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埃舍尔风格的多边形连缀与旋转变换可视化

埃舍尔风格的多边形连缀与旋转变换可视化
几何画板及绘图内容加载中，请稍等……
2023-03-20 23:29
多边形角向量变换几何作图
所属专题 geometriadinamica.es
该范例展示了如何用连续的旋转与平移，把基础多边形单元反复嵌合成类似埃舍尔（Escher）风格的几何连缀图案。核心数学概念包括：多边形的顶点构造、向量的平移表示、旋转变换的几何意义，以及通过变换参数生成重复结构（可理解为离散的“对称/拼砌”思想）。作图要点来自构造摘要：使用 Polygon 构造初始多边形单元；用 Vector 定义平移所需的方向与大小（由相应向量对象刻画）；用 Rotate 对图形进行绕给定中心的旋转复制；再结合 Translate 将图元按向量平移到新的位置，形成整体的嵌套与连续铺排。涉及的对象包含多组顶点/点（如 A,B,C…与其下标变体）以及若干旋转/平移相关的辅助量。适合中学高年级到大学基础层的几何作图、变换几何教学与编程式几何探索，亦可用于培养学生对对称性与几何构造的直观理解。

GeoGebra 命令及参数

  1. Polygon(A, B, K, L, M, N, O, P, Q, R, S, T, C, U, V, W, Y, Z, A_1, B_1, C_1, D_1, E_1, D, F_1, G_1, H_1, I_1, J_1, K_1, L_1, M_1, N_1, O_1, E, P_4, Q_1, R_1, S_1, T_1, U_1, V_1, W_1, Y_1, Z_1, F, A_2, B_2, C_2, D_2, E_2, G, H, I, J) → P_1, a, j, k, l, m, n, p, q, r, s, t, b, a_1, b_1, c_1, d_1, e_1, f_1, g_1, h_1, i_1, j_1, c, k_1, l_1, m_1, n_1, p_1, q_1, r_1, s_1, t_1, b_2, d, c_2, d_2, e_2, f_2, g_2, h_2, i_2, j_2, k_2, l_2, e, m_2, n_2, p_2, q_2, r_2, s_2, f, g, h, i
  2. Rotate(A, α, A) → A'
  3. Rotate(B, α, A) → B'
  4. Rotate(C, α, A) → C'
  5. Rotate(D, α, A) → D'
  6. Rotate(E, α, A) → E'
  7. Rotate(F, α, A) → F'
  8. Rotate(G, α, A) → G'
  9. Rotate(H, α, A) → H'
  10. Rotate(I, α, A) → I'
  11. Rotate(J, α, A) → J'
  12. Rotate(K, α, A) → K'
  13. Rotate(L, α, A) → L'
  14. Rotate(M, α, A) → M'
  15. Rotate(N, α, A) → N'
  16. Rotate(O, α, A) → O'
  17. Rotate(P, α, A) → P'
  18. Rotate(Q, α, A) → Q'
  19. Rotate(R, α, A) → R'
  20. Rotate(S, α, A) → S'
  21. Rotate(T, α, A) → T'
  22. Rotate(U, α, A) → U'
  23. Rotate(V, α, A) → V'
  24. Rotate(W, α, A) → W'
  25. Rotate(Y, α, A) → Y'
  26. Rotate(Z, α, A) → Z'
  27. Rotate(A_1, α, A) → A_1'
  28. Rotate(B_1, α, A) → B_1'
  29. Rotate(C_1, α, A) → C_1'
  30. Rotate(D_1, α, A) → D_1'
  31. Rotate(E_1, α, A) → E_1'
  32. Rotate(F_1, α, A) → F_1'
  33. Rotate(G_1, α, A) → G_1'
  34. Rotate(H_1, α, A) → H_1'
  35. Rotate(I_1, α, A) → I_1'
  36. Rotate(J_1, α, A) → J_1'
  37. Rotate(K_1, α, A) → K_1'
  38. Rotate(L_1, α, A) → L_1'
  39. Rotate(M_1, α, A) → M_1'
  40. Rotate(N_1, α, A) → N_1'
  41. Rotate(O_1, α, A) → O_1'
  42. Rotate(P_4, α, A) → P_1'
  43. Rotate(Q_1, α, A) → Q_1'
  44. Rotate(R_1, α, A) → R_1'
  45. Rotate(S_1, α, A) → S_1'
  46. Rotate(T_1, α, A) → T_1'
  47. Rotate(U_1, α, A) → U_1'
  48. Rotate(V_1, α, A) → V_1'
  49. Rotate(W_1, α, A) → W_1'
  50. Rotate(Y_1, α, A) → Y_1'
  51. Rotate(Z_1, α, A) → Z_1'
  52. Rotate(A_2, α, A) → A_2'
  53. Rotate(B_2, α, A) → B_2'
  54. Rotate(C_2, α, A) → C_2'
  55. Rotate(D_2, α, A) → D_2'
  56. Rotate(E_2, α, A) → E_2'
  57. Polygon(A', B', K', L', M', N', O', P', Q', R', S', T', C', U', V', W', Y', Z', A_1', B_1', C_1', D_1', E_1', D', F_1', G_1', H_1', I_1', J_1', K_1', L_1', M_1', N_1', O_1', E', P_1', Q_1', R_1', S_1', T_1', U_1', V_1', W_1', Y_1', Z_1', F', A_2', B_2', C_2', D_2', E_2', G', H', I', J') → P_2, a', j', k', l', m', n', o', p', q', r', s', b', t', u', v', w', y', z', a_1', b_1', c_1', d_1', c', e_1', f_1', g_1', h_1', i_1', j_1', k_1', l_1', m_1', n_1', d', o_1', p_1', q_1', r_1', s_1', t_1', u_1', v_1', w_1', y_1', e', z_1', a_2', b_2', c_2', d_2', e_2', f', g', h', i'
  58. Rotate(A', α, A) → A''
  59. Rotate(B', α, A) → B''
