三维无人机模型2

三维无人机模型2
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2019-12-13 17:30
①本范例演示了一个三维无人机模型的构建过程;②涉及的核心数学概念包括立体几何、平行四边形、余弦定理、椭圆、积分计算和分布;③作图要点提炼自构造摘要,使用了Circle(圆)、Point(点)、Polygon(多边形)、Rotate(旋转)、Intersect(相交)、Prism(棱柱)、Midpoint(中点)、Pyramid(金字塔)、Cylinder(圆柱)、Ray(射线)、Sphere(球体)、Line(线)、OrthogonalLine(垂线)、Plane(平面)、Mirror(镜像)、Segment(线段)等GeoGebra命令和对象;④适合高中及以上学段学习立体几何、积分计算和三维建模的学生,也可用于数学教学演示。

GeoGebra 命令及参数

  1. Circle(A, sqrt(20), xOyPlane) → d
  2. Point(d) → B
  3. Point(d) → C
  4. Point(d) → D
  5. Point(d) → E
  6. Polygon(B, E, D, C) → q1, b_1, e, d_1, c_1
  7. Rotate(q1, (-α), A) → q1'
  8. Rotate(B, (-α), A) → B'
  9. Rotate(C, (-α), A) → C'
  10. Rotate(E, (-α), A) → E'
  11. Rotate(D, (-α), A) → D'
  12. Circle(B', sqrt(5), xOyPlane) → f
  13. Circle(C', sqrt(5), xOyPlane) → g
  14. Intersect(f, g, 1) → F
  15. Point(zAxis) → G
  16. Prism(q1', k) → l, L, edge5, edge6, edge7, edge8, edgeLM, edgeMN, edgeNO, edgeLO, M, N, O, face5, face7, face8, face6, faceLMNO
  17. Prism(q1', m) → n, P, edge9, edge10, edge11, edge12, edgePQ, edgeQR, edgeRS, edgePS, Q, R, S, face9, face11, face12, face10, facePQRS
  18. Midpoint(B', C') → I
  19. Pyramid(facePQRS, G) → h, faceGPQ, faceGQR, faceGRS, faceGPS, edgeGP, edgeGQ, edgeGR, edgeGS
  20. Circle(I, C', xOyPlane) → p
  21. Cylinder(p, t) → v, e_1, a_1
  22. Cylinder(p, f_1) → g_1, h_1, i_1
  23. Midpoint(D', E') → H
  24. Midpoint(H, A) → J
  25. Midpoint(I, A) → K
  26. Midpoint(edgeGQ) → U
  27. Intersect(edgeRS, edgeGR) → V
  28. Midpoint(edgeGR) → Z
  29. Midpoint(edgeGS) → A_1
  30. Midpoint(edgeGP) → B_1
  31. Polygon(B_1, U, Z, A_1) → q2, i, u_1, z_1, s
  32. Ray(J, Z) → j_1
  33. Point(edge10) → C_1
  34. Polygon(U, C_1, V, Z) → q3, u_2, k_1, v_1, z_2
  35. Sphere(Z, 1) → o
  36. Intersect(j_1, o, 2) → D_1
  37. Line(D_1, k_1) → l_1
  38. Midpoint(A, J) → T
  39. Midpoint(z_1) → W
  40. Midpoint(W, Z) → E_1
  41. Ray(T, E_1) → m_1
  42. Line(D_1, i) → n_1
  43. Intersect(m_1, n_1) → F_1
  44. Line(F_1, l_1) → p_1
  45. Polygon(D_1, F_1, T, J) → q4, q_1, r_1, t_1, j_2
  46. Prism(q4, s_1) → w_1, K_1, edge18, edge20, edge19, edge17, edge21, edge23, edge24, edge22, L_1, M_1, N_1, face16, face17, face15, face14, face18
  47. Line(L_1, p_1) → f_2
  48. Line(K_1, p_1) → g_2
  49. Sphere(F_1, 1) → o_1
  50. Intersect(p_1, o_1, 2) → G_1
  51. Line(G_1, q_1) → h_2
  52. Intersect(h_2, l_1) → H_1
  53. Polygon(D_1, H_1, G_1, F_1) → q5, i_2, k_2, l_2, m_2
  54. Prism(q5, b_2) → c_2, Q_1, edge25, edge28, edge27, edge26, edge29, edge31, edge32, edge30, R_1, S_1, T_1, face20, face22, face21, face19, face23
  55. Midpoint(R_1, G_1) → J_1
