单元格排列的几何构造与平面变换

单元格排列的几何构造与平面变换
几何画板及绘图内容加载中,请稍等……
2020-08-17 14:58
本例演示如何通过单元格排列与几何变换构建复杂的平面图案。核心概念包括多边形构造、平面变换(镜像、旋转、平移)、序列生成及交点与对角线关系。作图要点涉及Polygon、Mirror、Rotate、Translate、Sequence、Intersect、OrthogonalLine等GeoGebra命令,通过单元格的重复与对称生成规则图案。适合高中几何、平面变换单元或数学建模入门,帮助学生探索对称性、规则排列与参数化图形的构建方法。

GeoGebra 命令及参数

  1. ConstructionStep() → stap
  2. Point(yAxis) → B
  3. Point(yAxis) → A
  4. Polygon(D, C, 4) → bas1, f, g, h, i, E, F
  5. Line(G, E) → di1
  6. Mirror(B, di1) → B'
  7. Mirror(B', yAxis) → B''
  8. Midpoint(B', B'') → H_6
  9. Mirror(A, di1) → A'
  10. Mirror(K_1, spieg) → Q_1
  11. Mirror(L, di1) → N
  12. Mirror(I_6, yAxis) → N_8
  13. Mirror(O_2, spieg) → R_2
  14. Rotate(I_6, 45°, H_6) → A_7
  15. Mirror(A_7, yAxis) → L_8
  16. Mirror(L_2, spieg) → P_2
  17. Rotate(I_6, 22.5°, I_6) → Z_6
  18. Mirror(L, Line[F, C]) → L'_1
  19. Mirror(W_1, spieg) → K_2
  20. Rotate(L'_1, (-(22.5°)), A_7) → B_7
  21. Segment(B_7, A_7) → f_{11}
  22. Rotate(L'_1, 22.5°, I_6) → W_6
  23. Segment(W_6, Z_6) → e_{10}
  24. Intersect(e_{10}, f_{11}) → C_7
  25. Rotate(C_7, (-(45°)), H_6) → Q_9
  26. Mirror(Q_9, yAxis) → R_9
  27. Mirror(S_2, spieg) → T_2
  28. Rotate(C_7, 45°, H_6) → O_8
  29. Mirror(C_7, yAxis) → M_8
  30. Mirror(N_2, spieg) → Q_2
  31. Rotate(L, 22.5°, D) → L'
  32. Segment(D, L') → n
  33. Line(L, xAxis) → p
  34. Intersect(p, n) → Q
  35. Mirror(B_2, spieg) → H_2
  36. Mirror(Q, x = ((-v2)) / 2) → U
  37. Mirror(D_2, spieg) → F_2
  38. Mirror(U, di1) → V
  39. Mirror(L_1, spieg) → R_1
  40. Mirror(Q, di1) → S
  41. Mirror(N_1, spieg) → T_1
  42. Mirror(Q, Line[F, C]) → Q'_1
  43. Mirror(Z_1, spieg) → J_2
  44. Mirror(Q'_1, di1) → J_3
  45. Mirror(O_1, spieg) → V_1
  46. Mirror(C, di1) → C'
  47. Polygon(E, L'_1, J_3, C') → bas11, e_5, d_4, f_5, g_5
  48. Polygon(A, C, D, B) → basvierhoek1, a, c, d, b
  49. Mirror(bas1, di1) → bas7
  50. Mirror(D, di1) → D'
  51. Polygon(A', C', D', B') → bas16, a', c', d', b'
  52. Mirror(bas1, yAxis) → bas9
  53. Mirror(A, yAxis) → A'_1
  54. Mirror(C, yAxis) → C'_1
  55. Mirror(D, yAxis) → D'_1
  56. Mirror(B, yAxis) → B'_1
  57. Polygon(A'_1, C'_1, D'_1, B'_1) → bas18, a'_1, c'_1, d'_1, b'_1
  58. Mirror(A', yAxis) → A''
  59. Mirror(C', yAxis) → C''
  60. Mirror(D', yAxis) → D''
  61. Polygon(A'', C'', D'', B'') → bas17, a'', c'', d'', b''
  62. Mirror(bas7, yAxis) → bas8
  63. Mirror(L, yAxis) → M
  64. Mirror(N, yAxis) → P
  65. Segment(D, L) → j
  66. Segment(L, B) → k
