积极 AI Logo 积极 AI

三维自行车模型

三维自行车模型
几何画板及绘图内容加载中，请稍等……
2016-05-10 20:51
向量三角函数解析几何立体几何
①本范例演示了如何在三维空间中构建自行车模型，灵感来源于四维框架操作工具；②涉及的核心数学概念包括向量、三角函数、解析几何和立体几何；③作图要点提炼自构造摘要，使用了Line（线）、Vector（向量）、Circle（圆）、Translate（平移）、Rotate（旋转）等GeoGebra命令和对象；④适合高中及以上学生学习和教师教学使用。

GeoGebra 命令及参数

  1. Line(D, yAxis) → i
  2. OrthogonalLine(D, yAxis, space) → b
  3. Intersect(i, b) → S
  4. Circle(I, (0.3 * r), yAxis) → e
  5. Plane(e) → j
  6. Line(I, G) → c
  7. OrthogonalLine(I, c, j) → l
  8. Intersect(l, e) → O, P
  9. Line(I, O) → q_1
  10. Intersect(xAxis, q_1) → T
  11. Vector(T, I) → u_1
  12. Circle(I, r, u_1) → p_2
  13. Vector(S, T) → v
  14. Circle(D, (0.25 * r), zAxis) → h
  15. Intersect(i, h) → B, F
  16. Translate(F, v) → F'_1
  17. Translate(F'_1, u_1) → E_2
  18. Midpoint(I, E_2) → G_2
  19. Circle(D, E, space) → f
  20. Circle(D, (0.8 * r), yAxis) → g
  21. Intersect(xAxis, zAxis) → C
  22. Polygon(F, G, A) → poly1, a_1, f_1, g_1
  23. Polygon(A, H, G) → poly2, g_2, a_2, h_1
  24. Polygon(I, A, G) → poly3, g_3, i_1, a_3
  25. Intersect(i, g_1) → J
  26. Plane(F, G, A) → d
  27. Plane(e) → k
  28. Intersect(c, e) → K, L
  29. AngularBisector(l, c) → m, n
  30. Intersect(m, e) → M, N
  31. Intersect(n, e) → Q, R
  32. Segment(R, Q) → p
  33. Segment(P, O) → q
  34. Segment(M, N) → s
  35. Segment(K, L) → t
  36. Segment(K, L) → b_1
  37. Line(G, q_1) → c_1
  38. Line(I, M) → d_1
  39. Vector(S, A) → u
  40. Segment(B, F) → e_1
  41. Translate(g, v) → g'
  42. Translate(B, u) → B'
  43. Translate(F, u) → F'
  44. Segment(B', F') → j_1
  45. Midpoint(A, F') → U
  46. Midpoint(B', A) → V
  47. Segment(F, U) → k_1
  48. Segment(V, B) → l_1
  49. Plane(A, G, F) → o
  50. Circle(G, (0.3 * r), o) → p_1
  51. Intersect(a_1, p_1) → W, Z
  52. Intersect(c_1, f_1) → A_1
  53. Intersect(c_1, f_1) → B_1
  54. Intersect(c_1, f_1) → C_1
  55. Intersect(c_1, p_1) → D_1, E_1
  56. Rotate(E_1, 45°, G, o) → F_1
  57. Rotate(F_1, 45°, G, o) → G_1
  58. Rotate(D_1, 45°, G, o) → H_1
  59. Rotate(H_1, 45°, G, o) → I_1
  60. Rotate(I_1, 45°, G, o) → J_1
  61. Segment(F_1, H_1) → m_1
  62. Segment(E_1, D_1) → n_1
  63. Segment(G_1, G) → r_1
  64. Segment(J_1, Z) → s_1
  65. Translate(B, v) → B'_1
  66. Segment(B'_1, F'_1) → b_2
  67. Segment(I, B'_1) → t_1
  68. Segment(I, F'_1) → c_2
  69. Plane(B'_1, I, K) → w
  70. Circle(I, (0.3 * r), w) → d_2
  71. Point(t) → K_1
  72. Point(t) → L_1
  73. Intersect(t_1, d_2) → O_1,
  74. Intersect(a_3, d_2) → P_1, Q_1
  75. Rotate(O_1, (-(45°)), I, w) → R_1
  76. Rotate(Q_1, (-(45°)), I, w) → S_1
  77. Rotate(S_1, (-(45°)), I, w) → T_1
  78. Rotate(T_1, (-(45°)), I, w) → U_1
  79. Rotate(U_1, (-(45°)), I, w) → V_1
  80. Rotate(V_1, (-(45°)), I, w) → W_1
  81. Segment(W_1, S_1) → e_2
  82. Segment(T_1, O_1) → f_2
  83. Segment(U_1, I) → h_2
  84. Segment(V_1, Q_1) → i_2
  85. Plane(F'_1, I, K) → o_1
  86. Circle(I, (0.3 * r), o_1) → k_2
  87. Rotate(K, 45°, I, o_1) → K'
  88. Rotate(K', 45°, I, o_1) → K''
  89. Rotate(K'', 45°, I, o_1) → K'''
  90. Rotate(K''', 45°, I, o_1) → Z_1
  91. Rotate(Z_1, 45°, I, o_1) → A_2
  92. Rotate(A_2, 45°, I, o_1) → B_2
  93. Rotate(B_2, 45°, I, o_1) → C_2
  94. Segment(C_2, K''') → j_2
  95. Segment(I, A_2) → l_2
  96. Segment(B_2, K'') → m_2
