滚动桥梁

滚动桥梁
几何画板及绘图内容加载中,请稍等……
2021-12-31 19:16
这个范例演示了一个桥梁的滚动过程。它涉及几何变换和轨迹的概念。通过使用GeoGebra命令如Rotate、Intersect、Polygon等,可以动态展示桥梁的滚动路径。适合高中几何和解析几何课程。

GeoGebra 命令及参数

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. Line(B, yAxis) → k
  4. Line(A, k) → l
  5. Rotate(B, (-α), l) → B'
  6. Line(B', l) → m
  7. Rotate(A, α, m) → A'
  8. Line(A', m) → n
  9. Rotate(B', α, n) → B''
  10. Line(B'', n) → p
  11. Rotate(A', α, p) → A''
  12. Line(A'', p) → q
  13. Rotate(B'', α, q) → B'''
  14. Line(B''', q) → r
  15. Rotate(A'', α, r) → A'''
  16. Line(A''', r) → s
  17. Rotate(B''', α, s) → E
  18. Intersect(k, g) → C
  19. Intersect(l, g) → D
  20. Intersect(m, g) → F
  21. Intersect(n, g) → G
  22. Intersect(p, q) → H
  23. Intersect(r, g) → I
  24. Intersect(p, g) → J
  25. Intersect(q, g) → K
  26. Intersect(s, g) → L
  27. Line(E, s) → h
  28. Intersect(h, g) → M
  29. Polygon(C, B, A, D) → q1, c, b, a, d
  30. Polygon(D, F, B', A) → q2, d_1, f_1, b', a_1
  31. Polygon(F, G, A', B') → q3, f_2, g_1, a', i
  32. Polygon(G, J, B'', A') → q4, g_2, j, b'', t
  33. Polygon(J, K, A'', B'') → q5, j_1, k_1, a'', e
  34. Polygon(K, I, B''', A'') → q6, k_2, i_1, b''', h_1
  35. Polygon(I, L, A''', B''') → q7, i_2, l_1, a''', m_1
  36. Polygon(L, M, E, A''') → q8, l_2, m_2, e_1, n_1
  37. Rotate(A, 67.5°, k) → A'_{1}
  38. Rotate(B, -67.5°, l) → B'_{1}
  39. Ray(A, B'_{1}) → q_1
  40. Rotate(B', 65°, l) → B''_{1}
  41. Ray(A, B''_{1}) → s_1
  42. Rotate(A, 67.5°, m) → A'_{2}
  43. Ray(B', A'_{2}) → t_1
  44. Rotate(A', -67.5°, m) → A''_{1}
  45. Rotate(A', -67.5°, m) → A''_{2}
  46. Rotate(B', 67.5°, n) → B''_{2}
  47. Rotate(B'', -67.5°, n) → B'''_{1}
  48. Ray(B', A''_{2}) → b_1
  49. Ray(A', B''_{2}) → c_1
  50. Ray(A', B'''_{1}) → h_2
  51. Rotate(A', 67.5°, p) → A''_{3}
  52. Ray(B'', A''_{3}) → j_2
  53. Rotate(A'', -67.5°, p) → A'''_{1}
  54. Rotate(B''', -67.5°, q) → R
  55. Rotate(A''', -67.5°, r) → S
  56. Rotate(E, -67.5°, s) → E'
  57. Ray(B'', A'''_{1}) → n_2
  58. Ray(A'', R) → q_2
  59. Ray(B''', S) → s_2
  60. Ray(A''', E') → a_2
  61. Rotate(B'', 67.5°, q) → B'''_{2}
  62. Ray(A'', B'''_{2}) → r_1
  63. Rotate(A'', 67.5°, r) → A'''_{2}
  64. Ray(B''', A'''_{2}) → p_2
  65. Rotate(B''', 67.5°, s) → O
  66. Ray(A''', O) → r_2
  67. Rotate(A''', 67.5°, h) → P
  68. Ray(E, P) → t_2
  69. Ray(B, A'_{1}) → p_1
  70. Sphere(B, sradius) → o
  71. Intersect(p_1, o) → N,
  72. Sphere(A, sradius) → u
  73. Intersect(q_1, u) → Q,
  74. Intersect(s_1, u) → T,
  75. Sphere(B', sradius) → v
  76. Sphere(A', sradius) → w
  77. Sphere(B'', sradius) → o_1
  78. Sphere(A'', sradius) → u_1
  79. Sphere(B''', sradius) → v_1
