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Collapsoid模型动画

Collapsoid模型动画
几何画板及绘图内容加载中，请稍等……
2020-07-17 00:40
立体几何几何作图
所属专题 Action Modular Origami
①本范例演示了一个从《Action Modular Origami》书中折纸模型（ISBN 9781911093947）的动态折叠过程；②涉及核心数学概念包括特殊点、加法、二次方程、相似三角形和函数；③作图要点提炼自GeoGebra命令：Point（点）、Dodecahedron（十二面体）、Midpoint（中点）、Sphere（球体）、PointIn（点在内部）、Line（线）、OrthogonalPlane（正交平面）、Plane（平面）、Circle（圆）、Center（中心）、Intersect（相交）、OrthogonalLine（正交线）、Rotate（旋转）、Polygon（多边形）、LineBisector（角平分线）、AngularBisector（角平分线）、Sequence（序列）、Vector（向量）、Translate（平移）、Mirror（镜像）；④适合高中及以上学段学习立体几何、几何作图及动画制作。

GeoGebra 命令及参数

  1. Point(Circle[((A * (1 - sqrt(5))) + (B * (3 + sqrt(5)))) / 4, (Distance[A, B] * sqrt(10 + (2 * sqrt(5))) / 4), Segment[A, B]]) → C
  2. Dodecahedron(A, B, C) → a, D, M, N, O, P, Q, R, S, T, faceABCDE, faceAEIOJ, E, faceABFKJ, faceBCGLF, faceCDHMG, faceDEINH, faceINSTO, faceJKPTO, faceFKPQL, faceGLQRM, faceHMRSN, facePQRST, F, edgeAE, edgeAB, edgeBC, edgeCD, edgeDE, edgeAJ, edgeEI, edgeIO, edgeJO, edgeJK, G, edgeFK, edgeBF, edgeFL, edgeGL, edgeCG, edgeGM, edgeHM, edgeDH, edgeHN, edgeIN, H, edgeNS, edgeST, edgeOT, edgePT, edgeKP, edgePQ, edgeLQ, edgeQR, edgeMR, edgeRS, I, J, K, L
  3. Midpoint(A, R) → OOO
  4. Sphere(OOO, Distance[OOO, A]) → b
  5. PointIn(b) → B_3
  6. PointIn(b) → N_2
  7. Line(P, D) → p
  8. OrthogonalPlane(OOO, p) → b_1
  9. PointIn(b_1) → L_1
  10. Plane(L_1, P, OOO) → e_1
  11. Circle(A, B, C) → c
  12. Center(c) → OO
  13. Line(OOO, OO) → f
  14. Intersect(f, b) → U, V
  15. Plane(P, U, D) → q
  16. OrthogonalLine(U, p, q) → h_1
  17. Intersect(p, h_1) → F_1
  18. OrthogonalPlane(F_1, p) → w
  19. Rotate(U, (-2 * β), F_1, w) → U'_1
  20. Polygon(P, OOO, U'_1) → poly7, j_1, k_1, l_1
  21. Rotate(U, (-β), F_1, w) → U'_3
  22. Polygon(U'_3, P, OOO) → poly3, ooo, u'_3, p_1
  23. LineBisector(P, H, q) → t
  24. Circle(OOO, P, q) → s
  25. Intersect(t, s) → C_1, D_1
  26. Polygon(OOO, C_1, U'_3) → poly4, u'_1, ooo_1, c_2
  27. OrthogonalLine(C_1, p, q) → i_1
  28. Intersect(p, i_1) → G_1
  29. OrthogonalPlane(G_1, p) → a_1
  30. Rotate(C_1, ((-3 * fac^(3)) * β), G_1, a_1) → J_1
  31. Polygon(OOO, U'_1, J_1) → poly12, j_2, ooo_8, u'_6
  32. Rotate(C_1, ((-2 * fac^(2)) * β), G_1, a_1) → H_1
  33. Polygon(OOO, H_1, U'_1) → poly10, u'_5, ooo_6, h_2
  34. Rotate(C_1, ((-fac) * β), G_1, a_1) → I_1
  35. Polygon(OOO, U'_1, I_1) → poly6, i_3, ooo_3, u'_4
  36. Polygon(OOO, I_1, U'_3) → poly5, u'_2, ooo_2, i_2
  37. AngularBisector(H, OOO, C_1) → f_1
  38. Intersect(f_1, s) → B_1, E_1
