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3D Drone Model 2

3D Drone Model 2
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2019-12-13 17:30
TrigonometryCoordinate GeometrySolid GeometryCalculusGeometric Construction
This example demonstrates the construction of a 3D drone model. It involves core mathematical concepts such as solid geometry, parallelogram, cosine theorem, ellipse, integral calculus, and distributions. The construction utilizes GeoGebra commands and objects like Circle, Point, Polygon, Rotate, Intersect, Prism, Midpoint, Pyramid, Cylinder, Ray, Sphere, Line, OrthogonalLine, Plane, Mirror, and Segment. It is suitable for high school and above students studying solid geometry, integral calculus, and 3D modeling, as well as for mathematical teaching demonstrations.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Draw a 3D drone model with a base, body, propellers, and tail. Start by drawing a circle d and selecting four points B, C, D, E to form a quadrilateral q1. Then rotate q1 and points B, C, D, E around point A to generate new shapes q1', B', C', E', D'. Next, draw two circles f and g with centers at B' and C', and find their intersection point F. Use point G on the z-axis as the apex to construct a pyramid h. Draw two cylinders v and g_1 with circle p as the base. Construct points H, J, K, U, V, Z, A_1, B_1, and use them to form new shapes q2, q3, q4, and a new prism w_1.
The prompt above was compiled from the original drawing commands and is for reference only.