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平移法镶嵌 by jahatch8

平移法镶嵌 by jahatch8
几何画板及绘图内容加载中，请稍等……
2014-03-30 05:25
测试改名0多边形向量变换几何作图
所属专题 Tesselation by Translation Tesselation by Translation
①本范例演示了如何通过平移操作创建平面镶嵌图案；②涉及的核心数学概念包括平移变换、等边三角形、中心对称、向量运算；③作图要点——使用了Polygon（多边形）、AttachCopyToView（视图附加复制）、Point（点）、Vector（向量）、Translate（平移）等GeoGebra命令与对象；④适合高中数学教学，用于理解几何变换与镶嵌图案的构成原理。

GeoGebra 命令及参数

  1. Polygon(A, B, 4) → poly1, a, b, c, d, C, D
  2. AttachCopyToView(PolyLine[(3.14, -4), (3.14, -4.12), (3.12, -4.18), (3.1, -4.28), (3.08, -4.34), (3.06, -4.4), (3.04, -4.46), (3.02, -4.58), (3, -4.68), (2.98, -4.74), (2.98, -4.82), (2.96, -4.88), (2.88, -4.88), (2.82, -4.9), (2.74, -4.9), (2.66, -4.9), (2.58, -4.92), (2.48, -4.92), (2.4, -4.92), (2.34, -4.94), (2.2600000000000002, -4.94), (2.18, -4.94), (2.1, -4.96), (2.06, -5.04), (2, -5.12), (1.96, -5.2), (1.9000000000000001, -5.28), (1.86, -5.34), (1.82, -5.4), (1.78, -5.46), (1.72, -5.5), (1.6600000000000001, -5.44), (1.62, -5.38), (1.56, -5.34), (1.54, -5.28), (1.52, -5.22), (1.58, -5.18), (1.62, -5.12), (1.68, -5.08), (1.72, -5.0200000000000005), (1.76, -4.96), (1.82, -4.94), (1.84, -4.88), (1.9000000000000001, -4.86), (1.96, -4.84), (2.02, -4.82), (2.08, -4.8), (2.14, -4.76), (2.2, -4.74), (2.2600000000000002, -4.7), (2.32, -4.68), (2.4, -4.64), (2.46, -4.6000000000000005), (2.44, -4.54), (2.38, -4.48), (2.32, -4.42), (2.2800000000000002, -4.36), (2.22, -4.34), (2.16, -4.28), (2.1, -4.22), (2.04, -4.2), (1.94, -4.14), (1.86, -4.1), (1.8, -4.0600000000000005), (1.72, -4.0200000000000005), (1.6600000000000001, -4), (1.6, -3.94), (1.54, -3.9), (1.48, -3.86), (1.52, -3.8000000000000003), (1.6, -3.7800000000000002), (1.6600000000000001, -3.7600000000000002), (1.72, -3.72), (1.78, -3.7), (1.84, -3.66), (1.9000000000000001, -3.64), (1.98, -3.6), (2.06, -3.58), (2.14, -3.54), (2.12, -3.48), (2.06, -3.46), (2, -3.44), (1.92, -3.38), (1.86, -3.3200000000000003), (1.8, -3.3000000000000003), (1.74, -3.24), (1.68, -3.2), (1.62, -3.14), (1.56, -3.1), (1.5, -3.04), (1.44, -3), (1.42, -2.94), (1.36, -2.96), (1.3, -2.98), (1.24, -3), (1.18, -3.02), (1.1, -3.02), (1.02, -3.04), (0.9400000000000001, -3.04), (0.86, -3.04), (0.8, -3.02), (0.72, -2.98), (0.66, -2.92), (0.6, -2.86), (0.56, -2.8000000000000003), (0.52, -2.72), (0.44, -2.62), (0.36, -2.56), (0.34, -2.5), (0.28, -2.44), (0.22, -2.42), (0.18, -2.48), (0.12, -2.54), (0.08, -2.6), (0.02, -2.64), (-0.02, -2.7), (-0.08, -2.74), (-0.14, -2.8000000000000003), (-0.2, -2.84), (-0.26, -2.86), (-0.34, -2.88), (-0.42, -2.88), (-0.5, -2.88), (-0.58, -2.88), (-0.66, -2.88), (-0.74, -2.92), (-0.78, -2.98), (-0.84, -3.02), (-0.9, -3.04), (-0.96, -3.08), (-0.98, -3.14), (-0.98, -3.22), (-0.98, -3.3000000000000003), (-0.96, -3.36), (-1.02, -3.42), (-1.08, -3.48), (-1.1400000000000001, -3.54), (-1.2, -3.58), (-1.26, -3.64), (-1.3, -3.7), (-1.32, -3.7600000000000002), (-1.28, -3.8200000000000003), (-1.26, -3.88), (-1.22, -3.94), true], 1, (-4.3, -7.96), (23.38, 6.3), (0, 713), (1384, 0)) → stroke1
  3. Point(a) → E
  4. Vector(E, F) → u
  5. Translate(stroke1, u) → stroke1'
