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伞形曲面

伞形曲面
几何画板及绘图内容加载中，请稍等……
2020-07-01 15:27
立体几何微积分概率统计
①本范例演示了伞形曲面的三维几何图形及其变化规律；②涉及的核心数学概念包括曲面、超几何分布、频率分布、均值、微积分和 planes；③作图要点使用了 Surface 和 Segment 命令，以及 m, n_2, n_3, n_1, f, O, R, nn, A, g, B, C, c, h, d, D, E, p, e, q, i, Color 等对象；④适合高中及以上学生学习和理解立体几何、微积分及概率统计相关内容。

GeoGebra 命令及参数

  1. Surface(x(A) + (((g(i) * R) * cos(i)) * cos(j)), y(A) + (((g(i) * R) * sin(i)) * cos(j)), z(O) + (R * sin(j)) + 2, i, 0, 6.28319, j, 0, π) → c
  2. Surface(x(C) + (((h(i) * R) * cos(i)) * cos(j)), y(C) + (((h(i) * R) * sin(i)) * cos(j)), z(C) + (R * sin(j)) + 2, i, 0, 6.28319, j, 0, π) → d
  3. Surface(x(D) + (((p(i) * R) * cos(i)) * cos(j)), y(D) + (((p(i) * R) * sin(i)) * cos(j)), z(D) + (R * sin(j)) + 2, i, 0.1, 6.283, j, 0.1, π) → e
  4. Surface(x(E) + (((q(i) * R) * cos(i)) * cos(j)), y(E) + (((q(i) * R) * sin(i)) * cos(j)), z(E) + (R * sin(j)) + 2, i, 0.1, 6.283, j, 0.1, π) → i
  5. Surface(x(O) + (((f(i) * R) * cos(i)) * cos(j)), y(O) + (((f(i) * R) * sin(i)) * cos(j)), z(O) + (R * sin(j)) + 2, i, A1, A2, j, 0, π) → B1
  6. Surface(x(O) + (((f(i) * R) * cos(i)) * cos(j)), y(O) + (((f(i) * R) * sin(i)) * cos(j)), z(O) + (R * sin(j)) + 2, i, A2, A3, j, 0, π) → B2
  7. Surface(x(O) + (((f(i) * R) * cos(i)) * cos(j)), y(O) + (((f(i) * R) * sin(i)) * cos(j)), z(O) + (R * sin(j)) + 2, i, A3, A4, j, 0, π) → B3
  8. Surface(x(O) + (((f(i) * R) * cos(i)) * cos(j)), y(O) + (((f(i) * R) * sin(i)) * cos(j)), z(O) + (R * sin(j)) + 2, i, A4, A5, j, 0, π) → B4
  9. Surface(x(O) + (((f(i) * R) * cos(i)) * cos(j)), y(O) + (((f(i) * R) * sin(i)) * cos(j)), z(O) + (R * sin(j)) + 2, i, A5, A6, j, 0, π) → B5
  10. Surface(x(O) + (((f(i) * R) * cos(i)) * cos(j)), y(O) + (((f(i) * R) * sin(i)) * cos(j)), z(O) + (R * sin(j)) + 2, i, A6, A7, j, 0, π) → B6
  11. Surface(x(O) + (((f(i) * R) * cos(i)) * cos(j)), y(O) + (((f(i) * R) * sin(i)) * cos(j)), z(O) + (R * sin(j)) + 2, i, A7, A8, j, 0, π) → B7
  12. Surface(x(O) + (((f(i) * R) * cos(i)) * cos(j)), y(O) + (((f(i) * R) * sin(i)) * cos(j)), z(O) + (R * sin(j)) + 2, i, A8, A9, j, 0, π) → B8
  13. Surface(x(O) + (((f(i) * R) * cos(i)) * cos(j)), y(O) + (((f(i) * R) * sin(i)) * cos(j)), z(O) + (R * sin(j)) + 2, i, A9, A10, j, 0, π) → B9
  14. Surface(x(O) + (((f(i) * R) * cos(i)) * cos(j)), y(O) + (((f(i) * R) * sin(i)) * cos(j)), z(O) + (R * sin(j)) + 2, i, A10, A11, j, 0, π) → B10
  15. Surface(x(O) + (((f(i) * R) * cos(i)) * cos(j)), y(O) + (((f(i) * R) * sin(i)) * cos(j)), z(O) + (R * sin(j)) + 2, i, A11, A12, j, 0, π) → B11
  16. Surface(x(O) + (((f(i) * R) * cos(i)) * cos(j)), y(O) + (((f(i) * R) * sin(i)) * cos(j)), z(O) + (R * sin(j)) + 2, i, A12, A13, j, 0, π) → B12
  17. Surface(x(O) + (((f(i) * R) * cos(i)) * cos(j)), y(O) + (((f(i) * R) * sin(i)) * cos(j)), z(O) + (R * sin(j)) + 2, i, A13, A14, j, 0, π) → B13
  18. Segment(O, O + (0, 0, 2)) → j
  19. Segment(A, A + (0, 0, 3.5)) → k
  20. Segment(D, D + (0, 0, 3.5)) → l
  21. Segment(E, E + (0, 0, 3.5)) → n
  22. Segment(C, C + (0, 0, 3.5)) → r

AI 绘图提示语参考

绘制一组三维伞状曲面，展示其变化模式。这些曲面由多个参数化方程生成，围绕中心轴旋转，高度随角度变化，形成伞状结构。曲面之间通过不同参数的调整产生层次感，整体呈现出复杂的几何形态。先绘制中心基准曲面，再围绕中心轴生成多个同心曲面，最后添加几条垂直于基面的线段，增强立体感。
以上提示语为根据原始绘图命令整理而来，仅供参考。