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玫瑰立方体：旋转花瓣与几何构造的融合

玫瑰立方体：旋转花瓣与几何构造的融合
几何画板及绘图内容加载中，请稍等……
2020-02-24 15:12
圆数列立体几何变换几何作图
① 本范例演示了一个名为“玫瑰立方体”的复合几何图形，它通过将立方体与一系列旋转的圆弧、椭圆和花瓣状曲线相结合，形成类似玫瑰花瓣的立体装饰效果。② 核心数学概念包括三维立体几何（立方体）、平面曲线（圆、椭圆、圆弧）、旋转变换、镜像对称、角平分线、切线以及序列生成的点列，体现了几何元素在空间中的动态组合。③ 作图要点：从构造摘要可见，使用了Segment（线段）、Rotate（旋转）、Intersect（交点）、Line（直线）、Circle（圆）、Point（点）、Tangent（切线）、OrthogonalLine（垂线）、AngularBisector（角平分线）、Mirror（镜像）、CircleArc（圆弧）、Sequence（序列）、Midpoint（中点）、Arc（弧）、Semicircle（半圆）、Cube（立方体）等GeoGebra命令，并涉及大量辅助点（如I_2, G_2, F_2等）和参数（如n, a_3, c等），通过序列和旋转生成对称的花瓣结构。④ 适合学段：适用于高中及以上学生，用于探索几何变换、立体与平面图形的结合，以及动态几何软件中的参数化构造，也可作为艺术数学或数学建模的创意案例。

GeoGebra 命令及参数

  1. Segment(G_2, F_2) → m_1
  2. Segment(F_2, I_2) → i_1
  3. Rotate((7, 0), 90° + (180°) / n) → B
  4. Intersect(xAxis, yAxis) → A
  5. Line(A, F_2) → a_3
  6. Line(F_2, A) → n_1
  7. Circle(A, B) → c
  8. Point(c) → S_4
  9. Tangent(S_4, c) → j_2,
  10. Intersect(j_2, m_1) → U_4
  11. Intersect(c, n_1, 1) → J_2
  12. OrthogonalLine(J_2, n_1) → a_2
  13. Intersect(a_2, i_1) → K_2
  14. AngularBisector(J_2, K_2, F_2) → b_2
  15. Intersect(n_1, b_2) → L_2
  16. Circle(L_2, J_2) → k_3
  17. Point(k_3) → R_4
  18. Tangent(R_4, k_3) → i_2,
  19. Intersect(i_2, j_2) → V_4
  20. Intersect(i_2, m_1) → T_4
  21. AngularBisector(T_4, V_4, U_4) → m_2
  22. AngularBisector(T_4, U_4, V_4) → l_2
  23. Intersect(l_2, m_2) → W_4
  24. OrthogonalLine(W_4, m_1) → n_2
  25. Intersect(m_1, n_2) → Z_4
  26. Circle(W_4, Z_4) → t_5
  27. Line(A, B) → b
  28. Rotate(b, (360°) / n) → b'
  29. Point(b) → C
  30. Rotate(C, (360°) / n) → C'
  31. Rotate(B, (180°) / n) → B'
  32. Line(A, B') → a
  33. Rotate(a, 30°, B') → a'
  34. Intersect(b, a') → E
  35. Mirror(E, a) → E'_1
  36. CircleArc(E'_1, E, B') → e
  37. CircleArc(E, B', E'_1) → f
  38. Sequence(Arc[Rotate[Circle[E'_1, E], (i * (360°) / n)], Rotate[E, (i * (360°) / n)], Rotate[B', (i * (360°) / n)]], i, 1, n) → list2
  39. Sequence(Arc[Rotate[Circle[E, B'], (i * (360°) / n)], Rotate[B', (i * (360°) / n)], Rotate[E'_1, (i * (360°) / n)]], i, 1, n) → list3
  40. Midpoint(B', B) → G
  41. Line(A, G) → g
  42. Intersect(e, g, 1) → H
  43. CircleArc(E'_1, E, H) → h
  44. Mirror(E'_1, g) → I
  45. Mirror(E, g) → E'
  46. Mirror(H, g) → H'
  47. Arc(Mirror[Circle[E'_1, E], g], E', H') → h'
  48. Semicircle(C', C) → d
  49. Sequence(Semicircle[Rotate[C', (i * (360°) / n)], Rotate[C, (i * (360°) / n)]], i, 1, n) → list1
  50. Intersect(d, a) → D,
  51. Circle(A, F) → k
  52. Intersect(k, b, 2) → J
  53. Mirror(E', a) → E''
  54. Mirror(H', a) → H''_1
  55. Arc(Mirror[Mirror[Circle[E'_1, E], g], a], E'', H''_1) → h''
  56. Sequence(Arc[Rotate[Mirror[Circle[E'_1, E], g], (i * (360°) / n)], Rotate[E', (i * (360°) / n)], Rotate[H', (i * (360°) / n)]], i, 1, n) → list4
