558 lines
19 KiB
HTML
558 lines
19 KiB
HTML
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<!DOCTYPE html>
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<html lang="zh-CN">
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<head>
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<meta charset="UTF-8">
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<meta name="viewport" content="width=device-width, initial-scale=1.0">
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<title>高级数学函数图像生成器</title>
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<script src="https://cdn.jsdelivr.net/npm/chart.js"></script>
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<script src="https://cdn.jsdelivr.net/npm/mathjs@11.6.0/lib/browser/math.js"></script>
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<style>
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:root {
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--primary-color: #4361ee;
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--secondary-color: #3f37c9;
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--accent-color: #4895ef;
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--light-color: #f8f9fa;
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--dark-color: #212529;
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--success-color: #4cc9f0;
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--warning-color: #f72585;
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}
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* {
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margin: 0;
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padding: 0;
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box-sizing: border-box;
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font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
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}
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body {
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background-color: #f5f7fa;
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color: var(--dark-color);
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line-height: 1.6;
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padding: 20px;
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min-width: 900px;
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}
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.container {
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max-width: 1400px;
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min-width: 900px;
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margin: 0 auto;
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padding: 30px;
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background-color: white;
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border-radius: 12px;
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box-shadow: 0 10px 30px rgba(0, 0, 0, 0.08);
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}
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header {
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text-align: center;
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margin-bottom: 30px;
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padding-bottom: 20px;
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border-bottom: 1px solid rgba(0, 0, 0, 0.1);
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}
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h1 {
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color: var(--primary-color);
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font-weight: 700;
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margin-bottom: 10px;
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font-size: 2.5rem;
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}
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.subtitle {
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color: #6c757d;
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font-size: 1.1rem;
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margin-bottom: 15px;
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}
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.intro-box {
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background-color: #f8f9fa;
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padding: 20px;
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border-radius: 8px;
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margin-bottom: 30px;
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border-left: 4px solid var(--accent-color);
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}
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.intro-box h3 {
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color: var(--primary-color);
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margin-bottom: 10px;
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}
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.intro-box ul {
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padding-left: 20px;
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}
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.intro-box li {
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margin-bottom: 5px;
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}
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.app-container {
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display: grid;
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grid-template-columns: 1fr 2fr;
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gap: 30px;
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}
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.control-panel {
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background-color: #f8f9fa;
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padding: 25px;
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border-radius: 10px;
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box-shadow: 0 4px 6px rgba(0, 0, 0, 0.05);
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min-width: 350px;
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}
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.form-group {
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margin-bottom: 20px;
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}
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label {
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display: block;
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margin-bottom: 8px;
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font-weight: 600;
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color: var(--dark-color);
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}
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input, select {
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width: 100%;
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padding: 12px 15px;
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border: 1px solid #ced4da;
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border-radius: 6px;