  60. Rotate(C', α, A) → C''
  61. Rotate(D', α, A) → D''
  62. Rotate(E', α, A) → E''
  63. Rotate(F', α, A) → F''
  64. Rotate(G', α, A) → G''
  65. Rotate(H', α, A) → H''
  66. Rotate(I', α, A) → I''
  67. Rotate(J', α, A) → J''
  68. Rotate(K', α, A) → K''
  69. Rotate(L', α, A) → L''
  70. Rotate(M', α, A) → M''
  71. Rotate(N', α, A) → N''
  72. Rotate(O', α, A) → O''
  73. Rotate(P', α, A) → P''
  74. Rotate(Q', α, A) → Q''
  75. Rotate(R', α, A) → R''
  76. Rotate(S', α, A) → S''
  77. Rotate(T', α, A) → T''
  78. Rotate(U', α, A) → U''
  79. Rotate(V', α, A) → V''
  80. Rotate(W', α, A) → W''
  81. Rotate(Y', α, A) → Y''
  82. Rotate(Z', α, A) → Z''
  83. Rotate(A_1', α, A) → A_1''
  84. Rotate(B_1', α, A) → B_1''
  85. Rotate(C_1', α, A) → C_1''
  86. Rotate(D_1', α, A) → D_1''
  87. Rotate(E_1', α, A) → E_1''
  88. Rotate(F_1', α, A) → F_1''
  89. Rotate(G_1', α, A) → G_1''
  90. Rotate(H_1', α, A) → H_1''
  91. Rotate(I_1', α, A) → I_1''
  92. Rotate(J_1', α, A) → J_1''
  93. Rotate(K_1', α, A) → K_1''
  94. Rotate(L_1', α, A) → L_1''
  95. Rotate(M_1', α, A) → M_1''
  96. Rotate(N_1', α, A) → N_1''
  97. Rotate(O_1', α, A) → O_1''
  98. Rotate(P_1', α, A) → P_1''
  99. Rotate(Q_1', α, A) → Q_1''
  100. Rotate(R_1', α, A) → R_1''
  101. Rotate(S_1', α, A) → S_1''
  102. Rotate(T_1', α, A) → T_1''
  103. Rotate(U_1', α, A) → U_1''
  104. Rotate(V_1', α, A) → V_1''
  105. Rotate(W_1', α, A) → W_1''
  106. Rotate(Y_1', α, A) → Y_1''
  107. Rotate(Z_1', α, A) → Z_1''
  108. Rotate(A_2', α, A) → A_2''
  109. Rotate(B_2', α, A) → B_2''
  110. Rotate(C_2', α, A) → C_2''
  111. Rotate(D_2', α, A) → D_2''
  112. Rotate(E_2', α, A) → E_2''
  113. Polygon(A'', B'', K'', L'', M'', N'', O'', P'', Q'', R'', S'', T'', C'', U'', V'', W'', Y'', Z'', A_1'', B_1'', C_1'', D_1'', E_1'', D'', F_1'', G_1'', H_1'', I_1'', J_1'', K_1'', L_1'', M_1'', N_1'', O_1'', E'', P_1'', Q_1'', R_1'', S_1'', T_1'', U_1'', V_1'', W_1'', Y_1'', Z_1'', F'', A_2'', B_2'', C_2'', D_2'', E_2'', G'', H'', I'', J'') → P_3, a'', j'', k'', l'', m'', n'', o'', p'', q'', r'', s'', b'', t'', u'', v'', w'', y'', z'', a_1'', b_1'', c_1'', d_1'', c'', e_1'', f_1'', g_1'', h_1'', i_1'', j_1'', k_1'', l_1'', m_1'', n_1'', d'', o_1'', p_1'', q_1'', r_1'', s_1'', t_1'', u_1'', v_1'', w_1'', y_1'', e'', z_1'', a_2'', b_2'', c_2'', d_2'', e_2'', f'', g'', h'', i''
  114. Vector(Y'', Y) → u
  115. Translate(A, Vector[(a_2 * u)]) → A'_1
  116. Translate(B, Vector[(a_2 * u)]) → B'_1
  117. Translate(C, Vector[(a_2 * u)]) → C'_1
  118. Translate(D, Vector[(a_2 * u)]) → D'_1
  119. Translate(E, Vector[(a_2 * u)]) → E'_1
  120. Translate(F, Vector[(a_2 * u)]) → F'_1
  121. Translate(G, Vector[(a_2 * u)]) → G'_1
  122. Translate(H, Vector[(a_2 * u)]) → H'_1
  123. Translate(I, Vector[(a_2 * u)]) → I'_1
  124. Translate(J, Vector[(a_2 * u)]) → J'_1
  125. Translate(K, Vector[(a_2 * u)]) → K'_1
  126. Translate(L, Vector[(a_2 * u)]) → L'_1
  127. Translate(M, Vector[(a_2 * u)]) → M'_1
  128. Translate(N, Vector[(a_2 * u)]) → N'_1
  129. Translate(O, Vector[(a_2 * u)]) → O'_1
  130. Translate(P, Vector[(a_2 * u)]) → P'_1
  131. Translate(Q, Vector[(a_2 * u)]) → Q'_1
  132. Translate(R, Vector[(a_2 * u)]) → R'_1
  133. Translate(S, Vector[(a_2 * u)]) → S'_1
