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追逐曲线

追逐曲线
几何画板及绘图内容加载中，请稍等……
2015-05-12 07:29
向量几何作图滑块动画
这是一个五只蚂蚁互相追逐的动态图形。演示了向量和几何变换的概念。通过使用Sequence和Polygon命令，可以观察到蚂蚁如何根据速度和步长进行移动。适合初中及以上学生学习几何变换和向量。

GeoGebra 命令及参数

  1. Sequence(Element[B1, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B1, Mod[i, 5] + 1], Element[B1, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B2
  2. Sequence(Element[B2, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B2, Mod[i, 5] + 1], Element[B2, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B3
  3. Sequence(Element[B3, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B3, Mod[i, 5] + 1], Element[B3, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B4
  4. Sequence(Element[B4, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B4, Mod[i, 5] + 1], Element[B4, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B5
  5. Sequence(Element[B5, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B5, Mod[i, 5] + 1], Element[B5, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B6
  6. Sequence(Element[B6, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B6, Mod[i, 5] + 1], Element[B6, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B7
  7. Sequence(Element[B7, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B7, Mod[i, 5] + 1], Element[B7, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B8
  8. Sequence(Element[B8, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B8, Mod[i, 5] + 1], Element[B8, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B9
  9. Sequence(Element[B9, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B9, Mod[i, 5] + 1], Element[B9, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B10
  10. Sequence(Element[B10, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B10, Mod[i, 5] + 1], Element[B10, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B11
  11. Sequence(Element[B11, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B11, Mod[i, 5] + 1], Element[B11, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B12
  12. Sequence(Element[B12, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B12, Mod[i, 5] + 1], Element[B12, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B13
  13. Sequence(Element[B13, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B13, Mod[i, 5] + 1], Element[B13, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B14
  14. Sequence(Element[B14, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B14, Mod[i, 5] + 1], Element[B14, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B15
  15. Sequence(Element[B15, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B15, Mod[i, 5] + 1], Element[B15, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B16
  16. Sequence(Element[B16, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B16, Mod[i, 5] + 1], Element[B16, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B17
  17. Sequence(Element[B17, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B17, Mod[i, 5] + 1], Element[B17, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B18
  18. Sequence(Element[B18, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B18, Mod[i, 5] + 1], Element[B18, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B19
  19. Sequence(Element[B19, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B19, Mod[i, 5] + 1], Element[B19, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B20
  20. Polygon(B1) → C1, D1, E1, F1, G1, H1
  21. Polygon(B2) → C2, D2, E2, F2, G2, H2
  22. Polygon(B3) → C3, D3, E3, F3, G3, H3
  23. Polygon(B4) → C4, D4, E4, F4, G4, H4
  24. Polygon(B5) → C5, D5, E5, F5, G5, H5
  25. Polygon(B6) → C6, D6, E6, F6, G6, H6
  26. Polygon(B7) → C7, D7, E7, F7, G7, H7
  27. Polygon(B8) → C8, D8, E8, F8, G8, H8
  28. Polygon(B9) → C9, D9, E9, F9, G9, H9
  29. Polygon(B10) → C10, D10, E10, F10, G10, H10
  30. Polygon(B11) → C11, D11, E11, F11, G11, H11
  31. Polygon(B12) → C12, D12, E12, F12, G12, H12
  32. Polygon(B13) → C13, D13, E13, F13, G13, H13
  33. Polygon(B14) → C14, D14, E14, F14, G14, H14
  34. Polygon(B15) → C15, D15, E15, F15, G15, H15
  35. Polygon(B16) → C16, D16, E16, F16, G16, H16
  36. Polygon(B17) → C17, D17, E17, F17, G17, H17
  37. Polygon(B18) → C18, D18, E18, F18, G18, H18
  38. Polygon(B19) → C19, D19, E19, F19, G19, H19
  39. Polygon(B20) → C20, D20, E20, F20, G20, H20
  40. Sequence(Segment[Element[B2, i], Element[B1, i]], i, 1, 5) → I2
  41. Sequence(Segment[Element[B3, i], Element[B2, i]], i, 1, 5) → I3
  42. Sequence(Segment[Element[B4, i], Element[B3, i]], i, 1, 5) → I4
  43. Sequence(Segment[Element[B5, i], Element[B4, i]], i, 1, 5) → I5
  44. Sequence(Segment[Element[B6, i], Element[B5, i]], i, 1, 5) → I6
  45. Sequence(Segment[Element[B7, i], Element[B6, i]], i, 1, 5) → I7
  46. Sequence(Segment[Element[B8, i], Element[B7, i]], i, 1, 5) → I8
  47. Sequence(Segment[Element[B9, i], Element[B8, i]], i, 1, 5) → I9
  48. Sequence(Segment[Element[B10, i], Element[B9, i]], i, 1, 5) → I10
  49. Sequence(Segment[Element[B11, i], Element[B10, i]], i, 1, 5) → I11
  50. Sequence(Segment[Element[B12, i], Element[B11, i]], i, 1, 5) → I12
  51. Sequence(Segment[Element[B13, i], Element[B12, i]], i, 1, 5) → I13
  52. Sequence(Segment[Element[B14, i], Element[B13, i]], i, 1, 5) → I14
  53. Sequence(Segment[Element[B15, i], Element[B14, i]], i, 1, 5) → I15
  54. Sequence(Segment[Element[B16, i], Element[B15, i]], i, 1, 5) → I16
  55. Sequence(Segment[Element[B17, i], Element[B16, i]], i, 1, 5) → I17
  56. Sequence(Segment[Element[B18, i], Element[B17, i]], i, 1, 5) → I18
  57. Sequence(Segment[Element[B19, i], Element[B18, i]], i, 1, 5) → I19
  58. Sequence(Segment[Element[B20, i], Element[B19, i]], i, 1, 5) → I20

AI 绘图提示语参考

画一个动态的蚂蚁追逐图案，展示五个蚂蚁互相追逐的轨迹，通过向量运算和几何变换实现。每个蚂蚁的位置基于前一个蚂蚁的位置和速度计算，使用序列命令生成每一步的位置，然后用多边形命令连接这些位置形成蚂蚁的路径。最后用线段连接相邻蚂蚁的路径，展示追逐关系。
以上提示语为根据原始绘图命令整理而来，仅供参考。