  80. Sphere(A''', sradius) → w_1
  81. Sphere(E, sradius) → b_2
  82. Intersect(t_1, v) → U,
  83. Intersect(b_1, v) → V,
  84. Intersect(c_1, w) → W,
  85. Intersect(h_2, w) → Z,
  86. Intersect(j_2, o_1) → A_1,
  87. Intersect(n_2, o_1) → B_1,
  88. Intersect(r_1, u_1) → C_1,
  89. Intersect(q_2, u_1) → D_1,
  90. Intersect(p_2, v_1) → E_1,
  91. Intersect(s_2, v_1) → F_1,
  92. Intersect(r_2, w_1) → G_1,
  93. Intersect(a_2, w_1) → H_1,
  94. Intersect(t_2, b_2) → I_1,
  95. Midpoint(H_1, G_1) → J_1
  96. Midpoint(F_1, E_1) → K_1
  97. Midpoint(D_1, C_1) → L_1
  98. Midpoint(B_1, A_1) → M_1
  99. Midpoint(Z, W) → N_1
  100. Midpoint(V, U) → O_1
  101. Midpoint(T, Q) → P_1
  102. Segment(I_1, E) → j_3
  103. Ray(A, P_1) → c_2
  104. Ray(A', N_1) → e_2
  105. Ray(B'', M_1) → f_3
  106. Ray(A'', L_1) → g_3
  107. Ray(B''', K_1) → h_3
  108. Ray(A''', J_1) → i_3
  109. Ray(B', O_1) → d_2
  110. Sphere(P_1, adjustment) → o_2
  111. Intersect(c_2, o_2) → Q_1, R_1
  112. Sphere(O_1, adjustment) → u_2
  113. Sphere(N_1, adjustment) → v_2
  114. Sphere(M_1, adjustment) → w_2
  115. Sphere(L_1, adjustment) → a_3
  116. Sphere(K_1, adjustment) → b_3
  117. Sphere(J_1, adjustment) → c_3
  118. Intersect(d_2, u_2) → S_1, T_1
  119. Intersect(e_2, v_2) → U_1, V_1
  120. Intersect(f_3, w_2) → W_1, Z_1
  121. Intersect(g_3, a_3) → A_2, B_2
  122. Intersect(h_3, b_3) → C_2, D_2
  123. Intersect(i_3, c_3) → E_2, F_2
  124. Segment(R_1, Q) → k_3
  125. Segment(R_1, T) → l_3
  126. Segment(T_1, U) → m_3
  127. Segment(T_1, V) → n_3
  128. Segment(V_1, W) → p_3
  129. Segment(V_1, Z) → q_3
  130. Segment(Z_1, A_1) → r_3
  131. Segment(Z_1, B_1) → s_3
  132. Segment(B_2, C_1) → t_3
  133. Segment(B_2, D_1) → d_3
  134. Segment(D_2, E_1) → e_3
  135. Segment(D_2, F_1) → f_4
  136. Segment(F_2, G_1) → g_4
  137. Segment(F_2, H_1) → h_4
  138. Segment(N, Q) → i_4
  139. Segment(T, U) → j_4
  140. Segment(V, W) → k_4
  141. Segment(Z, A_1) → l_4
  142. Segment(B_1, C_1) → m_4
  143. Segment(D_1, E_1) → n_4
  144. Segment(F_1, G_1) → p_4
  145. Segment(H_1, I_1) → q_4
  146. Segment(H_1, A''') → r_4
  147. Segment(G_1, A''') → s_4
  148. Segment(F_1, B''') → t_4
  149. Segment(B''', E_1) → a_4
  150. Segment(D_1, A'') → b_4
  151. Segment(A'', C_1) → c_4
  152. Segment(B_1, B'') → d_4
  153. Segment(B'', A_1) → e_4
  154. Segment(Z, A') → f_5
  155. Segment(A', W) → g_5
  156. Segment(V, B') → h_5
  157. Segment(B', U) → i_5
  158. Segment(T, A) → j_5
  159. Segment(A, Q) → k_5
  160. Segment(N, B) → l_5
  161. Segment(F_2, A''') → m_5
  162. Segment(D_2, B''') → n_5
  163. Segment(B_2, A'') → p_5
  164. Segment(Z_1, B'') → q_5
