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Pseudo-Fluxicube: Modular Origami Animation

Pseudo-Fluxicube: Modular Origami Animation
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2020-07-17 00:28
Coordinate GeometrySolid GeometryTransformationGeometric ConstructionSlider Animation
In collections Action Modular Origami
① This example demonstrates a modular origami model called the 'Pseudo-Fluxicube', animated in GeoGebra to show its folding and unfolding process in 3D. ② Core mathematical concepts include solid geometry of cubes, spatial transformations (translation, rotation, reflection), similarity transformations, and coordinate-based calculations, with elements of limits as the folding progresses continuously. ③ Construction highlights: Based on the summary, commands such as If, Vector, Point, Cube, Line, Translate, Plane, Mirror, Rotate, and Midpoint are used, creating multiple faces (faceABCD, faceADHE, etc.), edges (edgeAD, edgeAB, etc.), and list objects (listCube1, listCube2', listCube2''), with sliders (clock, vLift) driving the animation. ④ Suitable for high school or early university students to explore spatial transformations and dynamic modeling, and valuable for origami mathematics or STEAM education.

GeoGebra Commands & Parameters

  1. If(clock ≤ 1, 1, If[clock > 1 ∧ clock ≤ 2, 1 - (clock - 1) / 2, If[clock > 2 ∧ clock ≤ 3, 0.5, 0.5]]) → clock3_1
  2. If(clock < 3, 0, clock - 3) → clock4
  3. Vector((0, 0, (2 * clock4))) → vLift4
  4. Point(yAxis) → A
  5. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  6. 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
  7. Line(A, D) → g
  8. Translate({faceABCD, faceABFE, faceADHE, faceBCGF, faceCDHG, faceEFGH}, Vector[(0, 0, 0)]) → listCube1
  9. Line(C, D) → f
  10. Plane(C, G, H) → b
  11. Mirror(listCube1, b) → listCube2'
  12. If(clock ≤ 1, clock, 1) → clock1
  13. Vector((0, 0, clock1)) → vLift
  14. Translate(Rotate[listCube2', asin(clock1), f], vLift) → listCube2''
  15. If(clock ≤ 1, 0, If[clock > 1 ∧ clock ≤ 3, (clock - 1) / 2, 1]) → clock3
  16. Translate(listCube1, vLift) → listCube1'_1
  17. Rotate(listCube1'_1, (-α), g) → listCube1_3
  18. Translate(g, vLift) → g'
  19. Rotate(g', (-α), g) → g''
  20. Translate(f, vLift) → f'
  21. Rotate(f', (-α), g) → f''
  22. Translate(f'', vLift4) → f'''
  23. Translate(Rotate[listCube2'', (-α), g], vLift4) → listCube2'''
  24. Rotate(listCube2''', (-β), f''') → listCube2_4
  25. Translate(listCube1_3, vLift4) → listCube1_4
  26. Rotate(Translate[C, vLift], (-α), g) → C''
  27. Rotate(Translate[D, vLift], (-α), g) → D''
  28. If(x(C'') > x(D''), x(C''), x(D'')) → xMax
  29. Vector((cos((180° * clock3_1)), 0, 0)) → vShift
  30. Translate(listCube1_4, vShift) → list1
  31. Translate(listCube2_4, vShift) → list2
  32. Plane(E, A, H) → c
  33. Mirror(list2, c) → list2'
  34. Mirror(list1, c) → list1'
  35. Midpoint(E, H) → I
  36. Plane(I, b) → d
  37. Mirror(list2, d) → list2'_1
  38. Mirror(list2', d) → list2''
  39. Mirror(listCube1, b) → listFix0
  40. Mirror(listFix0, c) → listFix2
  41. Mirror(listFix0, d) → listFix4
  42. Mirror(listFix4, c) → listFix1

AI Drawing Prompt Reference

Create an animated 3D modular origami model called a 'pseudo-fluxicube'. Start with a solid cube composed of six colored faces. The animation unfolds in stages: first the cube translates upward, then rotates around one edge, while some faces mirror across an adjacent edge to create a folding effect. Next, the entire assembly translates and rotates further, with a set of faces reflecting across a diagonal plane, producing a symmetric unfolding. Finally, two mirrored halves shift apart horizontally, revealing the dynamic folding and unfolding process. Include semi-transparent faces, visible edges, and auxiliary planes to emphasize spatial transformations.
The prompt above was compiled from the original drawing commands and is for reference only.