  39. Polygon(OOO, I_1, B_1) → poly9, b_3, ooo_5, i_4
  40. Polygon(OOO, C_1, B_1) → poly8, b_2, ooo_4, c_3
  41. Line(OOO, M_1) → m_1
  42. Rotate(Mirror[I_1, e_1], 180°, m_1) → O_1
  43. Polygon(OOO, H_1, O_1) → poly11, o_1, ooo_7, h_3
  44. Circle(E, I, N) → d
  45. Center(d) → OO'
  46. Plane(N, OO', OOO) → o
  47. Plane(U, Q, L) → n
  48. Point(f) → Z
  49. Polygon(Z, E, OOO) → poly1, h, i, j
  50. Rotate(V, α, OOO, o) → E'
  51. Polygon(E, E', OOO) → poly2, k, l, m
  52. Sequence(Rotate[poly1, ((n * 360) * ° / 5), f], n, 0, 4, 1) → list1
  53. Point(list1) → W
  54. Line(OOO, B) → g
  55. Rotate(list1, 120°, g) → list1'
  56. Sequence(Rotate[list1', ((n * 360) * ° / 5), f], n, 0, 5, 1) → list2
  57. Vector(OO, OOO) → u
  58. Translate(xOyPlane, u) → xOyPlane'
  59. Rotate(Mirror[{list1, list2}, xOyPlane'], 36°, f) → list2'
  60. Sequence(Rotate[poly2, ((n * 360) * ° / 5), f], n, 0, 4, 1) → list01
  61. Plane(O, T, U) → e
  62. Rotate(Z, (-α), OOO, e) → Z'
  63. Rotate(Z, α, OOO, n) → Z'_1
  64. Intersect(l, f) → A_1
  65. Mirror(list01, o) → list01'
  66. OrthogonalLine(R, q) → r
  67. Translate({list01, list01', list1', list2, list2'}, Vector[(0, 0, 0)]) → pos02
  68. Sphere(OOO, P) → v
  69. OrthogonalLine(OOO, p, q) → g_1
  70. Mirror(U, g_1) → U'
  71. Circle(F_1, U, w) → c_1
  72. Circle(G_1, C_1, a_1) → d_1
  73. Rotate(U, (-3 * β), F_1, w) → U'_2
  74. Intersect(t, p) → K_1
  75. Translate({listCollapse, Mirror[listCollapse, e_1]}, Vector[(0, 0, 0)]) → pos04
  76. Rotate(Mirror[H_1, e_1], 180°, m_1) → N_1
  77. Polygon(H_1, OOO, N_1) → poly13, n_1, h_4, ooo_9
  78. Mirror(O_1, e_1) → P_1
  79. Mirror(N_1, e_1) → Q_1
  80. Mirror(I_1, e_1) → R_1
  81. Mirror(H_1, e_1) → S_1
  82. Rotate(Mirror[J_1, e_1], 180°, m_1) → T_1
  83. Rotate(Mirror[C_1, e_1], 180°, m_1) → U_1
  84. Mirror(U_1, e_1) → V_1
  85. Polygon(OOO, P_1, R_1) → poly14, r_1, ooo_{10}, p_2
  86. Rotate(Mirror[U, e_1], 180°, m_1) → W_1
  87. Rotate(Mirror[U'_1, e_1], 180°, m_1) → Z_1
  88. Rotate(Mirror[U'_2, e_1], 180°, m_1) → A_2
  89. Mirror(A_2, e_1) → B_2
  90. Mirror(Z_1, e_1) → C_2
  91. Mirror(W_1, e_1) → D_2
  92. Point(pos04) → E_2
  93. Polygon(V_1, D_2, E_2) → poly15, e_2, v_1, d_2
  94. Polygon(P_1, E_2, D_2) → poly16, d_3, p_3, e_3
  95. Translate(listCollapseFix, Vector[(0, 0, 0)]) → pos04Fix
  96. Translate({list1, list2, list2'}, Vector[(0, 0, 0)]) → pos01
  97. Point(pos01) → F_2
  98. PointIn(b) → G_2
  99. PointIn(b) → H_2
  100. PointIn(b) → I_2
  101. PointIn(b) → J_2
  102. PointIn(b) → K_2