  6. AttachCopyToView(PolyLine[(-1.2, -3.94), (-1.26, -4), (-1.3, -4.0600000000000005), (-1.34, -4.12), (-1.3800000000000001, -4.18), (-1.4000000000000001, -4.12), (-1.42, -4.0600000000000005), (-1.46, -4), (-1.5, -3.92), (-1.54, -3.86), (-1.58, -3.8000000000000003), (-1.62, -3.74), (-1.6, -3.64), (-1.54, -3.58), (-1.48, -3.54), (-1.42, -3.5), (-1.3800000000000001, -3.44), (-1.34, -3.36), (-1.34, -3.2800000000000002), (-1.32, -3.22), (-1.32, -3.14), (-1.3, -3.06), (-1.28, -3), (-1.28, -2.92), (-1.28, -2.84), (-1.28, -2.7600000000000002), (-1.22, -2.72), (-1.16, -2.7), (-1.08, -2.68), (-1.02, -2.62), (-0.96, -2.58), (-0.88, -2.5), (-0.8, -2.42), (-0.74, -2.38), (-0.66, -2.34), (-0.6, -2.3000000000000003), (-0.54, -2.2600000000000002), (-0.48, -2.22), (-0.42, -2.2), (-0.36, -2.16), (-0.3, -2.14), (-0.32, -2.08), (-0.36, -2.02), (-0.38, -1.96), (-0.44, -1.9000000000000001), (-0.48, -1.84), (-0.54, -1.78), (-0.6, -1.72), (-0.64, -1.6600000000000001), (-0.66, -1.6), (-0.72, -1.6600000000000001), (-0.74, -1.72), (-0.78, -1.8), (-0.84, -1.86), (-0.9, -1.9000000000000001), (-0.96, -1.94), (-1.02, -2), (-1.06, -2.06), (-1, -2.08), (-0.9400000000000001, -2.04), (-0.86, -2.02), (-0.78, -2.02), (-0.72, -2), (-0.66, -1.98), (-0.6, -1.96), (-0.58, -2.02), (-0.58, -2.1), (-0.6, -2.16), (-0.62, -2.22), (-0.7000000000000001, -2.22), (-0.78, -2.22), (-0.86, -2.22), (-0.92, -2.24), (-1, -2.2600000000000002), (-1.06, -2.2800000000000002), (-1.12, -2.3000000000000003), (-1.2, -2.3000000000000003), (-1.26, -2.32), (-1.34, -2.32), (-1.3800000000000001, -2.24), (-1.3800000000000001, -2.16), (-1.3800000000000001, -2.08), (-1.4000000000000001, -2.02), (-1.4000000000000001, -1.94), (-1.42, -1.8800000000000001), (-1.42, -1.8), (-1.36, -1.76), (-1.28, -1.68), (-1.22, -1.6400000000000001), (-1.16, -1.6), (-1.12, -1.54), (-1.08, -1.48), (-1.06, -1.42), (-1.04, -1.32), (-1.02, -1.26), (-1, -1.2), (-0.96, -1.12), (-0.9400000000000001, -1.06), (-0.86, -1.06), (-0.8, -1.08), (-0.72, -1.1), (-0.64, -1.12), (-0.58, -1.1400000000000001), (-0.52, -1.18), (-0.46, -1.22), (-0.38, -1.24), (-0.32, -1.26), (-0.26, -1.28), (-0.22, -1.22), (-0.2, -1.16), (-0.16, -1.08), (-0.12, -1.02), (-0.08, -0.96), (-0.04, -0.88), (0, -0.8200000000000001), (0.06, -0.78), (0.12, -0.7000000000000001), (0.16, -0.64), (0.22, -0.58), (0.28, -0.52), (0.32, -0.46), (0.38, -0.4), (0.44, -0.38), (0.5, -0.32), (0.56, -0.28), (0.6, -0.22), (0.6, -0.12), (0.64, 0.02), (0.64, 0.1), (0.68, 0.18), (0.7000000000000001, 0.26), (0.72, 0.34), (0.76, 0.42), (0.78, 0.52), (0.8200000000000001, 0.58), (0.84, 0.66), (0.86, 0.72), (0.78, 0.72), (0.7000000000000001, 0.72), (0.62, 0.76), (0.56, 0.8), (0.48, 0.8200000000000001), (0.4, 0.84), (0.34, 0.86), (0.28, 0.9), (0.22, 0.92), (0.16, 0.9400000000000001), (0.08, 0.96), (0.02, 0.98), (-0.06, 0.98), (-0.14, 0.96), (-0.2, 0.92), (-0.26, 0.86), (-0.28, 0.8), (-0.34, 0.76), (-0.38, 0.68), (-0.42, 0.62), (-0.46, 0.56), (-0.48, 0.5), (-0.54, 0.46), (-0.6, 0.44), (-0.68, 0.44), (-0.76, 0.44), (-0.84, 0.44), (-0.9, 0.42), (-0.98, 0.42), (-1.04, 0.4), (-1.12, 0.4), true], 1, (-4.3, -7.96), (23.38, 6.3), (0, 713), (1384, 0)) → stroke2
