生态景观造路
上传时间：2026-04-09 10:20 · 作者：ytry1983
最短距离：生态景观带路径 (第6题)
利用方向平移处理不同角度的固定路径段
📐 几何逻辑：分向平移
由于景观带 $l_1$ 和 $l_2$ 方向不同，我们需要进行分步平移：
- 将 $R$ 沿垂直于 $l_1$ 的方向平移，距离等于该处景观带宽度。
- 将 $S$ 沿垂直于 $l_2$ 的方向平移，距离等于该处景观带宽度。
连接两个平移点得到的线段 $R'S'$，其与两条内侧边界的交点就是廊道的最佳位置点。
💡 优化提示
如果画面仍有部分遮挡，您可以尝试上下滑动页面。当前的布局已将“酒店 S”及其作图痕迹提升到了安全高度（约 $y=410$），在大多数屏幕上均可完整显示。
查看解析页源码
<!DOCTYPE html>
<html lang="zh-CN">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>最短距离：多廊道平移问题演示</title>
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<style>
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0%, 100% { transform: scale(1); opacity: 1; }
50% { transform: scale(1.3); opacity: 0.7; }
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font-style: italic;
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<div class="max-w-4xl w-full bg-white rounded-2xl shadow-xl overflow-hidden border border-slate-200">
<!-- Header -->
<div class="bg-teal-600 p-6 text-white text-center">
<h1 class="text-2xl font-bold text-white">最短距离：生态景观带路径 (第6题)</h1>
<p class="mt-2 opacity-90 text-white">利用方向平移处理不同角度的固定路径段</p>
</div>
<!-- Animation Area -->
<div class="relative h-[600px] w-full bg-slate-50 border-y border-slate-200 overflow-hidden">
<!-- 增加 viewBox 高度到 650，并调整几何图形位置，避开底部的说明框 -->
<svg id="animation-svg" class="w-full h-full" viewBox="0 0 600 650" preserveAspectRatio="xMidYMid meet">
<!-- 景观带背景 - V型 (整体上移约 50px) -->
<!-- 景观带1 (斜向) -->
<path d="M 50 350 L 250 20 L 310 50 L 110 380 Z" fill="#ecfdf5" stroke="#10b981" stroke-width="1" />
<line x1="250" y1="20" x2="50" y2="350" stroke="#059669" stroke-width="2" stroke-dasharray="4" />
<line x1="310" y1="50" x2="110" y2="380" stroke="#059669" stroke-width="2" stroke-dasharray="4" />
<!-- 景观带2 (水平) -->
<path d="M 110 380 L 550 380 L 550 320 L 310 320 Z" fill="#ecfdf5" stroke="#10b981" stroke-width="1" />
<line x1="110" y1="380" x2="550" y2="380" stroke="#059669" stroke-width="2" stroke-dasharray="4" />
<line x1="310" y1="320" x2="550" y2="320" stroke="#059669" stroke-width="2" stroke-dasharray="4" />
<!-- 文字标注 -->
<text x="140" y="100" transform="rotate(-60, 140, 100)" class="text-[10px] fill-teal-700 font-bold italic">湖岸 l1</text>
<text x="450" y="395" class="text-[10px] fill-teal-700 font-bold italic">湖岸 l2</text>
<!-- 酒店 R 和 S -->
<g id="points-static">
<!-- 酒店 R 位置上移 -->
<rect x="200" y="60" width="12" height="12" fill="#ef4444" rx="2" />
<text x="180" y="70" class="font-bold fill-slate-800">酒店 R</text>
<!-- 酒店 S 位置上移至 410，确保在说明框上方 -->
<rect x="420" y="410" width="12" height="12" fill="#ef4444" rx="2" />
<text x="440" y="420" class="font-bold fill-slate-800">酒店 S</text>
</g>
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<g id="dynamic-layers"></g>
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<div id="info-box" class="absolute bottom-4 left-6 right-6 bg-white/80 backdrop-blur-sm p-4 rounded-xl shadow-lg border border-teal-100 transition-opacity duration-300 pointer-events-none">
<h3 id="step-title" class="text-lg font-bold text-teal-900"></h3>
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<div class="p-6 flex justify-between items-center bg-slate-50">
<button id="prev-btn" class="px-6 py-2 rounded-full border border-slate-300 text-slate-600 hover:bg-white transition-all active:scale-95 disabled:opacity-50">
上一步
</button>
