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鞍面在轴测投影中的等高线 by István Makai

鞍面在轴测投影中的等高线 by István Makai
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2020-04-22 04:30
向量函数三角函数解析几何立体几何
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、连续性、抛物线、随机变量和球面；③作图要点提炼自构造摘要，使用了线段、直线、交点、垂线、点、向量、平移、轨迹、多边形等 GeoGebra 命令/对象；④适合高中及以上数学学习者和教师用于理解空间几何和投影变换。

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(g, b) → G
  23. Line(B, j) → e
  24. Line(G, k) → i_1
  25. Intersect(j, i_1) → I
  26. Segment(G, I) → j_1
  27. Segment(E, G) → f_1
  28. Line(I, n) → l_1
  29. Intersect(t, l_1) → K
  30. Segment(K, I) → q_1
  31. Segment(K, I) → n_1
  32. Line(C, B) → c
  33. Intersect(c, q) → F
  34. Segment(C, F) → d
  35. OrthogonalLine(F, g) → g_1
  36. Intersect(g_1, f) → H
  37. Segment(F, H) → h_1
  38. Vector(A', H) → u
  39. Translate(A', u) → A''
  40. Translate(B, u) → B'
  41. Segment(A'', B') → g'
  42. OrthogonalLine(B', g) → k_1
  43. Intersect(s, k_1) → J
  44. Segment(J, B') → m_1
  45. Segment(I, B') → n_k
  46. Point(n_k) → L
  47. Line(L, j_1) → p_1
  48. Intersect(p_1, j) → M
  49. Intersect(g, p_1) → N
  50. Intersect(p, p_1) → O
  51. Intersect(p, n) → P
  52. Line(M, n) → t_1
  53. Line(N, t_1) → a_1
  54. Intersect(t, t_1) → Q
  55. Intersect(a_1, r) → R
  56. Segment(Q, R) → c_1
  57. Line(L, t_1) → d_1
  58. Intersect(c_1, d_1) → S
  59. Locus(S, L) → ponthalmaz1
  60. Segment(D, C) → r_1
  61. Segment(C, B) → s_1
  62. Segment(A, D) → b_1
  63. Intersect(r_1, b_1) → T
  64. Intersect(r_1, s_1) → U
  65. Point(r_1) → V
  66. Segment(A, B) → e_1
  67. Polygon(A, D, U, B) → q1, a_2, d_2, u_1, b_2
  68. Point(ponthalmaz1) → W
  69. Point(ponthalmaz1) → Z
  70. Point(ponthalmaz1) → A_1
  71. Point(ponthalmaz1) → B_1
  72. Point(ponthalmaz1) → C_1
  73. Point(ponthalmaz1) → D_1
  74. Point(ponthalmaz1) → E_1
  75. Point(ponthalmaz1) → F_1
  76. Point(ponthalmaz1) → G_1
  77. Point(ponthalmaz1) → H_1
  78. Point(ponthalmaz1) → I_1
  79. Point(ponthalmaz1) → J_1
  80. Polygon(U, K, G_1, H_1, I_1, J_1, J, W, Z, A_1, B_1, C_1, D_1, E_1, F_1) → poligon1, u_2, l_2, m_2, n_2, p_2, q_2, j_3, k_2, w, z_1, f_2, g_2, h_2, i_2, j_2