立方体切片与滑动演示

立方体切片与滑动演示
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2021-09-12 18:32
本范例通过GeoGebra动态演示立方体被平面切割后的截面变化现象。涉及的核心数学概念包括立体几何中的截面定理、二次函数与平面相交的解析几何方法,以及多项式函数的图像变换。作图要点包括使用Intersect命令计算平面与立方体面的交点,利用Cube和Sphere对象构建三维模型,通过OrthogonalPlane命令生成垂直截面,并用Mirror和Rotate命令实现平移动画。适合高中生学习立体几何与函数图像变换,或作为数学建模教学的辅助工具。

GeoGebra 命令及参数

  1. Intersect(yAxis, xAxis) → A
  2. Point(Circle[B, Distance[C, B], Segment[C, B]]) → D
  3. Cube(C, B, D) → b, E, faceDEIH, faceFGHI, edgeCE, edgeBC, edgeBD, edgeDE, edgeCF, edgeEI, edgeFI, edgeFG, F, edgeBG, edgeGH, edgeDH, edgeHI, G, H, I, faceBCED, faceCEIF, faceBCFG, faceBDHG
  4. Sphere(A, a) → c
  5. Line(G, H) → f
  6. Line(F, I) → g
  7. Line(H, I) → h
  8. Line(G, F) → i
  9. Line(G, B) → j
  10. Line(H, D) → k
  11. Line(B, D) → l
  12. Line(D, E) → m
  13. Line(C, B) → n
  14. Line(E, C) → p
  15. Intersect(p, xOyPlane) → J
  16. Intersect(p, xOyPlane) → K
  17. Line(I, E) → f_2
  18. Line(F, C) → g_2
  19. Intersect(zAxis, c) → L, M
  20. Intersect(yAxis, c) → N, O
  21. Intersect(xAxis, c, 2) → P
  22. Line(C, B) → s
  23. Line(F, G) → t
  24. Line(I, H) → d
  25. Line(E, D) → e
  26. Line(G, H) → f_1
  27. Line(F, I) → g_1
  28. Line(E, C) → h_1
  29. Line(D, B) → i_1
  30. Line(F, C) → q
  31. Line(G, B) → r
  32. Line(H, D) → j_1
  33. Line(I, E) → k_1
  34. OrthogonalPlane(M, k_1) → p_1
  35. Intersect(r, p_1) → Q
  36. Intersect(j_1, p_1) → R
  37. Intersect(k_1, p_1) → S
  38. Intersect(q, p_1) → T
  39. Sphere(M, 2) → o
  40. Intersect(zAxis, o, 2) → U
  41. OrthogonalPlane(U, k_1) → q_1
  42. Intersect(r, q_1) → V
  43. Intersect(q, q_1) → W
  44. Intersect(k_1, q_1) → Z
  45. Intersect(j_1, q_1) → A_1
  46. Mirror(V, g_3) → V'
  47. Mirror(W, g_3) → W'
  48. Mirror(Q, g_3) → Q'
  49. Mirror(T, g_3) → T'
  50. Mirror(R, g_3) → R'
  51. Mirror(S, g_3) → S'
  52. Mirror(Z, g_3) → Z'
  53. Line(O, N) → l_1
  54. Rotate(A_1, -90°, l_1) → B_1
  55. Rotate(V, -90°, l_1) → V'_{1}
  56. Rotate(Z, -90°, l_1) → Z'_{1}
  57. Rotate(W, -90°, l_1) → W'_{1}
  58. Rotate(Q, -90°, l_1) → Q'_{1}
  59. Rotate(R, -90°, l_1) → R'_{1}
  60. Rotate(S, -90°, l_1) → S'_{1}
  61. Rotate(T, -90°, l_1) → T'_{1}
  62. Mirror(B_1, eq1) → C_1
  63. Mirror(Z'_{1}, eq1) → D_1
  64. Mirror(W'_{1}, eq1) → E_1
  65. Mirror(V'_{1}, eq1) → F_1