  97. Translate(B'_1, u_1) → D_2
  98. Segment(D_2, E_2) → n_2
  99. Midpoint(n_2) → F_2
  100. Intersect(i_2, j_2) → I_2
  101. Mirror(G_2, a_3) → M_2
  102. Segment(E_2, I) → q_2
  103. Segment(I, D_2) → r_2
  104. Mirror(G, i_2) → G'
  105. Mirror(I, i_2) → I'
  106. Segment(G', I') → b_3
  107. Point(zAxis) → R_2
  108. Sphere(R_2, (0.8 * r)) → v_1
  109. Intersect(zAxis, v_1) → S_2, T_2
  110. OrthogonalPlane(S_2, zAxis) → w_1
  111. Ray(E, S) → d_3
  112. Intersect(d_3, g) → U_2, V_2
  113. Segment(U_2, E) → e_3
  114. Rotate(U_2, 45°, e_1) → W_2
  115. Rotate(E, 45°, e_1) → E'
  116. Segment(W_2, E') → f_3
  117. Rotate(W_2, 45°, e_1) → Z_2
  118. Rotate(E', 45°, e_1) → E''
  119. Segment(Z_2, E'') → h_3
  120. Rotate(Z_2, 45°, e_1) → A_3
  121. Rotate(E'', 45°, e_1) → E'''
  122. Segment(A_3, E''') → i_3
  123. Translate(U_2, v) → B_3
  124. Translate(E, v) → E'_1
  125. Segment(B_3, E'_1) → j_3
  126. Translate(W_2, v) → C_3
  127. Translate(E', v) → E''_1
  128. Segment(C_3, E''_1) → k_3
  129. Translate(Z_2, v) → D_3
  130. Translate(E'', v) → E'''_1
  131. Segment(D_3, E'''_1) → l_3
  132. Translate(A_3, v) → E_3
  133. Translate(E''', v) → F_3
  134. Segment(E_3, F_3) → m_3
  135. Cylinder(g, (-((0.08 * r)))) → o_2, p_3, u_2
  136. Cylinder(g, (-((-0.08 * r)))) → v_2, q_3, w_2
  137. Cylinder(g', (-((0.08 * r)))) → n_3, r_3, o_3
  138. Cylinder(g', (0.08 * r)) → s_3, t_3, u_3
  139. Plane(B, G, A) → v_3
  140. Circle(G, (0.3 * r), v_3) → c_4
  141. Intersect(f_1, h_1) → G_3
  142. Intersect(n_1, c_4) → H_3, I_3
  143. Rotate(H_3, 45°, G, v_3) → J_3
  144. Rotate(J_3, 45°, G, v_3) → K_3
  145. Rotate(K_3, 45°, G, v_3) → L_3
  146. Rotate(I_3, 45°, G, v_3) → M_3
  147. Rotate(M_3, 45°, G, v_3) → N_3
  148. Rotate(N_3, 45°, G, v_3) → O_3
  149. Segment(M_3, J_3) → a_4
  150. Segment(G, K_3) → b_4
  151. Segment(O_3, L_3) → d_4
  152. Mirror(G, E_1) → G'_1
  153. Midpoint(G'_1, E_1) → P_3
  154. Segment(P_3, G) → e_4
  155. OrthogonalPlane(P_3, e_4) → w_3
  156. Circle(P_3, (0.4 * r), w_3) → f_4
  157. Line(P_3, a_3) → g_4
  158. Intersect(g_4, f_4, 1) → Q_3
  159. Mirror(Q_3, P_3) → R_3
  160. Rotate(R_3, (-(60°)), P_3, w_3) → S_3
  161. Mirror(S_3, g_4) → T_3
  162. CircleSector(Q_3, S_3, T_3, w_3) → h_4
  163. Line(D_2, E_2) → s_2
  164. Intersect(s_2, p_2) → M_1, N_1
  165. Rotate(N_1, 30°, D_2, p_2) → H_2
  166. Ray(D_2, H_2) → t_2
  167. Intersect(t_2, p_2) → J_2,
  168. Segment(J_2, D_2) → c_3
  169. Mirror(J_2, b_3) → K_2
  170. Mirror(D_2, b_3) → L_2
  171. Segment(K_2, L_2) → i_4
  172. Circle(A, (0.3 * r), j_1) → k_4
  173. Intersect(f_1, k_4) → N_2, O_2
  174. Rotate(O_2, (-(45°)), A, k_4) → P_2
  175. Rotate(P_2, (-(45°)), A, k_4) → U_3
  176. Rotate(U_3, (-(45°)), A, k_4) → Q_2
  177. Rotate(Q_2, (-(45°)), A, k_4) → V_3
  178. Rotate(V_3, (-(45°)), A, k_4) → W_3
  179. Rotate(W_3, (-(45°)), A, k_4) → Z_3
  180. Rotate(Z_3, (-(45°)), A, k_4) → A_4
  181. Segment(A_4, Q_2) → j_4
  182. Segment(O_2, V_3) → l_4
  183. Segment(U_3, Z_3) → m_4
  184. Segment(P_2, W_3) → n_4
  185. Segment(V, U) → p_4

AI 绘图提示语参考

在三维空间中绘制一个自行车模型，包含多个圆柱体、球体和长方体，通过旋转和平移操作组合成车架、车轮和车座等部件。先绘制基本几何体，再通过直线和圆的相交确定关键点，最后用多边形和线段连接各部件，形成完整的自行车结构。
以上提示语为根据原始绘图命令整理而来，仅供参考。