Contour of Saddle Surface in Axonometry 2

Contour of Saddle Surface in Axonometry 2
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2020-04-22 04:25
This example demonstrates the contour lines of a saddle surface in axonometric projection. Key mathematical concepts include surfaces, axonometric projection, and geometric construction. It utilizes commands like Segment, Line, Intersect, OrthogonalLine, Point, Locus, and Polygon in GeoGebra to create the visualization. Suitable for high school and above students studying 3D geometry and projection transformations.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Draw an axonometric projection of a saddle surface showing its contour lines. Start with a quadrilateral base and its projection. From two base vertices, erect perpendiculars to define two elevated points, forming the surface edges. On the projection plane, use intersections and auxiliary lines to construct the main contour lines, then generate inner contours by connecting intersection points with parallels, completing the saddle-shaped outline.
The prompt above was compiled from the original drawing commands and is for reference only.