  134. Translate(T, Vector[(a_2 * u)]) → T'_1
  135. Translate(U, Vector[(a_2 * u)]) → U'_1
  136. Translate(V, Vector[(a_2 * u)]) → V'_1
  137. Translate(W, Vector[(a_2 * u)]) → W'_1
  138. Translate(Y, Vector[(a_2 * u)]) → Y'_1
  139. Translate(Z, Vector[(a_2 * u)]) → Z'_1
  140. Translate(A_1, Vector[(a_2 * u)]) → A_3
  141. Translate(B_1, Vector[(a_2 * u)]) → B_3
  142. Translate(C_1, Vector[(a_2 * u)]) → C_3
  143. Translate(D_1, Vector[(a_2 * u)]) → D_3
  144. Translate(E_1, Vector[(a_2 * u)]) → E_3
  145. Translate(F_1, Vector[(a_2 * u)]) → F_2
  146. Translate(G_1, Vector[(a_2 * u)]) → G_2
  147. Translate(H_1, Vector[(a_2 * u)]) → H_2
  148. Translate(I_1, Vector[(a_2 * u)]) → I_2
  149. Translate(J_1, Vector[(a_2 * u)]) → J_2
  150. Translate(K_1, Vector[(a_2 * u)]) → K_2
  151. Translate(L_1, Vector[(a_2 * u)]) → L_2
  152. Translate(M_1, Vector[(a_2 * u)]) → M_2
  153. Translate(N_1, Vector[(a_2 * u)]) → N_2
  154. Translate(O_1, Vector[(a_2 * u)]) → O_2
  155. Translate(P_4, Vector[(a_2 * u)]) → P_4'
  156. Translate(Q_1, Vector[(a_2 * u)]) → Q_2
  157. Translate(R_1, Vector[(a_2 * u)]) → R_2
  158. Translate(S_1, Vector[(a_2 * u)]) → S_2
  159. Translate(T_1, Vector[(a_2 * u)]) → T_2
  160. Translate(U_1, Vector[(a_2 * u)]) → U_2
  161. Translate(V_1, Vector[(a_2 * u)]) → V_2
  162. Translate(W_1, Vector[(a_2 * u)]) → W_2
  163. Translate(Y_1, Vector[(a_2 * u)]) → Y_3
  164. Translate(Z_1, Vector[(a_2 * u)]) → Z_3
  165. Translate(A_2, Vector[(a_2 * u)]) → A_4
  166. Translate(B_2, Vector[(a_2 * u)]) → B_4
  167. Translate(C_2, Vector[(a_2 * u)]) → C_4
  168. Translate(D_2, Vector[(a_2 * u)]) → D_4
  169. Translate(E_2, Vector[(a_2 * u)]) → E_4
  170. Polygon(A'_1, B'_1, K'_1, L'_1, M'_1, N'_1, O'_1, P'_1, Q'_1, R'_1, S'_1, T'_1, C'_1, U'_1, V'_1, W'_1, Y'_1, Z'_1, A_3, B_3, C_3, D_3, E_3, D'_1, F_2, G_2, H_2, I_2, J_2, K_2, L_2, M_2, N_2, O_2, E'_1, P_4', Q_2, R_2, S_2, T_2, U_2, V_2, W_2, Y_3, Z_3, F'_1, A_4, B_4, C_4, D_4, E_4, G'_1, H'_1, I'_1, J'_1) → P_5, a'_1, j'_1, k'_1, l'_1, m'_1, n'_1, o'_1, p'_1, q'_1, r'_1, s'_1, b'_1, t'_1, u'_1, v'_1, w'_1, y'_1, z'_1, a_3, b_3, c_3, d_3, c'_1, e_3, f_3, g_3, h_3, i_3, j_3, k_3, l_3, m_3, n_3, d'_1, o_2, p_4', q_3, r_3, s_3, t_2, u_2, v_2, w_2, y_3, e'_1, z_3, a_4, b_5, c_4, d_4, e_4, f'_1, g'_1, h'_1, i'_1
  171. Translate(A', Vector[(a_2 * u)]) → A''_1
  172. Translate(B', Vector[(a_2 * u)]) → B''_1
  173. Translate(C', Vector[(a_2 * u)]) → C''_1
  174. Translate(D', Vector[(a_2 * u)]) → D''_1
  175. Translate(E', Vector[(a_2 * u)]) → E''_1
  176. Translate(F', Vector[(a_2 * u)]) → F''_1
  177. Translate(G', Vector[(a_2 * u)]) → G''_1
  178. Translate(H', Vector[(a_2 * u)]) → H''_1
  179. Translate(I', Vector[(a_2 * u)]) → I''_1
  180. Translate(J', Vector[(a_2 * u)]) → J''_1
  181. Translate(K', Vector[(a_2 * u)]) → K''_1
  182. Translate(L', Vector[(a_2 * u)]) → L''_1
  183. Translate(M', Vector[(a_2 * u)]) → M''_1
  184. Translate(N', Vector[(a_2 * u)]) → N''_1
  185. Translate(O', Vector[(a_2 * u)]) → O''_1
  186. Translate(P', Vector[(a_2 * u)]) → P''_1
  187. Translate(Q', Vector[(a_2 * u)]) → Q''_1
  188. Translate(R', Vector[(a_2 * u)]) → R''_1
  189. Translate(S', Vector[(a_2 * u)]) → S''_1