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font-size: 1rem;
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transition: all 0.3s;
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}
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input:focus, select:focus {
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outline: none;
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border-color: var(--primary-color);
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box-shadow: 0 0 0 3px rgba(67, 97, 238, 0.2);
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}
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button {
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background-color: var(--primary-color);
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color: white;
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border: none;
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padding: 12px 20px;
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border-radius: 6px;
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cursor: pointer;
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font-size: 1rem;
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font-weight: 600;
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transition: all 0.3s;
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width: 100%;
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margin-top: 10px;
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}
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button:hover {
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background-color: var(--secondary-color);
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transform: translateY(-2px);
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}
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.chart-container {
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position: relative;
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height: 500px;
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background-color: white;
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border-radius: 10px;
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box-shadow: 0 4px 6px rgba(0, 0, 0, 0.05);
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padding: 15px;
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min-width: 500px;
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}
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.examples-panel {
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margin-top: 25px;
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padding-top: 20px;
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border-top: 1px solid rgba(0, 0, 0, 0.1);
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}
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.examples-header {
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display: flex;
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justify-content: space-between;
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align-items: center;
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margin-bottom: 15px;
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cursor: pointer;
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}
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.examples-header h3 {
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color: var(--primary-color);
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margin: 0;
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}
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.examples-content {
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display: none;
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padding: 10px;
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background-color: white;
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border-radius: 6px;
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}
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.examples-content.show {
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display: block;
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}
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.example-list {
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list-style: none;
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}
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.example-list li {
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margin-bottom: 10px;
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padding: 10px;
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background-color: white;
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border-radius: 6px;
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border-left: 4px solid var(--accent-color);
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cursor: pointer;
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transition: all 0.2s;
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}
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.example-list li:hover {
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background-color: #e9ecef;
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transform: translateX(5px);
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}
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.error-message {
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color: var(--warning-color);
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margin-top: 10px;
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font-size: 0.9rem;
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display: none;
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}
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.footer {
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text-align: center;
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margin-top: 40px;
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color: #6c757d;
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font-size: 0.9rem;
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}
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.toggle-icon {
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transition: transform 0.3s;
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}
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.toggle-icon.rotated {
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transform: rotate(180deg);
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}
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.real-time-btn {
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background-color: var(--accent-color);
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}
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.real-time-btn.active {
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background-color: var(--success-color);
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}
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.button-group {
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display: flex;
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gap: 10px;
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}
