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纸艺模型3D演示

纸艺模型3D演示
几何画板及绘图内容加载中，请稍等……
2020-07-17 00:34
向量立体几何几何作图
所属专题 Action Modular Origami
①这个范例演示了从书籍《Action Modular Origami》中折叠的纸艺模型的动画过程；②涉及的核心数学概念包括立体几何、向量运算、几何变换等；③作图要点提炼了OrthogonalLine, Dilate, Intersect, Line, Vector, Translate, Polygon, Midpoint, Rotate, Mirror, Sequence等GeoGebra命令和对象的使用；④适合高中及以上学段学习立体几何、几何作图及空间想象能力的学生。

GeoGebra 命令及参数

  1. OrthogonalLine(OOO, xOyPlane) → s
  2. Dilate(C, ribbonCut, B) → C'_1
  3. Intersect(xAxis, yAxis) → A
  4. Line(B, A) → q
  5. Vector(A, B) → v
  6. Translate(A, u) → D
  7. Polygon(A, D, nSides, xOyPlane) → poly2, f, F, G, H, I, J, g, h, i, j, k, l, m, E
  8. Midpoint(D, H) → OO
  9. Vector(OO, OOO) → w
  10. Rotate(B, rot, OO) → B'
  11. Polygon(A, B, C) → poly1, c, a, b
  12. OrthogonalLine(K, a, xOyPlane) → n
  13. Intersect(n, b) → L
  14. Rotate(L, 180°, A) → L'
  15. Rotate(L', rot, OO) → L''
  16. OrthogonalLine(L', n, xOyPlane) → p
  17. Intersect(p, q) → M
  18. Rotate(M, rot, OO) → M'
  19. Mirror(K, c) → K'
  20. Rotate(K', rot, OO) → K''
  21. Polygon(K'', L'', M', B') → base', k'', l'', m', b'
  22. Polygon(K', L', M, B) → base, k', l', m_1, b_1
  23. Intersect(k', k'') → P
  24. Vector(A, A'') → e
  25. Translate(B, e_2) → B'_2
  26. Translate(B, e_0) → B'_3
  27. Translate(K', e_0) → K''_2
  28. Translate(K', e_2) → K''_1
  29. Translate(C'_1, e_0) → C_1
  30. Translate(C'_1, e_2) → B_1
  31. Dilate(C, topCut, K) → C'
  32. Translate(C', e_0) → C''_1
  33. Translate(C', e_2) → C''
  34. Sequence(Polygon[Rotate[A, (n * rot), OO], Rotate[B, (n * rot), OO], Rotate[C, (n * rot), OO]], n, 0, nSides, 1) → list1
  35. Polygon(A, L, K, B) → ribbon, a_1, l_1, k_1, b_2
  36. OrthogonalLine(N, a, xOyPlane) → r
  37. Intersect(r, b) → O
  38. Polygon(K, L, O, N) → top, k_2, l_2, o, n_1
  39. Sequence(Polygon[Rotate[K', (n * rot), OO], Rotate[L', (n * rot), OO], Rotate[M, (n * rot), OO], Rotate[B, (n * rot), OO]], n, 0, nSides, 1) → list2
  40. Sequence(Polygon[Rotate[A, (n * rot), OO], Rotate[L, (n * rot), OO], Rotate[K, (n * rot), OO], Rotate[B, (n * rot), OO]], n, 0, nSides, 1) → list3
  41. Rotate(A, rot, OO) → A'
  42. Rotate(L, rot, OO) → L'_1
  43. Rotate(K, rot, OO) → K'_1
  44. Rotate(B, rot, OO) → B'_1
  45. Polygon(A', L'_1, K'_1, B'_1) → ribbon', a', l'_1, k'_1, b'_1
  46. Rotate(K, rot, OO) → K'_2
  47. Rotate(L, rot, OO) → L'_2
  48. Rotate(O, rot, OO) → O'
  49. Rotate(N, rot, OO) → N'
  50. Polygon(K'_2, L'_2, O', N') → top', k'_2, l'_2, o', n'
  51. Polygon(B, D, M', L'', A, L, K) → ribbonCut_1, b_3, d, m'_1, l''_1, a_2, l_3, k_3
  52. Polygon(P, L', M, L'') → baseCut, p_1, l'_3, m_2, l''_2
  53. Intersect(b, a_1) → Q
  54. Intersect(m', d) → R
  55. Intersect(b, a_1) → S
  56. Intersect(m', d) → T
  57. Intersect(m', d) → U
  58. Intersect(b, l_2) → V
  59. Intersect(m', d) → W
  60. Intersect(b, l_2) → Z
  61. Intersect(b, m') → A_1
  62. Polygon(B, D, A_1, L, C'_1) → ribbonLong, b_4, d_1, a_3, l_4, c'_1
  63. Translate(Sequence[Polygon[Rotate[B, (n * rot), OO], Rotate[D, (n * rot), OO], Rotate[A_1, (n * rot), OO], Rotate[L, (n * rot), OO], Rotate[C'_1, (n * rot), OO]], n, 0, nSides, 1], w) → listRibbonLong