  190. Translate(T', Vector[(a_2 * u)]) → T''_1
  191. Translate(U', Vector[(a_2 * u)]) → U''_1
  192. Translate(V', Vector[(a_2 * u)]) → V''_1
  193. Translate(W', Vector[(a_2 * u)]) → W''_1
  194. Translate(Y', Vector[(a_2 * u)]) → Y''_1
  195. Translate(Z', Vector[(a_2 * u)]) → Z''_1
  196. Translate(A_1', Vector[(a_2 * u)]) → A_5
  197. Translate(B_1', Vector[(a_2 * u)]) → B_5
  198. Translate(C_1', Vector[(a_2 * u)]) → C_5
  199. Translate(D_1', Vector[(a_2 * u)]) → D_5
  200. Translate(E_1', Vector[(a_2 * u)]) → E_5
  201. Translate(F_1', Vector[(a_2 * u)]) → F_3
  202. Translate(G_1', Vector[(a_2 * u)]) → G_3
  203. Translate(H_1', Vector[(a_2 * u)]) → H_3
  204. Translate(I_1', Vector[(a_2 * u)]) → I_3
  205. Translate(J_1', Vector[(a_2 * u)]) → J_3
  206. Translate(K_1', Vector[(a_2 * u)]) → K_3
  207. Translate(L_1', Vector[(a_2 * u)]) → L_3
  208. Translate(M_1', Vector[(a_2 * u)]) → M_3
  209. Translate(N_1', Vector[(a_2 * u)]) → N_3
  210. Translate(O_1', Vector[(a_2 * u)]) → O_3
  211. Translate(P_1', Vector[(a_2 * u)]) → P_6
  212. Translate(Q_1', Vector[(a_2 * u)]) → Q_3
  213. Translate(R_1', Vector[(a_2 * u)]) → R_3
  214. Translate(S_1', Vector[(a_2 * u)]) → S_3
  215. Translate(T_1', Vector[(a_2 * u)]) → T_3
  216. Translate(U_1', Vector[(a_2 * u)]) → U_3
  217. Translate(V_1', Vector[(a_2 * u)]) → V_3
  218. Translate(W_1', Vector[(a_2 * u)]) → W_3
  219. Translate(Y_1', Vector[(a_2 * u)]) → Y_4
  220. Translate(Z_1', Vector[(a_2 * u)]) → Z_4
  221. Translate(A_2', Vector[(a_2 * u)]) → A_6
  222. Translate(B_2', Vector[(a_2 * u)]) → B_6
  223. Translate(C_2', Vector[(a_2 * u)]) → C_6
  224. Translate(D_2', Vector[(a_2 * u)]) → D_6
  225. Translate(E_2', Vector[(a_2 * u)]) → E_6
  226. Polygon(A''_1, B''_1, K''_1, L''_1, M''_1, N''_1, O''_1, P''_1, Q''_1, R''_1, S''_1, T''_1, C''_1, U''_1, V''_1, W''_1, Y''_1, Z''_1, A_5, B_5, C_5, D_5, E_5, D''_1, F_3, G_3, H_3, I_3, J_3, K_3, L_3, M_3, N_3, O_3, E''_1, P_6, Q_3, R_3, S_3, T_3, U_3, V_3, W_3, Y_4, Z_4, F''_1, A_6, B_6, C_6, D_6, E_6, G''_1, H''_1, I''_1, J''_1) → P_2', a''_1, j''_1, k''_1, l''_1, m''_1, n''_1, o''_1, p''_1, q''_1, r''_1, s''_1, b''_1, t''_1, u''_1, v''_1, w''_1, y''_1, z''_1, a_5, b_6, c_5, d_5, c''_1, e_5, f_4, g_4, h_4, i_4, j_4, k_4, l_4, m_4, n_4, d''_1, o_3, p_6, q_4, r_4, s_4, t_3, u_3, v_3, w_3, y_4, e''_1, z_4, a_6, b_7, c_6, d_6, e_6, f''_1, g''_1, h''_1, i''_1
  227. Translate(A'', Vector[(a_2 * u)]) → A'''
  228. Translate(B'', Vector[(a_2 * u)]) → B'''
  229. Translate(C'', Vector[(a_2 * u)]) → C'''
  230. Translate(D'', Vector[(a_2 * u)]) → D'''
  231. Translate(E'', Vector[(a_2 * u)]) → E'''
  232. Translate(F'', Vector[(a_2 * u)]) → F'''
  233. Translate(G'', Vector[(a_2 * u)]) → G'''
  234. Translate(H'', Vector[(a_2 * u)]) → H'''
  235. Translate(I'', Vector[(a_2 * u)]) → I'''
  236. Translate(J'', Vector[(a_2 * u)]) → J'''
  237. Translate(K'', Vector[(a_2 * u)]) → K'''
  238. Translate(L'', Vector[(a_2 * u)]) → L'''
  239. Translate(M'', Vector[(a_2 * u)]) → M'''
  240. Translate(N'', Vector[(a_2 * u)]) → N'''
  241. Translate(O'', Vector[(a_2 * u)]) → O'''
  242. Translate(P'', Vector[(a_2 * u)]) → P'''
  243. Translate(Q'', Vector[(a_2 * u)]) → Q'''
  244. Translate(R'', Vector[(a_2 * u)]) → R'''
