美国航空标志构造

美国航空标志构造
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2020-01-01 01:22
这个范例演示了如何使用GeoGebra构造美国航空公司的标志。核心数学概念包括向量、几何变换和坐标几何。通过使用LineBisector、Line、Vector等命令,可以构造标志中的关键元素。适合高中几何和解析几何课程使用。

GeoGebra 命令及参数

  1. LineBisector(A, B) → m
  2. Line(A, B) → s
  3. OrthogonalLine(A, s) → b
  4. Vector(A, B) → u
  5. OrthogonalVector(u) → v
  6. OrthogonalLine(F, b) → r
  7. OrthogonalLine(I, b) → h
  8. Intersect(h, m) → S
  9. Midpoint(C, A) → J
  10. OrthogonalLine(N, b) → j
  11. LineBisector(A, C) → d
  12. Mirror(h, d) → h'_1
  13. OrthogonalLine(M, d) → i
  14. Intersect(i, h'_1) → G
  15. Segment(G, S) → k
  16. Intersect(r, k) → S_1
  17. Intersect(k, j) → R
  18. Vector(R, G) → a
  19. Intersect(i, h) → L
  20. Mirror(L, m) → L'_2
  21. Segment(K, L'_2) → l
  22. Intersect(r, l) → G_1
  23. Mirror(h, d) → h'
  24. Intersect(m, d) → E
  25. OrthogonalLine(C, v, xOyPlane) → f
  26. Intersect(f, m) → U
  27. Mirror(i, m) → i'
  28. OrthogonalLine(B, u, xOyPlane) → g
  29. Intersect(g, f) → D
  30. Mirror(M, m) → M'
  31. Polygon(A, B, D, C) → q11, a_3, b_2, d_2, c_3
  32. Translate(B, Vector[(-2.804024317353038, -0.08247130345155984)]) → B'
  33. OrthogonalLine(Q, b) → n
  34. Intersect(l, j) → T
  35. Vector(T, K) → w
  36. LineBisector(Z, V) → p
  37. LineBisector(B_1, A_1) → q
  38. Intersect(p, k) → C_1
  39. Intersect(q, l) → D_1
  40. Polygon(G, Z, V, T, A_1, B_1) → poly1, g_1, z_1, v_1, t, a_1, b_1
  41. Intersect(n, q) → E_1
  42. Vector(D_1, E_1) → u_1
  43. CircleArc(F_1, B_1, A_1) → e
  44. LineBisector(I_1, J_1) → f_1
  45. Intersect(f_1, r) → K_1
  46. CircleArc(K_1, I_1, J_1) → c_1
  47. Intersect(k, n) → M_1
  48. Intersect(d, l) → N_1
  49. LineBisector(M_1, N_1) → h_1
  50. Intersect(n, h_1) → O_1
  51. CircleArc(O_1, N_1, M_1) → d_1
  52. Polygon(M_1, I_1, J_1, L'_2, N_1) → poly2, m_1, i_1, j_1, l'_2, n_1
  53. CircleArc(C_1, V, Z) → c
  54. CurveCartesian(((1 - t)^(4) * M_1) + (((4 * (1 - t)^(3)) * t) * P_1) + (((6 * (1 - t)^(2)) * t^(2)) * Q_1) + (((4 * (1 - t)) * t^(3)) * H_1) + (t^(4) * L_1), t, 0, 1) → e_1
  55. Line(M_1, L_1) → k_1
  56. Intersect(k_1, l) → R_1
  57. Polygon(R_1, L_1, N_1) → t1, l_1, r_1, p_1
  58. CircleArc(O_1, N_1, M_1) → q_1
  59. Polygon(L'_2, G_1, S_1, I_1, J_1) → poly3, h_2, i_2, j_2, k_2, l_2
  60. Polygon(T, A_1, B_1, D_1) → q1, t_1, s_1, f_2, g_2
  61. Polygon(N_1, R_1, M_1) → t2, m_2, n_2, p_2
  62. OrthogonalLine(T_1, d) → q_2
  63. Mirror(q_2, m) → r_2
  64. OrthogonalLine(U_1, d) → s_2
  65. Mirror(s_2, m) → t_2
  66. LineBisector(T_1, U_1) → a_2
  67. Intersect(a_2, d) → V_1
  68. Intersect(q_2, h) → Z_1
  69. Line(Z_1, W_1) → c_2
  70. Line(A_2, c_2) → e_2
  71. Mirror(c_2, a_2) → f_3
  72. Mirror(e_2, a_2) → g_3
  73. Line(B_2, r) → h_3
  74. Intersect(r, e_2) → C_2
  75. Intersect(e_2, h_3) → F_2
  76. Intersect(e_2, g_3) → G_2
  77. Intersect(a_2, h_3) → H_2
  78. Intersect(a_2, r) → I_2
  79. Polygon(Z_1, A_2, C_2, I_2, H_2, F_2, G_2, V_1, W_1) → poly4, i_3, j_3, k_3, l_3, m_3, n_3, p_3, q_3, w_1
  80. Mirror(Z_1, a_2) → J_2
  81. Mirror(A_2, a_2) → K_2
  82. Mirror(C_2, a_2) → L_2
  83. Mirror(I_2, a_2) → M_2
  84. Mirror(H_2, a_2) → N_2
  85. Mirror(F_2, a_2) → O_2
  86. Mirror(G_2, a_2) → P_2
  87. Mirror(V_1, a_2) → Q_2
  88. Mirror(W_1, a_2) → R_2
  89. Polygon(J_2, K_2, L_2, M_2, N_2, O_2, P_2, Q_2, R_2) → poly4', r_3, s_3, t_3, b_3, d_3, o_2, e_3, f_4, g_4
  90. Intersect(t_2, d) → S_2
  91. Vector(Z_1, S_2) → u_2
  92. Translate(Z_1, u_2) → T_2
  93. Translate(A_2, u_2) → U_2
  94. Translate(C_2, u_2) → V_2
  95. Translate(I_2, u_2) → W_2
  96. Translate(H_2, u_2) → Z_2
  97. Translate(F_2, u_2) → A_3
  98. Translate(G_2, u_2) → B_3
  99. Translate(V_1, u_2) → C_3
  100. Translate(W_1, u_2) → D_3
  101. Polygon(T_2, U_2, V_2, W_2, Z_2, A_3, B_3, C_3, D_3) → poly4'_1, h_4, i_4, v_2, w_2, z_2, j_4, k_4, l_4, m_4
  102. Translate(J_2, u_2) → E_3
  103. Translate(K_2, u_2) → F_3
  104. Translate(L_2, u_2) → H_3
  105. Translate(M_2, u_2) → I_3
  106. Translate(N_2, u_2) → J_3
  107. Translate(O_2, u_2) → K_3
  108. Translate(P_2, u_2) → L_3
  109. Translate(Q_2, u_2) → M_3
  110. Translate(R_2, u_2) → N_3
  111. Polygon(E_3, F_3, H_3, I_3, J_3, K_3, L_3, M_3, N_3) → poly4'', n_4, p_4, q_4, r_4, s_4, t_4, a_4, b_4, c_4

AI 绘图提示语参考

绘制美国航空标志,首先通过点A和B绘制线段,然后构造线段的中垂线和垂线,接着利用向量和垂线构造其他关键点和线段,逐步构建标志的各个部分,最后通过镜像和旋转等变换完成标志的整体构造。
以上提示语为根据原始绘图命令整理而来,仅供参考。