鞍面在轴测投影中的等高线

鞍面在轴测投影中的等高线
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2020-04-22 04:25
①本范例演示了鞍面在轴测投影下的等高线图形;②涉及的核心数学概念包括曲面、轴测投影、几何作图;③作图要点——从下方『构造摘要』提炼用到了Segment(线段)、Line(直线)、Intersect(交点)、OrthogonalLine(垂线)、Point(点)、Locus(轨迹)、Polygon(多边形)等GeoGebra命令/对象;④适合高中及以上学生学习和理解三维几何与投影变换。

GeoGebra 命令及参数

  1. Segment(D, A') → f
  2. Segment(A', B) → g
  3. Line(B, f) → h
  4. Line(D, g) → i
  5. Intersect(h, i) → C'
  6. Segment(D, C') → j
  7. Segment(C', B) → k
  8. OrthogonalLine(A', g) → l
  9. OrthogonalLine(C', j) → m
  10. Point(l) → A
  11. Point(m) → C
  12. Segment(A, A') → n
  13. Segment(C, C') → p
  14. Segment(D, A) → q
  15. Segment(A, B) → r
  16. Segment(B, C) → s
  17. Segment(C, D) → t
  18. Line(D, C) → s_2
  19. Intersect(s_2, r) → E
  20. Segment(C, E) → a
  21. Line(E, n) → b
  22. Intersect(i, b) → F
  23. Intersect(g, b) → G
  24. Segment(E, F) → f_1
  25. Segment(F, C') → c
  26. Line(F, k) → d
  27. Line(B, j) → e
  28. Intersect(d, e) → H
  29. Segment(F, H) → g_1
  30. Segment(H, B) → h_1
  31. Line(G, k) → i_1
  32. Intersect(j, i_1) → I
  33. Segment(G, I) → j_1
  34. Segment(H, I) → k_1
  35. Intersect(k, k_1) → J
  36. Line(I, n) → l_1
  37. Line(J, l_1) → m_1
  38. Intersect(t, l_1) → K
  39. Intersect(s, m_1) → L
  40. Segment(K, I) → q_1
  41. Segment(L, J) → t_1
  42. Segment(J, I) → a_1
  43. Point(a_1) → M
  44. Line(M, j_1) → c_1
  45. Intersect(j, c_1) → N
  46. Intersect(c_1, g) → O
  47. Line(N, n) → d_1
  48. Line(O, d_1) → e_1
  49. Segment(K, I) → n_1
  50. Intersect(d_1, t) → P
  51. Intersect(e_1, r) → Q
  52. Segment(P, Q) → f_2
  53. Line(M, n) → g_2
  54. Intersect(g_2, f_2) → R
  55. Locus(R, M) → ponthalmaz1
  56. Segment(L, J) → p_1
  57. Segment(D, C) → r_1
  58. Segment(C, B) → s_1
  59. Segment(A, D) → b_1
  60. Intersect(r_1, b_1) → T
  61. Intersect(r_1, s_1) → U
  62. Point(r_1) → V
  63. Intersect(h_1, s_1) → S
  64. Segment(A, S) → h_2
  65. Intersect(b_1, h_2) → W
  66. Polygon(D, U, S, W) → q1, d_2, u, s_3, w
  67. Point(ponthalmaz1) → Z
  68. Point(ponthalmaz1) → A_1
  69. Point(ponthalmaz1) → B_1
  70. Point(ponthalmaz1) → C_1
  71. Point(ponthalmaz1) → D_1
  72. Point(ponthalmaz1) → E_1
  73. Point(ponthalmaz1) → F_1
  74. Point(ponthalmaz1) → G_1
  75. Point(ponthalmaz1) → H_1
  76. Polygon(U, S, G_1, H_1, K, L, Z, A_1, B_1, C_1, D_1, E_1, F_1) → poligon1, u_1, p_2, q_2, r_2, k_3, s_4, l_2, z_1, i_2, j_2, k_2, m_2, n_2

AI 绘图提示语参考

绘制一个鞍形曲面的轴测投影轮廓图。先构造一个空间四边形底面,并作出其轴测投影。从底面的两个顶点分别作垂线,确定曲面上两个高点,连接形成曲面边界。在投影面上,通过交点与辅助线,逐步构造出曲面的等高线:先画出两条主轮廓线,再通过交点与平行线,生成多条内部等高线,最终形成完整的鞍面轮廓。
以上提示语为根据原始绘图命令整理而来,仅供参考。