  57. Sequence(Arc[Rotate[Mirror[Mirror[Circle[E'_1, E], g], a], (i * (360°) / n)], Rotate[E'', (i * (360°) / n)], Rotate[H''_1, (i * (360°) / n)]], i, 1, n) → list5
  58. Sequence(Segment[Rotate[J, (i * (360°) / n)], Rotate[E, (i * (360°) / n)]], i, 1, n) → list6
  59. Sequence(Segment[Rotate[F, (i * (360°) / n)], Rotate[E', (i * (360°) / n)]], i, 1, n) → list7
  60. Midpoint(B', H') → K
  61. Line(E'_1, K) → i
  62. Intersect(h'', i, 1) → M
  63. Intersect(a, i) → L
  64. Circle(L, M) → p
  65. Intersect(p, a, 2) → N
  66. Sequence(Rotate[p, (i * (360°) / n)], i, 1, n) → list8
  67. Sequence(Segment[Rotate[N, (i * (360°) / n)], Rotate[B', (i * (360°) / n)]], i, 1, n) → list9
  68. OrthogonalLine(L, a) → j
  69. Midpoint(M, L) → O
  70. Rotate(O, 90°, L) → O'
  71. Rotate(O', 90°, L) → O''
  72. Rotate(O'', 90°, L) → O'''
  73. Semicircle(O', O) → q
  74. Semicircle(O'', O') → r
  75. Semicircle(O''', O'') → s
  76. Semicircle(O, O''') → t
  77. Sequence(Semicircle[Rotate[O', (i * (360°) / n)], Rotate[O, (i * (360°) / n)]], i, 1, n) → list10
  78. Sequence(Semicircle[Rotate[O'', (i * (360°) / n)], Rotate[O', (i * (360°) / n)]], i, 1, n) → list11
  79. Sequence(Semicircle[Rotate[O''', (i * (360°) / n)], Rotate[O'', (i * (360°) / n)]], i, 1, n) → list12
  80. Sequence(Semicircle[Rotate[O, (i * (360°) / n)], Rotate[O''', (i * (360°) / n)]], i, 1, n) → list13
  81. Midpoint(E'', E'_1) → P
  82. CircleArc(Q, E'', E'_1) → c_1
  83. Line(A, Q) → l
  84. Intersect(c_1, l, 1) → R
  85. Line(E'_1, R) → m
  86. Intersect(h'', m) → S,
  87. Midpoint(R, S) → T
  88. Circle(R, T) → d_1
  89. Intersect(c_1, d_1, 2) → U
  90. Intersect(c_1, d_1, 1) → V
  91. CircleArc(Q, E'', U) → e_1
  92. CircleArc(R, U, V) → f_1
  93. CircleArc(Q, V, E'_1) → g_1
  94. Sequence(Arc[Rotate[Circle[Q, E''], (i * (360°) / n)], Rotate[E'', (i * (360°) / n)], Rotate[U, (i * (360°) / n)]], i, 1, n) → list14
  95. Sequence(Arc[Rotate[Circle[R, U], (i * (360°) / n)], Rotate[U, (i * (360°) / n)], Rotate[V, (i * (360°) / n)]], i, 1, n) → list15
  96. Sequence(Arc[Rotate[Circle[Q, V], (i * (360°) / n)], Rotate[V, (i * (360°) / n)], Rotate[E'_1, (i * (360°) / n)]], i, 1, n) → list16
  97. Mirror(Q, a) → Q'_1
  98. Mirror(E'', a) → E'''
  99. Mirror(U, a) → U'_1
  100. Arc(Mirror[Circle[Q, E''], a], E''', U'_1) → h_1
  101. Mirror(R, a) → R'
  102. Mirror(U, a) → U'
  103. Mirror(V, a) → V'_1
  104. Arc(Mirror[Circle[R, U], a], U', V'_1) → k_1
  105. Mirror(Q, a) → Q'
  106. Mirror(V, a) → V'
  107. Mirror(E'_1, a) → W
  108. Arc(Mirror[Circle[Q, V], a], V', W) → p_1
  109. Sequence(Arc[Rotate[Mirror[Circle[Q, E''], a], (i * (360°) / n)], Rotate[E''', (i * (360°) / n)], Rotate[U'_1, (i * (360°) / n)]], i, 1, n) → list17
