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复数追踪路径：多智能体循环追逐问题

复数追踪路径：多智能体循环追逐问题
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2018-10-18 02:06
圆多边形数列复数轨迹
本范例演示如何利用复数运算模拟经典的追踪路径（pursuit path）问题。若干个智能体从正多边形顶点出发，每个智能体始终以恒定速率朝向相邻智能体移动，形成优美的闭合追逐轨迹。核心数学概念包括复数的几何意义、参数方程、极限与收敛、相似变换。通过GeoGebra的Sequence命令生成等距分布的多边形顶点，Polygon命令绘制追逐路径，Circle命令定义运动边界，Slider滑块参数n控制智能体数量。动态演示帮助学生直观理解复数在描述平面运动中的作用，感受离散到连续的数学思想，适合高中数学拓展课程、大学复变函数入门及数学建模爱好者研究使用。

GeoGebra 命令及参数

  1. Sequence((cos(w), sin(w)), w, (2 * π / n), (2 * π), (2 * π / n)) → L_1
  2. Polygon(L_1) → t1
  3. Polygon(A1) → B1
  4. Polygon(A2) → B2
  5. Polygon(A3) → B3
  6. Polygon(A4) → B4
  7. Polygon(A5) → B5
  8. Polygon(A6) → B6
  9. Polygon(A7) → B7
  10. Polygon(A8) → B8
  11. Polygon(A9) → B9
  12. Polygon(A10) → B10
  13. Polygon(A11) → B11
  14. Polygon(A12) → B12
  15. Polygon(A13) → B13
  16. Polygon(A14) → B14
  17. Polygon(A15) → B15
  18. Polygon(A16) → B16
  19. Polygon(A17) → B17
  20. Polygon(A18) → B18
  21. Polygon(A19) → B19
  22. Polygon(A20) → B20
  23. Polygon(A21) → B21
  24. Polygon(A22) → B22
  25. Polygon(A23) → B23
  26. Polygon(A24) → B24
  27. Polygon(A25) → B25
  28. Polygon(A26) → B26
  29. Polygon(A27) → B27
  30. Polygon(A28) → B28
  31. Polygon(A29) → B29
  32. Polygon(A30) → B30
  33. Polygon(A31) → B31
  34. Polygon(A32) → B32
  35. Polygon(A33) → B33
  36. Polygon(A34) → B34
  37. Polygon(A35) → B35
  38. Polygon(A36) → B36
  39. Polygon(A37) → B37
  40. Polygon(A38) → B38
  41. Polygon(A39) → B39
  42. Polygon(A40) → B40
  43. Polygon(A41) → B41
  44. Polygon(A42) → B42
  45. Polygon(A43) → B43
  46. Polygon(A44) → B44
  47. Polygon(A45) → B45
  48. Polygon(A46) → B46
  49. Polygon(A47) → B47
  50. Polygon(A48) → B48
  51. Polygon(A49) → B49
  52. Polygon(A50) → B50
  53. Polygon(A51) → B51
  54. Polygon(A52) → B52
  55. Polygon(A53) → B53
  56. Polygon(A54) → B54
  57. Polygon(A55) → B55
  58. Polygon(A56) → B56
  59. Polygon(A57) → B57
  60. Polygon(A58) → B58
  61. Polygon(A59) → B59
  62. Polygon(A60) → B60
  63. Polygon(A61) → B61
  64. Polygon(A62) → B62
  65. Polygon(A63) → B63
  66. Polygon(A64) → B64
  67. Polygon(A65) → B65
  68. Polygon(A66) → B66
  69. Polygon(A67) → B67
  70. Polygon(A68) → B68
  71. Polygon(A69) → B69
  72. Polygon(A70) → B70
  73. Polygon(A71) → B71
  74. Polygon(A72) → B72
  75. Polygon(A73) → B73
  76. Polygon(A74) → B74
  77. Polygon(A75) → B75
  78. Polygon(A76) → B76
  79. Polygon(A77) → B77
  80. Polygon(A78) → B78
  81. Polygon(A79) → B79
  82. Polygon(A80) → B80
  83. Polygon(A81) → B81
  84. Polygon(A82) → B82
  85. Polygon(A83) → B83
  86. Polygon(A84) → B84
  87. Polygon(A85) → B85
  88. Polygon(A86) → B86
  89. Polygon(A87) → B87
  90. Polygon(A88) → B88
  91. Polygon(A89) → B89
  92. Polygon(A90) → B90
  93. Polygon(A91) → B91
  94. Polygon(A92) → B92
  95. Polygon(A93) → B93
  96. Polygon(A94) → B94
  97. Polygon(A95) → B95
  98. Polygon(A96) → B96
  99. Polygon(A97) → B97
  100. Polygon(A98) → B98
  101. Polygon(A99) → B99
  102. Polygon(A100) → B100
  103. Circle((0, 0), 1) → c

AI 绘图提示语参考

绘制追及曲线图形。创建一个可调节的滑块参数n来控制智能体数量。在单位圆上生成n个均匀分布的顶点，每个智能体从各自顶点出发，以恒定速度持续朝向下一个智能体移动，形成优雅的封闭追及曲线。多个智能体的运动轨迹交织呈现出螺旋形的几何图案，展现从离散到连续的数学演变过程。
以上提示语为根据原始绘图命令整理而来，仅供参考。