达·芬奇的棱柱透视图

达·芬奇的棱柱透视图
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2020-05-04 14:10
这个范例演示了达·芬奇的棱柱透视图。核心数学概念包括几何、棱柱和透视。通过使用Mirror、Polygon、PointIn等GeoGebra命令,可以构造棱柱的透视图。适合初中及以上学生学习几何透视和立体几何。

GeoGebra 命令及参数

  1. Mirror(B, A) → B'
  2. Mirror(D, A) → D'
  3. Polygon(D', B', D, B) → poly1, d', b', d, b_1
  4. PointIn(poly1) → N
  5. PointIn(poly1) → L
  6. Polygon(L, N, 4, xOyPlane) → poly2, k, l, m, n, M, B_1
  7. Point(b') → E
  8. Segment(E, O) → f
  9. Point(f) → P
  10. Line(L, zAxis) → r_4
  11. Intersect(xAxis, yAxis) → E_1
  12. Mirror(F_1, yAxis) → G_1
  13. Mirror(FF, yAxis) → FF'
  14. Polygon(FF', FF, F_1, G_1) → poly5, ff', ff, f_2, g_2
  15. Midpoint(d) → F
  16. Segment(F, D) → c
  17. Point(c) → G
  18. Line(G, b') → e
  19. Intersect(e, d') → H
  20. Polygon(R, Q, H, G) → poly3, r, q, h, g
  21. Segment(L, E) → t
  22. Intersect(t, e) → U
  23. Line(U, f) → c_1
  24. Segment(P, L) → i
  25. Intersect(c_1, i) → V
  26. Line(V, q) → r_2
  27. Intersect(r_2, h) → B_2
  28. Segment(V, B_2) → t_2
  29. Mirror(H, D') → H'
  30. Midpoint(D', F) → I
  31. Midpoint(d') → J
  32. Segment(P, N) → j
  33. Intersect(e, h) → T
  34. Segment(P, B_1) → s
  35. Segment(N, E) → e_1
  36. Intersect(e_1, e) → A_1
  37. Line(A_1, f) → g_1
  38. Intersect(j, g_1) → C_1
  39. Segment(P, E) → i_1
  40. Segment(D, E) → j_1
  41. Line(C_1, V) → l_1
  42. Intersect(l_1, r) → J_1
  43. Intersect(l_1, h) → K_1
  44. Segment(R, J_1) → m_1
  45. Segment(G, K_1) → n_1
  46. Intersect(h, n_1) → M_1
  47. Intersect(h, poly1) → S_1, S_2
  48. Line(V, r) → q_2
  49. Intersect(q_2, poly3) → Z_1, A_2
  50. Segment(V, A_2) → s_2
  51. Line(VD, g_2) → a_3
  52. Line(VH, ff') → b_3
  53. Intersect(a_3, b_3) → C_2
  54. Line(C_1, r) → c_3
  55. Line(C_1, g) → d_3
  56. Intersect(h, poly1) → D_2, D_3
  57. Intersect(h, poly1) → E_2, E_3
  58. Intersect(c_3, q) → F_2
  59. Intersect(h, poly1) → G_2, G_3
  60. Intersect(d_3, h) → H_2
  61. Segment(F_2, C_1) → e_3
  62. Segment(C_1, H_2) → f_3
  63. Line(CH, ff') → g_3
  64. Line(CL, g_2) → h_3
  65. Intersect(g_3, h_3) → I_2
  66. Sequence(R + (i * Vector[R, Q]), i, 0, 1, 1 / o_1) → l1
  67. Sequence(G + (i * Vector[R, Q]), i, 0, 1, 1 / o_1) → l2
  68. Sequence(G + (i * Vector[G, R]), i, 0, 1, 1 / u_1) → l3
  69. Sequence(H + (i * Vector[G, R]), i, 0, 1, 1 / u_1) → l4
  70. Sequence(Segment[Element[l1, i], Element[l2, i]], i, 1, Length[l1]) → l5
  71. Sequence(Segment[Element[l3, i], Element[l4, i]], i, 1, Length[l3]) → l6
  72. Line(P, A) → j_3
  73. Point(j_3) → C
  74. Line(C, xAxis) → k_3
  75. Sphere(C, 0.2) → u_2
  76. Sphere(C - (0, 0.13, -0.05), 0.3) → o_2
  77. Point(r_4) → L_2
  78. Segment(L_2, P) → n_3
  79. Intersect(n_3, poly3) → P_2
  80. Segment(P, M) → p
  81. Intersect(p, poly3) → K
  82. Intersect(s, poly3) → S
  83. Polygon(K, C_1, V, S) → q1, k_1, f_1, v_1, s_1
  84. Prism(poly2, L_2) → a_1, W, arêteNW, arête2, arête3, arête4, arête6, arête7, arête5, D_1, I_1, face1, face2, face4, face3, face5, arête1
  85. Segment(P, I_1) → h_1
  86. Segment(P, D_1) → p_1
  87. Segment(P, W) → q_1
  88. Segment(E, A) → r_1
  89. Intersect(q_1, poly3) → L_1
  90. Intersect(p_1, poly3) → N_1
  91. Intersect(h_1, poly3) → O_1
  92. Polygon(N_1, L_1, P_2, O_1) → q2, t_1, d_1, p_2, h_2
  93. Polygon(N_1, K, C_1, L_1) → q3, i_2, k_2, j_2, l_2
  94. Polygon(L_1, C_1, V, P_2) → q4, m_2, n_2, v_2, a_2
  95. Polygon(N_1, O_1, S, K) → q5, b_2, c_2, s_3, k_4
  96. Polygon(O_1, P_2, V, S) → q6, d_2, e_2, v_3, s_4

AI 绘图提示语参考

绘制一个棱柱的透视示意图。先画一个四边形作为棱柱的底面,并在其内部取两个点。从这两个点出发,构建一个与水平面相关的四边形,形成棱柱的顶面。在底面的边上取点,连接该点与空间中的固定点,形成一条视线,并在视线上取点。接着,通过一系列辅助线与交点,逐步构建出棱柱的侧面和透视投影线,包括连接顶点与底边中点的线段、延长线及其交点,最终形成完整的透视棱柱图形,并标注出各关键交点。
以上提示语为根据原始绘图命令整理而来,仅供参考。