  66. Mirror(Q'_{1}, eq1) → G_1
  67. Mirror(T'_{1}, eq1) → H_1
  68. Mirror(S'_{1}, eq1) → I_1
  69. Mirror(R'_{1}, eq1) → J_1
  70. Rotate(Z, -90°, s_1) → Z'_{2}
  71. Rotate(W, -90°, s_1) → W'_{2}
  72. Rotate(V, -90°, s_1) → V'_{2}
  73. Rotate(A_1, -90°, s_1) → K_1
  74. Rotate(Q, -90°, s_1) → Q'_{2}
  75. Rotate(R, -90°, s_1) → R'_{2}
  76. Rotate(S, -90°, s_1) → S'_{2}
  77. Rotate(T, -90°, s_1) → T'_{2}
  78. Mirror(Q'_{2}, f_3) → L_1
  79. Mirror(V'_{2}, f_3) → M_1
  80. Mirror(R'_{2}, f_3) → N_1
  81. Mirror(K_1, f_3) → O_1
  82. Mirror(T'_{2}, f_3) → P_1
  83. Mirror(S'_{2}, f_3) → Q_1
  84. Mirror(Z'_{2}, f_3) → R_1
  85. Mirror(W'_{2}, f_3) → S_1
  86. Line(Z, W) → m_1
  87. Line(S, T) → n_1
  88. Line(R, Q) → t_1
  89. Line(A_1, V) → a_1
  90. Line(Q'_{1}, R'_{1}) → b_1
  91. Line(V'_{1}, B_1) → c_1
  92. Line(W'_{1}, Z'_{1}) → d_1
  93. Line(T'_{1}, S'_{1}) → e_1
  94. Intersect(e_1, t_1) → T_1
  95. Intersect(a_1, b_1) → U_1
  96. Intersect(c_1, a_1) → V_1
  97. Intersect(c_1, t_1) → W_1
  98. Intersect(n_1, d_1) → Z_1
  99. Intersect(n_1, e_1) → A_2
  100. Intersect(t_1, b_1) → B_2
  101. Intersect(e_1, m_1) → C_2
  102. Intersect(d_1, m_1) → D_2
  103. Rotate(W_1, 90°, l_1) → E_2
  104. Rotate(Z_1, 90°, l_1) → F_2
  105. Rotate(A_2, 90°, l_1) → G_2
  106. Rotate(B_2, 90°, l_1) → H_2
  107. Rotate(V_1, 90°, l_1) → I_2
  108. Rotate(D_2, 90°, l_1) → J_2
  109. Rotate(C_2, 90°, l_1) → K_2
  110. Rotate(U_1, 90°, l_1) → L_2
  111. Polygon(J_2, K_2, G_2, F_2) → q1, j_2, k_2, h_2, i_2
  112. Polygon(I_2, L_2, H_2, E_2) → q2, l_2, m_2, n_2, e_2
  113. Polygon(U_1, B_2, W_1, V_1) → q3, u_1, b_2, w_1, v_1
  114. Polygon(C_2, A_2, Z_1, D_2) → q4, c_2, a_2, z_1, d_2
  115. Mirror(I_2, g_3) → M_2
  116. Mirror(E_2, g_3) → N_2
  117. Mirror(L_2, g_3) → O_2
  118. Mirror(H_2, g_3) → P_2
  119. Mirror(q2, g_3) → q2'
  120. Mirror(q1, g_3) → q1'
  121. Mirror(J_2, g_3) → Q_2
  122. Mirror(F_2, g_3) → R_2
  123. Mirror(G_2, g_3) → S_2
  124. Mirror(K_2, g_3) → T_2
  125. Mirror(q3, g_3) → q3'
  126. Mirror(q4, g_3) → q4'
  127. Mirror(U_1, g_3) → U_2
  128. Mirror(V_1, g_3) → V_2
  129. Mirror(B_2, g_3) → W_2
  130. Mirror(D_2, g_3) → Z_2
  131. Mirror(C_2, g_3) → A_3
  132. Mirror(A_2, g_3) → B_3
  133. Mirror(Z_1, g_3) → C_3
  134. Midpoint(A_1, W) → D_3