  7. Point(d) → G
  8. Point(b) → H
  9. Vector(G, H) → v
  10. Translate(stroke2, v) → stroke2'
  11. Vector(A, D) → w
  12. Translate(stroke1, w) → stroke1'_1
  13. Translate(stroke1', w) → stroke1''
  14. Translate(stroke2, w) → stroke2'_1
  15. Translate(stroke2', w) → stroke2''
  16. Translate(B, w) → B'
  17. Translate(C, w) → C'
  18. Translate(E, w) → E'
  19. Translate(F, w) → F'
  20. Translate(G, w) → G'
  21. Translate(H, w) → H'
  22. Point(stroke1') → I
  23. Point(stroke1') → J
  24. Point(stroke1') → K
  25. Point(stroke1') → L
  26. Point(stroke1') → M
  27. Point(stroke1'_1) → N
  28. Point(stroke1') → O
  29. Point(stroke1') → P
  30. Point(stroke1') → Q
  31. Point(stroke1') → R
  32. Point(stroke1') → S
  33. Point(stroke1') → T
  34. Point(stroke1'_1) → U
  35. Point(stroke1') → V
  36. Point(stroke1') → W
  37. Point(stroke1') → Z
  38. Point(stroke2') → A_1
  39. Point(stroke2') → B_1
  40. Point(stroke2') → C_1
  41. Point(stroke2') → D_1
  42. Point(stroke2') → E_1
  43. Point(stroke2') → F_1
  44. Point(stroke2') → G_1
  45. Point(stroke2') → H_1
  46. Point(stroke2') → I_1
  47. Point(stroke2') → J_1
  48. Point(stroke2') → K_1
  49. Point(stroke2') → L_1
  50. Point(stroke2') → M_1
  51. Point(stroke2') → P_1
  52. Point(stroke2') → Q_1
  53. Point(stroke2') → R_1
  54. Point(stroke2') → S_1
  55. Point(stroke2') → T_1
  56. Point(stroke1) → U_1
  57. Point(stroke1) → V_1
  58. Point(stroke1) → W_1
  59. Point(stroke1) → Z_1
  60. Point(stroke1) → A_2
  61. Point(stroke1) → B_2
  62. Point(stroke1) → C_2
  63. Point(stroke1) → D_2
  64. Point(stroke1) → E_2
  65. Point(stroke1) → F_2
  66. Point(stroke1) → G_2
  67. Point(stroke1) → H_2
  68. Point(stroke1) → J_2
  69. Point(stroke1) → K_2
  70. Point(stroke1) → L_2
  71. Point(stroke2) → M_2
  72. Point(stroke2) → O_2
  73. Point(stroke2) → P_2
  74. Point(stroke2) → Q_2
  75. Point(stroke2) → S_2
  76. Point(stroke2) → T_2
  77. Point(stroke2) → U_2
  78. Point(stroke2) → V_2
  79. Point(stroke2) → W_2
  80. Point(stroke2) → Z_2
  81. Point(stroke2) → B_3
  82. Point(stroke2) → C_3
  83. Point(stroke2) → D_3
  84. Point(stroke2) → E_3
  85. Point(stroke2) → F_3
  86. Polygon(D, I, R, S, T, U, V, W, Z, H, C, A_1, J, B_1, C_1, D_1, E_1, F_1, G_1, H_1, I_1, J_1, K_1, K, M_1, N_1, O_1, P_1, Q_1, R_1, S_1, T_1, B, U_1, L, V_1, W_1, Z_1, A_2, B_2, C_2, D_2, E_2, F_2, G_2, M, H_2, I_2, J_2, K_2, L_2, A, M_2, N_2, O_2, P_2, N, Q_2, R_2, S_2, T_2, U_2, V_2, W_2, Z_2, A_3, B_3, O, F, E', D_3, E_3, F_3, P, Q) → poly2, d_1, q, r, s, t, u_1, v_1, w_1, z, h, c_1, i, a_1, b_1, c_2, d_2, e_1, f_1, g_1, h_1, i_1, j_1, j, k_1, m_1, n_1, o_1, p_1, q_1, r_1, s_1, t_1, b_2, k, u_2, v_2, w_2, z_1, a_2, b_3, c_3, d_3, e_2, f_2, l, g_2, h_2, i_2, j_2, k_2, l_2, a_3, m_2, n_2, o_2, m, p_2, q_2, r_2, s_2, t_2, u_3, v_3, w_3, z_2, a_4, n, b_4, f, e', d_4, e_3, f_3, o, p

AI 绘图提示语参考

画一个由多个四边形组成的平面镶嵌图案，这些四边形通过平移操作相互连接。首先绘制一个四边形，然后以该四边形的一个顶点为起点，绘制一条曲线。接着，从曲线的起点出发，绘制一个向量，并使用该向量平移四边形，得到一个新的四边形。重复此过程，使用新四边形的顶点和向量进行平移，创建更多的四边形，最终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。