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.button-group button {
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margin-top: 0;
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}
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</style>
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</head>
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<body>
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<div class="container">
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<header>
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<h1>数学函数图像生成器</h1>
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<p class="subtitle">拥有基本运算，输入框不支持更高级参数填入</p>
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</header>
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<div class="intro-box">
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<h3>使用说明</h3>
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<p>手机请缩小屏幕，输入数学函数表达式，设置参数范围，即可生成精美的函数图像。</p>
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<h3>支持的运算符和函数：</h3>
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<ul>
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<li>基本运算: +, -, *, /, ^ (幂)</li>
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<li>三角函数: sin, cos, tan, asin, acos, atan</li>
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<li>对数函数: log, log10, ln</li>
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<li>其他函数: sqrt, abs, ceil, floor, round</li>
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<li>常数: pi, e</li>
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</ul>
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<h3>注意事项：</h3>
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<ul>
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<li>使用 x 作为变量，区分大小写</li>
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<li>不支持隐式乘法，必须使用 * 运算符</li>
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<li>不支持分段函数和条件表达式</li>
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<li>程序预留有示例方案</li>
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<li>某些函数在特定区间可能无定义(如log(0))</li>
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<li>复数结果将显示为NaN</li>
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<li>无法生成创意图案，因为输入框限制，而且这个不是直角系</li>
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<li>千万不要把所有数值输入过大和过小，否则会卡</li>
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</ul>
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</div>
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<div class="app-container">
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<div class="control-panel">
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<div class="form-group">
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<label for="function-input">函数表达式 (使用 x 作为变量)</label>
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<input type="text" id="function-input" placeholder="例如: sin(x), x^2 + 2*x + 1" value="sin(x)">
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</div>
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<div class="form-group">
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<label for="x-min">X 最小值</label>
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<input type="number" id="x-min" value="-10" step="0.1">
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</div>
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<div class="form-group">
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<label for="x-max">X 最大值</label>
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<input type="number" id="x-max" value="10" step="0.1">
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</div>
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<div class="form-group">
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<label for="step">步长 (精度)</label>
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<input type="number" id="step" value="0.1" step="0.01" min="0.01">
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</div>
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<div class="form-group">
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<label for="line-color">线条颜色</label>
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<select id="line-color">
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<option value="#4361ee">蓝色</option>
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<option value="#f72585">粉色</option>
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<option value="#4cc9f0">青色</option>
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<option value="#7209b7">紫色</option>
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<option value="#3a0ca3">深蓝</option>
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</select>
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</div>
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<div class="button-group">
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<button id="plot-button">绘制函数图像</button>
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<button id="real-time-btn" class="real-time-btn">实时生成图像</button>
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</div>
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<div id="error-message" class="error-message"></div>
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<div class="examples-panel">
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<div class="examples-header" id="examples-toggle">
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<h3>示例函数</h3>
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<svg class="toggle-icon" width="16" height="16" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round">
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<polyline points="6 9 12 15 18 9"></polyline>
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</svg>
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</div>
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<div class="examples-content" id="examples-content">
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<ul class="example-list">
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<li onclick="useExample('sin(x)')">正弦函数: sin(x)</li>
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<li onclick="useExample('cos(x)')">余弦函数: cos(x)</li>
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<li onclick="useExample('tan(x)')">正切函数: tan(x)</li>
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<li onclick="useExample('x^2')">二次函数: x^2</li>
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<li onclick="useExample('x^3 - 3*x')">三次函数: x^3 - 3*x</li>
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<li onclick="useExample('sqrt(x)')">平方根函数: sqrt(x)</li>
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<li onclick="useExample('log(x)')">自然对数: log(x)</li>
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<li onclick="useExample('log10(x)')">常用对数: log10(x)</li>
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<li onclick="useExample('exp(x)')">指数函数: exp(x)</li>
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<li onclick="useExample('abs(x)')">绝对值函数: abs(x)</li>
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<li onclick="useExample('sin(x)/x')">sinc函数: sin(x)/x</li>