  135. Line(D_3, L) → p_2
  136. Rotate(q2, 90°, p_2) → q2'_{1}
  137. Rotate(q1, 90°, p_2) → q1'_{1}
  138. Rotate(I_2, 90°, p_2) → E_3
  139. Rotate(E_2, 90°, p_2) → F_3
  140. Rotate(L_2, 90°, p_2) → G_3
  141. Rotate(H_2, 90°, p_2) → H_3
  142. Rotate(J_2, 90°, p_2) → I_3
  143. Rotate(F_2, 90°, p_2) → J_3
  144. Rotate(K_2, 90°, p_2) → K_3
  145. Rotate(G_2, 90°, p_2) → L_3
  146. Mirror(q2'_{1}, g_3) → q5
  147. Mirror(q1'_{1}, g_3) → q6
  148. Mirror(K_3, g_3) → M_3
  149. Mirror(L_3, g_3) → N_3
  150. Mirror(J_3, g_3) → O_3
  151. Mirror(I_3, g_3) → P_3
  152. Mirror(H_3, g_3) → Q_3
  153. Mirror(E_3, g_3) → R_3
  154. Mirror(G_3, g_3) → S_3
  155. Mirror(q2'_{1}, f_3) → q7
  156. Mirror(q1'_{1}, f_3) → q8
  157. Mirror(q6, f_3) → q6'
  158. Mirror(R_3, f_3) → T_3
  159. Mirror(q5, f_3) → q5'
  160. Mirror(I_3, f_3) → U_3
  161. Mirror(K_3, f_3) → V_3
  162. Mirror(L_3, f_3) → W_3
  163. Mirror(J_3, f_3) → Z_3
  164. Mirror(E_3, f_3) → A_4
  165. Mirror(F_3, f_3) → B_4
  166. Mirror(H_3, f_3) → C_4
  167. Mirror(G_3, f_3) → D_4
  168. Mirror(S_3, f_3) → E_4
  169. Mirror(M_3, f_3) → F_4
  170. Mirror(P_3, f_3) → G_4
  171. Mirror(Q_3, f_3) → H_4
  172. Mirror(O_3, f_3) → I_4
  173. Mirror(N_3, f_3) → J_4
  174. Mirror(F_3, g_3) → K_4
  175. Line(A_4, U_3) → q_2
  176. Line(B_4, Z_3) → r_2
  177. Line(C_4, W_3) → s_2
  178. Line(D_4, V_3) → t_2
  179. Line(E_2, F_2) → h_3
  180. Line(I_2, J_2) → i_3
  181. Line(L_2, K_2) → j_3
  182. Line(H_2, G_2) → k_3
  183. Intersect(h_3, q_2) → L_4
  184. Intersect(q_2, i_3) → M_4
  185. Intersect(r_2, i_3) → N_4
  186. Intersect(s_2, j_3) → O_4
  187. Intersect(k_3, s_2) → P_4
  188. Intersect(k_3, t_2) → Q_4
  189. Intersect(r_2, h_3) → R_4
  190. Intersect(t_2, j_3) → S_4
  191. Polygon(M_4, S_4, O_4, N_4) → q9, m_4, s_4, o_4, n_4
  192. Polygon(L_4, Q_4, P_4, R_4) → q10, l_4, q_4, p_4, r_4
  193. Mirror(q9, f_3) → q9'
  194. Mirror(q10, f_3) → q10'
  195. Mirror(M_4, f_3) → T_4
  196. Mirror(N_4, f_3) → U_4
  197. Mirror(S_4, f_3) → V_4
  198. Mirror(O_4, f_3) → W_4
  199. Mirror(L_4, f_3) → Z_4
  200. Mirror(R_4, f_3) → A_5
  201. Mirror(P_4, f_3) → B_5
  202. Mirror(Q_4, f_3) → C_5
  203. Mirror(q9', eq1) → q9''
  204. Mirror(U_4, eq1) → D_5
  205. Mirror(W_4, eq1) → E_5
  206. Mirror(V_4, eq1) → F_5
