两点透视立方体绘制谜题

两点透视立方体绘制谜题
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2020-10-03 02:17
①本范例演示了如何在两点透视下绘制立方体,通过动态模型展示透视原理;②涉及核心数学概念包括立体几何、几何作图、坐标几何;③作图要点提炼自构造摘要,使用了线段、直线、中点、交点、多边形等 GeoGebra 命令与对象;④适合高中阶段学生或数学爱好者学习空间几何与透视技巧,提升几何作图能力。

GeoGebra 命令及参数

  1. Segment(A, B) → f
  2. Segment(C, D) → g
  3. Line(D, A) → h
  4. Midpoint(g) → E
  5. Segment(I, F) → i
  6. Segment(J, G) → j
  7. Segment(K, H) → k
  8. Segment(H, D) → l
  9. Segment(K, C) → m
  10. Midpoint(k) → L
  11. Segment(L, E) → n
  12. Intersect(n, j) → M
  13. Intersect(n, i) → N
  14. Segment(D, P) → p
  15. Segment(C, Q) → q
  16. Segment(Q, P) → r
  17. Segment(R, O) → s
  18. Midpoint(r) → S
  19. Segment(E, S) → t
  20. Intersect(t, s) → T
  21. Line(H, B) → a
  22. Line(P, A) → b
  23. Intersect(a, b) → U
  24. Line(Q, A) → c
  25. Line(K, B) → d
  26. Intersect(d, c) → V
  27. Segment(K, V) → e
  28. Segment(V, Q) → f_1
  29. Line(J, B) → g_1
  30. Line(I, B) → h_1
  31. Midpoint(e) → W
  32. Segment(R, W) → i_1
  33. Intersect(g_1, f_1) → Z
  34. Intersect(h_1, f_1) → A_1
  35. Segment(J, Z) → j_1
  36. Segment(I, A_1) → k_1
  37. Intersect(j_1, i_1) → B_1
  38. Intersect(k_1, i_1) → C_1
  39. Segment(U, V) → l_1
  40. Midpoint(l_1) → D_1
  41. Segment(L, D_1) → m_1
  42. Segment(D_1, S) → n_1
  43. Segment(U, H) → p_1
  44. Segment(U, P) → q_1
  45. Midpoint(p_1) → E_1
  46. Segment(O, E_1) → r_1
  47. Line(G, B) → s_1
  48. Line(F, B) → t_1
  49. Intersect(s_1, q_1) → F_1
  50. Intersect(t_1, q_1) → G_1
  51. Segment(G, F_1) → a_1
  52. Segment(F, G_1) → b_1
  53. Segment(W, E_1) → c_1
  54. Intersect(m_1, c_1) → H_1
  55. Segment(Z, F_1) → d_1
  56. Segment(A_1, G_1) → e_1
  57. Intersect(n_1, d_1) → I_1
  58. Intersect(e_1, n_1) → J_1
  59. Segment(H_1, T) → f_2
  60. Segment(N, J_1) → g_2
  61. Segment(M, I_1) → h_2
  62. Intersect(f_2, h_2) → K_1
  63. Intersect(g_2, f_2) → L_1
  64. Intersect(a_1, r_1) → M_1
  65. Intersect(b_1, r_1) → N_1
  66. Segment(L, H) → m_2
  67. Segment(O, T) → n_2
  68. Segment(T, L_1) → q_2
  69. Segment(L_1, N_1) → a_2
  70. Segment(W, V) → b_2
  71. Segment(V, Z) → c_2
  72. Segment(W, B_1) → d_2
  73. Segment(B_1, Z) → e_2
  74. Segment(W, H_1) → f_3
  75. Segment(H_1, L) → g_3
  76. Segment(H_1, K_1) → h_3
  77. Segment(K_1, B_1) → i_3