  110. Sequence(Arc[Rotate[Mirror[Circle[R, U], a], (i * (360°) / n)], Rotate[U', (i * (360°) / n)], Rotate[V'_1, (i * (360°) / n)]], i, 1, n) → list18
  111. Sequence(Arc[Rotate[Mirror[Circle[Q, V], a], (i * (360°) / n)], Rotate[V', (i * (360°) / n)], Rotate[W, (i * (360°) / n)]], i, 1, n) → list19
  112. Intersect(k, b, 1) → Z
  113. Midpoint(W, Z) → A_1
  114. Intersect(k, a, 1) → B_1
  115. Midpoint(E''', B_1) → C_1
  116. Circle(A_1, E''') → q_1
  117. Circle(E''', A_1) → r_1
  118. Intersect(r_1, q_1) → D_1, E_1, ,
  119. CircleArc(E_1, A_1, E''') → s_1
  120. Line(H', A) → a_1
  121. Intersect(s_1, a_1, 1) → F_1
  122. Mirror(E_1, a_1) → G_1
  123. CircleArc(E_1, A_1, F_1) → t_1
  124. CircleArc(G_1, F_1, C_1) → c_2
  125. Sequence(Arc[Rotate[Circle[E_1, A_1], (i * (360°) / n)], Rotate[A_1, (i * (360°) / n)], Rotate[F_1, (i * (360°) / n)]], i, 1, n) → list20
  126. Sequence(Arc[Rotate[Circle[G_1, F_1], (i * (360°) / n)], Rotate[F_1, (i * (360°) / n)], Rotate[C_1, (i * (360°) / n)]], i, 1, n) → list21
  127. Mirror(E_1, a) → H_1
  128. Mirror(A_1, a) → I_1
  129. Mirror(F_1, a) → J_1
  130. Arc(Mirror[Circle[E_1, A_1], a], I_1, J_1) → d_2
  131. Mirror(G_1, a) → K_1
  132. Mirror(F_1, a) → L_1
  133. Mirror(C_1, a) → M_1
  134. Arc(Mirror[Circle[G_1, F_1], a], L_1, M_1) → e_2
  135. Sequence(Arc[Rotate[Mirror[Circle[E_1, A_1], a], (i * (360°) / n)], Rotate[I_1, (i * (360°) / n)], Rotate[J_1, (i * (360°) / n)]], i, 1, n) → list22
  136. Sequence(Arc[Rotate[Mirror[Circle[G_1, F_1], a], (i * (360°) / n)], Rotate[L_1, (i * (360°) / n)], Rotate[M_1, (i * (360°) / n)]], i, 1, n) → list23
  137. Mirror(E'_1, b) → N_1
  138. Line(E'_1, B) → b_1
  139. Intersect(e, b_1, 1) → O_1
  140. Circle(B, O_1) → f_2
  141. Intersect(f_2, b, 1) → P_1
  142. Circle(P_1, B) → g_2
  143. Intersect(f_2, g_2) → Q_1, R_1, ,
  144. Circle(R_1, P_1) → h_2
  145. Circle(Q_1, P_1) → k_2
  146. Intersect(f_2, h_2, 2) → S_1
  147. Intersect(f_2, k_2, 2) → T_1
  148. Intersect(f_2, b, 2) → U_1
  149. Intersect(c, f_2, 1) → V_1
  150. Intersect(c, f_2, 2) → W_1
  151. Circle(W_1, P_1) → p_2
  152. Circle(V_1, P_1) → q_2
  153. Intersect(f_2, q_2, 2) → Z_1
  154. Intersect(f_2, p_2, 2) → A_2
  155. Circle(A_2, W_1) → r_2
  156. Circle(Z_1, V_1) → s_2
  157. Intersect(p_2, s_2, 1) → B_2
  158. Intersect(q_2, r_2, 2) → C_2
  159. CircleArc(W_1, B_2, P_1) → t_2
  160. Sequence(Arc[Rotate[Circle[W_1, B_2], (i * (360°) / n)], Rotate[B_2, (i * (360°) / n)], Rotate[P_1, (i * (360°) / n)]], i, 1, n) → list24
  161. CircleArc(B, V_1, W_1) → c_3
  162. Sequence(Arc[Rotate[Circle[B, V_1], (i * (360°) / n)], Rotate[V_1, (i * (360°) / n)], Rotate[W_1, (i * (360°) / n)]], i, 1, n) → list25
  163. CircleArc(V_1, P_1, C_2) → d_3
