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平移镶嵌

平移镶嵌
几何画板及绘图内容加载中，请稍等……
2014-03-30 05:24
多边形解析几何变换
所属专题 Tesselation by Translation Tesselation by Translation
这个范例演示了通过平移生成镶嵌图形的过程。核心数学概念包括平移变换和几何作图。使用了Polygon, AttachCopyToView, Point, Vector, Translate等GeoGebra命令。适合初中及以上学生学习几何变换和镶嵌图形。

GeoGebra 命令及参数

  1. Polygon(A, B, 4) → poly1, a, b, c, d, C, D
  2. AttachCopyToView(PolyLine[(2.86, -2.88), (2.7800000000000002, -2.88), (2.7, -2.88), (2.62, -2.9), (2.56, -2.94), (2.52, -3), (2.48, -3.06), (2.44, -3.12), (2.4, -3.18), (2.38, -3.24), (2.36, -3.3000000000000003), (2.36, -3.38), (2.36, -3.46), (2.36, -3.54), (2.36, -3.62), (2.3000000000000003, -3.68), (2.24, -3.7), (2.18, -3.72), (2.12, -3.74), (2.06, -3.7600000000000002), (1.98, -3.8200000000000003), (1.92, -3.86), (1.86, -3.92), (1.8, -3.96), (1.74, -4.0200000000000005), (1.6600000000000001, -4.0200000000000005), (1.6, -4.08), (1.54, -4.1), (1.5, -4.16), (1.44, -4.22), (1.42, -4.28), (1.4000000000000001, -4.34), (1.4000000000000001, -4.42), (1.3800000000000001, -4.48), (1.32, -4.44), (1.32, -4.34), (1.3, -4.28), (1.3, -4.2), (1.3, -4.12), (1.3, -4.04), (1.32, -3.98), (1.34, -3.92), (1.4000000000000001, -3.86), (1.46, -3.8200000000000003), (1.54, -3.8200000000000003), (1.56, -3.7600000000000002), (1.6, -3.7), (1.6600000000000001, -3.66), (1.72, -3.6), (1.78, -3.58), (1.84, -3.54), (1.9000000000000001, -3.5), (1.84, -3.48), (1.76, -3.48), (1.7, -3.46), (1.6400000000000001, -3.44), (1.58, -3.4), (1.52, -3.36), (1.46, -3.3000000000000003), (1.44, -3.24), (1.44, -3.16), (1.44, -3.08), (1.44, -3), (1.44, -2.92), (1.44, -2.84), (1.46, -2.7600000000000002), (1.48, -2.7), (1.52, -2.64), (1.56, -2.58), (1.58, -2.52), (1.6400000000000001, -2.48), (1.58, -2.5), (1.52, -2.52), (1.44, -2.52), (1.36, -2.52), (1.28, -2.52), (1.2, -2.52), (1.1400000000000001, -2.5), (1.08, -2.48), (1.04, -2.42), (1, -2.36), (0.96, -2.3000000000000003), (0.9, -2.24), (0.9, -2.16), (0.86, -2.1), (0.86, -2.02), (0.84, -1.96), (0.84, -1.8800000000000001), (0.78, -1.86), (0.76, -1.92), (0.7000000000000001, -1.94), (0.64, -1.96), (0.58, -1.98), (0.52, -2), (0.44, -2.02), (0.34, -2.02), (0.26, -2.02), (0.2, -2), (0.16, -1.94), (0.12, -1.8800000000000001), (0.1, -1.82), (0.06, -1.76), (0, -1.72), (-0.06, -1.76), (-0.1, -1.82), (-0.16, -1.84), (-0.18, -1.9000000000000001), (-0.24, -1.94), (-0.3, -1.98), (-0.36, -2.02), (-0.42, -2.04), (-0.5, -2.04), (-0.58, -2.04), (-0.6, -1.98), (-0.62, -1.92), (-0.64, -1.86), (-0.64, -1.78), (-0.64, -1.7), (-0.7000000000000001, -1.74), (-0.72, -1.8), (-0.74, -1.9000000000000001), (-0.74, -1.98), (-0.76, -2.04), (-0.78, -2.1), (-0.8, -2.18), (-0.8200000000000001, -2.24), (-0.9, -2.2600000000000002), (-0.96, -2.3000000000000003), (-1.02, -2.32), (-1.08, -2.34), (-1.1400000000000001, -2.36), (-1.2, -2.38), (-1.28, -2.38), (-1.28, -2.46), (-1.28, -2.54), (-1.3, -2.6), (-1.4000000000000001, -2.62), (-1.46, -2.64), (-1.54, -2.64), (-1.6, -2.68), (-1.68, -2.68), (-1.74, -2.7), (-1.8, -2.72), (-1.86, -2.74), (-1.8800000000000001, -2.8000000000000003), (-1.86, -2.86), (-1.8, -2.92), true], 1, (-4.3, -7.96), (23.38, 6.3), (0, 713), (1384, 0)) → stroke1
  3. Point(a) → E
  4. Point(c) → F
  5. Vector(E, F) → u
  6. Translate(stroke1, u) → stroke1'
  7. AttachCopyToView(PolyLine[(-1.74, -2.9), (-1.82, -2.9), (-1.8800000000000001, -2.94), (-1.92, -3), (-1.98, -2.98), (-2, -2.92), (-2, -2.84), (-2.02, -2.7800000000000002), (-2.04, -2.72), (-2.06, -2.66), (-2.08, -2.56), (-2.04, -2.5), (-1.98, -2.46), (-1.94, -2.4), (-1.8800000000000001, -2.36), (-1.8, -2.36), (-1.72, -2.36), (-1.6600000000000001, -2.38), (-1.58, -2.38), (-1.56, -2.3000000000000003), (-1.54, -2.24), (-1.52, -2.18), (-1.5, -2.12), (-1.44, -2.1), (-1.3800000000000001, -2.08), (-1.32, -2.04), (-1.26, -2.02), (-1.22, -1.96), (-1.2, -1.9000000000000001), (-1.16, -1.84), (-1.1400000000000001, -1.76), (-1.1, -1.7), (-1.08, -1.62), (-1.06, -1.56), (-1.04, -1.5), (-1.02, -1.44), (-0.98, -1.3800000000000001), (-0.92, -1.32), (-0.86, -1.28), (-0.78, -1.26), (-0.72, -1.24), (-0.7000000000000001, -1.18), (-0.66, -1.12), (-0.66, -1.04), (-0.66, -0.9400000000000001), (-0.66, -0.86), (-0.68, -0.8), (-0.72, -0.74), (-0.78, -0.72), (-0.84, -0.7000000000000001), (-0.9, -0.68), (-0.96, -0.66), (-1.04, -0.66), (-1.12, -0.66), (-1.2, -0.66), (-1.28, -0.7000000000000001), (-1.34, -0.72), (-1.4000000000000001, -0.76), (-1.48, -0.8200000000000001), (-1.54, -0.88), (-1.56, -0.9400000000000001), (-1.6, -1), (-1.6, -1.08), (-1.56, -1.1400000000000001), (-1.48, -1.1400000000000001), (-1.4000000000000001, -1.1), (-1.36, -1.04), (-1.34, -0.98), (-1.32, -0.92), (-1.32, -1), (-1.3, -1.06), (-1.3, -1.1400000000000001), (-1.3, -1.22), (-1.32, -1.3), (-1.3800000000000001, -1.34), (-1.48, -1.34), (-1.56, -1.34), (-1.6400000000000001, -1.34), (-1.72, -1.34), (-1.8, -1.32), (-1.82, -1.26), (-1.84, -1.2), (-1.86, -1.1400000000