  103. PointIn(b) → L_2
  104. PointIn(b) → M_2
  105. OrthogonalPlane(OOO, p) → q_1
  106. Intersect(g_1, b) → O_2, P_2
  107. Circle(OOO, P_2, q_1) → s_1
  108. PointIn(b) → Q_2
  109. PointIn(b) → R_2
  110. Polygon(OOO, H_2, J_2) → poly17, j_3, ooo_{11}, h_5
  111. Polygon(OOO, K_2, J_2) → poly18, k_2, s_2, t_2
  112. Polygon(G_2, K_2, OOO) → poly19, ooo_{13}, g_2, k_3
  113. Polygon(OOO, L_2, G_2) → poly20, g_3, ooo_{14}, l_2
  114. Polygon(L_2, M_2, OOO) → poly21, ooo_{15}, l_3, m_2
  115. Polygon(B_3, N_2, OOO) → poly23, n_2, p_4, q_4
  116. Polygon(M_2, K_2, OOO) → poly22, ooo_{16}, m_3, k_4
  117. Polygon(N_2, OOO, Q_2) → poly24, a_2, f_3, n_3
  118. OrthogonalLine(OOO, g_1, q_1) → t_1
  119. Intersect(t_1, s_1) → U_2, V_2
  120. Plane(L_2, V_2, OOO) → u_1
  121. Circle(OOO, L_2, u_1) → f_2
  122. Circle(OOO, O_2, e_1) → q_2
  123. Polygon(OOO, G_2, H_2) → poly25, h_7, ooo_{19}, g_4
  124. PointIn(b) → W_2
  125. Polygon(M_2, W_2, OOO) → poly26, ooo_{20}, m_4, w_2
  126. Polygon(W_2, N_2, OOO) → poly27, ooo_{21}, w_1, n_4
  127. Polygon(N_2, R_2, OOO) → poly28, ooo_{22}, n_5, r_2
  128. PointIn(b) → C_3
  129. PointIn(b) → D_3
  130. PointIn(b) → E_3
  131. PointIn(b) → F_3
  132. PointIn(b) → G_3
  133. PointIn(b) → H_3
  134. Intersect(h_5, p) → I_3
  135. Polygon(G_3, OOO, G_2) → poly29, g_5, g_6, ooo_{12}
  136. Intersect(h_5, f_3) → J_3
  137. Polygon(G_3, H_3, OOO) → poly30, ooo_{18}, g_7, h_6
  138. Intersect(f_3, p) → K_3
  139. Polygon(H_3, OOO, L_2) → poly31, l_4, h_8, ooo_{23}
  140. Intersect(h_5, p) → L_3
  141. Polygon(D_3, M_2, OOO) → poly32, q_3, r_3, s_3
  142. Intersect(h_5, p) → M_3
  143. Polygon(D_3, M_2, OOO) → poly33, ooo_{25}, d_5, m_5
  144. Intersect(h_5, f_3) → N_3
  145. Polygon(D_3, E_3, OOO) → poly34, ooo_{26}, d_6, e_4
  146. Intersect(f_3, n_5) → O_3
  147. Polygon(E_3, W_2, OOO) → poly35, ooo_{27}, e_5, w_3
  148. Intersect(h_5, p) → P_3
  149. Polygon(N_2, OOO, I_2) → poly36, t_3, a_3, f_4
  150. Intersect(f_3, p) → Q_3
  151. Intersect(a_3, p) → R_3
  152. Polygon(OOO, I_2, J_2) → poly37, j_4, ooo_{24}, i_5
  153. Intersect(a_3, h_5) → S_3
  154. Polygon(OOO, G_2, C_3) → poly38, c_4, ooo_{28}, g_8
  155. Intersect(h_5, a_3) → T_2
  156. Polygon(OOO, J_2, B_3) → poly39, b_4, ooo_{17}, j_5
  157. Intersect(f_3, p) → Z_2
  158. Intersect(a_3, p) → A_3
  159. Polygon(OOO, B_3, M_2) → poly40, m_6, ooo_{29}, b_5
  160. Polygon(E_3, OOO, R_2) → poly41, r_4, e_6, ooo_{30}
  161. Intersect(q_4, p) → T_3
  162. Polygon(OOO, H_3, D_3) → poly42, s_4, t_4, a_4