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<li onclick="useExample('1/x')">反比例函数: 1/x</li>
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</ul>
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</div>
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</div>
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</div>
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<div class="chart-container">
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<canvas id="function-chart"></canvas>
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</div>
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</div>
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<div class="footer">
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<p>© 2023 高级数学可视化工具 | 使用 Chart.js 和 Math.js 构建 | 支持缩放和平移功能</p>
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</div>
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</div>
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<script>
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// 初始化图表
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const ctx = document.getElementById('function-chart').getContext('2d');
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let chart = new Chart(ctx, {
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type: 'line',
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data: {
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datasets: [{
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label: '函数图像(支持横向触摸图像有信息跟踪)',
|
|||
|
|
borderColor: '#4361ee',
|
|||
|
|
borderWidth: 3,
|
|||
|
|
pointRadius: 0,
|
|||
|
|
fill: false,
|
|||
|
|
tension: 0.1
|
|||
|
|
}]
|
|||
|
|
},
|
|||
|
|
options: {
|
|||
|
|
responsive: true,
|
|||
|
|
maintainAspectRatio: false,
|
|||
|
|
scales: {
|
|||
|
|
x: {
|
|||
|
|
title: {
|
|||
|
|
display: true,
|
|||
|
|
text: 'X轴',
|
|||
|
|
font: {
|
|||
|
|
size: 14,
|
|||
|
|
weight: 'bold'
|
|||
|
|
}
|
|||
|
|
},
|
|||
|
|
grid: {
|
|||
|
|
color: 'rgba(0, 0, 0, 0.05)'
|
|||
|
|
}
|
|||
|
|
},
|
|||
|
|
y: {
|
|||
|
|
title: {
|
|||
|
|
display: true,
|
|||
|
|
text: 'Y轴',
|
|||
|
|
font: {
|
|||
|
|
size: 14,
|
|||
|
|
weight: 'bold'
|
|||
|
|
}
|
|||
|
|
},
|
|||
|
|
grid: {
|
|||
|
|
color: 'rgba(0, 0, 0, 0.05)'
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
},
|
|||
|
|
plugins: {
|
|||
|
|
legend: {
|
|||
|
|
position: 'top',
|
|||
|
|
labels: {
|
|||
|
|
font: {
|
|||
|
|
size: 14
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
},
|
|||
|
|
tooltip: {
|
|||
|
|
mode: 'index',
|
|||
|
|
intersect: false,
|
|||
|
|
callbacks: {
|
|||
|
|
label: function(context) {
|
|||
|
|
return `f(${context.parsed.x.toFixed(2)}) = ${context.parsed.y.toFixed(4)}`;
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
},
|
|||
|
|
zoom: {
|
|||
|
|
zoom: {
|
|||
|
|
wheel: {
|
|||
|
|
enabled: true,
|
|||
|
|
},
|
|||
|
|
pinch: {
|
|||
|
|
enabled: true
|
|||
|
|
},
|
|||
|
|
mode: 'xy',
|
|||
|
|
},
|
|||
|
|
pan: {
|
|||
|
|
enabled: true,
|
|||
|
|
mode: 'xy',
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
});
|
|||
|
|
|
|||
|
|
// 实时生成状态
|
|||
|
|
let isRealTime = false;
|
|||
|
|
let inputElements = [
|
|||
|
|
document.getElementById('function-input'),
|
|||
|
|
document.getElementById('x-min'),
|
|||
|
|
document.getElementById('x-max'),
|
|||
|
|
document.getElementById('step'),
|
|||
|
|
document.getElementById('line-color')
|
|||
|
|
];
|
|||
|
|
|
|||
|
|
// 防抖函数，避免频繁更新
|
|||
|
|
function debounce(func, wait) {
|
|||
|
|
let timeout;
|
|||
|
|
return function() {
|
|||
|
|
const context = this;
|
|||
|
|
const args = arguments;
|
|||
|
|
clearTimeout(timeout);
|
|||
|
|
timeout = setTimeout(() => {
|
|||
|
|
func.apply(context, args);
|
|||
|
|
}, wait);
|
|||
|
|
};
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// 绘制函数
|
|||
|
|
function plotFunction() {
|
|||
|
|
const funcInput = document.getElementById('function-input').value;
|
|||
|
|
const xMin = parseFloat(document.getElementById('x-min').value);
|
|||
|
|
const xMax = parseFloat(document.getElementById('x-max').value);
|
|||
|
|
const step = parseFloat(document.getElementById('step').value);
|
|||
|
|
const lineColor = document.getElementById('line-color').value;
|
|||
|
|
|
|||
|
|
const errorElement = document.getElementById('error-message');
|
|||
|
|
errorElement.style.display = 'none';
|
|||
|
|
|
|||
|
|
try {
|
|||
|
|
// 生成x值数组
|
|||
|
|
const xValues = [];
|
|||
|
|
for (let x = xMin; x <= xMax; x += step) {
|
|||
|
|
xValues.push(x);
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// 计算y值
|
|||
|
|
const yValues = [];
|
|||
|
|
const scope = {};
|
|||
|
|
|
|||
|
|
for (let i = 0; i < xValues.length; i++) {
|
|||
|
|
scope.x = xValues[i];
|
|||
|
|
try {
|
|||
|
|
const y = math.evaluate(funcInput, scope);
|
|||
|
|
yValues.push(y);
|
|||
|
|
} catch (e) {
|
|||
|
|
// 对于某些x值可能无法计算（如log(0)）
|
|||
|
|
yValues.push(NaN);
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// 更新图表
|
|||
|
|
chart.data.labels = xValues;
|
|||
|
|
chart.data.datasets[0].data = yValues.map((y, i) => ({x: xValues[i], y: y}));
|
|||
|
|
chart.data.datasets[0].borderColor = lineColor;
|
|||
|
|
chart.update();
|
|||
|
|
|
|||
|
|
} catch (error) {
|
|||
|
|
errorElement.textContent = `错误: ${error.message}`;
|
|||
|
|
errorElement.style.display = 'block';
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// 使用示例函数
|
|||
|
|
function useExample(func) {
|
|||
|
|
document.getElementById('function-input').value = func;
|
|||
|
|
if (isRealTime) {
|
|||
|
|
plotFunction();
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// 切换实时生成模式
|
|||
|
|
function toggleRealTime() {
|
|||
|
|
const realTimeBtn = document.getElementById('real-time-btn');
|
|||
|
|
isRealTime = !isRealTime;
|
|||
|
|
|
|||
|
|
if (isRealTime) {
|
|||
|
|
realTimeBtn.classList.add('active');
|
|||
|
|
realTimeBtn.textContent = '实时生成中...';
|
|||
|
|
// 立即绘制一次
|
|||
|
|
plotFunction();
|
|||
|
|
} else {
|
|||
|
|
realTimeBtn.classList.remove('active');
|
|||
|
|
realTimeBtn.textContent = '实时生成图像';
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// 设置输入框监听
|
|||
|
|
function setupInputListeners() {
|
|||
|
|
const debouncedPlot = debounce(plotFunction, 500);
|
|||
|
|
|
|||
|
|
inputElements.forEach(element => {
|
|||
|
|
element.addEventListener('input', () => {
|
|||
|
|
if (isRealTime) {
|
|||
|
|
debouncedPlot();
|
|||
|
|
}
|
|||
|
|
});
|
|||
|
|
});
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// 切换示例面板
|
|||
|
|
document.getElementById('examples-toggle').addEventListener('click', function() {
|
|||
|
|
const content = document.getElementById('examples-content');
|
|||
|
|
const icon = this.querySelector('.toggle-icon');
|
|||
|
|
content.classList.toggle('show');
|
|||
|
|
icon.classList.toggle('rotated');
|
|||
|
|
});
|
|||
|
|
|
|||
|
|
// 事件监听
|
|||
|
|
document.getElementById('plot-button').addEventListener('click', plotFunction);
|
|||
|
|
document.getElementById('real-time-btn').addEventListener('click', toggleRealTime);
|
|||
|
|
|
|||
|
|
// 设置输入监听
|
|||
|
|
setupInputListeners();
|
|||
|
|
|
|||
|
|
// 初始绘制
|
|||
|
|
plotFunction();
|
|||
|
|
</script>
|
|||
|
|
</body>
|
|||
|
|
</html>
|