  164. CircleArc(A_2, C_2, W_1) → e_3
  165. Sequence(Arc[Rotate[Circle[A_2, C_2], (i * (360°) / n)], Rotate[C_2, (i * (360°) / n)], Rotate[W_1, (i * (360°) / n)]], i, 1, n) → list27
  166. CircleArc(Z_1, V_1, B_2) → f_3
  167. Sequence(Arc[Rotate[Circle[Z_1, V_1], (i * (360°) / n)], Rotate[V_1, (i * (360°) / n)], Rotate[B_2, (i * (360°) / n)]], i, 1, n) → list28
  168. Circle(B, B_2) → g_3
  169. Intersect(c, g_3, 1) → D_2
  170. Intersect(c, g_3, 2) → E_2
  171. CircleArc(B, D_2, E_2) → h_3
  172. Sequence(Arc[Rotate[Circle[B, D_2], (i * (360°) / n)], Rotate[D_2, (i * (360°) / n)], Rotate[E_2, (i * (360°) / n)]], i, 1, n) → list29
  173. Segment(H_2, I_2) → j_1
  174. Segment(H_2, G_2) → l_1
  175. Rotate(J_2, 90°, L_2) → O_2
  176. Rotate(J_2, 270°, L_2) → U_2
  177. Circle(U_2, J_2) → p_3
  178. Intersect(k_3, p_3, 2) → M_2
  179. CircleArc(U_2, J_2, M_2) → q_3
  180. CircleArc(O_2, M_2, J_2) → r_3
  181. Rotate(O_2, 60°, L_2) → N_2
  182. Rotate(M_2, 60°, L_2) → P_2
  183. Rotate(J_2, 60°, L_2) → Q_2
  184. Arc(Rotate[Circle[O_2, M_2], 60°, L_2], P_2, Q_2) → s_3
  185. Rotate(O_2, 120°, L_2) → R_2
  186. Rotate(M_2, 120°, L_2) → S_2
  187. Rotate(J_2, 120°, L_2) → T_2
  188. Arc(Rotate[Circle[O_2, M_2], 120°, L_2], S_2, T_2) → t_3
  189. Rotate(U_2, 60°, L_2) → V_2
  190. Rotate(J_2, 60°, L_2) → W_2
  191. Rotate(M_2, 60°, L_2) → Z_2
  192. Arc(Rotate[Circle[U_2, J_2], 60°, L_2], W_2, Z_2) → c_4
  193. Rotate(U_2, 120°, L_2) → A_3
  194. Rotate(J_2, 120°, L_2) → B_3
  195. Rotate(M_2, 120°, L_2) → C_3
  196. Arc(Rotate[Circle[U_2, J_2], 120°, L_2], B_3, C_3) → d_4
  197. Rotate(k_3, 90°, A) → e_4
  198. Rotate(e_4, 90°, A) → f_4
  199. Rotate(f_4, 90°, A) → g_4
  200. Rotate(S_2, 90°, A) → D_3
  201. Rotate(T_2, 90°, A) → E_3
  202. Arc(Rotate[Rotate[Circle[O_2, M_2], 120°, L_2], 90°, A], D_3, E_3) → h_4
  203. Rotate(B_3, 90°, A) → F_3
  204. Rotate(C_3, 90°, A) → G_3
  205. Arc(Rotate[Rotate[Circle[U_2, J_2], 120°, L_2], 90°, A], F_3, G_3) → k_4
  206. Rotate(U_2, 90°, A) → H_3
  207. Rotate(J_2, 90°, A) → I_3
  208. Rotate(M_2, 90°, A) → J_3
  209. Arc(Rotate[Circle[U_2, J_2], 90°, A], I_3, J_3) → p_4
  210. Rotate(O_2, 90°, A) → K_3
  211. Rotate(M_2, 90°, A) → L_3
  212. Rotate(J_2, 90°, A) → M_3
  213. Arc(Rotate[Circle[O_2, M_2], 90°, A], L_3, M_3) → q_4
  214. Rotate(P_2, 90°, A) → N_3
  215. Rotate(Q_2, 90°, A) → O_3
  216. Arc(Rotate[Rotate[Circle[O_2, M_2], 60°, L_2], 90°, A], N_3, O_3) → r_4
  217. Rotate(W_2, 90°, A) → P_3
  218. Rotate(Z_2, 90°, A) → Q_3
  219. Arc(Rotate[Rotate[Circle[U_2, J_2], 60°, L_2], 90°, A], P_3, Q_3) → s_4
  220. Rotate(P_3, 90°, A) → R_3
  221. Rotate(Q_3, 90°, A) → S_3
  222. Arc(Rotate[Rotate[Rotate[Circle[U_2, J_2], 60°, L_2], 90°, A], 90°, A], R_3, S_3) → t_4
  223. Rotate(N_3, 90°, A) → T_3