  56. Line(J_1, p_1) → n_2
  57. Sphere(J_1, 5) → a_2
  58. Intersect(n_2, a_2) → O_1, P_1
  59. Midpoint(J_1, P_1) → U_1
  60. OrthogonalLine(U_1, q2) → p_2
  61. Sphere(U_1, 0.4) → d_2
  62. Intersect(p_2, d_2, 1) → V_1
  63. Intersect(p_2, d_2, 2) → W_1
  64. Cylinder(V_1, W_1, 2.5) → e_2, q_2, r_2, o_2
  65. Rotate(P_1, (-β), p_2) → Z_1
  66. Rotate(Z_1, 15°, p_2) → A_2
  67. Polygon(A_2, U_1, Z_1) → t1, s_2, t_2, f_3
  68. Sphere(U_1, 2.2) → v_2
  69. Intersect(t_2, v_2, 1) → B_2
  70. Intersect(s_2, v_2) → C_2, H_2
  71. Polygon(B_2, C_2, U_1) → t2, g_3, h_3, i_3
  72. Rotate(t2, -90°, p_2) → t2'
  73. Rotate(t2, 180°, p_2) → t2'_1
  74. Rotate(t2, -270°, p_2) → t2'_2
  75. Line(V_1, n_2) → j_3
  76. Cylinder(V_1, W_1, 0.1) → w_2, c_3, d_3, a_3
  77. Intersect(j_3, face18) → D_2
  78. Point(j_3) → E_2
  79. Intersect(j_3, q4) → F_2
  80. Midpoint(F_2, D_2) → G_2
  81. Midpoint(B_1, A_1) → I_2
  82. Plane(I_2, A, H) → p_3
  83. Mirror(o_2, p_3) → b_3
  84. Mirror(t2'_1, p_3) → t3
  85. Mirror(t2'_2, p_3) → t4
  86. Mirror(t2', p_3) → t2''
  87. Mirror(t2, p_3) → t2'_3
  88. Mirror(a_3, p_3) → e_3
  89. Mirror(d_3, p_3) → q_3
  90. Mirror(c_3, p_3) → r_3
  91. Mirror(r_2, p_3) → k_3
  92. Mirror(q_2, p_3) → s_3
  93. Intersect(j_3, q_2) → J_2,
  94. Point(q_2) → K_2
  95. Point(j_3) → L_2
  96. Midpoint(N_1, M_1) → M_2
  97. Cylinder(M_2, V_1, 0.15) → l_3, t_3, c_4, m_3
  98. Sphere(V_1, 0.2) → n_3
  99. Mirror(m_3, p_3) → o_3
  100. Mirror(n_3, p_3) → u_3
  101. Intersect(edgePS, edgePQ) → N_2
  102. Intersect(edgePS, edge12) → O_2
  103. Segment(O_2, A_1) → f_4
  104. Segment(B_1, N_2) → g_4
  105. Mirror(q4, p_3) → q4'
  106. Mirror(q5, p_3) → q5'
  107. Mirror(R_1, p_3) → P_2
  108. Mirror(Q_1, p_3) → Q_2
  109. Segment(P_2, Q_2) → edge29'
  110. Mirror(K_1, p_3) → R_2
  111. Mirror(N_1, p_3) → S_2
  112. Segment(R_2, S_2) → edge22'
  113. Mirror(face23, p_3) → face23'
  114. Mirror(face18, p_3) → face18'
  115. Mirror(K_1, p_3) → T_2
  116. Mirror(N_1, p_3) → U_2
  117. Segment(T_2, U_2) → edge22'_1
  118. Mirror(face20, p_3) → face20'
  119. Mirror(face14, p_3) → face14'
  120. Mirror(D_1, p_3) → V_2
  121. Mirror(H_1, p_3) → W_2
  122. Segment(V_2, W_2) → h_4
  123. Mirror(Q_1, p_3) → Z_2
  124. Mirror(D_1, p_3) → A_3
  125. Segment(Z_2, A_3) → edge25'
  126. Mirror(R_1, p_3) → B_3
  127. Mirror(Q_1, p_3) → C_3
  128. Segment(B_3, C_3) → edge29'_1
  129. Mirror(K_1, p_3) → D_3
  130. Mirror(N_1, p_3) → E_3
  131. Segment(D_3, E_3) → edge22'_2
  132. Intersect(edgeQR, k_1) → F_3
  133. Midpoint(F_3, O_2) → G_3
  134. Midpoint(G_3, O_2) → H_3
  135. Midpoint(G_3, H_3) → I_3
  136. Midpoint(I_3, H_3) → J_3