  78. Segment(K_1, I_1) → j_3
  79. Segment(I_1, Z) → k_3
  80. Segment(L, N) → i_2
  81. Segment(H, F) → l_2
  82. Segment(N, F) → m_3
  83. Segment(N, L_1) → n_3
  84. Segment(F, N_1) → p_3
  85. Segment(N_1, O) → q_3
  86. Segment(O, P) → j_2
  87. Segment(I_1, S) → k_2
  88. Segment(S, P) → p_2
  89. Segment(S, T) → r_2
  90. Intersect(m_2, g_3) → O_1
  91. Intersect(f_3, g_3) → P_1
  92. Intersect(h_3, i_3) → Q_1
  93. Intersect(j_3, k_3) → R_1
  94. Intersect(k_2, p_2) → S_1
  95. Intersect(n_2, q_2) → T_1
  96. Intersect(q_2, a_2) → U_1
  97. Intersect(i_2, m_3) → V_1
  98. Polygon(O_1, P_1, Q_1, R_1, S_1, T_1, U_1, V_1) → poly1, o_1, s_2, t_2, l_3, r_3, s_3, u_1, v_1
  99. Intersect(n_2, q_2) → W_1
  100. Intersect(k_2, p_2) → Z_1
  101. Intersect(j_2, p_2) → A_2
  102. Intersect(n_2, q_3) → B_2
  103. Polygon(W_1, Z_1, A_2, B_2) → q1, w_1, z_1, t_3, a_3
  104. Intersect(i_2, m_3) → C_2
  105. Intersect(q_2, a_2) → D_2
  106. Intersect(a_2, p_3) → E_2
  107. Intersect(l_2, m_3) → F_2
  108. Polygon(C_2, D_2, E_2, F_2) → q2, b_3, c_3, d_3, e_3
  109. Intersect(d_2, e_2) → G_2
  110. Intersect(c_2, e_2) → H_2
  111. Intersect(j_3, k_3) → I_2
  112. Intersect(h_3, i_3) → J_2
  113. Polygon(G_2, H_2, I_2, J_2) → q3, f_4, g_4, h_4, i_4
  114. Intersect(b_2, d_2) → K_2
  115. Intersect(b_2, c_2) → L_2
  116. Intersect(c_2, e_2) → M_2
  117. Intersect(d_2, e_2) → N_2
  118. Polygon(K_2, L_2, M_2, N_2) → q4, j_4, k_4, l_4, m_4
  119. Intersect(m_2, l_2) → O_2
  120. Intersect(m_2, g_3) → P_2
  121. Intersect(i_2, m_3) → Q_2
  122. Intersect(l_2, m_3) → R_2
  123. Polygon(O_2, P_2, Q_2, R_2) → q5, o_2, n_4, p_4, q_4
  124. Intersect(f_3, g_3) → S_2
  125. Intersect(b_2, d_2) → T_2
  126. Intersect(d_2, e_2) → U_2
  127. Intersect(h_3, i_3) → V_2
  128. Polygon(S_2, T_2, U_2, V_2) → q6, r_4, s_4, u_2, v_2
  129. Intersect(a_2, p_3) → W_2
  130. Intersect(q_2, a_2) → Z_2
  131. Intersect(n_2, q_2) → A_3
  132. Intersect(n_2, q_3) → B_3
  133. Polygon(W_2, Z_2, A_3, B_3) → q7, w_2, z_2, t_4, a_4
  134. Intersect(l, p) → C_3
  135. Segment(C, C_3) → b_4

AI 绘图提示语参考

绘制一个使用两点透视法的立方体。首先,画出立方体的前后面,然后画出侧面,确保所有线段和点都符合透视原则。先画出点A、B、C、D,然后画出线段AB、CD,接着画出线段DA,找到线段CD的中点E,再画出线段IF、IJ、JK、HK、KP、KQ、QR、RO,找到线段JK的中点L,画出线段LE,找到线段IJ和线段FK的交点M,找到线段LE和线段FI的交点N。继续按照这个顺序,逐步完成立方体的透视构造。
以上提示语为根据原始绘图命令整理而来,仅供参考。