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平移镶嵌 by jahatch8 (2)

平移镶嵌 by jahatch8 (2)
几何画板及绘图内容加载中，请稍等……
2014-03-30 05:26
多边形向量变换
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多边形。通过使用GeoGebra命令如Polygon、Translate等，可以创建平移镶嵌。适合初中及以上学生学习几何变换和镶嵌图案。

GeoGebra 命令及参数

  1. Polygon(A, B, 4) → poly1, a, b, c, d, C, D
  2. AttachCopyToView(PolyLine[(2.74, -3.06), (2.68, -3.08), (2.62, -3.14), (2.56, -3.2), (2.52, -3.2600000000000002), (2.46, -3.2800000000000002), (2.38, -3.34), (2.32, -3.38), (2.2600000000000002, -3.44), (2.22, -3.5), (2.18, -3.56), (2.08, -3.56), (1.98, -3.56), (1.8800000000000001, -3.56), (1.82, -3.54), (1.76, -3.52), (1.6600000000000001, -3.48), (1.6, -3.46), (1.54, -3.44), (1.46, -3.44), (1.3800000000000001, -3.46), (1.32, -3.5), (1.26, -3.54), (1.24, -3.6), (1.16, -3.66), (1.1, -3.74), (1.04, -3.8200000000000003), (0.98, -3.86), (0.96, -3.8000000000000003), (0.92, -3.72), (0.9, -3.66), (0.84, -3.6), (0.9, -3.54), (0.96, -3.46), (1.02, -3.44), (1.04, -3.38), (1.1, -3.34), (1.16, -3.3000000000000003), (1.22, -3.24), (1.26, -3.18), (1.32, -3.12), (1.3800000000000001, -3.1), (1.3800000000000001, -3.02), (1.36, -2.96), (1.32, -2.9), (1.26, -2.84), (1.2, -2.7800000000000002), (1.16, -2.72), (1.1, -2.7), (1.04, -2.64), (0.98, -2.58), (0.92, -2.52), (0.86, -2.44), (0.8, -2.36), (0.74, -2.32), (0.68, -2.24), (0.62, -2.18), (0.56, -2.1), (0.5, -2.02), (0.46, -1.96), (0.42, -1.9000000000000001), (0.38, -1.84), (0.34, -1.78), (0.28, -1.8), (0.22, -1.82), (0.14, -1.84), (0.06, -1.8800000000000001), (0, -1.9000000000000001), (-0.08, -1.94), (-0.12, -2), (-0.2, -2.04), (-0.28, -2.06), (-0.36, -2.06), (-0.42, -2.08), (-0.48, -2.1), (-0.56, -2.14), (-0.62, -2.16), (-0.68, -2.18), (-0.78, -2.18), (-0.86, -2.18), (-0.9400000000000001, -2.18), (-0.98, -2.24), (-0.98, -2.32), (-0.98, -2.4), (-1, -2.48), (-1.06, -2.5), (-1.12, -2.52), (-1.18, -2.56), (-1.24, -2.6), (-1.3, -2.62), (-1.32, -2.68), (-1.3800000000000001, -2.72), (-1.4000000000000001, -2.7800000000000002), (-1.44, -2.84), (-1.5, -2.88), (-1.46, -2.94), (-1.4000000000000001, -2.98), 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[(-1.3800000000000001, -2.98), (-1.46, -3), (-1.52, -3.02), (-1.58, -3.04), (-1.6600000000000001, -3.04), (-1.68, -2.98), (-1.68, -2.88), (-1.7, -2.82), (-1.68, -2.72), (-1.6400000000000001, -2.66), (-1.6, -2.6), (-1.54, -2.56), (-1.5, -2.5), (-1.48, -2.44), (-1.44, -2.36), (-1.4000000000000001, -2.3000000000000003), (-1.36, -2.2), (-1.36, -2.12), (-1.34, -2), (-1.3, -1.94), (-1.24, -1.92), (-1.18, -1.9000000000000001), (-1.12, -1.86), (-1.06, -1.82), (-1, -1.8), (-0.9400000000000001, -1.78), (-0.86, -1.76), (-0.8, -1.74), (-0.72, -1.68), (-0.66, -1.6400000000000001), (-0.6, -1.58), (-0.58, -1.52), (-0.58, -1.44), (-0.58, -1.36), (-0.58, -1.28), (-0.6, -1.18), (-0.62, -1.12), (-0.64, -1.06), (-0.7000000000000001, -1.04), (-0.76, -1.06), (-0.84, -1.08), (-0.92, -1.08), (-1, -1.08), (-1.06, -1.1), (-1.12, -1.12), (-1.2, -1.12), (-1.28, -1.12), (-1.36, -1.12), (-1.44, -1.12), (-1.5, -1.1400000000000001), (-1.44, -1.16), (-1.36, -1.16), (-1.3, -1.2), (-1.22, -1.2), (-1.18, -1.26), (-1.12, -1.3), (-1.1, -1.36), (-1.02, -1.36), (-0.96, -1.3800000000000001), (-0.9400000000000001, -1.44), (-0.96, -1.52), (-1.02, -1.56), (-1.1, -1.56), (-1.2, -1.56), (-1.28, -1.56), (-1.36, -1.56), (-1.42, -1.54), (-1.48, -1.52), (-1.54, -1.5), (-1.62, -1.5), (-1.68, -1.48), (-1.74, -1.46), (-1.78, -1.4000000000000001), (-1.8, -1.34), (-1.82, -1.28), (-1.82, -1.2), (-1.8, -1.1400000000000001), (-1.78, -1.06), (-1.76, -1), (-1.76, -0.92), (-1.7, -0.9), (-1.6400000000000001, -0.88), (-1.56, -0.88), (-1.48, -0.88), (-1.42, -0.8200000000000001), (-1.34, -0.78), (-1.28, -0.74), (-1.2, -0.7000000000000001), (-1.1400000000000001, -0.66), (-1.08, -0.6), (-1.02, -0.58), (-0.96, -0.56), (-0.9, -0.52), (-0.8200000000000001, -0.52), (-0.76, -0.48), (-0.72, -0.42), (-0.66, -0.4), (-0.6, -0.38), (-0.54, -0.32), (-0.5, -0.26), (-0.48, -0.2), (-0.46, -0.14), (-0.46, -0.04), (-0.44, 0.04), (-0.4, 0.14), (-0.36, 0.24), (-0.34, 0.3), (-0.28, 0.36), (-0.22, 0.42), (-0.16, 0.48), (-0.1, 0.5), (-0.04, 0.54), (0.02, 0.62), (0.08, 0.7000000000000001), (0.12, 0.78), (0.14, 0.84), (0.12, 0.92), (0.1, 0.98), (0.08, 1.04), (0.06, 1.1), (0.04, 1.16), (0.04, 1.24), (0.04, 1.32), (0.02, 1.3800000000000001), (0.02, 1.46), (-0.04, 1.42), (-0.06, 1.36), (-0.12, 1.3), (-0.2, 1.26), (-0.26, 1.22), (-0.32, 1.2), (-0.4, 1.2), (-0.48, 1.2), (-0.56, 1.2), (-0.64, 1.2), (-0.7000000000000001, 1.1400000000000001), (-0.76, 1.12), (-0.8200000000000001, 1.08), (-0.9, 1.08), (-0.98, 1.08), (-1.06, 1.08), (-1.1400000000000001, 1.08), (-1.22, 1.08), (-1.3, 1.08), (-1.36, 1.04), 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. Point(stroke1') → J
  12. Point(stroke1') → K
  13. Point(stroke1') → M
  14. Point(stroke1') → N
  15. Point(stroke1') → O
  16. Point(stroke1') → P
  17. Point(stroke1') → Q
  18. Point(stroke1') → S
  19. Point(stroke1') → T
  20. Point(stroke1') → U
  21. Point(stroke2') → V
  22. Point(stroke2') → W
  23. Point(stroke2') → A_1
  24. Point(stroke2') → B_1
  25. Point(stroke2') → C_1
  26. Point(stroke2') → D_1
  27. Point(stroke2') → F_1
  28. Point(stroke2') → G_1
  29. Point(stroke2') → H_1
  30. Point(stroke2') → I_1
  31. Point(stroke2') → J_1
  32. Point(stroke2') → K_1
  33. Point(stroke2') → L_1
  34. Point(stroke2') → M_1
  35. Point(stroke1) → N_1
  36. Point(stroke1) → O_1
  37. Point(stroke1) → P_1
  38. Point(stroke1) → Q_1
  39. Point(stroke1) → S_1
  40. Point(stroke1) → T_1
  41. Point(stroke1) → U_1
  42. Point(stroke1) → V_1
  43. Point(stroke2) → W_1
  44. Point(stroke2) → Z_1
  45. Point(stroke2) → A_2
  46. Point(stroke2) → B_2
  47. Point(stroke2) → C_2
  48. Point(stroke2) → D_2
  49. Point(stroke2) → E_2
  50. Point(stroke2) → F_2
  51. Point(stroke2) → G_2
  52. Point(stroke2) → H_2
  53. Point(stroke2) → I_2
  54. Point(stroke2) → J_2
  55. Point(stroke2) → K_2