  67. Segment(B, M) → l
  68. Segment(M, D'_1) → m
  69. Mirror(Q, yAxis) → R
  70. Mirror(S, yAxis) → T
  71. Segment(B', N) → q
  72. Segment(N, S) → r
  73. Segment(S, C') → s
  74. Segment(N, D') → t
  75. Segment(C, Q) → e
  76. Segment(Q, L) → f_1
  77. Mirror(V, yAxis) → W
  78. Mirror(U, yAxis) → Z
  79. Segment(L, U) → g_1
  80. Segment(U, A) → h_1
  81. Segment(A, Z) → i_1
  82. Segment(Z, M) → j_1
  83. Segment(M, R) → k_1
  84. Segment(R, C'_1) → l_1
  85. Segment(C'', T) → m_1
  86. Segment(T, P) → n_1
  87. Segment(P, W) → p_1
  88. Segment(W, A'') → q_1
  89. Segment(P, B'') → r_1
  90. Segment(P, D'') → s_1
  91. Segment(N, V) → j_2
  92. Segment(V, A') → k_2
  93. Plane(L, L + (0, 0, 1), L + (0, 1, 0)) → vlakL
  94. Mirror(D, vlakL) → D'_2
  95. Polygon(A, B, D'_1, C'_1, R, M, Z) → bas2, a_2, b_2, r_2, s_2, r_3, m_3, z_1
  96. Polygon(D, B, A, U, Q, C) → bas21, d_2, b_3, a_3, u, q_3, c_2
  97. Mirror(A, di1) → A'_2
  98. Mirror(C, di1) → C'_2
  99. Polygon(C'', D'', B'', A'', W, T) → bas22, t_2, e_2, f_3, g_3, w, t_3
  100. Polygon(E, C, Q'_1, L'_1) → bas10, e_4, c_5, q'_1, l'_1
  101. Mirror(E, yAxis) → E'
  102. Mirror(C, yAxis) → C'_3
  103. Mirror(Q'_1, yAxis) → K_3
  104. Mirror(L'_1, yAxis) → L_3
  105. Polygon(E', C'_3, K_3, L_3) → bas19, e', c'_3, h_5, i_5
  106. Mirror(E, yAxis) → E'_1
  107. Mirror(L'_1, yAxis) → M_3
  108. Mirror(J_3, yAxis) → N_3
  109. Mirror(C', yAxis) → C''_1
  110. Polygon(E'_1, M_3, N_3, C''_1) → bas20, e'_1, j_5, k_5, c''_1
  111. Intersect(l'_1, e_5) → A_4
  112. Intersect(l'_1, e_5) → B_4
  113. Midpoint(d'') → T_5
  114. PolyLine(B', H, E, F, K, J, I, B'') → h_{10}
  115. Line(H_6, H_6 + (0, 0, 1)) → rot
  116. Polygon(I_6, A', V, N) → bas12, m_{10}, n_{10}, v_{10}, n_{11}
  117. Sequence(Polygon[Rotate[I_6, (nn * 45°), rot], Rotate[A', (nn * 45°), rot], Rotate[V, (nn * 45°), rot], Rotate[N, (nn * 45°), rot]], nn, 1, 3) → l1
  118. Polygon(I_6, N, S, C') → bas13, p_{10}, n_{12}, s_{10}, q_{10}
  119. Sequence(Polygon[Rotate[I_6, (nn * 45°), rot], Rotate[N, (nn * 45°), rot], Rotate[S, (nn * 45°), rot], Rotate[C', (nn * 45°), rot]], nn, 1, 3) → l2
  120. Polygon(I_6, C', J_3, L'_1) → bas14, r_{10}, t_{10}, a_{10}, b_{10}
  121. Sequence(Polygon[Rotate[I_6, (nn * 45°), rot], Rotate[C', (nn * 45°), rot], Rotate[J_3, (nn * 45°), rot], Rotate[L'_1, (nn * 45°), rot]], nn, 1, 3) → l3
  122. Polygon(I_6, L'_1, A_7, C_7) → bas15, g_{11}, h_{11}, i_{11}, j_{11}
