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edu-solid-geometry

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把一道立体几何题解成一个自包含的交互教学网页：左侧 MathJax 分步解析， 右侧 Three.js 可交互 3D 模型（分步高亮 + 镜头切换）。支持三种入口——给定文字题目、 随机出题、上传题目图片识别后解题。覆盖正方体/长方体、棱锥/棱柱、圆柱/圆锥上的线面角、 二面角、异面直线夹角、点到平面距离、体积等题型，统一用"建系+向量法"，并由 sympy 精确 计算驱动（答案、3D 坐标、步骤数值同源一致）。其他 agent 也可调用本技能生成此类网页。 触发词：立体几何, 线面角, 二面角, 异面直线, 点到平面距离, 正四棱锥, 正方体求角, 解这道几何题, 随机出一道立体几何题, 这张图里的立体几何题; solid geometry, line-plane angle, dihedral angle, angle between skew lines, distance to plane, interactive geometry solution page.

skills/edu-solid-geometry/SKILL.md

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# 立体几何解题 → 交互网页

## 这个技能产出什么
一个可直接用浏览器打开的单页 HTML：左侧题面/答案/分步解析（公式用 MathJax），
右侧是题目对应的 3D 模型（Three.js，可旋转缩放，分步高亮关键元素并切换镜头）。
形态与 `template/lesson.html` 一致。

## 依赖（重要）
计算核心 `lib/geometry_kernel.py` 依赖 **sympy**。运行脚本前先确认有一个能 import sympy 的
`python3`：跑 `python3 -c "import sympy"`。

**缺库时的处理（重要）**：若 import 报错（sympy 或后续用到的任何库都同理），**先询问用户是否安装**，
得到同意后再帮忙安装（`python3 -m pip install <库名>`），或换一个已装该库的解释器；**不要未经询问直接装**。
下文命令里的 `python3` 均指这个能跑通依赖的解释器。
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