  137. OrthogonalLine(J_3, p_3) → i_4
  138. Point(i_4) → K_3
  139. OrthogonalLine(E_3, edgeMN, space) → j_4
  140. Line(K_3, edge8) → k_4
  141. Point(k_4) → L_3
  142. Plane(L_3, J_3, K_3) → p_4
  143. Mirror(o_2, p_4) → v_3
  144. Mirror(r_2, p_4) → d_4
  145. Mirror(F_1, p_4) → M_3
  146. Mirror(T, p_4) → T'
  147. Segment(M_3, T') → l_4
  148. Mirror(t2', p_4) → t2''_1
  149. Mirror(t2'_1, p_4) → t5
  150. Mirror(t2'_2, p_4) → t6
  151. Mirror(t2, p_4) → t2'_4
  152. Mirror(d_3, p_4) → e_4
  153. Mirror(n_3, p_4) → w_3
  154. Mirror(m_3, p_4) → a_4
  155. Mirror(a_3, p_4) → b_4
  156. Mirror(e_3, p_4) → m_4
  157. Mirror(b_3, p_4) → n_4
  158. Mirror(k_3, p_4) → q_4
  159. Mirror(t4, p_4) → t4'
  160. Mirror(t2'_3, p_4) → t7
  161. Mirror(t2'', p_4) → t2'''
  162. Mirror(o_3, p_4) → o_4
  163. Mirror(u_3, p_4) → r_4
  164. Mirror(t3, p_4) → t3'
  165. Mirror(q_3, p_4) → s_4
  166. Mirror(face18, p_4) → face18'_1
  167. Mirror(face23, p_4) → face23'_1
  168. Mirror(R_1, p_4) → N_3
  169. Mirror(Q_1, p_4) → O_3
  170. Segment(N_3, O_3) → edge29'_2
  171. Mirror(K_1, p_4) → P_3
  172. Mirror(N_1, p_4) → Q_3
  173. Segment(P_3, Q_3) → edge22'_3
  174. Mirror(q_2, p_4) → t_4
  175. Mirror(s_3, p_4) → c_5
  176. Mirror(B_3, p_4) → R_3
  177. Mirror(C_3, p_4) → S_3
  178. Mirror(D_3, p_4) → T_3
  179. Mirror(E_3, p_4) → U_3
  180. Mirror(face14, p_4) → face14'_1
  181. Mirror(J, p_3) → J'
  182. Mirror(D_1, p_3) → V_3
  183. Segment(J', V_3) → h_5
  184. Mirror(q4, p_4) → q4'_1
  185. Mirror(q5, p_4) → q5'_1
  186. Mirror(F_1, p_4) → W_3
  187. Mirror(T, p_4) → T'_1
  188. Segment(W_3, T'_1) → i_5
  189. Mirror(G_1, p_4) → Z_3
  190. Mirror(F_1, p_4) → A_4
  191. Segment(Z_3, A_4) → j_5
  192. Mirror(D_1, p_4) → B_4
  193. Mirror(H_1, p_4) → C_4
  194. Segment(B_4, C_4) → k_5
  195. Mirror(J, p_4) → J'_1
  196. Mirror(D_1, p_4) → D_4
  197. Segment(J'_1, D_4) → l_5
  198. Mirror(F_1, p_4) → E_4
  199. Mirror(D_1, p_4) → F_4
  200. Segment(E_4, F_4) → m_5
  201. Mirror(M_1, p_4) → G_4
  202. Mirror(L_1, p_4) → H_4
  203. Segment(G_4, H_4) → edge23'
  204. Mirror(K_1, p_4) → I_4
  205. Mirror(N_1, p_4) → J_4
  206. Segment(I_4, J_4) → edge22'_4
  207. Mirror(B_4, p_3) → K_4
  208. Mirror(C_4, p_3) → L_4
  209. Segment(K_4, L_4) → f_5
  210. Mirror(q5'_1, p_3) → q6
  211. Mirror(W_3, p_3) → M_4
  212. Mirror(T'_1, p_3) → N_4
  213. Segment(M_4, N_4) → g_5
  214. Mirror(J'_1, p_3) → O_4
  215. Mirror(D_4, p_3) → P_4
  216. Segment(O_4, P_4) → n_5
  217. Mirror(E_4, p_3) → Q_4
  218. Mirror(F_4, p_3) → R_4
  219. Segment(Q_4, R_4) → p_5
  220. Mirror(q4'_1, p_3) → q7
  221. Mirror(I_4, p_3) → S_4