  245. Translate(S'', Vector[(a_2 * u)]) → S'''
  246. Translate(T'', Vector[(a_2 * u)]) → T'''
  247. Translate(U'', Vector[(a_2 * u)]) → U'''
  248. Translate(V'', Vector[(a_2 * u)]) → V'''
  249. Translate(W'', Vector[(a_2 * u)]) → W'''
  250. Translate(Y'', Vector[(a_2 * u)]) → Y'''
  251. Translate(Z'', Vector[(a_2 * u)]) → Z'''
  252. Translate(A_1'', Vector[(a_2 * u)]) → A_1'''
  253. Translate(B_1'', Vector[(a_2 * u)]) → B_1'''
  254. Translate(C_1'', Vector[(a_2 * u)]) → C_1'''
  255. Translate(D_1'', Vector[(a_2 * u)]) → D_1'''
  256. Translate(E_1'', Vector[(a_2 * u)]) → E_1'''
  257. Translate(F_1'', Vector[(a_2 * u)]) → F_1'''
  258. Translate(G_1'', Vector[(a_2 * u)]) → G_1'''
  259. Translate(H_1'', Vector[(a_2 * u)]) → H_1'''
  260. Translate(I_1'', Vector[(a_2 * u)]) → I_1'''
  261. Translate(J_1'', Vector[(a_2 * u)]) → J_1'''
  262. Translate(K_1'', Vector[(a_2 * u)]) → K_1'''
  263. Translate(L_1'', Vector[(a_2 * u)]) → L_1'''
  264. Translate(M_1'', Vector[(a_2 * u)]) → M_1'''
  265. Translate(N_1'', Vector[(a_2 * u)]) → N_1'''
  266. Translate(O_1'', Vector[(a_2 * u)]) → O_1'''
  267. Translate(P_1'', Vector[(a_2 * u)]) → P_1'''
  268. Translate(Q_1'', Vector[(a_2 * u)]) → Q_1'''
  269. Translate(R_1'', Vector[(a_2 * u)]) → R_1'''
  270. Translate(S_1'', Vector[(a_2 * u)]) → S_1'''
  271. Translate(T_1'', Vector[(a_2 * u)]) → T_1'''
  272. Translate(U_1'', Vector[(a_2 * u)]) → U_1'''
  273. Translate(V_1'', Vector[(a_2 * u)]) → V_1'''
  274. Translate(W_1'', Vector[(a_2 * u)]) → W_1'''
  275. Translate(Y_1'', Vector[(a_2 * u)]) → Y_1'''
  276. Translate(Z_1'', Vector[(a_2 * u)]) → Z_1'''
  277. Translate(A_2'', Vector[(a_2 * u)]) → A_2'''
  278. Translate(B_2'', Vector[(a_2 * u)]) → B_2'''
  279. Translate(C_2'', Vector[(a_2 * u)]) → C_2'''
  280. Translate(D_2'', Vector[(a_2 * u)]) → D_2'''
  281. Translate(E_2'', Vector[(a_2 * u)]) → E_2'''
  282. Polygon(A''', B''', K''', L''', M''', N''', O''', P''', Q''', R''', S''', T''', C''', U''', V''', W''', Y''', Z''', A_1''', B_1''', C_1''', D_1''', E_1''', D''', F_1''', G_1''', H_1''', I_1''', J_1''', K_1''', L_1''', M_1''', N_1''', O_1''', E''', P_1''', Q_1''', R_1''', S_1''', T_1''', U_1''', V_1''', W_1''', Y_1''', Z_1''', F''', A_2''', B_2''', C_2''', D_2''', E_2''', G''', H''', I''', J''') → P_3', a''', j''', k''', l''', m''', n''', o''', p''', q''', r''', s''', b''', t''', u''', v''', w''', y''', z''', a_1''', b_1''', c_1''', d_1''', c''', e_1''', f_1''', g_1''', h_1''', i_1''', j_1''', k_1''', l_1''', m_1''', n_1''', d''', o_1''', p_1''', q_1''', r_1''', s_1''', t_1''', u_1''', v_1''', w_1''', y_1''', e''', z_1''', a_2''', b_2''', c_2''', d_2''', e_2''', f''', g''', h''', i'''
  283. Vector(Y', Y) → v
  284. Translate(A, Vector[(b_4 * v)]) → A'_2
  285. Translate(B, Vector[(b_4 * v)]) → B'_2
  286. Translate(C, Vector[(b_4 * v)]) → C'_2
  287. Translate(D, Vector[(b_4 * v)]) → D'_2
  288. Translate(E, Vector[(b_4 * v)]) → E'_2
  289. Translate(F, Vector[(b_4 * v)]) → F'_2
  290. Translate(G, Vector[(b_4 * v)]) → G'_2
  291. Translate(H, Vector[(b_4 * v)]) → H'_2
  292. Translate(I, Vector[(b_4 * v)]) → I'_2
  293. Translate(J, Vector[(b_4 * v)]) → J'_2
  294. Translate(K, Vector[(b_4 * v)]) → K'_2