  207. Mirror(T_4, eq1) → G_5
  208. Mirror(q10', eq1) → q10''
  209. Mirror(Z_4, eq1) → H_5
  210. Mirror(C_5, eq1) → I_5
  211. Mirror(A_5, eq1) → J_5
  212. Mirror(B_5, eq1) → K_5
  213. Mirror(q9'', f_3) → q9'''
  214. Mirror(q10'', f_3) → q10'''
  215. Mirror(D_5, f_3) → L_5
  216. Mirror(G_5, f_3) → M_5
  217. Mirror(F_5, f_3) → N_5
  218. Mirror(H_5, f_3) → O_5
  219. Mirror(E_5, f_3) → P_5
  220. Mirror(I_5, f_3) → Q_5
  221. Mirror(K_5, f_3) → R_5
  222. Mirror(J_5, f_3) → S_5
  223. Mirror(q9, g_3) → q9'_{1}
  224. Mirror(q10, g_3) → q10'_{1}
  225. Mirror(O_4, g_3) → T_5
  226. Mirror(S_4, g_3) → U_5
  227. Mirror(M_4, g_3) → V_5
  228. Mirror(N_4, g_3) → W_5
  229. Mirror(R_4, g_3) → Z_5
  230. Mirror(L_4, g_3) → A_6
  231. Mirror(Q_4, g_3) → B_6
  232. Mirror(P_4, g_3) → C_6
  233. Mirror(q10''', g_3) → q11
  234. Mirror(q9''', g_3) → q12
  235. Mirror(L_5, g_3) → D_6
  236. Mirror(M_5, g_3) → E_6
  237. Mirror(N_5, g_3) → F_6
  238. Mirror(P_5, g_3) → G_6
  239. Mirror(Q_5, g_3) → H_6
  240. Mirror(O_5, g_3) → I_6
  241. Mirror(S_5, g_3) → J_6
  242. Mirror(R_5, g_3) → K_6
  243. Mirror(q9', g_3) → q9''_{1}
  244. Mirror(q10', g_3) → q10''_{1}
  245. Mirror(U_4, g_3) → L_6
  246. Mirror(T_4, g_3) → M_6
  247. Mirror(V_4, g_3) → N_6
  248. Mirror(W_4, g_3) → O_6
  249. Mirror(Z_4, g_3) → P_6
  250. Mirror(A_5, g_3) → Q_6
  251. Mirror(B_5, g_3) → R_6
  252. Mirror(C_5, g_3) → S_6
  253. Mirror(q9'', g_3) → q9'''_{1}
  254. Mirror(q10'', g_3) → q10'''_{1}
  255. Mirror(E_5, g_3) → T_6
  256. Mirror(F_5, g_3) → U_6
  257. Mirror(G_5, g_3) → V_6
  258. Mirror(D_5, g_3) → W_6
  259. Mirror(I_5, g_3) → Z_6
  260. Mirror(H_5, g_3) → A_7
  261. Mirror(J_5, g_3) → B_7
  262. Mirror(K_5, g_3) → C_7
  263. Polygon(R'_{2}, S'_{2}, Z'_{2}, K_1) → q13, r'_{2}, s'_{2}, z'_{2}, l_3
  264. Polygon(Q'_{2}, T'_{2}, W'_{2}, V'_{2}) → q14, q'_{2}, t'_{2}, w'_{2}, v'_{2}
  265. Polygon(A_1, R, S, Z) → q15, m_3, r_3, s_3, z_2
  266. Polygon(V, Q, T, W) → q16, v, q_3, t_3, w
  267. Polygon(K_2, L_2, I_2, J_2) → q17, n_3, p_3, a_3, b_3
  268. Polygon(L_2, H_2, G_2, K_2) → q18, c_3, d_3, e_3, f_4
  269. Polygon(J_2, I_2, E_2, F_2) → q19, g_4, h_4, i_4, j_4
  270. Polygon(F_2, G_2, H_2, E_2) → q20, k_4, t_4, a_4, b_4
  271. Polygon(J_1, C_1, F_1, G_1) → q21, c_4, d_4, e_4, f_5
