纸艺八面体折纸动画

纸艺八面体折纸动画
几何画板及绘图内容加载中,请稍等……
2020-07-17 00:30
本范例演示了来自《Action Modular Origami》一书的纸艺八面体折纸过程。核心数学概念包括几何作图和变换。使用了Point, Intersect, Line, Polygon, Dilate, Plane, Mirror, OrthogonalLine, Sequence, Vector, Translate, Rotate等GeoGebra命令。适合用于几何学教学,特别是立体几何和几何作图的教学。

GeoGebra 命令及参数

  1. Point(zAxis) → A
  2. Point(yAxis) → B
  3. Point(xAxis) → C
  4. Point(yAxis) → D
  5. Point(xAxis) → E
  6. Point(zAxis) → F
  7. Intersect(zAxis, xOyPlane) → O
  8. Line(O, Z) → a
  9. Polygon(B, C, D, E) → poly1, b, c, d, e
  10. Polygon(B, F, D, A) → poly2, b_1, f, d_1, a_1
  11. Polygon(E, F, C, A) → poly3, e_1, f_1, c_1, a_2
  12. Dilate(A, scalefactor, O) → A'
  13. Dilate(B, scalefactor, O) → B'
  14. Dilate(C, scalefactor, O) → C'
  15. Dilate(D, scalefactor, O) → D'
  16. Dilate(E, scalefactor, O) → E'
  17. Dilate(F, scalefactor, O) → F'
  18. Plane(F', C', D') → g
  19. Mirror(O, g) → O'
  20. Line(E, C) → h
  21. Line(B, D) → i
  22. OrthogonalLine(C', h, xOyPlane) → j
  23. Intersect(j, b) → G
  24. Intersect(j, c) → H
  25. OrthogonalLine(G, i, xOyPlane) → k
  26. Intersect(i, yAxis) → I
  27. Intersect(i, yAxis) → J
  28. Intersect(k, i) → K
  29. Polygon(O, C', H, C, G, K) → poly10, o, c'_2, h_1, c_2, g_1, k_1
  30. Mirror(G, i) → G'
  31. Polygon(B, G, K, O, E', G') → poly11, b_2, g_2, k_2, o_1, e', g'
  32. Sequence(Rotate[poly10, (n * 180°), O], n, 0, 2) → ListPolyXY1
  33. Sequence(Rotate[poly11, (n * 180°), O], n, 0, 2) → ListPolyXY2
  34. Vector((0, 0, 0), (0, 0, sep)) → u
  35. Translate(ListPolyXY1, u) → ListPolyXY1'_1
  36. Translate(ListPolyXY2, u) → ListPolyXY2'_1
  37. Rotate(ListPolyXY1'_1, 180°, h) → ListPolyXY1'
  38. Rotate(ListPolyXY2'_1, 180°, h) → ListPolyXY2'
  39. Translate({ListPolyXY1, ListPolyXY1'}, Vector[(0, 0, 0), (0, 0, 0)]) → ListPoly1
  40. Translate({ListPolyXY2, ListPolyXY2'}, Vector[(0, 0, 0), (0, 0, 0)]) → ListPoly2
  41. Line(O, F) → m
  42. Rotate(ListPoly1, 120°, a) → ListPoly1'
  43. Rotate(ListPoly2, 120°, a) → ListPoly2'
  44. Rotate(ListPoly1', 120°, a) → ListPoly1''
  45. Rotate(ListPoly2', 120°, a) → ListPoly2''
  46. Line(O, F) → l
  47. Rotate({ListPoly1'', ListPoly2'}, α, l) → list2
  48. Rotate({ListPoly1', ListPoly2}, α, l) → list1
  49. Rotate({ListPoly1, ListPoly2''}, α, l) → list0

AI 绘图提示语参考

绘制一个由六个顶点构成的正八面体骨架,其中三个顶点分别位于三条坐标轴的正半轴,另三个位于负半轴。以原点为中心,将各顶点按比例缩放,形成内部缩小的八面体。连接内外对应顶点,构造出多个三角形和四边形面片,并沿坐标轴旋转复制,形成对称的折叠结构。最后,将整体绕一条竖直轴旋转一定角度,并沿该轴平移,展示八面体的折叠动画效果。
以上提示语为根据原始绘图命令整理而来,仅供参考。