  123. Sequence(Polygon[Rotate[I_6, (nn * 45°), rot], Rotate[L'_1, (nn * 45°), rot], Rotate[A_7, (nn * 45°), rot], Rotate[C_7, (nn * 45°), rot]], nn, 1, 2) → l4
  124. Polygon(A', B', W, T, N_3, L_3, K_3, R, Z, A, U, Q, H, Q'_1, L'_1, J_3, S, V, E, F, K, J, I, B'', A'') → basveelhoek5, p_{11}, s_{11}, w_9, t_{11}, a_{11}, b_{11}, c_{11}, r_{12}, z_2, a_{12}, u_{10}, q_{11}, q_{12}, d_{11}, g_{12}, l_{12}, s_{12}, v_{11}, h_{12}, e_{11}, f_{12}, k_{12}, j_{12}, i_{12}, r_{11}
  125. Translate(E, Vector[(0, 0, 2)]) → E'_2
  126. Translate(F, Vector[(0, 0, 2)]) → F'
  127. Polygon(A', V, R, K_3, L_3, N_3, T, W, A'', N_8, M_8, O_8, S, A_7, C_7, I_6, J_3, L'_1, Q'_1, Q, U, A, Z) → bas3, e_{12}, z_3, r_{13}, i_{13}, j_{13}, k_{13}, t_{13}, w_{10}, l_{13}, m_{13}, n_{13}, v_{12}, o_8, p_{13}, b_{13}, c_{13}, s_{13}, f_{13}, g_{13}, h_{13}, q_{13}, u_{11}, a_{13}
  128. Translate(E, Vector[(0, 0, 2)]) → E'_3
  129. Translate(F, Vector[(0, 0, 2)]) → F'_1
  130. Rotate(P_9, (-(45°)), H_6) → S_9
  131. Ray(C, A_7) → i_{16}
  132. Intersect(i_{16}, yAxis) → T_9
  133. Segment(I_6, S_9) → j_{16}
  134. Segment(I_6, P_9) → k_{16}
  135. OrthogonalLine(P_9, j_{16}) → l_{16}
  136. OrthogonalLine(S_9, k_{16}) → m_{16}
  137. Intersect(l_{16}, m_{16}) → U_9
  138. Segment(S_9, U_9) → n_{16}
  139. Segment(U_9, P_9) → p_{16}
  140. Segment(Q_9, S_9) → q_{16}
  141. Segment(I_6, Q_9) → r_{16}
  142. Segment(A', Q_9) → s_{16}
  143. Mirror(A_7, yAxis) → V_9
  144. Mirror(C_7, yAxis) → W_9
  145. Mirror(I_6, yAxis) → Z_9
  146. Segment(A'', R_9) → t_{16}
  147. Segment(R_9, Z_9) → a_{16}
  148. Mirror(P_9, yAxis) → A_{10}
  149. Mirror(U_9, yAxis) → B_{10}
  150. Mirror(S_9, yAxis) → C_{10}
  151. Segment(C_{10}, R_9) → b_{16}
  152. Segment(C_{10}, B_{10}) → c_{16}
  153. Segment(B_{10}, A_{10}) → d_{16}
  154. Segment(A_{10}, Z_9) → e_{16}
  155. Segment(C_{10}, Z_9) → f_{17}
  156. Segment(P_9, A_7) → g_{17}
  157. Segment(A_{10}, V_9) → h_{17}
  158. Segment(T_9, V_9) → j_{17}
  159. Segment(A_7, T_9) → i_{17}
  160. Rotate(U_9, 45°, H_6) → D_{10}
  161. Rotate(U_9, 90°, H_6) → E_{10}
  162. Segment(P_9, D_{10}) → k_{17}
  163. Segment(D_{10}, T_9) → l_{17}
  164. Segment(T_9, E_{10}) → m_{17}
  165. Segment(E_{10}, A_{10}) → n_{17}
  166. Segment(S_9, C_{10}) → i_{21}
  167. Segment(P_9, H_6) → j_{21}
  168. Segment(T_9, H_6) → k_{21}
  169. Polygon(A', I_6, Q_9) → basdriehoek1, r_{17}, s_{17}, t_{17}
  170. Mirror(A', yAxis) → A''_5
