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金字塔变形构造

金字塔变形构造
几何画板及绘图内容加载中，请稍等……
2015-06-22 01:11
函数三角函数立体几何参数方程几何作图
所属专题 surface 3D surface 3D
①本范例演示了通过单一表面变形生成金字塔的过程；②涉及核心数学概念包括立体几何、三角函数、函数图像及参数方程；③构造要点运用了Append, Function, CurveCartesian, Angle, Sequence, Polygon, Element, Surface等GeoGebra命令与对象；④适合高中及以上学生及数学爱好者用于理解三维图形的动态变化与数学建模。

GeoGebra 命令及参数

  1. First({A, B, C, D, E, F, G, H, I, J, K, L}, n) → P_0
  2. Append(P_0, A) → P
  3. Function(Join[{{0, n}, Px}]) → fbx
  4. Function(Join[{{0, n}, Py}]) → fby
  5. CurveCartesian(fbx(t), fby(t), t, 0, n) → cb
  6. Angle((0, 0, 0), S, A) → α
  7. Sequence(Surface[(fbx(u) * (1 - v)) + (v * x(S)), (fby(u) * (1 - v)) + (v * y(S)), (ceil((v * m)) / m * z(S)), u, 0, U, v, ((i - 1) * V / m), (i * V / m)], i, 1, m) → liste1
  8. Sequence(CurveCartesian[(fbx(u) * (1 - v)) + (v * x(S)), (fby(u) * (1 - v)) + (v * y(S)), (ceil((v * m)) / m * z(S)), v, 0, V], u, 0, U, U / n) → liste3
  9. Sequence(CurveCartesian[(fbx(u) * (1 - v)) + (v * x(S)), (fby(u) * (1 - v)) + (v * y(S)), (ceil((v * m)) / m * z(S)), u, 0, U], v, 0, V, 1 / m) → liste2
  10. Polygon(P_0) → poly1
  11. Element({f1, f2, f3}, selec) → f
  12. Surface((((fbx(u) * (1 - v)) + (v * x(S))) * cos((w * v))) - (sin((w * v)) * ((fby(u) * (1 - v)) + (v * y(S)))), (((fbx(u) * (1 - v)) + (v * x(S))) * sin((w * v))) + (cos((w * v)) * ((fby(u) * (1 - v)) + (v * y(S)))), f(v), u, 0, U, v, 0.01, V) → d
  13. Surface((((fbx(u) * (1 - v)) + (v * x(S))) * cos((w * v))) - (sin((w * v)) * ((fby(u) * (1 - v)) + (v * y(S)))), (((fbx(u) * (1 - v)) + (v * x(S))) * sin((w * v))) + (cos((w * v)) * ((fby(u) * (1 - v)) + (v * y(S)))), f(v), u, 0, U, v, 0, V) → a
  14. Surface((((fbx(u) * (1 - v)) + (v * x(S))) * cos((w * v))) - (sin((w * v)) * ((fby(u) * (1 - v)) + (v * y(S)))), (((fbx(u) * (1 - v)) + (v * x(S))) * sin((w * v))) + (cos((w * v)) * ((fby(u) * (1 - v)) + (v * y(S)))), f(v), u, 0.03, U, v, 0, V) → b
  15. Sequence(CurveCartesian[(fbx(u) * (1 - v)) + (v * x(S)), (fby(u) * (1 - v)) + (v * y(S)), (ceil((v * m)) / m * z(S)), u, 0, U], v, 0.01, V, 1 / m) → liste4