometryJSON</p>
</div>
<div style="padding:1.5rem;background:var(--bg-card);border:1px solid var(--border);border-radius:var(--radius);border-top:3px solid #FF6B6B;">
<div style="font-size:0.75rem;color:#FF6B6B;font-weight:700;margin-bottom:0.3rem;">Phase 3</div>
<h4 style="font-size:0.95rem;margin-bottom:0.3rem;">Flutter 引擎实现</h4>
<p style="font-size:0.82rem;color:var(--text-secondary);">CustomPainter 渲染 + GestureDetector 交互 + 约束求解器</p>
</div>
<div style="padding:1.5rem;background:var(--bg-card);border:1px solid var(--border);border-radius:var(--radius);border-top:3px solid #FDCB6E;">
<div style="font-size:0.75rem;color:#FDCB6E;font-weight:700;margin-bottom:0.3rem;">Phase 4</div>
<h4 style="font-size:0.95rem;margin-bottom:0.3rem;">UI/UX 打磨</h4>
<p style="font-size:0.82rem;color:var(--text-secondary);">流式渲染、触觉反馈、实时 LaTeX 标签、异常降级处理</p>
</div>
</div>
</div>
</div>
</section>
<div class="section-divider"></div>
<!-- ====== Section 3: 外源库引用 ====== -->
<section class="section" id="libraries">
<div class="container">
<div class="section-header fade-in">
<div class="header-glow"></div><div class="header-glow"></div><div class="header-glow"></div>
<div class="section-label">External Libraries</div>
<h2>外源库引用清单</h2>
<p>所有第三方依赖均经过选型评估，按需引入</p>
</div>
<h3 class="fade-in" style="font-size:1.05rem;margin-top:2rem;margin-bottom:0.8rem;display:flex;align-items:center;gap:0.5rem;">
<span style="width:8px;height:8px;border-radius:50%;background:#6C5CE7;"></span>
核心框架
</h3>
<table class="lib-table fade-in">
<thead>
<tr><th>库名</th><th>版本</th><th>用途</th></tr>
</thead>
<tbody>
<tr><td class="lib-name">Flutter SDK</td><td class="lib-version">Dart ^3.11.3</td><td>跨平台 UI 框架，Android / iOS / Web / Desktop 全平台构建</td></tr>
<tr><td class="lib-name">flutter_localizations</td><td class="lib-version">SDK 内置</td><td>多语言本地化支持（zh_CN / en_US）</td></tr>
<tr><td class="lib-name">cupertino_icons</td><td class="lib-version">^1.0.8</td><td>iOS 风格图标集（CupertinoIcons）</td></tr>
<tr><td class="lib-name">http</td><td class="lib-version">^1.1.0</td><td>HTTP 客户端，调用 DeepSeek / 火山引擎 / Qwen API</td></tr>
<tr><td class="lib-name">path</td><td class="lib-version">^1.9.1</td><td>跨平台路径操作工具（文件路径拼接、解析）</td></tr>
<tr><td class="lib-name">flutter_dotenv</td><td class="lib-version">^5.2.1</td><td>从 <code>.env</code> 文件加载 API 密钥，安全隔离敏感配置</td></tr>
</tbody>
</table>
<h3 class="fade-in" style="font-size:1.05rem;margin-top:2rem;margin-bottom:0.8rem;display:flex;align-items:center;gap:0.5rem;">
<span style="width:8px;height:8px;border-radius:50%;background:#00CEC9;"></span>
AI 与数据处理
</h3>
<table class="lib-table fade-in">
<thead>
<tr><th>库名</th><th>版本</th><th>用途</th></tr>
</thead>
<tbody>
<tr><td class="lib-name">flutter_math_fork</td><td class="lib-version">^0.7.2+1</td><td>LaTeX / MathML 数学公式渲染（计划迁移至 flutter_tex）</td></tr>
<tr><td class="lib-name">flutter_markdown_plus</td><td class="lib-version">^1.0.7</td><td>Markdown 内容渲染，支持代码高亮和 LaTeX 行内公式</td></tr>
<tr><td class="lib-name">image</td><td class="lib-version">^4.5.4</td><td>图像处理库，用于拍照后的裁剪、缩放、预处理</td></tr>
</tbody>
</table>
<h3 class="fade-in" style="font-size:1.05rem;margin-top:2rem;margin-bottom:0.8rem;display:flex;align-items:center;gap:0.5rem;">