  295. Translate(L, Vector[(b_4 * v)]) → L'_2
  296. Translate(M, Vector[(b_4 * v)]) → M'_2
  297. Translate(N, Vector[(b_4 * v)]) → N'_2
  298. Translate(O, Vector[(b_4 * v)]) → O'_2
  299. Translate(P, Vector[(b_4 * v)]) → P'_2
  300. Translate(Q, Vector[(b_4 * v)]) → Q'_2
  301. Translate(R, Vector[(b_4 * v)]) → R'_2
  302. Translate(S, Vector[(b_4 * v)]) → S'_2
  303. Translate(T, Vector[(b_4 * v)]) → T'_2
  304. Translate(U, Vector[(b_4 * v)]) → U'_2
  305. Translate(V, Vector[(b_4 * v)]) → V'_2
  306. Translate(W, Vector[(b_4 * v)]) → W'_2
  307. Translate(Y, Vector[(b_4 * v)]) → Y'_2
  308. Translate(Z, Vector[(b_4 * v)]) → Z'_2
  309. Translate(A_1, Vector[(b_4 * v)]) → A_7
  310. Translate(B_1, Vector[(b_4 * v)]) → B_7
  311. Translate(C_1, Vector[(b_4 * v)]) → C_7
  312. Translate(D_1, Vector[(b_4 * v)]) → D_7
  313. Translate(E_1, Vector[(b_4 * v)]) → E_7
  314. Translate(F_1, Vector[(b_4 * v)]) → F_4
  315. Translate(G_1, Vector[(b_4 * v)]) → G_4
  316. Translate(H_1, Vector[(b_4 * v)]) → H_4
  317. Translate(I_1, Vector[(b_4 * v)]) → I_4
  318. Translate(J_1, Vector[(b_4 * v)]) → J_4
  319. Translate(K_1, Vector[(b_4 * v)]) → K_4
  320. Translate(L_1, Vector[(b_4 * v)]) → L_4
  321. Translate(M_1, Vector[(b_4 * v)]) → M_4
  322. Translate(N_1, Vector[(b_4 * v)]) → N_4
  323. Translate(O_1, Vector[(b_4 * v)]) → O_4
  324. Translate(P_4, Vector[(b_4 * v)]) → P_7
  325. Translate(Q_1, Vector[(b_4 * v)]) → Q_4
  326. Translate(R_1, Vector[(b_4 * v)]) → R_4
  327. Translate(S_1, Vector[(b_4 * v)]) → S_4
  328. Translate(T_1, Vector[(b_4 * v)]) → T_4
  329. Translate(U_1, Vector[(b_4 * v)]) → U_4
  330. Translate(V_1, Vector[(b_4 * v)]) → V_4
  331. Translate(W_1, Vector[(b_4 * v)]) → W_4
  332. Translate(Y_1, Vector[(b_4 * v)]) → Y_5
  333. Translate(Z_1, Vector[(b_4 * v)]) → Z_5
  334. Translate(A_2, Vector[(b_4 * v)]) → A_8
  335. Translate(B_2, Vector[(b_4 * v)]) → B_8
  336. Translate(C_2, Vector[(b_4 * v)]) → C_8
  337. Translate(D_2, Vector[(b_4 * v)]) → D_8
  338. Translate(E_2, Vector[(b_4 * v)]) → E_8
  339. Polygon(A'_2, B'_2, K'_2, L'_2, M'_2, N'_2, O'_2, P'_2, Q'_2, R'_2, S'_2, T'_2, C'_2, U'_2, V'_2, W'_2, Y'_2, Z'_2, A_7, B_7, C_7, D_7, E_7, D'_2, F_4, G_4, H_4, I_4, J_4, K_4, L_4, M_4, N_4, O_4, E'_2, P_7, Q_4, R_4, S_4, T_4, U_4, V_4, W_4, Y_5, Z_5, F'_2, A_8, B_8, C_8, D_8, E_8, G'_2, H'_2, I'_2, J'_2) → P_8, a'_2, j'_2, k'_2, l'_2, m'_2, n'_2, o'_2, p'_2, q'_2, r'_2, s'_2, b'_2, t'_2, u'_2, v'_2, w'_2, y'_2, z'_2, a_7, b_8, c_7, d_7, c'_2, e_7, f_5, g_5, h_5, i_5, j_5, k_5, l_5, m_5, n_5, d'_2, o_4, p_7, q_5, r_5, s_5, t_4, u_4, v_4, w_4, y_5, e'_2, z_5, a_8, b_9, c_8, d_8, e_8, f'_2, g'_2, h'_2, i'_2
  340. Translate(A', Vector[(b_4 * v)]) → A''_2
  341. Translate(B', Vector[(b_4 * v)]) → B''_2
  342. Translate(C', Vector[(b_4 * v)]) → C''_2
  343. Translate(D', Vector[(b_4 * v)]) → D''_2
  344. Translate(E', Vector[(b_4 * v)]) → E''_2
  345. Translate(F', Vector[(b_4 * v)]) → F''_2
  346. Translate(G', Vector[(b_4 * v)]) → G''_2
  347. Translate(H', Vector[(b_4 * v)]) → H''_2
  348. Translate(I', Vector[(b_4 * v)]) → I''_2
  349. Translate(J', Vector[(b_4 * v)]) → J''_2
  350. Translate(K', Vector[(b_4 * v)]) → K''_2
  351. Translate(L', Vector[(b_4 * v)]) → L''_2