  171. Segment(H_6, A_{10}) → l_{21}
  172. Mirror(I_6, yAxis) → A_{11}
  173. Mirror(Q_9, yAxis) → B_{11}
  174. Polygon(A''_5, A_{11}, B_{11}) → basdriehoek1', c_{17}, a''_5, d_{17}
  175. PolyLine(S_9, U_9, D_{10}, E_{10}, B_{10}, C_{10}) → e_{17}
  176. PolyLine(Q_9, C_7, W_{11}, W_9, R_9) → g_{18}
  177. Polygon(Q_9, C_7, S_9, W_{11}, W_9, R_9, C_{10}, B_{10}, E_{10}, D_{10}, U_9) → bas4, j_{18}, t_{18}, a_{18}, k_{18}, l_{18}, m_{18}, n_{18}, p_{18}, q_{18}, r_{18}, s_{18}
  178. Polygon(A', V, R, K_3, L_3, N_3, T, W, A'', R_9, W_9, W_{11}, S, C_7, Q_9, J_3, L'_1, Q'_1, Q, U, A, Z) → bas5, b_{18}, z_4, r_{19}, f_{19}, g_{19}, h_{19}, t_{19}, w_{16}, i_{19}, j_{19}, k_{19}, v_{16}, l_{19}, m_{19}, n_{19}, s_{19}, c_{18}, d_{18}, e_{18}, q_{19}, u_{16}, a_{19}
  179. Polygon(S_9, U_9, P_9, D_{10}, E_{10}, B_{10}, C_{10}) → bas6, g_{20}, h_{20}, i_{20}, j_{20}, k_{20}, l_{20}, m_{20}
  180. Segment(S_9, C_{10}) → n_{20}
  181. Mirror(C'', yAxis) → C'''
  182. Mirror(D'', yAxis) → D'''
  183. Mirror(B'', yAxis) → B'''
  184. Mirror(A'', yAxis) → A'''
  185. Mirror(W, yAxis) → W'
  186. Mirror(T, yAxis) → T'
  187. Polygon(C''', D''', B''', A''', W', T') → bas23, c''', d''', b''', a''', w', t'
  188. Translate(baspa, Vector[(-ver)]) → baspa'
  189. Translate(bas5, Vector[(-ver)]) → bas5'
  190. Translate(bas4, Vector[(-ver)]) → bas4'
  191. Mirror(N, yAxis) → N'
  192. Mirror(I_6, yAxis) → G_3
  193. Segment(N', G_3) → t_{26}
  194. Mirror(C', yAxis) → C''_2
  195. Mirror(I_6, yAxis) → H_3
  196. Segment(C''_2, H_3) → a_{26}
  197. Mirror(L'_1, yAxis) → I_3
  198. Mirror(I_6, yAxis) → O_3
  199. Segment(I_3, O_3) → b_{26}
  200. Mirror(L'_1, yAxis) → P_3
  201. Mirror(A_7, yAxis) → Q_3
  202. Segment(P_3, Q_3) → c_{26}
  203. Intersect(n_{13}, o_8) → R_3
  204. Intersect(h_1, i_1) → S_3
  205. Segment(R_3, S_3) → d_{26}
  206. Segment(A_7, C) → e_{26}
  207. Segment(A_7, L) → f_{27}
  208. Mirror(A_7, yAxis) → T_3
  209. Mirror(C, yAxis) → C'_4
  210. Segment(T_3, C'_4) → g_{27}
  211. Mirror(A_7, yAxis) → U_3
  212. Mirror(L, yAxis) → L'_2
  213. Segment(U_3, L'_2) → h_{27}
  214. Translate(S_9, Vector[(-ver)]) → V_3
  215. Translate(U_9, Vector[(-ver)]) → W_3
  216. Translate(P_9, Vector[(-ver)]) → Z_3
  217. Translate(D_{10}, Vector[(-ver)]) → C_4
  218. Translate(E_{10}, Vector[(-ver)]) → D_4
  219. Translate(B_{10}, Vector[(-ver)]) → E_4
  220. Translate(C_{10}, Vector[(-ver)]) → F_4
