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Paper Model Animation

Paper Model Animation
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2020-07-17 00:31
PolygonVectorSolid GeometryTransformationGeometric Construction
In collections Action Modular Origami
This example demonstrates the transformation of a paper model from the book 'Action Modular Origami' into a dynamic 3D model using GeoGebra. It involves core mathematical concepts such as solid geometry, vector operations, transformations, and polygon construction. Key GeoGebra commands and objects used in the construction include Line, OrthogonalPlane, Vector, Plane, Rotate, Translate, Midpoint, Dilate, Polygon, OrthogonalLine, Intersect, and Angle. It is suitable for high school students and mathematics enthusiasts to understand the principles of spatial geometry and dynamic transformations, serving as an example for teaching applications of solid geometry and vectors.

GeoGebra Commands & Parameters

  1. Line(A, B) → lx
  2. OrthogonalPlane(B, lx) → xx
  3. Vector(B, A) → u
  4. Plane(A, B, Bkeep) → zz
  5. Rotate(A, (-(90°)), B, zz) → C
  6. Translate(C, u) → D
  7. Rotate(B, (-(90°)), C, xx) → G
  8. Translate(G, u) → H
  9. Rotate(C, 90°, B, xx) → F
  10. Translate(F, u) → E
  11. Midpoint(C, G) → CG
  12. Midpoint(H, G) → GH
  13. Midpoint(F, G) → FG
  14. Midpoint(A, B) → AB
  15. Midpoint(A, E) → AE
  16. Midpoint(A, D) → AD
  17. Midpoint(B, F) → BF
  18. Midpoint(A, G) → O
  19. Dilate(GH, b, O) → GH'
  20. Dilate(AD, b, O) → AD'
  21. Dilate(BF, b, O) → BF'
  22. Midpoint(D, H) → DH
  23. Dilate(DH, b, O) → DH'
  24. Midpoint(E, H) → EH
  25. Midpoint(C, D) → CD
  26. Midpoint(B, C) → BC
  27. Dilate(BC, b, O) → BC'
  28. Midpoint(E, F) → EF
  29. Dilate(EF, b, O) → EF'
  30. Dilate(CD, b, O) → CD'
  31. Dilate(AE, b, O) → AE'
  32. Dilate(FG, b, O) → FG'
  33. Dilate(EH, b, O) → EH'
  34. Dilate(CG, b, O) → CG'
  35. Dilate(AB, b, O) → AB'
  36. Polygon(AE, BF, CG, DH) → poly1, i, j, k, l
  37. Polygon(AE', EF, FG', CG, CD', AD) → poly2, t, a_1, b_1, c_1, d_1, e_1
  38. Polygon(EH, EF', BF, BC', CD, DH') → poly4, f_1, g_1, h_1, i_1, j_1, k_1
  39. Polygon(GH', FG, BF', AB, AD', DH) → poly5, h, m, n, p, q, r
  40. Polygon(AB, EF, GH, CD) → poly1', i', j', k', l'
  41. Polygon(EH', GH, CG', BC, AB', AE) → poly3, c, d, e, f, g, s
  42. Polygon(AD, BC, FG, EH) → poly1'_1, i'_1, j'_1, k'_1, l'_1
  43. OrthogonalLine(A, zz) → lz
  44. Plane(A, B, F) → yy
  45. OrthogonalLine(A, yy) → l_1
  46. Line(O, lz) → lzz
  47. Line(O, lx) → lxx
  48. Line(O, l_1) → lyy
  49. Rotate(GH, α, lzz) → GH'_1
  50. Rotate(FG, α, lzz) → FG'_1
  51. Rotate(EF, α, lzz) → EF'_1
  52. Rotate(EH, α, lzz) → EH'_1
  53. Polygon(GH', EH'_1, O) → poly6, o, gh', eh'_1
  54. Polygon(FG', GH'_1, O) → poly7, o_1, fg', gh'_1
  55. Polygon(EF', FG'_1, O) → poly8, o_2, ef', fg'_1
  56. Intersect(lyy, lzz) → I
  57. Polygon(EH', EF'_1, O) → poly9, o_3, eh', ef'_1
  58. Rotate(poly9, β, fg'_1) → poly9'
  59. Rotate(poly6, β, ef'_1) → poly6'
  60. Rotate(poly7, β, eh'_1) → poly7'
  61. Rotate(poly8, β, gh'_1) → poly8'
  62. Rotate(poly9, β, ef'_1) → poly9'_1
  63. Rotate(poly6, β, eh'_1) → poly6'_1
  64. Rotate(poly7, β, gh'_1) → poly7'_1
  65. Rotate(poly8, β, fg'_1) → poly8'_1
  66. Rotate(poly7, β, eh'_1) → poly7'_2
  67. Line(AE', CG') → a
  68. Line(DH', BF') → m_1
  69. Rotate(poly6', (-β), a) → poly6''
  70. Rotate(poly6'_1, β, a) → poly10
  71. Rotate(poly9'_1, β, m_1) → poly11
  72. Rotate(poly8', β, a) → poly8''
  73. Rotate(poly9', β, m_1) → poly9''
  74. OrthogonalLine(O, zz) → n_1
  75. Rotate(poly7', (-β), m_1) → poly7''
  76. Rotate(poly7'_1, β, m_1) → poly12
  77. Rotate(poly8'_1, (-β), a) → poly13
  78. Line(O, CD') → p_1
  79. Line(O, EH') → q_1
  80. Rotate(poly9'', (-β), q_1) → poly9'''
  81. Line(O, GH') → r_1
  82. Rotate(poly6'', (-β), r_1) → poly6'''
  83. Rotate(poly12, (-β), r_1) → poly12'
  84. Line(AD', O) → s_1
  85. Rotate(poly13, (-β), s_1) → poly13'
  86. Angle(O, EF', FG'_1, poly8'_1) → γ
  87. Rotate({poly10, poly6, poly6', poly6'', poly6''', poly6'_1}, spin, zAxis) → list1
  88. Rotate({poly11, poly9, poly9', poly9'', poly9''', poly9'_1}, spin, zAxis) → list2
  89. Rotate({poly13, poly13', poly8', poly8'', poly8, poly8'_1}, spin, zAxis) → list4
  90. Rotate({poly12, poly12', poly7, poly7', poly7'_2, poly7'_1, poly7''}, spin, zAxis) → list3

AI Drawing Prompt Reference

Draw a 3D origami-like geometric model composed of multiple triangular and quadrilateral faces, forming a symmetric polyhedral structure. Start with two base points, rotate one around the other in a perpendicular plane to create a new vertex, then translate it along the initial vector to get its counterpart. Repeat rotations and translations to generate a set of vertices. Connect these vertices to form polygons, including quadrilaterals and triangles. Take midpoints of edges, then dilate these midpoint segments toward the model's center by a scale factor to create inward crease effects. Finally, draw three reference lines from the center along orthogonal directions to indicate spatial orientation.
The prompt above was compiled from the original drawing commands and is for reference only.