  224. Rotate(O_3, 90°, A) → U_3
  225. Arc(Rotate[Rotate[Rotate[Circle[O_2, M_2], 60°, L_2], 90°, A], 90°, A], T_3, U_3) → c_5
  226. Rotate(D_3, 90°, A) → V_3
  227. Rotate(E_3, 90°, A) → W_3
  228. Arc(Rotate[Rotate[Rotate[Circle[O_2, M_2], 120°, L_2], 90°, A], 90°, A], V_3, W_3) → d_5
  229. Rotate(F_3, 90°, A) → Z_3
  230. Rotate(G_3, 90°, A) → A_4
  231. Arc(Rotate[Rotate[Rotate[Circle[U_2, J_2], 120°, L_2], 90°, A], 90°, A], Z_3, A_4) → e_5
  232. Rotate(I_3, 90°, A) → B_4
  233. Rotate(J_3, 90°, A) → C_4
  234. Arc(Rotate[Rotate[Circle[U_2, J_2], 90°, A], 90°, A], B_4, C_4) → f_5
  235. Rotate(L_3, 90°, A) → D_4
  236. Rotate(M_3, 90°, A) → E_4
  237. Arc(Rotate[Rotate[Circle[O_2, M_2], 90°, A], 90°, A], D_4, E_4) → g_5
  238. Rotate(Z_3, 90°, A) → F_4
  239. Rotate(A_4, 90°, A) → G_4
  240. Arc(Rotate[Rotate[Rotate[Rotate[Circle[U_2, J_2], 120°, L_2], 90°, A], 90°, A], 90°, A], F_4, G_4) → h_5
  241. Rotate(V_3, 90°, A) → H_4
  242. Rotate(W_3, 90°, A) → I_4
  243. Arc(Rotate[Rotate[Rotate[Rotate[Circle[O_2, M_2], 120°, L_2], 90°, A], 90°, A], 90°, A], H_4, I_4) → k_5
  244. Rotate(D_4, 90°, A) → J_4
  245. Rotate(E_4, 90°, A) → K_4
  246. Arc(Rotate[Rotate[Rotate[Circle[O_2, M_2], 90°, A], 90°, A], 90°, A], J_4, K_4) → p_5
  247. Rotate(B_4, 90°, A) → L_4
  248. Rotate(C_4, 90°, A) → M_4
  249. Arc(Rotate[Rotate[Rotate[Circle[U_2, J_2], 90°, A], 90°, A], 90°, A], L_4, M_4) → q_5
  250. Rotate(T_3, 90°, A) → N_4
  251. Rotate(U_3, 90°, A) → O_4
  252. Arc(Rotate[Rotate[Rotate[Rotate[Circle[O_2, M_2], 60°, L_2], 90°, A], 90°, A], 90°, A], N_4, O_4) → r_5
  253. Rotate(R_3, 90°, A) → P_4
  254. Rotate(S_3, 90°, A) → Q_4
  255. Arc(Rotate[Rotate[Rotate[Rotate[Circle[U_2, J_2], 60°, L_2], 90°, A], 90°, A], 90°, A], P_4, Q_4) → s_5
  256. Rotate(t_5, 90°) → d_6
  257. Rotate(t_5, 180°) → e_6
  258. Rotate(t_5, 270°) → f_6
  259. Mirror(t_5, a_3) → c_6
  260. Rotate(c_6, 90°) → g_6
  261. Rotate(c_6, 180°) → h_6
  262. Rotate(c_6, 270°) → k_6
  263. Mirror(Z_4, W_4) → A_5
  264. Rotate(A_5, 90°, W_4) → B_5
  265. Mirror(B_5, W_4) → C_5
  266. Semicircle(B_5, Z_4) → p_6
  267. Semicircle(Z_4, C_5) → q_6
  268. Semicircle(C_5, A_5) → r_6
  269. Semicircle(A_5, B_5) → s_6
  270. Mirror(B_5, a_3) → D_5
  271. Mirror(Z_4, a_3) → E_5
  272. Semicircle(E_5, D_5) → t_6
  273. Mirror(C_5, a_3) → F_5
  274. Mirror(A_5, a_3) → G_5
  275. Semicircle(G_5, F_5) → c_7
  276. Mirror(Z_4, a_3) → H_5
  277. Mirror(C_5, a_3) → I_5
  278. Semicircle(I_5, H_5) → d_7
  279. Mirror(A_5, a_3) → J_5
  280. Mirror(B_5, a_3) → K_5
  281. Semicircle(K_5, J_5) → e_7
  282. Rotate(B_5, 90°) → L_5
  283. Rotate(Z_4, 90°) → M_5
  284. Semicircle(L_5, M_5) → f_7
  285. Rotate(Z_4, 90°) → N_5
  286. Rotate(C_5, 90°) → O_5