  64. Rotate(Translate[Sequence[Polygon[Rotate[B, (n * rot), OO], Rotate[D, (n * rot), OO], Rotate[M', (n * rot), OO], Rotate[L'', (n * rot), OO], Rotate[A, (n * rot), OO], Rotate[L, (n * rot), OO], Rotate[K, (n * rot), OO]], n, 0, nSides, 2], w], α, s) → listRibbonCut
  65. Rotate(Translate[Sequence[Polygon[Rotate[K, (n * rot), OO], Rotate[L, (n * rot), OO], Rotate[O, (n * rot), OO], Rotate[N, (n * rot), OO]], n, 0, nSides, 2], w], α, s) → listTop
  66. Rotate(Translate[Translate[Sequence[Polygon[Rotate[P, (n * rot), OO], Rotate[L', (n * rot), OO], Rotate[M, (n * rot), OO], Rotate[L'', (n * rot), OO]], n, 1, nSides, 2], w], Vector[(-3 * e_0)]], α, s) → listBaseCut2
  67. Rotate(Translate[Translate[Sequence[Polygon[Rotate[B, (n * rot), OO], Rotate[D, (n * rot), OO], Rotate[M', (n * rot), OO], Rotate[L'', (n * rot), OO], Rotate[A, (n * rot), OO], Rotate[L, (n * rot), OO], Rotate[K, (n * rot), OO]], n, 1, nSides, 2], Vector[(-e_0)]], w], α, s) → listRibbonCut2
  68. Rotate(Translate[Sequence[Polygon[Rotate[K, (n * rot), OO], Rotate[L, (n * rot), OO], Rotate[O, (n * rot), OO], Rotate[N, (n * rot), OO]], n, 1, nSides, 2], w], α, s) → listTop2
  69. Translate(listTop2, e) → listTop2'
  70. Translate(listTop, e) → listTop'
  71. Polygon(C''_1, C_1, B_1, C'') → SideTop, t, f_1, g_1, h_1
  72. Polygon(B_1, B'_2, B'_3, C_1) → SideRibbon, i_1, j_1, q_1, r_1
  73. Translate(O, e_2) → O'_1
  74. Polygon(O, C', C'', O'_1) → SideCut, o_1, c'_3, c''_1, o'_1
  75. Polygon(B'_2, K''_1, K''_2, B'_3) → SideBase, s_1, t_1, c_1, e_1
  76. Translate(Sequence[Rotate[SideCut, (n * rot), OO], n, 0, nSides, 2], w) → listSideCut
  77. Translate(Sequence[Rotate[SideCut, (n * rot), OO], n, 1, nSides, 2], w) → listSideCut2
  78. Rotate(Translate[Translate[Sequence[Polygon[Rotate[P, (n * rot), OO], Rotate[L', (n * rot), OO], Rotate[M, (n * rot), OO], Rotate[L'', (n * rot), OO]], n, 0, nSides, 2], w], Vector[(-2 * e_0)]], α, s) → listBaseCut
  79. Translate(listRibbonCut2, Vector[e + (2 * e_0)]) → listRibbonCut2'
  80. Rotate(Translate[Sequence[Rotate[SideTop, (n * rot), OO], n, 0, nSides, 2], w], α, s) → listSideTop
  81. Rotate(Translate[Sequence[Rotate[SideTop, (n * rot), OO], n, 1, nSides, 2], w], α, s) → listSideTop2
  82. Rotate(Translate[Sequence[Rotate[SideRibbon, (n * rot), OO], n, 0, nSides, 2], w], α, s) → listSideRibbon
  83. Rotate(Translate[Sequence[Rotate[SideBase, (n * rot), OO], n, 0, nSides, 2], w], α, s) → listSideBase
  84. Rotate(Translate[Sequence[Rotate[SideRibbon, (n * rot), OO], n, 1, nSides, 2], w], α, s) → listSideRibbon2
  85. Rotate(Translate[Sequence[Rotate[SideBase, (n * rot), OO], n, 1, nSides, 2], w], α, s) → listSideBase2
  86. Translate(listRibbonCut, e) → listRibbonCut'
  87. Translate(listBaseCut, Vector[e + (6 * e_0)]) → listBaseCut'
  88. Translate(listBaseCut2, Vector[e + (5 * e_0)]) → listBaseCut2'

AI 绘图提示语参考

绘制一个由纸折叠而成的三维模型动画，展示其展开和折叠的过程。模型基于《Action Modular Origami》一书中的描述，包含多个几何面和边，通过旋转和镜像操作形成。动画展示模型从平面图形逐渐折叠成立体形态，过程中涉及多个几何变换，如平移、旋转和镜像，以及向量运算和几何构造。
以上提示语为根据原始绘图命令整理而来，仅供参考。