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<button id="next-btn" class="px-6 py-2 rounded-full bg-teal-600 text-white hover:bg-teal-700 transition-all shadow-lg shadow-teal-200 active:scale-95">
下一步
</button>
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</div>
<!-- Explanation -->
<div class="mt-8 grid grid-cols-1 md:grid-cols-2 gap-6 max-w-4xl w-full pb-12">
<div class="bg-white p-6 rounded-xl shadow-sm border border-slate-200">
<h4 class="font-bold text-teal-800 flex items-center gap-2 text-teal-800">
<span>📐</span> 几何逻辑：分向平移
</h4>
<div class="text-sm text-slate-600 mt-2 space-y-2 leading-relaxed">
<p>由于景观带 $l_1$ 和 $l_2$ 方向不同，我们需要进行分步平移：</p>
<ul class="list-disc list-inside bg-teal-50 p-2 rounded text-teal-900">
<li>将 $R$ 沿垂直于 $l_1$ 的方向平移，距离等于该处景观带宽度。</li>
<li>将 $S$ 沿垂直于 $l_2$ 的方向平移，距离等于该处景观带宽度。</li>
</ul>
<p>连接两个平移点得到的线段 $R'S'$，其与两条内侧边界的交点就是廊道的最佳位置点。</p>
</div>
</div>
<div class="bg-white p-6 rounded-xl shadow-sm border border-slate-200">
<h4 class="font-bold text-teal-800 flex items-center gap-2">
<span>💡</span> 优化提示
</h4>
<p class="text-sm text-slate-600 mt-2">
如果画面仍有部分遮挡，您可以尝试上下滑动页面。当前的布局已将“酒店 S”及其作图痕迹提升到了安全高度（约 $y=410$），在大多数屏幕上均可完整显示。
</p>
</div>
</div>
<script>
const steps = [
{ title: "1. 场景分析", desc: "路径 R→C→D→P→Q→S 中，CD 和 PQ 是长度固定的廊道（宽度）。我们需要找到最优的 D 和 P 点。" },
{ title: "2. 垂直平移 R", desc: "将点 R 沿垂直于斜岸 l1 的方向向内平移，得到点 R'。这抵消了廊道 CD 对路径方向的影响。" },
{ title: "3. 垂直平移 S", desc: "将点 S 沿垂直于水平岸 l2 的方向向上平移，得到点 S'。这抵消了廊道 PQ 对路径方向的影响。" },
{ title: "4. 连接 R'S' 确定交点", desc: "连接 R'S'，其与 l1 内侧交点为 D，与 l2 内侧交点为 P。直线 A-B 最短原理在此生效。" },
{ title: "5. 还原路径与证明", desc: "完成作图。橙色平行四边形展示了 AM=A'N 的等价性，红色折线即为所求的最短观光路径。" }
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// 几何定义 (整体 y 上移 50)
const pR = { x: 206, y: 66 };
const pS = { x: 426, y: 416 };
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const pRPrime = { x: pR.x + v1.dx, y: pR.y + v1.dy };
const v2 = { dx: 0, dy: -60 };
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const pD = { x: 285, y: 135 };
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createSVGElement('circle', { cx: pD.x, cy: pD.y, r: 4, fill: '#10b981' });
createSVGElement('circle', { cx: pP.x, cy: pP.y, r: 4, fill: '#10b981' });
createSVGElement('text', { x: pD.x + 10, y: pD.y, class: 'fill-emerald-700 text-[10px] font-bold', textContent: 'D' });
createSVGElement('text', { x: pP.x - 5, y: pP.y - 10, class: 'fill-emerald-700 text-[10px] font-bold', textContent: 'P' });
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const poly2 = `${pS.x},${pS.y} ${pSPrime.x},${pSPrime.y} ${pP.x},${pP.y} ${pQ.x},${pQ.y}`;
createSVGElement('polygon', { points: poly1, fill: '#fbbf24', opacity: 0.15, stroke: '#d97706', 'stroke-width': 1, 'stroke-dasharray': '2' });
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createSVGElement('line', { x1: pC.x, y1: pC.y, x2: pD.x, y2: pD.y, stroke: '#10b981', 'stroke-width': 4 });
createSVGElement('line', { x1: pP.x, y1: pP.y, x2: pQ.x, y2: pQ.y, stroke: '#10b981', 'stroke-width': 4 });
createSVGElement('text', { x: pC.x - 10, y: pC.y, class: 'fill-emerald-700 text-[10px] font-bold', textContent: 'C' });
createSVGElement('text', { x: pQ.x + 10, y: pQ.y + 15, class: 'fill-emerald-700 text-[10px] font-bold', textContent: 'Q' });
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