  287. Semicircle(N_5, O_5) → g_7
  288. Rotate(C_5, 90°) → P_5
  289. Rotate(A_5, 90°) → Q_5
  290. Semicircle(P_5, Q_5) → h_7
  291. Rotate(A_5, 90°) → R_5
  292. Rotate(B_5, 90°) → S_5
  293. Semicircle(R_5, S_5) → k_7
  294. Rotate(B_5, 180°) → T_5
  295. Rotate(Z_4, 180°) → U_5
  296. Semicircle(T_5, U_5) → p_7
  297. Rotate(Z_4, 180°) → V_5
  298. Rotate(C_5, 180°) → W_5
  299. Semicircle(V_5, W_5) → q_7
  300. Rotate(C_5, 180°) → Z_5
  301. Rotate(A_5, 180°) → A_6
  302. Semicircle(Z_5, A_6) → r_7
  303. Rotate(A_5, 180°) → B_6
  304. Rotate(B_5, 180°) → C_6
  305. Semicircle(B_6, C_6) → s_7
  306. Rotate(B_5, 270°) → D_6
  307. Rotate(Z_4, 270°) → E_6
  308. Semicircle(D_6, E_6) → t_7
  309. Rotate(Z_4, 270°) → F_6
  310. Rotate(C_5, 270°) → G_6
  311. Semicircle(F_6, G_6) → c_8
  312. Rotate(C_5, 270°) → H_6
  313. Rotate(A_5, 270°) → I_6
  314. Semicircle(H_6, I_6) → d_8
  315. Rotate(A_5, 270°) → J_6
  316. Rotate(B_5, 270°) → K_6
  317. Semicircle(J_6, K_6) → e_8
  318. Rotate(E_5, 90°) → L_6
  319. Rotate(D_5, 90°) → M_6
  320. Semicircle(L_6, M_6) → f_8
  321. Rotate(E_5, 180°) → N_6
  322. Rotate(D_5, 180°) → O_6
  323. Semicircle(N_6, O_6) → g_8
  324. Rotate(E_5, 270°) → P_6
  325. Rotate(D_5, 270°) → Q_6
  326. Semicircle(P_6, Q_6) → h_8
  327. Rotate(G_5, 90°) → R_6
  328. Rotate(F_5, 90°) → S_6
  329. Semicircle(R_6, S_6) → k_8
  330. Rotate(I_5, 90°) → T_6
  331. Rotate(H_5, 90°) → U_6
  332. Semicircle(T_6, U_6) → p_8
  333. Rotate(K_5, 90°) → V_6
  334. Rotate(J_5, 90°) → W_6
  335. Semicircle(V_6, W_6) → q_8
  336. Rotate(G_5, 180°) → Z_6
  337. Rotate(F_5, 180°) → A_7
  338. Semicircle(Z_6, A_7) → r_8
  339. Rotate(I_5, 180°) → B_7
  340. Rotate(H_5, 180°) → C_7
  341. Semicircle(B_7, C_7) → s_8
  342. Rotate(K_5, 180°) → D_7
  343. Rotate(J_5, 180°) → E_7
  344. Semicircle(D_7, E_7) → t_8
  345. Rotate(G_5, 270°) → F_7
  346. Rotate(F_5, 270°) → G_7
  347. Semicircle(F_7, G_7) → c_9
  348. Rotate(I_5, 270°) → H_7
  349. Rotate(H_5, 270°) → I_7
  350. Semicircle(H_7, I_7) → d_9
  351. Rotate(K_5, 270°) → J_7
  352. Rotate(J_5, 270°) → K_7
  353. Semicircle(J_7, K_7) → e_9
  354. Point(t_5) → L_7
  355. Point(c) → M_7
  356. Tangent(M_7, c) → b_3,
  357. Tangent(L_7, t_5) → i_3,
  358. Intersect(b_3, i_3) → N_7
  359. Intersect(b_3, m_1) → O_7
  360. Intersect(m_1, i_3) → P_7
  361. AngularBisector(P_7, O_7, N_7) → j_3
  362. AngularBisector(N_7, P_7, O_7) → l_3
  363. Intersect(j_3, l_3) → Q_7
  364. OrthogonalLine(Q_7, m_1) → m_3
  365. Intersect(m_3, m_1) → R_7
  366. Circle(Q_7, R_7) → f_9
  367. Point(f_9) → S_7
  368. Point(c) → T_7
  369. Tangent(T_7, c) → n_3,
  370. Tangent(S_7, f_9) → a_4,
  371. Intersect(a_4, n_3) → U_7
  372. Intersect(m_1, a_4) → V_7
  373. Intersect(m_1, n_3) → W_7
