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Fluxicube Animation

Fluxicube Animation
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2020-07-17 00:29
VectorSolid GeometryGeometric Construction
This example demonstrates the dynamic folding process of the paper model 'Fluxicube' from the book 'Action Modular Origami'. It involves core mathematical concepts like vectors, geometric transformations, solid geometry, and parametric animations. GeoGebra commands and objects such as If, Vector, Point, Translate, Line, Cube, Rotate, Plane, Angle, OrthogonalLine, Intersect, PointIn, Polygon, Circle, Center, Mirror, Midpoint, Segment, and Dilate are used in the construction. Suitable for high school students and math enthusiasts studying spatial geometry and dynamic transformations.

GeoGebra Commands & Parameters

  1. If(clock0 ≥ 1 ∧ clock0 < 2 ∨ clock0 ≥ 3 ∧ clock0 < 5, 1 - fractionalPart(clock0), fractionalPart(clock0)) → clock
  2. If(clock ≤ 1, 1, If[clock > 1 ∧ clock ≤ 2, 1 - (clock - 1) / 2, If[clock > 2 ∧ clock ≤ 3, 0.5, 0.5]]) → clock3_1
  3. Vector((cos((180° * clock3_1)), 0, 0)) → vShift
  4. If(clock ≤ 1, clock, 1) → clock1_1
  5. Vector((0, 0, clock1_1)) → vLift
  6. If(clock ≤ 1, 0, If[clock > 1 ∧ clock ≤ 3, (clock - 1) / 2, 1]) → clock3
  7. If(clock ≤ 1, 90° + (30° * (1 - clock)^(0.29)), 120°) → γ
  8. Point(yAxis) → A
  9. Translate(A, vLift) → A'
  10. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  11. Translate(C, vShift) → C'
  12. Line(C', ZZZ) → g_1
  13. Cube(A, B, C) → a, D, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH, edgeEH, edgeEF, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  14. Line(A, D) → g
  15. Rotate(Translate[C, vLift], (-α), g) → C''
  16. Line(C, D) → f
  17. Plane(C, G, H) → b
  18. Translate(Rotate[Mirror[F, b], asin(clock1_1), f], vLift) → J
  19. Translate(Rotate[Mirror[B, b], asin(clock1_1), f], vLift) → K
  20. Line(K, J) → h
  21. Translate(Rotate[Mirror[A, b], asin(clock1_1), f], vLift) → M
  22. Angle(A, M, A') → δ
  23. Rotate(M, (-γ), h) → M'
  24. Line(K, M) → r
  25. Rotate(M', (-δ), r) → M''
  26. OrthogonalLine(M'', xOyPlane) → h_1
  27. Plane(M'', b) → o
  28. Intersect(g_1, o) → W
  29. OrthogonalLine(W, h_1, o) → i_1
  30. Intersect(h_1, i_1) → A_1
  31. Angle(M'', W, A_1, o) → η
  32. Rotate(Rotate[Rotate[Translate[F, vLift], (-α), g], (-δ), r], η, g_1) → Z_1
  33. Rotate(Rotate[Rotate[Translate[B, vLift], (-α), g], (-δ), r], η, g_1) → N_1
  34. Line(Z_1, N_1) → b_1
  35. Rotate(Rotate[C'', (-δ), r], η, g_1) → K_1
  36. Plane(K_1, xOyPlane) → a_1
  37. PointIn(a_1) → I_2
  38. Intersect(b_1, a_1) → C_2
  39. Polygon(K_1, C_2, 3, a_1) → poly5, l_2, m_2, n_2, E_2
  40. Polygon(K_1, E_2, 3, a_1) → poly6, p_2, q_2, r_2, F_2
  41. Circle(K_1, F_2, E_2) → c_2
  42. Center(c_2) → G_2
  43. Rotate(Translate[D, vLift], (-α), g) → D''
  44. Rotate(Rotate[D'', (-δ), r], η, g_1) → L_1
  45. OrthogonalLine(L_1, xOyPlane) → t_1
  46. Intersect(t_1, xOyPlane) → B_2
  47. Circle(F_1, H_1, G_1) → e_1
  48. Point(e_1) → A_2
  49. Rotate(Rotate[Rotate[Translate[A, vLift], (-α), g], (-δ), r], η, g_1) → M_1
  50. OrthogonalLine(K_1, xOyPlane) → n_1
  51. Intersect(n_1, xOyPlane) → P_1
  52. OrthogonalLine(N_1, xOyPlane) → m_1
  53. Intersect(m_1, xOyPlane) → O_1
  54. Vector(O_1, P_1) → u_1
  55. Translate(P_1, u_1) → R_1
  56. Polygon(R_1, O_1, 3, xOyPlane) → poly3, p_1, q_1, r_1, S_1
  57. Circle(R_1, O_1, S_1) → s_1
  58. Center(s_1) → T_1
  59. Translate(Rotate[Mirror[H, b], asin(clock1_1), f], vLift) → L
  60. Rotate(L, (-γ) - 90°, h) → L'_1
  61. Translate(Rotate[Mirror[E, b], asin(clock1_1), f], vLift) → E'''
  62. Rotate(E''', (-γ), h) → N
  63. Vector(N, P) → u
  64. Translate(L'_1, u) → Q
  65. Vector(N, L'_1) → v
  66. Translate(K, v) → K'
  67. OrthogonalLine(K', xOyPlane) → j_1
  68. Intersect(j_1, xOyPlane) → B_1