000001), (-1.86, -1.06), (-1.8800000000000001, -1), (-1.8800000000000001, -0.92), (-1.86, -0.84), (-1.8, -0.8), (-1.74, -0.76), (-1.68, -0.72), (-1.62, -0.66), (-1.58, -0.6), (-1.52, -0.56), (-1.48, -0.5), (-1.44, -0.42), (-1.4000000000000001, -0.36), (-1.34, -0.32), (-1.26, -0.32), (-1.18, -0.32), (-1.1, -0.32), (-1.02, -0.32), (-0.96, -0.34), (-0.9, -0.36), (-0.8200000000000001, -0.36), (-0.74, -0.36), (-0.66, -0.36), (-0.58, -0.36), (-0.5, -0.36), (-0.42, -0.36), (-0.38, -0.3), (-0.32, -0.24), (-0.26, -0.18), (-0.22, -0.12), (-0.18, -0.02), (-0.14, 0.06), (-0.1, 0.14), (-0.04, 0.18), (0.02, 0.22), (0.1, 0.28), (0.14, 0.34), (0.18, 0.42), (0.2, 0.5), (0.24, 0.6), (0.28, 0.68), (0.34, 0.78), (0.4, 0.86), (0.44, 0.92), (0.48, 1), (0.5, 1.06), (0.52, 1.12), (0.58, 1.16), (0.64, 1.2), (0.7000000000000001, 1.24), (0.78, 1.32), (0.8, 1.3800000000000001), (0.8, 1.46), (0.8, 1.54), (0.78, 1.6), (0.74, 1.6600000000000001), (0.7000000000000001, 1.72), (0.68, 1.78), (0.66, 1.84), (0.66, 1.92), (0.64, 1.98), (0.58, 2), (0.48, 2), (0.42, 1.96), (0.34, 1.96), (0.28, 1.94), (0.22, 1.92), (0.14, 1.92), (0.08, 1.8800000000000001), (0.06, 1.82), (0, 1.78), (-0.04, 1.72), (-0.1, 1.7), (-0.18, 1.68), (-0.24, 1.6600000000000001), (-0.32, 1.68), (-0.38, 1.72), (-0.44, 1.76), (-0.52, 1.76), (-0.6, 1.76), (-0.68, 1.76), (-0.76, 1.76), (-0.8200000000000001, 1.72), (-0.88, 1.7), (-0.96, 1.7), (-1.02, 1.68), (-1.08, 1.6600000000000001), (-1.1400000000000001, 1.6400000000000001), (-1.2, 1.6), (-1.28, 1.6), (-1.36, 1.6), (-1.44, 1.6), (-1.52, 1.6), (-1.6, 1.6), (-1.68, 1.6), (-1.72, 1.6600000000000001), true], 1, (-4.3, -7.96), (23.38, 6.3), (0, 713), (1384, 0)) → stroke2
  8. Point(d) → G
  9. Point(b) → H
  10. Vector(G, H) → v
  11. Translate(stroke2, v) → stroke2'
  12. Point(stroke1') → J
  13. Point(stroke1') → L
  14. Point(stroke1') → M
  15. Point(stroke1') → N
  16. Point(stroke1') → O
  17. Point(stroke1') → P
  18. Point(stroke1') → Q
  19. Point(stroke1') → R
  20. Point(stroke1') → S
  21. Point(stroke1') → T
  22. Point(stroke1') → U
  23. Point(stroke1') → V
  24. Point(stroke1') → W
  25. Point(stroke1') → Z
  26. Point(stroke1') → A_1
  27. Point(stroke1') → B_1
  28. Point(stroke1') → C_1
  29. Point(stroke1') → D_1
  30. Point(stroke1') → E_1
  31. Point(stroke2') → F_1
  32. Point(stroke2') → G_1
  33. Point(stroke2') → H_1
  34. Point(stroke2') → I_1
  35. Point(stroke2') → J_1
  36. Point(stroke2') → K_1