  221. Polygon(V_3, W_3, Z_3, C_4, D_4, E_4, F_4) → bas6', v_3, i_{27}, j_{27}, k_{27}, l_{27}, m_{27}, n_{27}
  222. Polygon(H, D_1, C_1, B') → pa44, h_4, f_2, g_2, i_2
  223. Polygon(H, E, E + ver, D_1) → pa42, h_2, e_1, t_1, d_1
  224. Polygon(E, E_1, F_1, F) → pa43, e_3, a_1, b_1, f_4
  225. Polygon(F, K, G_1, F_1) → pa45, f_6, k_3, c_1, l_2
  226. Polygon(K, J, H_1, G_1) → pa46, k_4, j_3, m_2, n_2
  227. Polygon(J, I, I_1, H_1) → pa47, j_4, i_3, p_2, q_2
  228. Polygon(I, B'', J_1, I_1) → pa48, i_4, h_3, l_3, n_3
  229. Polygon(B', K_1, L_1) → pa1, p_3, s_3, c_3
  230. Polygon(B', L_1, M_1) → pa2, d_3, g_4, l_4
  231. Polygon(D', B', M_1) → pa3, m_4, n_4, p_4
  232. Polygon(D', M_1, N_1) → pa4, q_4, r_4, s_4
  233. Polygon(D', N_1, P_1) → pa5, t_4, a_4, b_4
  234. Polygon(D', P_1, H) → pa6, h_6, c_4, l_5
  235. Polygon(E, H, P_1) → pa7, m_5, e_6, h_7
  236. Mirror(M_1, spieg) → S_1
  237. Mirror(P_1, spieg) → U_1
  238. Polygon(E, P_1, O_1) → pa8, o_1, e_7, d_5
  239. Polygon(E, O_1, W_1) → pa9, w_1, e_8, g_6
  240. Polygon(E, W_1, Z_1) → pa10, i_6, e_9, j_6
  241. Polygon(E, Z_1, A_2) → pa11, k_6, e_{13}, l_6
  242. Polygon(F, E, A_2) → pa12, m_6, f_7, e_{14}
  243. Polygon(F, A_2, D) → pa13, d_6, f_8, n_6
  244. Polygon(F, A_2, D) → pa14, d_7, f_9, p_6
  245. Polygon(D, A_2, B_2) → pa15, n_5, d_8, p_5
  246. Polygon(D, B_2, C_2) → pa16, q_5, d_9, r_5
  247. Polygon(D, C_2, B) → pa17, b_5, d_{10}, s_5
  248. Mirror(pa1, spieg) → pa31
  249. Mirror(pa2, spieg) → pa34
  250. Mirror(pa3, spieg) → pa35
  251. Mirror(pa4, spieg) → pa36
  252. Mirror(pa5, spieg) → pa37
  253. Mirror(pa6, spieg) → pa38
  254. Mirror(pa7, spieg) → pa39
  255. Mirror(pa8, spieg) → pa40
  256. Mirror(pa9, spieg) → pa21
  257. Mirror(pa10, spieg) → pa22
  258. Mirror(pa11, spieg) → pa23
  259. Mirror(pa12, spieg) → pa24
  260. Mirror(pa13, spieg) → pa25
  261. Mirror(pa14, spieg) → pa26
  262. Mirror(pa15, spieg) → pa27
  263. Mirror(pa16, spieg) → pa28
  264. Mirror(pa17, spieg) → pa29
  265. Polygon(B, D_2, C_2) → pa18, t_5, b_6, a_5
  266. Polygon(B, E_2, D_2) → pa19, q_6, b_7, r_6
  267. Mirror(pa18, spieg) → pa30
  268. Mirror(pa19, spieg) → pa32
  269. Polygon(B', C_1, K_1) → pa20, s_6, t_6, a_6
  270. Mirror(pa20, spieg) → pa33
  271. Mirror(C_2, spieg) → G_2
  272. Mirror(A_2, spieg) → I_2
  273. Polygon(K_1, L_1, E_2, F_2, H_2, J_2, K_2, V_1, T_1, R_1, Q_1, J_1, M_1, I_1, H_1, G_1, F_1, E_1, D_1, C_1, N_1, P_1, O_1, W_1, Z_1, B_2, D_2) → pa41, c_6, q_7, r_7, s_7, t_7, a_7, c_7, v_1, g_8, h_8, i_8, g_7, j_8, k_8, l_8, m_8, n_8, p_8, q_8, r_8, i_7, j_7, k_7, l_7, m_7, n_7, p_7
