可见性实验：灰色点能看到的世界
几何画板及绘图内容加载中，请稍等……
① 本范例演示一个交互式可见性实验，用户只能看到灰色点所“看见”的区域，直观展示视线遮挡与可见范围的概念。② 核心数学概念包括视线、遮挡、多边形区域、角度与几何变换，涉及点、线段、多边形、圆等基本几何元素及其相互关系。③ 作图要点：使用GeoGebra命令Polygon（多边形）、Ray（射线）、Intersect（求交点）、Circle（圆）、Segment（线段）构造场景；对象包括多个点（A1至N1）、线段（c1至n2）、多边形（q1至q5）以及圆等，通过射线与多边形求交实现可见区域的动态计算。④ 适合中学几何教学、数学实验课或计算机图形学入门，帮助学生理解空间感知与几何可视化的结合，也可用于探索遮挡问题的数学建模。
GeoGebra 命令及参数
Polygon(C_{1}, D_{1}, E_{1}, F_{1}) → q1_{1}, c_{1}, d_{1}, e_{1}, f_{2}Ray(G_{1}, E_{1}) → g_{1}Ray(G_{1}, D_{1}) → h_{1}Ray(G_{1}, C_{1}) → i_{1}Intersect(g_{1}, i_{1}) → H_{1}Ray(G_{1}, F_{1}) → j_{1}Circle(I_{1}, J_{1}) → f_{1}Intersect(f_{1}, i_{1}, 1) → K_{1}Intersect(f_{1}, j_{1}, 1) → L_{1}Intersect(f_{1}, g_{1}, 1) → M_{1}Intersect(f_{1}, h_{1}, 1) → N_{1}Polygon(L_{1}, F_{1}, C_{1}, K_{1}) → q2_{1}, l_{1}, f_{3}, c_{2}, k_{1}Polygon(D_{1}, N_{1}, K_{1}, C_{1}) → q3_{1}, d_{2}, n_{1}, k_{2}, c_{3}Polygon(N_{1}, M_{1}, E_{1}, D_{1}) → q4_{1}, n_{2}, m_{1}, e_{2}, d_{3}Polygon(F_{1}, L_{1}, M_{1}, E_{1}) → q5_{1}, f_{4}, l_{2}, m_{2}, e_{3}Segment(O_{1}, P_{1}) → p_{1}Ray(G_{1}, P_{1}) → q_{1}Ray(G_{1}, O_{1}) → r_{1}Polygon(Q_{1}, R_{1}, S_{1}, T_{1}, U_{1}, I_{1}, V_{1}, W_{1}) → poly1_{1}, q_{2}, r_{2}, s_{1}, t_{1}, u_{1}, i_{2}, v_{1}, w_{1}Intersect(f_{1}, r_{1}, 1) → Z_{1}Intersect(f_{1}, q_{1}, 1) → A_{2}Polygon(Z_{1}, A_{2}, P_{1}, O_{1}) → q6_{1}, z_{1}, a_{2}, p_{2}, o_{1}Ray(G_{1}, U_{1}) → a_{1}Ray(G_{1}, Q_{1}) → b_{1}Ray(G_{1}, R_{1}) → g_{2}Ray(G_{1}, W_{1}) → h_{2}Ray(G_{1}, S_{1}) → j_{2}Ray(G_{1}, T_{1}) → s_{2}Ray(G_{1}, I_{1}) → t_{2}Ray(G_{1}, V_{1}) → b_{2}Intersect(f_{1}, h_{2}, 1) → B_{2}Intersect(f_{1}, b_{1}, 1) → C_{2}Polygon(W_{1}, B_{2}, C_{2}, Q_{1}) → q7_{1}, w_{2}, g_{3}, h_{3}, q_{3}Intersect(f_{1}, g_{2}, 1) → D_{2}Polygon(Q_{1}, C_{2}, D_{2}, R_{1}) → q8_{1}, q_{4}, i_{3}, j_{3}, r_{3}Intersect(f_{1}, j_{2}, 1) → E_{2}Polygon(D_{2}, E_{2}, S_{1}, R_{1}) → q9_{1}, k_{3}, l_{3}, s_{3}, r_{4}Intersect(f_{1}, s_{2}, 1) → F_{2}Polygon(S_{1}, E_{2}, F_{2}, T_{1}) → q10_{1}, s_{4}, m_{3}, n_{3}, t_{3}Intersect(f_{1}, a_{1}, 1) → G_{2}Polygon(T_{1}, F_{2}, G_{2}, U_{1}) → q11_{1}, t_{4}, p_{3}, a_{3}, u_{2}Intersect(f_{1}, t_{2}, 1) → H_{2}Polygon(G_{2}, H_{2}, I_{1}, U_{1}) → q12_{1}, b_{3}, g_{4}, i_{4}, u_{3}Intersect(f_{1}, b_{2}, 1) → I_{2}Polygon(I_{1}, H_{2}, I_{2}, V_{1}) → q13_{1}, i_{5}, h_{4}, j_{4}, v_{2}Polygon(V_{1}, I_{2}, B_{2}, W_{1}) → q14_{1}, v_{3}, k_{4}, l_{4}, w_{3}
AI 绘图提示语参考
绘制一个由多个点和线段构成的复杂图形，其中包括五个可见区域（q1到q5），每个区域由多个顶点和线段组成。首先绘制五个多边形（q1到q5），然后通过线段和射线的交点确定每个区域的边界。最后，使用射线和圆的交点来定义每个区域的可见部分。
以上提示语为根据原始绘图命令整理而来，仅供参考。