  352. Translate(M', Vector[(b_4 * v)]) → M''_2
  353. Translate(N', Vector[(b_4 * v)]) → N''_2
  354. Translate(O', Vector[(b_4 * v)]) → O''_2
  355. Translate(P', Vector[(b_4 * v)]) → P''_2
  356. Translate(Q', Vector[(b_4 * v)]) → Q''_2
  357. Translate(R', Vector[(b_4 * v)]) → R''_2
  358. Translate(S', Vector[(b_4 * v)]) → S''_2
  359. Translate(T', Vector[(b_4 * v)]) → T''_2
  360. Translate(U', Vector[(b_4 * v)]) → U''_2
  361. Translate(V', Vector[(b_4 * v)]) → V''_2
  362. Translate(W', Vector[(b_4 * v)]) → W''_2
  363. Translate(Y', Vector[(b_4 * v)]) → Y''_2
  364. Translate(Z', Vector[(b_4 * v)]) → Z''_2
  365. Translate(A_1', Vector[(b_4 * v)]) → A_9
  366. Translate(B_1', Vector[(b_4 * v)]) → B_9
  367. Translate(C_1', Vector[(b_4 * v)]) → C_9
  368. Translate(D_1', Vector[(b_4 * v)]) → D_9
  369. Translate(E_1', Vector[(b_4 * v)]) → E_9
  370. Translate(F_1', Vector[(b_4 * v)]) → F_5
  371. Translate(G_1', Vector[(b_4 * v)]) → G_5
  372. Translate(H_1', Vector[(b_4 * v)]) → H_5
  373. Translate(I_1', Vector[(b_4 * v)]) → I_5
  374. Translate(J_1', Vector[(b_4 * v)]) → J_5
  375. Translate(K_1', Vector[(b_4 * v)]) → K_5
  376. Translate(L_1', Vector[(b_4 * v)]) → L_5
  377. Translate(M_1', Vector[(b_4 * v)]) → M_5
  378. Translate(N_1', Vector[(b_4 * v)]) → N_5
  379. Translate(O_1', Vector[(b_4 * v)]) → O_5
  380. Translate(P_1', Vector[(b_4 * v)]) → P_9
  381. Translate(Q_1', Vector[(b_4 * v)]) → Q_5
  382. Translate(R_1', Vector[(b_4 * v)]) → R_5
  383. Translate(S_1', Vector[(b_4 * v)]) → S_5
  384. Translate(T_1', Vector[(b_4 * v)]) → T_5
  385. Translate(U_1', Vector[(b_4 * v)]) → U_5
  386. Translate(V_1', Vector[(b_4 * v)]) → V_5
  387. Translate(W_1', Vector[(b_4 * v)]) → W_5
  388. Translate(Y_1', Vector[(b_4 * v)]) → Y_6
  389. Translate(Z_1', Vector[(b_4 * v)]) → Z_6
  390. Translate(A_2', Vector[(b_4 * v)]) → A_{10}
  391. Translate(B_2', Vector[(b_4 * v)]) → B_{10}
  392. Translate(C_2', Vector[(b_4 * v)]) → C_{10}
  393. Translate(D_2', Vector[(b_4 * v)]) → D_{10}
  394. Translate(E_2', Vector[(b_4 * v)]) → E_{10}
  395. Polygon(A''_2, B''_2, K''_2, L''_2, M''_2, N''_2, O''_2, P''_2, Q''_2, R''_2, S''_2, T''_2, C''_2, U''_2, V''_2, W''_2, Y''_2, Z''_2, A_9, B_9, C_9, D_9, E_9, D''_2, F_5, G_5, H_5, I_5, J_5, K_5, L_5, M_5, N_5, O_5, E''_2, P_9, Q_5, R_5, S_5, T_5, U_5, V_5, W_5, Y_6, Z_6, F''_2, A_{10}, B_{10}, C_{10}, D_{10}, E_{10}, G''_2, H''_2, I''_2, J''_2) → P_{10}, a''_2, j''_2, k''_2, l''_2, m''_2, n''_2, o''_2, p''_2, q''_2, r''_2, s''_2, b''_2, t''_2, u''_2, v''_2, w''_2, y''_2, z''_2, a_9, b_{10}, c_9, d_9, c''_2, e_9, f_6, g_6, h_6, i_6, j_6, k_6, l_6, m_6, n_6, d''_2, o_5, p_9, q_6, r_6, s_6, t_5, u_5, v_5, w_5, y_6, e''_2, z_6, a_{10}, b_{11}, c_{10}, d_{10}, e_{10}, f''_2, g''_2, h''_2, i''_2
  396. Translate(A'', Vector[(b_4 * v)]) → A'''_1
  397. Translate(B'', Vector[(b_4 * v)]) → B'''_1
  398. Translate(C'', Vector[(b_4 * v)]) → C'''_1
  399. Translate(D'', Vector[(b_4 * v)]) → D'''_1
  400. Translate(E'', Vector[(b_4 * v)]) → E'''_1
  401. Translate(F'', Vector[(b_4 * v)]) → F'''_1
  402. Translate(G'', Vector[(b_4 * v)]) → G'''_1
  403. Translate(H'', Vector[(b_4 * v)]) → H'''_1
  404. Translate(I'', Vector[(b_4 * v)]) → I'''_1
  405. Translate(J'', Vector[(b_4 * v)]) → J'''_1