  274. Polygon(R_9, N_8 + ver, A'') → driehoek22, s_8, r_9, t_8
  275. Polygon(A, Z, L_8 + ver) → ro1, a_8, b_8, c_8
  276. Polygon(M, Z, L_8 + ver) → ro2, g_9, m_9, z_5
  277. Polygon(M, R, L_8 + ver) → ro3, h_9, m_{11}, r_{14}
  278. Polygon(R, C'_3, L_8 + ver) → ro4, i_9, r_{15}, j_9
  279. Mirror(ro1, spieg) → driehoek23'
  280. Mirror(ro2, spieg) → driehoek24'
  281. Mirror(ro3, spieg) → driehoek25'
  282. Mirror(ro4, spieg) → driehoek26'
  283. Polygon(C'_3, K_3, L_8 + ver) → ro5, k_9, l_9, n_9
  284. Polygon(L_3, K_3, L_8 + ver) → ro6, p_9, q_9, s_9
  285. Mirror(ro5, spieg) → driehoek27'
  286. Mirror(ro6, spieg) → driehoek28'
  287. Polygon(A, L_2, M_2) → ro7, t_9, a_9, b_9
  288. Mirror(ro7, spieg) → driehoek29'
  289. Polygon(L_3, N_3, O_2) → ro8, o_2, c_9, f_{10}
  290. Polygon(L_2, L_3, N_2) → ro9, g_{10}, i_{10}, j_{10}
  291. Polygon(L_3, O_2, N_2) → ro10, k_{10}, l_{10}, c_{10}
  292. Polygon(N_3, C'', O_2) → ro11, k_{11}, l_{11}, m_{12}
  293. Polygon(C'', T, O_2) → ro12, p_{12}, t_{12}, t_{14}
  294. Polygon(T, P, O_2) → ro13, b_{12}, t_{15}, p_{14}
  295. Polygon(P, W, O_2) → ro14, c_{12}, p_{15}, w_2
  296. Polygon(W, A'', O_2) → ro15, d_{12}, w_3, d_{13}
  297. Polygon(A'', R_9, O_2) → driehoek38, f_{14}, g_{14}, h_{14}
  298. Mirror(ro8, spieg) → driehoek30'
  299. Mirror(ro9, spieg) → driehoek31'
  300. Mirror(ro10, spieg) → driehoek32'
  301. Mirror(ro11, spieg) → driehoek33'
  302. Mirror(ro12, spieg) → driehoek34'
  303. Mirror(ro13, spieg) → driehoek35'
  304. Mirror(ro14, spieg) → driehoek36'
  305. Mirror(ro15, spieg) → driehoek37'
  306. Mirror(driehoek38, spieg) → driehoek38'
  307. Polygon(A'', Q_1, R_1, W) → ro20, i_{14}, j_{14}, k_{14}, w_4
  308. Polygon(O_2, S_2, A'') → ro16, s_{14}, a_{14}, b_{14}
  309. Mirror(ro16, spieg) → driehoek39'
  310. Polygon(A'', S_2, Q_1) → ro17, c_{14}, d_{14}, f_{15}
  311. Mirror(ro17, spieg) → driehoek40'
  312. Polygon(W, T, T_1, R_1) → ro22, w_5, t_{20}, g_{15}, h_{15}
  313. Mirror(ro22, spieg) → ro30
  314. Mirror(ro20, spieg) → ro28
  315. Polygon(T, N_3, V_1, T_1) → ro21, t_{21}, l_{14}, m_{14}, n_{14}
  316. Mirror(ro21, spieg) → ro29
  317. Polygon(N_3, L_3, K_2, V_1) → ro23, q_{14}, i_{15}, j_{15}, k_{15}
  318. Mirror(ro23, spieg) → ro31
  319. Polygon(L_3, K_3, J_2, K_2) → ro24, l_{15}, m_{15}, n_{15}, q_{15}
  320. Mirror(ro24, spieg) → ro32
