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环绕环面纽结的舞动立方体

环绕环面纽结的舞动立方体
几何画板及绘图内容加载中，请稍等……
2018-10-22 18:26
解析几何立体几何变换
这个范例展示了立方体在环面纽结上的动态变换。它涉及到了立方体、解析几何和变换等核心数学概念。通过使用GeoGebra中的Point, Cube, CurveCartesian, Rotate等命令，可以构造出立方体在环面纽结上的动态轨迹。适合高中或大学的几何与变换课程使用。

GeoGebra 命令及参数

  1. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  2. 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
  3. CurveCartesian(((2 + cos((((q * i) * 2) * π))) * cos((((p * i) * 2) * π))), ((2 + cos((((q * i) * 2) * π))) * sin((((p * i) * 2) * π))), sin((((q * i) * 2) * π)), i, 0, 1) → knot
  4. Rotate(Translate[a, Vector[(0, 0, 0), knot(0 / n)]], t + 0, knot(0 / n)) → A0
  5. Rotate(Translate[a, Vector[(0, 0, 0), knot(1 / n)]], t + 1, knot(1 / n)) → A1
  6. Rotate(Translate[a, Vector[(0, 0, 0), knot(2 / n)]], t + 2, knot(2 / n)) → A2
  7. Rotate(Translate[a, Vector[(0, 0, 0), knot(3 / n)]], t + 3, knot(3 / n)) → A3
  8. Rotate(Translate[a, Vector[(0, 0, 0), knot(4 / n)]], t + 4, knot(4 / n)) → A4
  9. Rotate(Translate[a, Vector[(0, 0, 0), knot(5 / n)]], t + 5, knot(5 / n)) → A5
  10. Rotate(Translate[a, Vector[(0, 0, 0), knot(6 / n)]], t + 6, knot(6 / n)) → A6
  11. Rotate(Translate[a, Vector[(0, 0, 0), knot(7 / n)]], t + 7, knot(7 / n)) → A7
  12. Rotate(Translate[a, Vector[(0, 0, 0), knot(8 / n)]], t + 8, knot(8 / n)) → A8
  13. Rotate(Translate[a, Vector[(0, 0, 0), knot(9 / n)]], t + 9, knot(9 / n)) → A9
  14. Rotate(Translate[a, Vector[(0, 0, 0), knot(10 / n)]], t + 10, knot(10 / n)) → A10
  15. Rotate(Translate[a, Vector[(0, 0, 0), knot(11 / n)]], t + 11, knot(11 / n)) → A11
  16. Rotate(Translate[a, Vector[(0, 0, 0), knot(12 / n)]], t + 12, knot(12 / n)) → A12
  17. Rotate(Translate[a, Vector[(0, 0, 0), knot(13 / n)]], t + 13, knot(13 / n)) → A13
  18. Rotate(Translate[a, Vector[(0, 0, 0), knot(14 / n)]], t + 14, knot(14 / n)) → A14
  19. Rotate(Translate[a, Vector[(0, 0, 0), knot(15 / n)]], t + 15, knot(15 / n)) → A15
  20. Rotate(Translate[a, Vector[(0, 0, 0), knot(16 / n)]], t + 16, knot(16 / n)) → A16
  21. Rotate(Translate[a, Vector[(0, 0, 0), knot(17 / n)]], t + 17, knot(17 / n)) → A17
  22. Rotate(Translate[a, Vector[(0, 0, 0), knot(18 / n)]], t + 18, knot(18 / n)) → A18
  23. Rotate(Translate[a, Vector[(0, 0, 0), knot(19 / n)]], t + 19, knot(19 / n)) → A19
  24. Rotate(Translate[a, Vector[(0, 0, 0), knot(20 / n)]], t + 20, knot(20 / n)) → A20
  25. Rotate(Translate[a, Vector[(0, 0, 0), knot(21 / n)]], t + 21, knot(21 / n)) → A21
  26. Rotate(Translate[a, Vector[(0, 0, 0), knot(22 / n)]], t + 22, knot(22 / n)) → A22