  374. AngularBisector(V_7, W_7, U_7) → b_4
  375. AngularBisector(U_7, V_7, W_7) → i_4
  376. Intersect(b_4, i_4) → Z_7
  377. OrthogonalLine(Z_7, m_1) → j_4
  378. Intersect(j_4, m_1) → A_8
  379. Circle(Z_7, A_8) → g_9
  380. Intersect(f_9, m_1, 1) → B_8
  381. Rotate(B_8, 120°, Q_7) → C_8
  382. Rotate(C_8, 120°, Q_7) → D_8
  383. CircleArc(D_8, B_8, C_8) → h_9
  384. CircleArc(B_8, C_8, D_8) → k_9
  385. CircleArc(C_8, D_8, B_8) → p_9
  386. Line(C_8, B_8) → l_4
  387. Line(B_8, D_8) → m_4
  388. Line(D_8, C_8) → n_4
  389. Mirror(B_8, n_4) → E_8
  390. Mirror(C_8, n_4) → F_8
  391. Mirror(D_8, n_4) → G_8
  392. Arc(Mirror[Circle[B_8, C_8], n_4], F_8, G_8) → q_9
  393. Mirror(C_8, m_4) → H_8
  394. Mirror(D_8, m_4) → I_8
  395. Mirror(B_8, m_4) → J_8
  396. Arc(Mirror[Circle[C_8, D_8], m_4], I_8, J_8) → r_9
  397. Mirror(D_8, l_4) → K_8
  398. Mirror(B_8, l_4) → L_8
  399. Mirror(C_8, l_4) → M_8
  400. Arc(Mirror[Circle[D_8, B_8], l_4], L_8, M_8) → s_9
  401. Mirror(f_9, a_3) → t_9
  402. Mirror(g_9, a_3) → c_{10}
  403. Mirror(F_8, a_3) → N_8
  404. Mirror(G_8, a_3) → O_8
  405. Arc(Mirror[Mirror[Circle[B_8, C_8], n_4], a_3], N_8, O_8) → d_{10}
  406. Mirror(L_8, a_3) → P_8
  407. Mirror(M_8, a_3) → Q_8
  408. Arc(Mirror[Mirror[Circle[D_8, B_8], l_4], a_3], P_8, Q_8) → e_{10}
  409. Mirror(I_8, a_3) → R_8
  410. Mirror(J_8, a_3) → S_8
  411. Arc(Mirror[Mirror[Circle[C_8, D_8], m_4], a_3], R_8, S_8) → f_{10}
  412. Rotate(f_9, 90°) → g_{10}
  413. Rotate(f_9, 180°) → h_{10}
  414. Rotate(f_9, 270°) → k_{10}
  415. Rotate(t_9, 90°) → p_{10}
  416. Rotate(t_9, 180°) → q_{10}
  417. Rotate(t_9, 270°) → r_{10}
  418. Rotate(g_9, 270°) → s_{10}
  419. Rotate(g_9, 180°) → t_{10}
  420. Rotate(g_9, 90°) → c_{11}
  421. Rotate(c_{10}, 90°) → d_{11}
  422. Rotate(c_{10}, 180°) → e_{11}
  423. Rotate(c_{10}, 270°) → f_{11}
  424. Rotate(F_8, 90°) → T_8
  425. Rotate(G_8, 90°) → U_8
  426. Arc(Rotate[Mirror[Circle[B_8, C_8], n_4], 90°], T_8, U_8) → g_{11}
  427. Rotate(I_8, 90°) → V_8
  428. Rotate(J_8, 90°) → W_8
  429. Arc(Rotate[Mirror[Circle[C_8, D_8], m_4], 90°], V_8, W_8) → h_{11}
  430. Rotate(L_8, 90°) → Z_8
  431. Rotate(M_8, 90°) → A_9
  432. Arc(Rotate[Mirror[Circle[D_8, B_8], l_4], 90°], Z_8, A_9) → k_{11}
  433. Rotate(L_8, 180°) → B_9
  434. Rotate(M_8, 180°) → C_9
  435. Arc(Rotate[Mirror[Circle[D_8, B_8], l_4], 180°], B_9, C_9) → p_{11}
  436. Rotate(F_8, 180°) → D_9
  437. Rotate(G_8, 180°) → E_9
  438. Arc(Rotate[Mirror[Circle[B_8, C_8], n_4], 180°], D_9, E_9) → q_{11}
  439. Rotate(I_8, 180°) → F_9
  440. Rotate(J_8, 180°) → G_9
  441. Arc(Rotate[Mirror[Circle[C_8, D_8], m_4], 180°], F_9, G_9) → r_{11}
  442. Rotate(I_8, 270°) → H_9
  443. Rotate(J_8, 270°) → I_9