  222. Mirror(J_4, p_3) → T_4
  223. Segment(S_4, T_4) → q_5
  224. Mirror(N_3, p_3) → U_4
  225. Mirror(O_3, p_3) → V_4
  226. Segment(U_4, V_4) → r_5
  227. Mirror(face23'_1, p_3) → q8
  228. Mirror(face18'_1, p_3) → q9
  229. Mirror(W_3, p_3) → W_4
  230. Mirror(T'_1, p_3) → Z_4
  231. Segment(W_4, Z_4) → s_5
  232. Mirror(Z_3, p_3) → A_5
  233. Mirror(A_4, p_3) → B_5
  234. Segment(A_5, B_5) → t_5
  235. Mirror(G_4, p_3) → C_5
  236. Mirror(H_4, p_3) → D_5
  237. Segment(C_5, D_5) → edge23''
  238. Mirror(T_1, p_4) → E_5
  239. Mirror(S_1, p_4) → F_5
  240. Segment(E_5, F_5) → edge32'
  241. Mirror(p_4, p_3) → p_6
  242. Mirror(E_5, p_3) → G_5
  243. Mirror(F_5, p_3) → H_5
  244. Segment(G_5, H_5) → edge32''
  245. Mirror(T_1, p_3) → I_5
  246. Mirror(S_1, p_3) → J_5
  247. Segment(I_5, J_5) → edge32'_1
  248. Mirror(M_1, p_3) → K_5
  249. Mirror(L_1, p_3) → L_5
  250. Segment(K_5, L_5) → edge23'_1
  251. Mirror(N_3, p_3) → M_5
  252. Mirror(O_3, p_3) → N_5
  253. Segment(M_5, N_5) → a_5
  254. Mirror(I_4, p_3) → O_5
  255. Mirror(J_4, p_3) → P_5
  256. Segment(O_5, P_5) → b_5
  257. Line(A, T) → d_5
  258. Point(d_5) → Q_5
  259. Prism(face7, v_4) → w_4, W_5, edge33, edge34, edge36, edge35, edge37, edge39, edge40, edge38, Z_5, A_6, B_6, face24, face26, face27, face25, face28
  260. Intersect(edge6, edge35) → S_5
  261. Point(edgeMN) → T_5
  262. Line(Q_5, i) → e_5
  263. Polygon(C_1, S_5, T_5, F_3) → q10, f_6, g_6, h_6, i_6
  264. Pyramid(q10, v_5) → w_5, V_5, face29, face31, face30, face13, edge13, edge15, edge16, edge14
  265. Line(Z, z_1) → j_6
  266. Line(U, i) → k_6
  267. Intersect(j_6, i_5) → C_6
  268. Intersect(k_6, s_5) → U_5
  269. Line(C_6, zAxis) → l_6
  270. Point(l_6) → D_6
  271. Line(D_6, yAxis) → r_6
  272. Intersect(z_2, j_2) → E_6
  273. Line(E_6, l_6) → m_6
  274. Line(U_5, l_6) → n_6
  275. Line(U, l_6) → q_6
  276. Intersect(m_6, r_6) → F_6
  277. Segment(E_6, F_6) → t_6
  278. Segment(C_6, D_6) → b_6
  279. Sphere(F_6, 1) → u_4
  280. Intersect(r_6, u_4, 1) → G_6
  281. Sphere(D_6, 1) → c_6
  282. Intersect(r_6, c_6, 2) → H_6
  283. Segment(G_6, H_6) → s_6
  284. Mirror(G_6, eq1) → I_6
  285. Mirror(H_6, eq1) → J_6
  286. Segment(I_6, J_6) → d_6
  287. Mirror(E_6, eq1) → K_6
  288. Mirror(F_6, eq1) → L_6
  289. Segment(K_6, L_6) → e_6
  290. Mirror(C_6, eq1) → M_6
  291. Mirror(D_6, eq1) → N_6
  292. Segment(M_6, N_6) → f_7

AI 绘图提示语参考

绘制一个3D无人机模型,包含底座、机身、螺旋桨和尾翼。首先画一个圆d,从中选取四个点B、C、D、E,构成一个四边形q1。然后围绕点A旋转q1和点B、C、D、E,生成新的图形q1'、B'、C'、E'、D'。接着画两个以B'、C'为圆心的圆f和g,求交点F。使用z轴上的点G作为顶点,构造一个金字塔h。画一个以I为圆心的圆p,围绕它画两个圆柱v和g_1。构造点H、J、K、U、V、Z、A_1、B_1,使用这些点构造新的图形q2、q3、q4,并围绕它们构造新的棱柱w_1。
以上提示语为根据原始绘图命令整理而来,仅供参考。