  321. Polygon(K_3, R, H_2, J_2) → ro25, s_{15}, r_{20}, a_{15}, b_{15}
  322. Mirror(ro25, spieg) → ro33
  323. Polygon(R, Z, F_2, H_2) → ro26, r_{21}, z_6, c_{15}, d_{15}
  324. Mirror(ro26, spieg) → ro34
  325. Polygon(Z, A, E_2, F_2) → ro27, z_7, a_{17}, e_{15}, f_{16}
  326. Polygon(S_2, O_2, L_1, N_1, O_1, W_1, Z_1, B_2, D_2, E_2, F_2, H_2, N_2, J_2, K_2, V_1, T_1, R_1, Q_1, L_2, M_2, P_2, Q_2, R_2, T_2, K_1) → ro19, g_{16}, b_{19}, c_{19}, d_{19}, e_{19}, f_{20}, p_{20}, q_{20}, s_{20}, a_{20}, b_{20}, h_{16}, c_{20}, d_{20}, e_{20}, f_{21}, g_{21}, h_{21}, q_{21}, p_{17}, q_{17}, b_{17}, f_{18}, h_{18}, i_{18}, p_{19}
  327. Mirror(ro27, spieg) → ro35
  328. Mirror(ro2, spieg) → ro2_2
  329. Mirror(ro3, spieg) → ro3_2
  330. Mirror(ro1, spieg) → ro1_2
  331. Mirror(ro4, spieg) → ro4_2
  332. Mirror(ro5, spieg) → ro5_2
  333. Mirror(ro6, spieg) → ro6_2
  334. Mirror(ro7, spieg) → ro7_2
  335. Mirror(ro8, spieg) → ro8_2
  336. Mirror(ro9, spieg) → ro9_2
  337. Mirror(ro10, spieg) → ro10_2
  338. Mirror(ro11, spieg) → ro11_2
  339. Mirror(ro12, spieg) → ro12_2
  340. Mirror(ro13, spieg) → ro13_2
  341. Mirror(ro14, spieg) → ro14_2
  342. Mirror(ro15, spieg) → ro15_2
  343. Mirror(ro16, spieg) → ro16_2
  344. Polygon(A', K_1, T_2) → ro18, m_{21}, n_{21}, p_{21}
  345. Polygon(R_9, N_8, U_2) → geel1, u_2, s_{21}, a_{21}
  346. Polygon(N_8, V_2, U_2) → geel2, b_{21}, c_{21}, v_2
  347. Polygon(N_8, W_2, V_2) → geel3, d_{21}, e_{21}, f_{22}
  348. Polygon(N_8, M_8, W_2) → geel4, g_{22}, h_{22}, i_{22}
  349. Polygon(M_8, L_8, W_2) → geel5, j_{22}, k_{22}, l_{22}
  350. Polygon(L_8, Z_2, W_2) → geel6, m_{22}, n_{22}, p_{22}
  351. Polygon(L_8, B_3, Z_2) → geel7, q_{22}, r_{22}, s_{22}
  352. Polygon(L_8, O_8, B_3) → geel8, t_{22}, a_{22}, b_{22}
  353. Mirror(geel1, spieg) → geel10
  354. Mirror(geel2, spieg) → geel11
  355. Mirror(geel3, spieg) → geel12
  356. Mirror(geel4, spieg) → geel13
  357. Mirror(geel5, spieg) → geel14
  358. Mirror(geel6, spieg) → geel15
  359. Mirror(geel7, spieg) → geel16
  360. Mirror(geel8, spieg) → geel17
  361. Polygon(R_9, U_2, S_2) → geel9, c_{22}, d_{22}, e_{22}
  362. Mirror(geel9, spieg) → geel18
  363. Polygon(R_9, N_8, O_2, S_2) → geel19, f_{23}, g_{23}, h_{23}, i_{23}
  364. Mirror(geel19, spieg) → geel22
  365. Polygon(N_8, M_8, N_2, O_2) → geel20, j_{23}, k_{23}, l_{23}, m_{23}
  366. Mirror(geel20, spieg) → geel23
  367. Polygon(M_8, O_8, M_2, N_2) → geel21, n_{23}, p_{23}, q_{23}, r_{23}