  165. Segment(V_1, A') → r_5
  166. Segment(T_1, B') → s_5
  167. Segment(R_1, A) → t_5
  168. Ray(B, N) → b_5
  169. Line(C, B) → c_5
  170. Line(B, N) → a_5
  171. Sphere(N, adjustment) → o_3
  172. Intersect(a_5, o_3) → G_2, H_2
  173. Segment(B, H_2) → d_5
  174. Ray(E, I_1) → e_5
  175. Sphere(I_1, adjustment) → u_3
  176. Intersect(e_5, u_3) → I_2, J_2
  177. Segment(J_2, E) → f_6
  178. Segment(R_1, A) → g_6
  179. Mirror(J_2, h_6) → K_2
  180. Mirror(J_2, h_6) → L_2
  181. Mirror(E, h_6) → E'_{1}
  182. Segment(L_2, E'_{1}) → i_6
  183. Mirror(H_1, h_6) → M_2
  184. Mirror(H_1, h_6) → N_2
  185. Mirror(I_1, h_6) → O_2
  186. Segment(N_2, O_2) → j_6
  187. Mirror(H_1, h_6) → P_2
  188. Mirror(A''', h_6) → Q_2
  189. Segment(P_2, Q_2) → k_6
  190. Mirror(F_2, h_6) → R_2
  191. Mirror(A''', h_6) → S_2
  192. Segment(R_2, S_2) → l_6
  193. Mirror(F_2, h_6) → T_2
  194. Mirror(G_1, h_6) → U_2
  195. Segment(T_2, U_2) → m_6
  196. Mirror(G_1, h_6) → V_2
  197. Mirror(A''', h_6) → W_2
  198. Segment(V_2, W_2) → n_6
  199. Mirror(F_1, h_6) → Z_2
  200. Mirror(G_1, h_6) → A_3
  201. Segment(Z_2, A_3) → p_6
  202. Mirror(D_2, h_6) → B_3
  203. Mirror(F_1, h_6) → C_3
  204. Segment(B_3, C_3) → q_6
  205. Mirror(D_2, h_6) → D_3
  206. Mirror(E_1, h_6) → E_3
  207. Segment(D_3, E_3) → r_6
  208. Mirror(D_2, h_6) → F_3
  209. Mirror(B''', h_6) → G_3
  210. Segment(F_3, G_3) → s_6
  211. Mirror(B''', h_6) → H_3
  212. Mirror(E_1, h_6) → I_3
  213. Segment(H_3, I_3) → t_6
  214. Mirror(D_1, h_6) → J_3
  215. Mirror(E_1, h_6) → K_3
  216. Segment(J_3, K_3) → a_6
  217. Mirror(B_2, h_6) → L_3
  218. Mirror(C_1, h_6) → M_3
  219. Segment(L_3, M_3) → b_6
  220. Mirror(B_2, h_6) → N_3
  221. Mirror(D_1, h_6) → O_3
  222. Segment(N_3, O_3) → c_6
  223. Mirror(B_2, h_6) → P_3
  224. Mirror(A'', h_6) → A'''_{3}
  225. Segment(P_3, A'''_{3}) → d_6
  226. Mirror(A'', h_6) → A'''_{4}
  227. Mirror(C_1, h_6) → Q_3
  228. Segment(A'''_{4}, Q_3) → e_6
  229. Mirror(B_1, h_6) → R_3
  230. Mirror(C_1, h_6) → S_3
  231. Segment(R_3, S_3) → f_7
  232. Mirror(Z_1, h_6) → T_3
  233. Mirror(B_1, h_6) → U_3
  234. Segment(T_3, U_3) → g_7
  235. Mirror(Z_1, h_6) → V_3
  236. Mirror(A_1, h_6) → W_3
  237. Segment(V_3, W_3) → h_7
  238. Mirror(Z_1, h_6) → Z_3
  239. Mirror(B'', h_6) → B'''_{3}
  240. Segment(Z_3, B'''_{3}) → i_7
  241. Mirror(B'', h_6) → B'''_{4}
  242. Mirror(A_1, h_6) → A_4
  243. Segment(B'''_{4}, A_4) → j_7
  244. Mirror(B_1, h_6) → B_4
  245. Mirror(B'', h_6) → B'''_{5}
  246. Segment(B_4, B'''_{5}) → k_7
  247. Mirror(Z, h_6) → Z'
  248. Mirror(A_1, h_6) → C_4
  249. Segment(Z', C_4) → l_7
