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3D Bike Model

3D Bike Model
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2016-05-10 20:51
VectorTrigonometryCoordinate GeometrySolid Geometry
This example demonstrates the construction of a bike model in three-dimensional space, inspired by the 4D Frame manipulative. It involves core math concepts like vectors, trigonometry, coordinate geometry, and solid geometry. Construction highlights include commands like Line, Vector, Circle, Translate, and Rotate from GeoGebra. Suitable for high school students and educators.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Draw a 3D bike model in space, combining cylinders, spheres, and cuboids through rotation and translation to form the frame, wheels, and seat. Start by creating basic shapes, then determine key points by intersecting lines and circles, and finally connect the parts with polygons and lines to complete the bike structure.
The prompt above was compiled from the original drawing commands and is for reference only.