  272. Polygon(I_1, H_1, E_1, D_1) → q22, g_5, h_5, i_5, j_5
  273. Polygon(Z'_{1}, W'_{1}, T'_{1}, S'_{1}) → q23, z'_{1}, w'_{1}, t'_{1}, s'_{1}
  274. Polygon(B_1, V'_{1}, Q'_{1}, R'_{1}) → q24, k_5, v'_{1}, q'_{1}, r'_{1}
  275. Polygon(L_1, P_1, S_1, M_1) → q25, l_5, m_5, n_5, p_5
  276. Polygon(N_1, Q_1, R_1, O_1) → q26, q_5, r_5, s_5, o_1
  277. Polygon(G_1, H_1, E_1, F_1) → q27, t_5, a_5, b_5, c_5
  278. Polygon(J_1, I_1, H_1, G_1) → q28, d_5, e_5, f_6, g_6
  279. Polygon(C_1, D_1, I_1, J_1) → q29, h_6, i_6, j_6, k_6
  280. Polygon(C_1, F_1, E_1, D_1) → q30, l_6, m_6, n_6, p_6
  281. Polygon(I_3, E_3, F_3, J_3) → q31, q_6, r_6, s_6, t_6
  282. Polygon(K_3, G_3, E_3, I_3) → q32, a_6, b_6, c_6, d_6
  283. Polygon(K_3, L_3, H_3, G_3) → q33, e_6, f_7, g_7, h_7
  284. Polygon(J_3, L_3, H_3, F_3) → q34, i_7, j_7, k_7, l_7
  285. Polygon(V_4, C_5, Z_4, T_4) → q35, v_4, m_7, z_4, n_7
  286. Polygon(U_4, A_5, Z_4, T_4) → q36, u_4, p_7, q_7, r_7
  287. Polygon(V_4, C_5, B_5, W_4) → q37, s_7, t_7, a_7, w_4
  288. Polygon(H_5, G_5, D_5, J_5) → q38, b_7, c_7, d_7, e_7
  289. Polygon(K_5, E_5, F_5, I_5) → q39, f_8, g_8, h_8, i_8
  290. Polygon(H_5, I_5, F_5, G_5) → q40, j_8, k_8, l_8, m_8
  291. Polygon(J_5, K_5, E_5, D_5) → q41, n_8, p_8, q_8, r_8
  292. Polygon(B_2, A_2, C_2, U_1) → q42, s_8, t_8, a_8, b_8
  293. Polygon(V_1, W_1, Z_1, D_2) → q43, c_8, d_8, e_8, f_9
  294. Polygon(W_1, B_2, A_2, Z_1) → q44, g_9, h_9, i_9, j_9
  295. Polygon(U_1, C_2, D_2, V_1) → q45, k_9, l_9, m_9, n_9
  296. Polygon(A_1, V, W, Z) → q46, p_9, v_2, w_2, z_3
  297. Polygon(R, Q, T, S) → q47, r_9, q_9, t_9, s_9
  298. Polygon(Z, S, T, W) → q48, z_5, s_{10}, t_{10}, w_3
  299. Polygon(A_1, R, Q, V) → q49, a_9, r_{10}, q_{10}, v_3
  300. Polygon(S_5, L_5, M_5, O_5) → q50, b_9, c_9, d_9, o_5
  301. Polygon(R_5, P_5, N_5, Q_5) → q51, e_9, f_{10}, g_{10}, h_{10}
  302. Polygon(R_5, P_5, L_5, S_5) → q52, i_{10}, j_{10}, k_{10}, l_{10}
  303. Polygon(O_5, Q_5, N_5, M_5) → q53, m_{10}, n_{10}, p_{10}, a_{10}
  304. Polygon(D_4, V_3, W_3, C_4) → q54, b_{10}, c_{10}, d_{10}, e_{10}
  305. Polygon(U_3, V_3, D_4, A_4) → q55, u_3, f_{11}, g_{11}, h_{11}
  306. Polygon(Z_3, B_4, C_4, W_3) → q56, i_{11}, j_{11}, k_{11}, l_{11}
  307. Polygon(Z_3, B_4, A_4, U_3) → q57, m_{11}, n_{11}, p_{11}, q_{11}