  27. Rotate(Translate[a, Vector[(0, 0, 0), knot(23 / n)]], t + 23, knot(23 / n)) → A23
  28. Rotate(Translate[a, Vector[(0, 0, 0), knot(24 / n)]], t + 24, knot(24 / n)) → A24
  29. Rotate(Translate[a, Vector[(0, 0, 0), knot(25 / n)]], t + 25, knot(25 / n)) → A25
  30. Rotate(Translate[a, Vector[(0, 0, 0), knot(26 / n)]], t + 26, knot(26 / n)) → A26
  31. Rotate(Translate[a, Vector[(0, 0, 0), knot(27 / n)]], t + 27, knot(27 / n)) → A27
  32. Rotate(Translate[a, Vector[(0, 0, 0), knot(28 / n)]], t + 28, knot(28 / n)) → A28
  33. Rotate(Translate[a, Vector[(0, 0, 0), knot(29 / n)]], t + 29, knot(29 / n)) → A29
  34. Rotate(Translate[a, Vector[(0, 0, 0), knot(30 / n)]], t + 30, knot(30 / n)) → A30
  35. Rotate(Translate[a, Vector[(0, 0, 0), knot(31 / n)]], t + 31, knot(31 / n)) → A31
  36. Rotate(Translate[a, Vector[(0, 0, 0), knot(32 / n)]], t + 32, knot(32 / n)) → A32
  37. Rotate(Translate[a, Vector[(0, 0, 0), knot(33 / n)]], t + 33, knot(33 / n)) → A33
  38. Rotate(Translate[a, Vector[(0, 0, 0), knot(34 / n)]], t + 34, knot(34 / n)) → A34
  39. Rotate(Translate[a, Vector[(0, 0, 0), knot(35 / n)]], t + 35, knot(35 / n)) → A35
  40. Rotate(Translate[a, Vector[(0, 0, 0), knot(36 / n)]], t + 36, knot(36 / n)) → A36
  41. Rotate(Translate[a, Vector[(0, 0, 0), knot(37 / n)]], t + 37, knot(37 / n)) → A37
  42. Rotate(Translate[a, Vector[(0, 0, 0), knot(38 / n)]], t + 38, knot(38 / n)) → A38
  43. Rotate(Translate[a, Vector[(0, 0, 0), knot(39 / n)]], t + 39, knot(39 / n)) → A39
  44. Rotate(Translate[a, Vector[(0, 0, 0), knot(40 / n)]], t + 40, knot(40 / n)) → A40
  45. Rotate(Translate[a, Vector[(0, 0, 0), knot(41 / n)]], t + 41, knot(41 / n)) → A41
  46. Rotate(Translate[a, Vector[(0, 0, 0), knot(42 / n)]], t + 42, knot(42 / n)) → A42
  47. Rotate(Translate[a, Vector[(0, 0, 0), knot(43 / n)]], t + 43, knot(43 / n)) → A43
  48. Rotate(Translate[a, Vector[(0, 0, 0), knot(44 / n)]], t + 44, knot(44 / n)) → A44
  49. Rotate(Translate[a, Vector[(0, 0, 0), knot(45 / n)]], t + 45, knot(45 / n)) → A45
  50. Rotate(Translate[a, Vector[(0, 0, 0), knot(46 / n)]], t + 46, knot(46 / n)) → A46
  51. Rotate(Translate[a, Vector[(0, 0, 0), knot(47 / n)]], t + 47, knot(47 / n)) → A47
  52. Rotate(Translate[a, Vector[(0, 0, 0), knot(48 / n)]], t + 48, knot(48 / n)) → A48
  53. Rotate(Translate[a, Vector[(0, 0, 0), knot(49 / n)]], t + 49, knot(49 / n)) → A49
  54. Rotate(Translate[a, Vector[(0, 0, 0), knot(50 / n)]], t + 50, knot(50 / n)) → A50
  55. Rotate(Translate[a, Vector[(0, 0, 0), knot(51 / n)]], t + 51, knot(51 / n)) → A51
  56. Rotate(Translate[a, Vector[(0, 0, 0), knot(52 / n)]], t + 52, knot(52 / n)) → A52