  444. Arc(Rotate[Mirror[Circle[C_8, D_8], m_4], 270°], H_9, I_9) → s_{11}
  445. Rotate(L_8, 270°) → J_9
  446. Rotate(M_8, 270°) → K_9
  447. Arc(Rotate[Mirror[Circle[D_8, B_8], l_4], 270°], J_9, K_9) → t_{11}
  448. Rotate(F_8, 270°) → L_9
  449. Rotate(G_8, 270°) → M_9
  450. Arc(Rotate[Mirror[Circle[B_8, C_8], n_4], 270°], L_9, M_9) → c_{12}
  451. Rotate(N_8, 90°) → N_9
  452. Rotate(O_8, 90°) → O_9
  453. Arc(Rotate[Mirror[Mirror[Circle[B_8, C_8], n_4], a_3], 90°], N_9, O_9) → d_{12}
  454. Rotate(P_8, 90°) → P_9
  455. Rotate(Q_8, 90°) → Q_9
  456. Arc(Rotate[Mirror[Mirror[Circle[D_8, B_8], l_4], a_3], 90°], P_9, Q_9) → e_{12}
  457. Rotate(R_8, 90°) → R_9
  458. Rotate(S_8, 90°) → S_9
  459. Arc(Rotate[Mirror[Mirror[Circle[C_8, D_8], m_4], a_3], 90°], R_9, S_9) → f_{12}
  460. Rotate(R_8, 180°) → T_9
  461. Rotate(S_8, 180°) → U_9
  462. Arc(Rotate[Mirror[Mirror[Circle[C_8, D_8], m_4], a_3], 180°], T_9, U_9) → g_{12}
  463. Rotate(P_8, 180°) → V_9
  464. Rotate(Q_8, 180°) → W_9
  465. Arc(Rotate[Mirror[Mirror[Circle[D_8, B_8], l_4], a_3], 180°], V_9, W_9) → h_{12}
  466. Rotate(N_8, 180°) → Z_9
  467. Rotate(O_8, 180°) → A_{10}
  468. Arc(Rotate[Mirror[Mirror[Circle[B_8, C_8], n_4], a_3], 180°], Z_9, A_{10}) → k_{12}
  469. Rotate(N_8, 270°) → B_{10}
  470. Rotate(O_8, 270°) → C_{10}
  471. Arc(Rotate[Mirror[Mirror[Circle[B_8, C_8], n_4], a_3], 270°], B_{10}, C_{10}) → p_{12}
  472. Rotate(P_8, 270°) → D_{10}
  473. Rotate(Q_8, 270°) → E_{10}
  474. Arc(Rotate[Mirror[Mirror[Circle[D_8, B_8], l_4], a_3], 270°], D_{10}, E_{10}) → q_{12}
  475. Rotate(R_8, 270°) → F_{10}
  476. Rotate(S_8, 270°) → G_{10}
  477. Arc(Rotate[Mirror[Mirror[Circle[C_8, D_8], m_4], a_3], 270°], F_{10}, G_{10}) → r_{12}
  478. Line(G_2, F_2) → i_5
  479. Rotate(l1, 90°, i_5) → l1'
  480. Line(F_2, I_2) → j_5
  481. Intersect(j_1, l_1) → H_{10}
  482. Line(I_2, xAxis) → l_5
  483. Line(G_2, yAxis) → m_5
  484. Rotate(l1, (-(90°)), l_5) → l1'_1
  485. Rotate(l1, 90°, j_5) → l1'_2
  486. Rotate(l1, (-(90°)), m_5) → l1'_3
  487. Point(Circle[F_2, Distance[G_2, F_2], Segment[G_2, F_2]]) → I_{10}
  488. Cube(G_2, F_2, I_{10}) → o, J_{10}, face5, face6, arête2, arête1, arête4, arête6, arête3, arête8, arête10, arête9, K_{10}, arête5, arête11, arête7, arête12, L_{10}, M_{10}, N_{10}, face1, face3, face2, face4
  489. Rotate(l2, 90°, i_5) → l2'
  490. Rotate(l2, (-(90°)), l_5) → l2'_1
  491. Rotate(l2, 90°, j_5) → l2'_2
  492. Rotate(l2, (-(90°)), m_5) → l2'_3
  493. Line(L_{10}, M_{10}) → n_5
  494. Rotate(l1'_2, 90°, n_5) → l3
  495. Rotate(l2'_2, 90°, n_5) → l4

AI 绘图提示语参考

绘制一个三维玫瑰立方体：以立方体为基础，在其表面或空间中生成对称的旋转花瓣结构。从中心点出发，构建多条辅助线与圆，通过旋转和镜像操作，生成一系列椭圆弧、圆弧和花瓣状曲线，并围绕中心轴按等分角度重复排列，形成多层嵌套的玫瑰花瓣效果。图形包含立方体框架、多个相交的圆与椭圆、切线、角平分线以及由序列生成的对称弧线，整体呈现几何变换与对称美。
以上提示语为根据原始绘图命令整理而来，仅供参考。