  406. Translate(K'', Vector[(b_4 * v)]) → K'''_1
  407. Translate(L'', Vector[(b_4 * v)]) → L'''_1
  408. Translate(M'', Vector[(b_4 * v)]) → M'''_1
  409. Translate(N'', Vector[(b_4 * v)]) → N'''_1
  410. Translate(O'', Vector[(b_4 * v)]) → O'''_1
  411. Translate(P'', Vector[(b_4 * v)]) → P'''_1
  412. Translate(Q'', Vector[(b_4 * v)]) → Q'''_1
  413. Translate(R'', Vector[(b_4 * v)]) → R'''_1
  414. Translate(S'', Vector[(b_4 * v)]) → S'''_1
  415. Translate(T'', Vector[(b_4 * v)]) → T'''_1
  416. Translate(U'', Vector[(b_4 * v)]) → U'''_1
  417. Translate(V'', Vector[(b_4 * v)]) → V'''_1
  418. Translate(W'', Vector[(b_4 * v)]) → W'''_1
  419. Translate(Y'', Vector[(b_4 * v)]) → Y'''_1
  420. Translate(Z'', Vector[(b_4 * v)]) → Z'''_1
  421. Translate(A_1'', Vector[(b_4 * v)]) → A_{11}
  422. Translate(B_1'', Vector[(b_4 * v)]) → B_{11}
  423. Translate(C_1'', Vector[(b_4 * v)]) → C_{11}
  424. Translate(D_1'', Vector[(b_4 * v)]) → D_{11}
  425. Translate(E_1'', Vector[(b_4 * v)]) → E_{11}
  426. Translate(F_1'', Vector[(b_4 * v)]) → F_6
  427. Translate(G_1'', Vector[(b_4 * v)]) → G_6
  428. Translate(H_1'', Vector[(b_4 * v)]) → H_6
  429. Translate(I_1'', Vector[(b_4 * v)]) → I_6
  430. Translate(J_1'', Vector[(b_4 * v)]) → J_6
  431. Translate(K_1'', Vector[(b_4 * v)]) → K_6
  432. Translate(L_1'', Vector[(b_4 * v)]) → L_6
  433. Translate(M_1'', Vector[(b_4 * v)]) → M_6
  434. Translate(N_1'', Vector[(b_4 * v)]) → N_6
  435. Translate(O_1'', Vector[(b_4 * v)]) → O_6
  436. Translate(P_1'', Vector[(b_4 * v)]) → P_{11}
  437. Translate(Q_1'', Vector[(b_4 * v)]) → Q_6
  438. Translate(R_1'', Vector[(b_4 * v)]) → R_6
  439. Translate(S_1'', Vector[(b_4 * v)]) → S_6
  440. Translate(T_1'', Vector[(b_4 * v)]) → T_6
  441. Translate(U_1'', Vector[(b_4 * v)]) → U_6
  442. Translate(V_1'', Vector[(b_4 * v)]) → V_6
  443. Translate(W_1'', Vector[(b_4 * v)]) → W_6
  444. Translate(Y_1'', Vector[(b_4 * v)]) → Y_7
  445. Translate(Z_1'', Vector[(b_4 * v)]) → Z_7
  446. Translate(A_2'', Vector[(b_4 * v)]) → A_{12}
  447. Translate(B_2'', Vector[(b_4 * v)]) → B_{12}
  448. Translate(C_2'', Vector[(b_4 * v)]) → C_{12}
  449. Translate(D_2'', Vector[(b_4 * v)]) → D_{12}
  450. Translate(E_2'', Vector[(b_4 * v)]) → E_{12}
  451. Polygon(A'''_1, B'''_1, K'''_1, L'''_1, M'''_1, N'''_1, O'''_1, P'''_1, Q'''_1, R'''_1, S'''_1, T'''_1, C'''_1, U'''_1, V'''_1, W'''_1, Y'''_1, Z'''_1, A_{11}, B_{11}, C_{11}, D_{11}, E_{11}, D'''_1, F_6, G_6, H_6, I_6, J_6, K_6, L_6, M_6, N_6, O_6, E'''_1, P_{11}, Q_6, R_6, S_6, T_6, U_6, V_6, W_6, Y_7, Z_7, F'''_1, A_{12}, B_{12}, C_{12}, D_{12}, E_{12}, G'''_1, H'''_1, I'''_1, J'''_1) → P_{12}, a'''_1, j'''_1, k'''_1, l'''_1, m'''_1, n'''_1, o'''_1, p'''_1, q'''_1, r'''_1, s'''_1, b'''_1, t'''_1, u'''_1, v'''_1, w'''_1, y'''_1, z'''_1, a_{11}, b_{12}, c_{11}, d_{11}, c'''_1, e_{11}, f_7, g_7, h_7, i_7, j_7, k_7, l_7, m_7, n_7, d'''_1, o_6, p_{11}, q_7, r_7, s_7, t_6, u_6, v_6, w_6, y_7, e'''_1, z_7, a_{12}, b_{13}, c_{12}, d_{12}, e_{12}, f'''_1, g'''_1, h'''_1, i'''_1

AI 绘图提示语参考

画一个类似埃舍尔风格的多边形镶嵌图案，包含多个重复的镶嵌结构，通过旋转和平移来构造。图案中包含多个多边形，包括一个初始多边形和其旋转和平移后的多个拷贝。每个多边形都有多个顶点，顶点之间有特定的关系和连接。图案的构造顺序是先创建初始多边形，然后通过旋转和平移来创建其拷贝，最后通过连接顶点来形成镶嵌结构。
以上提示语为根据原始绘图命令整理而来，仅供参考。