  368. Mirror(geel21, spieg) → geel24
  369. Polygon(U_2, V_2, S_2, Z_2, A_3, D_3, E_3, T_2, Q_2, M_2, N_2) → geel25, s_{23}, h_{24}, i_{24}, t_{23}, a_{23}, b_{23}, c_{23}, d_{23}, e_{23}, f_{24}, g_{24}
  370. Polygon(C_{10}, F_3, B_{10}) → groen1, j_{24}, k_{24}, l_{24}
  371. Polygon(B_{10}, A_{10}, F_3) → groen2, m_{24}, n_{24}, p_{24}
  372. Polygon(A_{10}, E_{10}, F_3) → groen3, q_{24}, r_{24}, s_{24}
  373. Polygon(E_{10}, T_9, F_3) → groen4, t_{24}, a_{24}, b_{24}
  374. Polygon(T_9, D_{10}, F_3) → groen5, c_{24}, d_{24}, e_{24}
  375. Polygon(D_{10}, F_3, P_9) → groen6, f_{25}, g_{25}, h_{25}
  376. Polygon(P_9, F_3, U_9) → groen7, u_9, i_{25}, j_{25}
  377. Polygon(S_9, U_9, F_3) → groen8, k_{25}, l_{25}, m_{25}
  378. Polygon(C_{10}, F_3, U_2) → groen9, n_{25}, p_{25}, q_{25}
  379. Polygon(S_9, E_3, F_3) → groen10, r_{25}, s_{25}, t_{25}
  380. Polygon(C_{10}, B_{10}, V_2, U_2) → groen11, a_{25}, b_{25}, c_{25}, d_{25}
  381. Mirror(groen11, spieg) → groen14
  382. Polygon(B_{10}, E_{10}, Z_2, V_2) → groen12, e_{25}, f_{26}, g_{26}, h_{26}
  383. Mirror(groen12, spieg) → groen15
  384. Polygon(E_{10}, D_{10}, A_3, Z_2) → groen13, i_{26}, j_{26}, k_{26}, l_{26}
  385. Polygon(U_2, E_3, D_3, A_3, Z_2, V_2) → groenboven, m_{26}, n_{26}, p_{26}, q_{26}, r_{26}, s_{26}
  386. Translate(groewand, Vector[(-ver)]) → groewand'
  387. Translate(gewand, Vector[(-ver)]) → gewand'
  388. Translate(rowand, Vector[(-ver)]) → rowand'
  389. Translate(pawand, Vector[(-ver)]) → pawand'
  390. If(ss < 1, Translate[rolijst, Vector[((2 * ss) * ver)]], Translate[rolijst, Vector[(2 * ver)]]) → rolijstdyn
  391. If(ss < 1, Translate[rowand', Vector[((2 * ss) * ver)]], Translate[rowand', Vector[(2 * ver)]]) → rowanddyn
  392. If(ss ≤ 1, geellijst, If[1 < ss < 2, Translate[geellijst, Vector[(((ss - 1) * 4) * ver)]], Translate[geellijst, Vector[(4 * ver)]]]) → geellijstdyn
  393. If(ss ≤ 1, gewand', If[1 < ss < 2, Translate[gewand', Vector[(((ss - 1) * 4) * ver)]], Translate[gewand', Vector[(4 * ver)]]]) → gewanddyn
  394. If(ss ≤ 2, groelijst, If[2 < ss, Translate[groelijst, Vector[(((ss - 2) * 6) * ver)]]]) → groelijstdyn
  395. If(ss ≤ 2, groewand', If[2 < ss, Translate[groewand', Vector[(((ss - 2) * 6) * ver)]]]) → groewanddyn

AI 绘图提示语参考

利用多边形构造和几何变换(如镜像、旋转、移动)来构建复杂的平面图案。重点在于细胞重复和对称性,通过多边形、交点和对角线的关系生成规则图案。构造顺序包括初始点定位、多边形创建、镜像和旋转操作、交点计算以及最终多边形生成。适合用于探索对称、规则排列和参数化形状的数学建模。
以上提示语为根据原始绘图命令整理而来,仅供参考。