  308. Polygon(Q_4, S_4, M_4, L_4) → q58, r_{11}, s_{11}, t_{11}, a_{11}
  309. Polygon(S_4, O_4, P_4, Q_4) → q59, b_{11}, c_{11}, d_{11}, e_{11}
  310. Polygon(N_4, R_4, P_4, O_4) → q60, f_{12}, g_{12}, h_{12}, i_{12}
  311. Polygon(N_4, R_4, L_4, M_4) → q61, j_{12}, k_{12}, l_{12}, m_{12}
  312. Polygon(M_2, Q_2, R_2, N_2) → q62, n_{12}, p_{12}, q_{12}, r_{12}
  313. Polygon(O_2, M_2, Q_2, T_2) → q63, o_2, s_{12}, t_{12}, a_{12}
  314. Polygon(P_2, N_2, R_2, S_2) → q64, b_{12}, c_{12}, d_{12}, e_{12}
  315. Polygon(P_2, O_2, T_2, S_2) → q65, f_{13}, g_{13}, h_{13}, i_{13}
  316. Polygon(C_6, T_5, U_5, B_6) → q66, j_{13}, k_{13}, u_5, l_{13}
  317. Polygon(C_6, Z_5, W_5, T_5) → q67, m_{13}, n_{13}, w_5, p_{13}
  318. Polygon(B_6, A_6, V_5, U_5) → q68, q_{13}, r_{13}, v_5, s_{13}
  319. Polygon(O_6, R_6, Q_6, L_6) → q69, o_6, t_{13}, a_{13}, b_{13}
  320. Polygon(P_6, Q_6, L_6, M_6) → q70, c_{13}, d_{13}, e_{13}, f_{14}
  321. Polygon(N_6, M_6, P_6, S_6) → q71, g_{14}, h_{14}, i_{14}, j_{14}
  322. Polygon(N_6, O_6, R_6, S_6) → q72, k_{14}, l_{14}, m_{14}, n_{14}
  323. Polygon(K_4, O_3, P_3, R_3) → q73, p_{14}, o_3, q_{14}, r_{14}
  324. Polygon(N_3, O_3, K_4, Q_3) → q74, s_{14}, t_{14}, a_{14}, b_{14}
  325. Polygon(M_3, S_3, R_3, P_3) → q75, c_{14}, d_{14}, e_{14}, f_{15}
  326. Polygon(N_3, M_3, S_3, Q_3) → q76, g_{15}, h_{15}, i_{15}, j_{15}
  327. Polygon(E_6, I_6, J_6, D_6) → q77, k_{15}, l_{15}, m_{15}, n_{15}
  328. Polygon(G_6, D_6, J_6, K_6) → q78, p_{15}, q_{15}, r_{15}, s_{15}
  329. Polygon(F_6, H_6, K_6, G_6) → q79, t_{15}, a_{15}, b_{15}, c_{15}
  330. Polygon(W_6, B_7, C_7, T_6) → q80, w_6, d_{15}, e_{15}, f_{16}
  331. Polygon(V_6, W_6, B_7, A_7) → q81, v_6, g_{16}, h_{16}, i_{16}
  332. Polygon(U_6, Z_6, C_7, T_6) → q82, u_6, z_6, j_{16}, k_{16}
  333. Polygon(U_6, V_6, A_7, Z_6) → q83, l_{16}, m_{16}, n_{16}, p_{16}
  334. Polygon(S', Z', W', T') → q84, s', z', w', t'
  335. Polygon(P_1, Q_1, N_1, L_1) → q85, q_{16}, r_{16}, s_{16}, t_{16}
  336. Polygon(M_1, O_1, R_1, S_1) → q86, a_{16}, b_{16}, c_{16}, d_{16}
  337. Polygon(P_1, Q_1, R_1, S_1) → q87, e_{16}, f_{17}, g_{17}, h_{17}
  338. Polygon(L_1, M_1, O_1, N_1) → q88, i_{17}, j_{17}, k_{17}, l_{17}
  339. Mirror(A_1, g_3) → D_7
  340. Polygon(D_7, Z', W', V') → q89, m_{17}, n_{17}, p_{17}, v'