  57. Rotate(Translate[a, Vector[(0, 0, 0), knot(53 / n)]], t + 53, knot(53 / n)) → A53
  58. Rotate(Translate[a, Vector[(0, 0, 0), knot(54 / n)]], t + 54, knot(54 / n)) → A54
  59. Rotate(Translate[a, Vector[(0, 0, 0), knot(55 / n)]], t + 55, knot(55 / n)) → A55
  60. Rotate(Translate[a, Vector[(0, 0, 0), knot(56 / n)]], t + 56, knot(56 / n)) → A56
  61. Rotate(Translate[a, Vector[(0, 0, 0), knot(57 / n)]], t + 57, knot(57 / n)) → A57
  62. Rotate(Translate[a, Vector[(0, 0, 0), knot(58 / n)]], t + 58, knot(58 / n)) → A58
  63. Rotate(Translate[a, Vector[(0, 0, 0), knot(59 / n)]], t + 59, knot(59 / n)) → A59
  64. Rotate(Translate[a, Vector[(0, 0, 0), knot(60 / n)]], t + 60, knot(60 / n)) → A60
  65. Rotate(Translate[a, Vector[(0, 0, 0), knot(61 / n)]], t + 61, knot(61 / n)) → A61
  66. Rotate(Translate[a, Vector[(0, 0, 0), knot(62 / n)]], t + 62, knot(62 / n)) → A62
  67. Rotate(Translate[a, Vector[(0, 0, 0), knot(63 / n)]], t + 63, knot(63 / n)) → A63
  68. Rotate(Translate[a, Vector[(0, 0, 0), knot(64 / n)]], t + 64, knot(64 / n)) → A64
  69. Rotate(Translate[a, Vector[(0, 0, 0), knot(65 / n)]], t + 65, knot(65 / n)) → A65
  70. Rotate(Translate[a, Vector[(0, 0, 0), knot(66 / n)]], t + 66, knot(66 / n)) → A66
  71. Rotate(Translate[a, Vector[(0, 0, 0), knot(67 / n)]], t + 67, knot(67 / n)) → A67
  72. Rotate(Translate[a, Vector[(0, 0, 0), knot(68 / n)]], t + 68, knot(68 / n)) → A68
  73. Rotate(Translate[a, Vector[(0, 0, 0), knot(69 / n)]], t + 69, knot(69 / n)) → A69
  74. Rotate(Translate[a, Vector[(0, 0, 0), knot(70 / n)]], t + 70, knot(70 / n)) → A70
  75. Rotate(Translate[a, Vector[(0, 0, 0), knot(71 / n)]], t + 71, knot(71 / n)) → A71
  76. Rotate(Translate[a, Vector[(0, 0, 0), knot(72 / n)]], t + 72, knot(72 / n)) → A72
  77. Rotate(Translate[a, Vector[(0, 0, 0), knot(73 / n)]], t + 73, knot(73 / n)) → A73
  78. Rotate(Translate[a, Vector[(0, 0, 0), knot(74 / n)]], t + 74, knot(74 / n)) → A74
  79. Rotate(Translate[a, Vector[(0, 0, 0), knot(75 / n)]], t + 75, knot(75 / n)) → A75
  80. Rotate(Translate[a, Vector[(0, 0, 0), knot(76 / n)]], t + 76, knot(76 / n)) → A76
  81. Rotate(Translate[a, Vector[(0, 0, 0), knot(77 / n)]], t + 77, knot(77 / n)) → A77
  82. Rotate(Translate[a, Vector[(0, 0, 0), knot(78 / n)]], t + 78, knot(78 / n)) → A78
  83. Rotate(Translate[a, Vector[(0, 0, 0), knot(79 / n)]], t + 79, knot(79 / n)) → A79

AI 绘图提示语参考

在三维空间中绘制一条环面纽结曲线，然后让一个立方体沿着这条纽结曲线移动，在移动过程中立方体持续旋转，形成一系列动态排列的立方体轨迹。立方体从曲线起点开始，每经过曲线的一定比例就放置一个旋转过的立方体副本，整体呈现出立方体在环形纽结上舞蹈般的视觉效果。
以上提示语为根据原始绘图命令整理而来，仅供参考。