  69. Translate(F, vLift) → F'
  70. Translate(B, vLift) → B'
  71. Plane(F', B', Q) → i
  72. Mirror(C'', i) → C'''
  73. OrthogonalLine(C''', xOyPlane) → k_1
  74. Intersect(k_1, xOyPlane) → C_1
  75. Circle(B_1, C, C_1) → d_1
  76. Center(d_1) → OOO
  77. Rotate(OOO, η, g_1) → OOO'
  78. OrthogonalLine(OOO', xOyPlane) → l_1
  79. Intersect(l_1, xOyPlane) → E_1
  80. If(clock < 3, 0, clock - 3) → clock4
  81. Vector((0, 0, (2 * clock4))) → vLift4
  82. Translate({faceABCD, faceABFE, faceADHE, faceBCGF, faceCDHG, faceEFGH}, Vector[(0, 0, 0)]) → listCube1
  83. Mirror(listCube1, b) → listCube2'
  84. Translate(Rotate[listCube2', asin(clock1_1), f], vLift) → listCube2''
  85. Translate(listCube1, vLift) → listCube1'_1
  86. Translate(g, vLift) → g'
  87. Rotate(g', (-α), g) → g''
  88. Translate(f, vLift) → f'
  89. Rotate(f', (-α), g) → f''
  90. Translate(f'', vLift4) → f'''
  91. If(x(C'') > x(D''), x(C''), x(D'')) → xMax
  92. Plane(E, A, H) → c
  93. Midpoint(E, H) → I
  94. Plane(I, b) → d
  95. Translate(D, vLift) → D'
  96. Translate(E, vLift) → E'
  97. Translate(G, vLift) → G'
  98. Translate(H, vLift) → H'
  99. Translate(I, vLift) → I'
  100. Plane(E''', J, K) → e
  101. Mirror(listCube2'', e) → listCube2'''
  102. Rotate(listCube2''', (-γ), h) → listCube3
  103. Translate(Rotate[Mirror[G, b], asin(clock1_1), f], vLift) → O
  104. Translate(J, v) → J'
  105. Mirror(listCube1'_1, i) → list1
  106. Mirror(listCube2'', i) → listCube2'''_1
  107. Mirror(listCube3, i) → listCube3'
  108. Plane(A', M, M') → j
  109. Plane(Q, M', N) → k
  110. Vector(ZZZ) → vShift4
  111. Translate(j, vShift4) → j'
  112. OrthogonalLine(A', j) → l
  113. OrthogonalLine(D'', j) → m
  114. Intersect(m, j) → R
  115. Intersect(l, xOyPlane) → S
  116. Intersect(m, xOyPlane) → T
  117. OrthogonalLine(M', xOyPlane) → n
  118. Intersect(n, xOyPlane) → U
  119. Segment(M', S) → p
  120. Segment(A', M) → q
  121. Rotate({list1, listCube1'_1, listCube2'', listCube2'''_1, listCube3, listCube3'}, (-δ), r) → listAllCubes
  122. Polygon(K, B, 3, xOyPlane) → poly1, s, t, f_1, V
  123. Angle(A', V, A) → ε
  124. Angle(C', Q, C'') → ζ
  125. Intersect(h_1, xAxis) → Z
  126. Rotate(listAllCubes, η, g_1) → listAllCubes'
  127. Circle(J, V, B) → c_1
  128. Vector(B_2, A_2) → w
  129. Intersect(l_1, xOyPlane) → D_1
  130. Polygon(F_1, G_1, H_1) → poly2, h_2, f_2, g_2
  131. Center(e_1) → I_1
  132. Rotate(poly2, 180°, A) → poly2'
  133. Rotate(Rotate[A, (-δ), r], η, g_1) → J_1
  134. Dilate(N_1, 2, K_1) → Q_1
  135. Rotate(Rotate[Rotate[Translate[E, vLift], (-α), g], (-δ), r], η, g_1) → U_1
  136. Rotate(Rotate[Rotate[Translate[H, vLift], (-α), g], (-δ), r], η, g_1) → V_1
  137. Rotate(Rotate[Rotate[Translate[G, vLift], (-α), g], (-δ), r], η, g_1) → W_1
  138. Polygon(K_1, N_1, 3, a_1) → poly4, i_2, j_2, k_2, D_2
  139. OrthogonalLine(M_1, xOyPlane) → s_2
  140. Intersect(s_2, a_1) → H_2
  141. Vector(G_2, I_2) → v_1
  142. Translate(listAllCubes', v_1) → pos3
  143. OrthogonalLine(I_2, xOyPlane) → t_2
  144. Rotate(pos3, 180°, t_2) → pos1
  145. Plane(W_1, xOyPlane) → o_1
  146. OrthogonalLine(W_1, o_1) → a_2
  147. Intersect(a_2, xOyPlane) → J_2
  148. Midpoint(W_1, J_2) → K_2
  149. Plane(K_2, xOyPlane) → w_1
  150. Rotate(Mirror[pos1, w_1], 180°, t_2) → pos2
  151. Rotate(Mirror[pos3, w_1], 180°, t_2) → pos4

AI Drawing Prompt Reference

Create an animation of a modular origami cube folding dynamically. Start with a cube whose vertices lift and shift horizontally over time. One face is mirrored and rotated to create folding triangular panels, with auxiliary lines, planes, and circles for positioning. The final view shows multiple rotated polygonal faces and a circle, illustrating spatial transformations and parametric motion.
The prompt above was compiled from the original drawing commands and is for reference only.