  341. Polygon(Q', V', W', T') → q90, q', q_{17}, r_{17}, s_{17}
  342. Polygon(R', D_7, V', Q') → q91, r', t_{17}, a_{17}, b_{17}
  343. Polygon(R', S', Z', D_7) → q92, c_{17}, d_{17}, e_{17}, f_{18}
  344. Mirror(B_4, g_3) → E_7
  345. Polygon(I_4, E_7, H_4, J_4) → q93, g_{18}, h_{18}, i_{18}, j_{18}
  346. Polygon(J_4, F_4, E_4, H_4) → q94, k_{18}, l_{18}, m_{18}, n_{18}
  347. Polygon(I_4, G_4, T_3, E_7) → q95, p_{18}, q_{18}, r_{18}, s_{18}
  348. Polygon(F_4, G_4, T_3, E_4) → q96, t_{18}, a_{18}, b_{18}, c_{18}
  349. Mirror(W_1, g_3) → F_7
  350. Polygon(B_3, W_2, F_7, C_3) → q97, d_{18}, e_{18}, f_{19}, g_{19}
  351. Polygon(A_3, U_2, W_2, B_3) → q98, h_{19}, u_2, i_{19}, j_{19}
  352. Polygon(A_3, U_2, V_2, Z_2) → q99, k_{19}, l_{19}, m_{19}, n_{19}
  353. Polygon(C_3, Z_2, V_2, F_7) → q100, p_{19}, q_{19}, r_{19}, s_{19}
  354. Polygon(S'_{2}, T'_{2}, W'_{2}, Z'_{2}) → q101, t_{19}, a_{19}, b_{19}, c_{19}
  355. Polygon(R'_{2}, Q'_{2}, T'_{2}, S'_{2}) → q102, d_{19}, e_{19}, f_{20}, g_{20}
  356. Polygon(R'_{2}, K_1, V'_{2}, Q'_{2}) → q103, h_{20}, i_{20}, j_{20}, k_{20}
  357. Polygon(K_1, Z'_{2}, W'_{2}, V'_{2}) → q104, l_{20}, m_{20}, n_{20}, p_{20}
  358. Polygon(T'_{1}, Q'_{1}, R'_{1}, S'_{1}) → q105, q_{20}, r_{20}, s_{20}, t_{20}
  359. Polygon(Z'_{1}, B_1, R'_{1}, S'_{1}) → q106, a_{20}, b_{20}, c_{20}, d_{20}
  360. Polygon(T'_{1}, Q'_{1}, V'_{1}, W'_{1}) → q107, e_{20}, f_{21}, g_{21}, h_{21}
  361. Polygon(Z'_{1}, B_1, V'_{1}, W'_{1}) → q108, i_{21}, j_{21}, k_{21}, l_{21}
  362. Line(M_5, N_5) → m_{21}
  363. Line(L_5, P_5) → n_{21}
  364. Line(S_5, R_5) → p_{21}
  365. Line(O_5, Q_5) → q_{21}
  366. Line(K_1, V'_{2}) → r_{21}
  367. Line(Z'_{2}, W'_{2}) → s_{21}
  368. Line(S'_{2}, T'_{2}) → t_{21}
  369. Line(R'_{2}, Q'_{2}) → a_{21}
  370. Intersect(q_{21}, s_{21}) → G_7
  371. Intersect(s_{21}, m_{21}) → H_7
  372. Intersect(n_{21}, t_{21}) → I_7
  373. Intersect(p_{21}, t_{21}) → J_7
  374. Intersect(q_{21}, r_{21}) → K_7
  375. Intersect(p_{21}, a_{21}) → L_7
  376. Intersect(a_{21}, n_{21}) → M_7
  377. Intersect(r_{21}, m_{21}) → N_7
  378. Polygon(G_7, H_7, I_7, J_7) → q109, b_{21}, c_{21}, d_{21}, e_{21}
  379. Polygon(K_7, N_7, M_7, L_7) → q110, f_{22}, g_{22}, h_{22}, i_{22}
  380. Midpoint(J_1, H_1) → O_7