  250. Mirror(V_1, h_6) → D_4
  251. Mirror(W, h_6) → W'
  252. Segment(D_4, W') → m_7
  253. Mirror(Z, h_6) → Z'_{1}
  254. Mirror(V_1, h_6) → E_4
  255. Mirror(Z, h_6) → Z'_{2}
  256. Segment(E_4, Z'_{2}) → n_7
  257. Mirror(V_1, h_6) → F_4
  258. Mirror(A', h_6) → A''_{4}
  259. Segment(F_4, A''_{4}) → p_7
  260. Mirror(A', h_6) → A''_{5}
  261. Mirror(W, h_6) → W'_{1}
  262. Segment(A''_{5}, W'_{1}) → q_7
  263. Mirror(Z, h_6) → Z'_{3}
  264. Mirror(A', h_6) → A''_{6}
  265. Segment(Z'_{3}, A''_{6}) → r_7
  266. Mirror(A''_{6}, h_6) → G_4
  267. Mirror(V, h_6) → V'
  268. Mirror(B', h_6) → B''_{3}
  269. Segment(V', B''_{3}) → s_7
  270. Mirror(B', h_6) → B''_{4}
  271. Mirror(U, h_6) → U'
  272. Segment(B''_{4}, U') → t_7
  273. Mirror(T_1, h_6) → H_4
  274. Mirror(U, h_6) → U'_{1}
  275. Segment(H_4, U'_{1}) → a_7
  276. Mirror(T_1, h_6) → I_4
  277. Mirror(B', h_6) → B''_{5}
  278. Segment(I_4, B''_{5}) → b_7
  279. Mirror(T_1, h_6) → J_4
  280. Mirror(V, h_6) → V'_{1}
  281. Segment(J_4, V'_{1}) → c_7
  282. Mirror(T, h_6) → T'
  283. Mirror(U, h_6) → U'_{2}
  284. Segment(T', U'_{2}) → d_7
  285. Mirror(R_1, h_6) → K_4
  286. Mirror(Q, h_6) → Q'
  287. Segment(K_4, Q') → e_7
  288. Mirror(T, h_6) → T'_{1}
  289. Mirror(R_1, h_6) → L_4
  290. Mirror(A, h_6) → A'_{3}
  291. Segment(L_4, A'_{3}) → f_8
  292. Mirror(R_1, h_6) → M_4
  293. Mirror(T, h_6) → T'_{2}
  294. Segment(M_4, T'_{2}) → g_8
  295. Mirror(A, h_6) → A'_{4}
  296. Mirror(Q, h_6) → Q'_{1}
  297. Segment(A'_{4}, Q'_{1}) → h_8
  298. Mirror(T, h_6) → T'_{3}
  299. Mirror(A, h_6) → A'_{5}
  300. Segment(T'_{3}, A'_{5}) → i_8
  301. Mirror(B, h_6) → B'_{2}
  302. Mirror(H_2, h_6) → N_4
  303. Segment(B'_{2}, N_4) → j_8
  304. Mirror(N, h_6) → N'
  305. Mirror(Q, h_6) → Q'_{2}
  306. Segment(N', Q'_{2}) → k_8
  307. Mirror(D_1, h_6) → O_4
  308. Mirror(A'', h_6) → A'''_{5}
  309. Segment(O_4, A'''_{5}) → l_8
  310. Mirror(V, h_6) → V'_{2}
  311. Mirror(W, h_6) → W'_{2}
  312. Segment(V'_{2}, W'_{2}) → m_8
  313. Mirror(F_2, h_6) → P_4
  314. Mirror(H_1, h_6) → Q_4
  315. Segment(P_4, Q_4) → n_8
  316. Mirror(F_1, h_6) → R_4
  317. Mirror(B''', h_6) → S_4
  318. Segment(R_4, S_4) → p_8
  319. Polygon(T_4, U_4, V_4, Z_4) → q9, q_8, u_4, v_4, z_4
  320. Prism(q9, -7) → w_3, D_5, edge9, edge10, edge12, edge11, edge13, edge15, edge16, edge14, E_5, F_5, G_5, face6, face8, face9, face7, face10
  321. Mirror(w_3, eq1) → v_3

AI 绘图提示语参考

在坐标平面内先给出一对互相垂直的坐标轴,并取两点分别落在 x 轴上用于确定初始折线方向;通过连接该点与垂直于对应轴的直线,得到多条基准直线。随后围绕相应的交点做连续旋转,逐步生成一串新的顶点与其对应的直线,使前后两段都以固定角度逐次折转。用这些旋转得到的多段直线的两两交点形成一组端点,再用端点依次拼接成多块四边形构成“滚动桥”的轮廓,最后再加上从关键端点出发的附加线段形成延伸结构。
以上提示语为根据原始绘图命令整理而来,仅供参考。