  37. Point(stroke2') → L_1
  38. Point(stroke2') → M_1
  39. Point(stroke2') → N_1
  40. Point(stroke2') → O_1
  41. Point(stroke2') → P_1
  42. Point(stroke2') → Q_1
  43. Point(stroke2') → R_1
  44. Point(stroke2') → S_1
  45. Point(stroke2') → T_1
  46. Point(stroke2') → U_1
  47. Point(stroke2') → V_1
  48. Point(stroke2') → W_1
  49. Point(stroke2') → Z_1
  50. Point(stroke2') → A_2
  51. Point(stroke2') → B_2
  52. Point(stroke2') → D_2
  53. Point(stroke2') → E_2
  54. Point(stroke1) → F_2
  55. Point(stroke1) → G_2
  56. Point(stroke1) → H_2
  57. Point(stroke1) → I_2
  58. Point(stroke1) → J_2
  59. Point(stroke1) → K_2
  60. Point(stroke1) → L_2
  61. Point(stroke1) → M_2
  62. Point(stroke1) → N_2
  63. Point(stroke1) → O_2
  64. Point(stroke1) → Q_2
  65. Point(stroke1) → T_2
  66. Point(stroke1) → U_2
  67. Point(stroke1) → V_2
  68. Point(stroke1) → Z_2
  69. Point(stroke1) → A_3
  70. Point(stroke2) → C_3
  71. Point(stroke2) → D_3
  72. Point(stroke2) → F_3
  73. Point(stroke2) → G_3
  74. Point(stroke2) → H_3
  75. Point(stroke2) → I_3
  76. Point(stroke2) → J_3
  77. Point(stroke2) → K_3
  78. Point(stroke2) → L_3
  79. Point(stroke2) → M_3
  80. Point(stroke2) → N_3
  81. Point(stroke2) → O_3
  82. Point(stroke2) → P_3
  83. Point(stroke2) → Q_3
  84. Point(stroke2) → R_3
  85. Point(stroke2) → S_3
  86. Point(stroke2) → T_3
  87. Point(stroke2) → U_3
  88. Point(stroke2) → V_3
  89. Point(stroke2) → W_3
  90. Polygon(D, I, R, S, T, U, V, W, Z, A_1, B_1, C_1, J, D_1, E_1, C, F_1, G_1, H_1, I_1, J_1, K_1, L_1, K, M_1, N_1, O_1, P_1, Q_1, R_1, S_1, T_1, U_1, V_1, L, W_1, Z_1, A_2, B_2, C_2, D_2, E_2, F_2, G_2, H_2, M, I_2, J_2, K_2, L_2, M_2, N_2, O_2, P_2, Q_2, R_2, N, S_2, T_2, U_2, V_2, W_2, Z_2, A_3, B_3, A, C_3, O, D_3, E_3, F_3, G_3, H_3, I_3, J_3, K_3, L_3, M_3, P, N_3, O_3, P_3, Q_3, R_3, S_3, T_3, F, U_3, V_3, Q, W_3) → poly2, d_1, q, r, s, t, u_1, v_1, w, z, a_1, b_1, i, c_1, d_2, e_1, c_2, f_1, g_1, h_1, i_1, j_1, k_1, j, l_1, m_1, n_1, o_1, p_1, q_1, r_1, s_1, t_1, u_2, k, v_2, w_1, z_1, a_2, b_2, c_3, d_3, e_2, f_2, g_2, l, h_2, i_2, j_2, k_2, l_2, m_2, n_2, o_2, p_2, q_2, m, r_2, s_2, t_2, u_3, v_3, w_2, z_2, a_3, b_3, a_4, n, c_4, d_4, e_3, f_3, g_3, h_3, i_3, j_3, k_3, l_3, o, m_3, n_3, o_3, p_3, q_3, r_3, s_3, t_3, f, u_4, p, v_4, w_3

AI 绘图提示语参考

绘制一个通过平移生成的镶嵌图案。首先画一个四边形，然后沿着一个向量平移这个四边形，接着画另一个四边形，并沿另一个向量平移。最后，将平移后的四边形重复平移，形成一个完整的镶嵌图案。
以上提示语为根据原始绘图命令整理而来，仅供参考。