  381. Mirror(q110, eq1) → q110'
  382. Mirror(q109, eq1) → q109'
  383. Mirror(K_7, eq1) → P_7
  384. Mirror(L_7, eq1) → Q_7
  385. Mirror(M_7, eq1) → R_7
  386. Mirror(N_7, eq1) → S_7
  387. Mirror(G_7, eq1) → T_7
  388. Mirror(J_7, eq1) → U_7
  389. Mirror(I_7, eq1) → V_7
  390. Mirror(H_7, eq1) → W_7
  391. Polygon(L_7, J_7, I_7, M_7) → q111, j_{22}, k_{22}, l_{22}, m_{22}
  392. Polygon(K_7, G_7, H_7, N_7) → q112, n_{22}, p_{22}, q_{22}, r_{22}
  393. Polygon(K_7, G_7, J_7, L_7) → q113, s_{22}, t_{22}, a_{22}, b_{22}
  394. Polygon(M_7, N_7, H_7, I_7) → q114, c_{22}, d_{22}, e_{22}, f_{23}
  395. Polygon(S_7, W_7, V_7, R_7) → q115, g_{23}, w_7, v_7, h_{23}
  396. Polygon(R_7, V_7, U_7, Q_7) → q116, i_{23}, j_{23}, u_7, k_{23}
  397. Polygon(P_7, T_7, U_7, Q_7) → q117, l_{23}, m_{23}, n_{23}, p_{23}
  398. Polygon(S_7, W_7, T_7, P_7) → q118, q_{23}, r_{23}, s_{23}, t_{23}
  399. Mirror(q112, f_3) → q112'
  400. Mirror(q111, f_3) → q111'
  401. Mirror(N_7, f_3) → Z_7
  402. Mirror(K_7, f_3) → A_8
  403. Mirror(H_7, f_3) → B_8
  404. Mirror(G_7, f_3) → C_8
  405. Mirror(M_7, f_3) → D_8
  406. Mirror(I_7, f_3) → E_8
  407. Mirror(J_7, f_3) → F_8
  408. Mirror(L_7, f_3) → G_8
  409. Polygon(D_8, Z_7, A_8, G_8) → q119, a_{23}, z_7, b_{23}, c_{23}
  410. Polygon(F_8, C_8, A_8, G_8) → q120, d_{23}, e_{23}, f_{24}, g_{24}
  411. Polygon(F_8, C_8, B_8, E_8) → q121, h_{24}, i_{24}, j_{24}, k_{24}
  412. Polygon(D_8, E_8, B_8, Z_7) → q122, l_{24}, m_{24}, n_{24}, p_{24}
  413. Mirror(q115, f_3) → q115'
  414. Mirror(q117, f_3) → q117'
  415. Mirror(P_7, f_3) → H_8
  416. Mirror(S_7, f_3) → I_8
  417. Mirror(R_7, f_3) → J_8
  418. Mirror(Q_7, f_3) → K_8
  419. Mirror(W_7, f_3) → L_8
  420. Mirror(T_7, f_3) → M_8
  421. Mirror(U_7, f_3) → N_8
  422. Mirror(V_7, f_3) → O_8
  423. Polygon(N_8, O_8, J_8, K_8) → q123, q_{24}, o_8, r_{24}, s_{24}
  424. Polygon(N_8, O_8, L_8, M_8) → q124, t_{24}, a_{24}, b_{24}, c_{24}
  425. Polygon(K_8, H_8, I_8, J_8) → q125, d_{24}, e_{24}, f_{25}, g_{25}
  426. Polygon(H_8, M_8, L_8, I_8) → q126, h_{25}, i_{25}, j_{25}, k_{25}

AI 绘图提示语参考

绘制一个三维立方体被球体和多个平面切割的动态模型。先定义一个以坐标原点附近某点为球心、半径可变的球体,再构建一个立方体使其与球体相交。创建多个正交平面,使其依次切割立方体的不同边,形成变化的截面多边形。显示球体与坐标轴的交点,以及平面与立方体各边的交点序列。可通过滑动条控制球体半径或平面位置,观察立方体内部截面形状随切割位置变化的动态过程,体现立体几何中截面与函数变换的关系。
以上提示语为根据原始绘图命令整理而来,仅供参考。