  56. Polygon(D, I, R, S, T, U, C, V, W, Z, A_1, B_1, J, C_1, D_1, E_1, F_1, G_1, H_1, I_1, J_1, K_1, L_1, K, M_1, B, N_1, O_1, P_1, Q_1, R_1, S_1, T_1, U_1, L, V_1, A, W_1, Z_1, A_2, B_2, C_2, D_2, E_2, F_2, M, G_2, H_2, I_2, F, J_2, K_2, N, O, P, Q) → poly2, d_1, q, r, s, t, u_1, c_1, v_1, w, z, a_1, i, b_1, c_2, d_2, e_1, f_1, g_1, h_1, i_1, j_1, k_1, j, l_1, m_1, b_2, n_1, o_1, p_1, q_1, r_1, s_1, t_1, k, u_2, v_2, a_2, w_1, z_1, a_3, b_3, c_3, d_3, e_2, l, f_2, g_2, h_2, i_2, f, j_2, k_2, m, n, o, p
  57. Vector(W_1, I) → e
  58. Translate(stroke1, e) → stroke1'_1
  59. Translate(stroke1', e) → stroke1''
  60. Translate(stroke2, e) → stroke2'_1
  61. Translate(stroke2', e) → stroke2''
  62. Translate(D, e) → D'
  63. Translate(I, e) → I'
  64. Translate(J, e) → J'
  65. Translate(K, e) → K'
  66. Translate(L, e) → L'
  67. Translate(M, e) → M'
  68. Translate(N, e) → N'
  69. Translate(O, e) → O'
  70. Translate(P, e) → P'
  71. Translate(Q, e) → Q'
  72. Translate(R, e) → R'
  73. Translate(S, e) → S'
  74. Translate(T, e) → T'
  75. Translate(U, e) → U'
  76. Translate(C, e) → C'
  77. Translate(V, e) → V'
  78. Translate(W, e) → W'
  79. Translate(Z, e) → Z'
  80. Translate(A_1, e) → L_2
  81. Translate(B_1, e) → M_2
  82. Translate(C_1, e) → N_2
  83. Translate(D_1, e) → O_2
  84. Translate(E_1, e) → P_2
  85. Translate(F_1, e) → Q_2
  86. Translate(G_1, e) → R_2
  87. Translate(H_1, e) → S_2
  88. Translate(I_1, e) → T_2
  89. Translate(J_1, e) → U_2
  90. Translate(K_1, e) → V_2
  91. Translate(L_1, e) → W_2
  92. Translate(M_1, e) → Z_2
  93. Translate(B, e) → B'
  94. Translate(N_1, e) → A_3
  95. Translate(O_1, e) → B_3
  96. Translate(P_1, e) → C_3
  97. Translate(Q_1, e) → D_3
  98. Translate(R_1, e) → E_3
  99. Translate(S_1, e) → F_3
  100. Translate(T_1, e) → G_3
  101. Translate(U_1, e) → H_3
  102. Translate(V_1, e) → I_3
  103. Translate(A, e) → A'
  104. Translate(W_1, e) → J_3
  105. Translate(Z_1, e) → K_3
  106. Translate(A_2, e) → L_3
  107. Translate(B_2, e) → M_3
  108. Translate(C_2, e) → N_3
  109. Translate(D_2, e) → O_3
  110. Translate(E_2, e) → P_3
  111. Translate(F_2, e) → Q_3
  112. Translate(G_2, e) → R_3
  113. Translate(H_2, e) → S_3
  114. Translate(I_2, e) → T_3
  115. Translate(F, e) → F'
  116. Translate(J_2, e) → U_3
  117. Translate(K_2, e) → V_3
  118. Polygon(D', I', R', S', T', U', C', V', W', Z', L_2, M_2, J', N_2, O_2, P_2, Q_2, R_2, S_2, T_2, U_2, V_2, W_2, K', Z_2, B', A_3, B_3, C_3, D_3, E_3, F_3, G_3, H_3, L', I_3, A', J_3, K_3, L_3, M_3, N_3, O_3, P_3, Q_3, M', R_3, S_3, T_3, F', U_3, V_3, N', O', P', Q') → poly2', d', q', r', s', t', u', c', v', w', z', l_2, i', m_2, n_2, o_2, p_2, q_2, r_2, s_2, t_2, u_3, v_3, j', w_2, z_2, b', a_4, b_4, c_4, d_4, e_3, f_3, g_3, k', h_3, i_3, a', j_3, k_3, l_3, m_3, n_3, o_3, p_3, l', q_3, r_3, s_3, t_3, f', u_4, v_4, m', n', o', p'
  119. Translate(E, e) → E'
  120. Translate(G, e) → G'
  121. Translate(H, e) → H'

AI 绘图提示语参考

绘制一个通过平移变换形成的镶嵌图案。首先绘制一个四边形，然后通过平移该四边形来创建一个重复的图案。接着，使用平移后的四边形再次平移，形成更复杂的镶嵌图案。最后，标记出平移后的关键点，如J、K、M、N等。
以上提示语为根据原始绘图命令整理而来，仅供参考。