  163. PointIn(b) → V_3
  164. PointIn(b) → W_3
  165. PointIn(b) → Z_3
  166. PointIn(b) → A_4
  167. PointIn(b) → B_4
  168. PointIn(b) → C_4
  169. PointIn(b) → D_4
  170. Intersect(m_4, w_3) → E_4
  171. Polygon(V_3, U_3, H_3) → poly43, p_5, q_5, r_5
  172. Polygon(E_3, V_3, U_3) → poly44, d_4, k_5, l_5
  173. Polygon(H_3, F_3, OOO) → poly45, ooo_{31}, h_9, f_5
  174. Polygon(V_3, Z_3, OOO) → poly46, ooo_{32}, v_3, z_3
  175. Polygon(Z_3, W_3, OOO) → poly47, ooo_{33}, z_1, w_4
  176. Polygon(W_3, E_3, OOO) → poly48, ooo_{34}, w_5, e_7
  177. Polygon(J_2, D_4, OOO) → poly49, ooo_{35}, j_6, d_7
  178. Mirror(c_1, q_1) → c_5
  179. Mirror(d_1, q_1) → s_5
  180. OrthogonalPlane(OOO, g_1) → o_2
  181. PointIn(b) → F_4
  182. PointIn(b) → G_4
  183. PointIn(b) → H_4
  184. PointIn(b) → I_4
  185. PointIn(b) → J_4
  186. PointIn(b) → K_4
  187. PointIn(b) → L_4
  188. PointIn(b) → M_4
  189. Intersect(a_3, j_6) → N_4
  190. Polygon(OOO, K_4, D_4) → poly51, d_8, ooo_{37}, k_6
  191. Intersect(a_3, d_8) → O_4
  192. Polygon(OOO, I_2, K_4) → poly52, i_6, a_6, c_6
  193. Intersect(d_8, p) → P_4
  194. Polygon(K_4, Q_2, OOO) → poly54, q_6, f_7, k_7
  195. Intersect(d_8, p) → Q_4
  196. Intersect(d_8, p) → R_4
  197. Polygon(OOO, R_2, M_4) → poly57, m_7, ooo_{43}, r_6
  198. Circle(OOO, V_2, o_2) → t_5
  199. Polygon(OOO, Q_2, M_4) → poly58, m_8, ooo_{44}, q_7
  200. Polygon(OOO, M_4, I_4) → poly59, i_8, ooo_{45}, m_9
  201. Polygon(OOO, I_4, K_4) → poly53, k_8, ooo_{39}, i_7
  202. Polygon(OOO, W_3, M_4) → poly55, m_{10}, ooo_{38}, w_6
  203. Polygon(OOO, F_4, F_3) → poly56, f_6, ooo_{40}, f_8
  204. Polygon(OOO, F_4, V_3) → poly50, v_2, ooo_{36}, f_9
  205. Polygon(OOO, I_4, J_4) → poly60, j_7, ooo_{41}, i_9
  206. Polygon(OOO, G_4, J_4) → poly61, j_8, ooo_{42}, g_9
  207. Polygon(OOO, M_4, G_4) → poly62, g_{10}, ooo_{46}, m_{11}
  208. Polygon(W_3, OOO, H_4) → poly63, h_{10}, w_7, ooo_{47}
  209. Polygon(H_4, G_4, OOO) → poly64, ooo_{48}, h_{11}, g_{11}
  210. Polygon(OOO, J_4, A_4) → poly65, a_5, ooo_{49}, j_9
  211. Polygon(OOO, L_4, G_4) → poly66, g_{12}, ooo_{50}, l_6
  212. Polygon(OOO, L_4, A_4) → poly67, a_7, ooo_{51}, l_7
  213. Rotate(listMiddle, 180°, g_1) → listMiddle'
  214. Translate({listMiddle, listMiddle'}, Vector[(0, 0, 0)]) → pos03
  215. Rotate(pos04, 180°, m_1) → pos04'

AI 绘图提示语参考

绘制一个由纸模型动态折叠过程的动画，展示从书中《Action Modular Origami》的模型。包含一个十二面体，其核心点、中点、球体、线段、平面、圆等几何元素。通过旋转和镜像操作，逐步构建出复杂的折叠结构，体现特殊点、相似三角形和函数的应用，适合高中及以上学习固体几何和几何构造。
以上提示语为根据原始绘图命令整理而来，仅供参考。