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船体网格动画

船体网格动画
几何画板及绘图内容加载中，请稍等……
2016-05-28 03:25
向量解析几何参数方程几何作图
①本范例演示了参数方程在几何图形中的应用，通过动态展示船体在网格中的运动轨迹；②涉及核心数学概念包括参数方程、向量运算、几何变换及导数应用；③构造过程中运用了正交线、点、旋转、圆弧、圆、交点、角度、射线、向量、条件语句、扇形、数列、线段、多边形等GeoGebra命令与对象；④适合高中及以上数学学习者，用于理解参数方程与动态几何关系的实际应用。

GeoGebra 命令及参数

  1. OrthogonalLine(C0, xAxis) → c
  2. Point(c) → Zcenit
  3. Rotate(Zcenit, 75.00000000000001°, C0) → Zangmin
  4. CircleArc(C0, Zcenit, Zangmin) → f
  5. Point(f) → Z
  6. Circle(C0, Zcenit) → e
  7. OrthogonalLine(C0, c) → d
  8. Intersect(e, d, 2) → Zang0
  9. Angle(Z, C0, Zang0) → α
  10. Point(yAxis) → B_1
  11. Ray(B_1, B_2) → a
  12. Vector(B_1, B_2) → v
  13. Point(xAxis) → A_1
  14. Ray(A_1, A_2) → b
  15. Intersect(a, b) → C
  16. Vector(B14, C) → v4
  17. Vector(B13, C) → v3
  18. Vector(B_1, C) → v1
  19. Vector(A_1, A_2) → u
  20. Vector(A14, C) → u4
  21. Vector(A13, C) → u3
  22. If((tB3 ≤ tA3) ∧ (tA3 ≤ tB4), tA3, If[(tA3 ≤ tB3) ∧ (tB3 ≤ tA4), tB3, 1000]) → tImpacto
  23. If(t < tImpacto, B0, B_1 + (tImpacto * v)) → B
  24. Vector(B'_1, B') → uB
  25. Vector(B', B' - (0, 200)) → wB
  26. Angle(wB, uB) → βB3
  27. Rotate(B4', ((-βB3) * If[t - tImpacto < tGiro, t - tImpacto, 1]), B') → B4Proa
  28. Rotate(B4', ((180° - βB3) * If[t - tImpacto < tGiro, t - tImpacto, 1]), B') → B4Popa
  29. If(tB < tImpacto, B4Popa, B4Proa) → B4''
  30. If(t < tImpacto, B4', If[t - tImpacto < tGiro, B4'', If[y(B4') - y(B4''') < 200 - Ship_B / 2, B4''', B' - (0, 200 - Ship_B / 2)]]) → BB4Proa
  31. Rotate(B3', ((-βB3) * If[t - tImpacto < tGiro, t - tImpacto, 1]), B') → B3Proa
  32. Rotate(B3', ((180° - βB3) * If[t - tImpacto < tGiro, t - tImpacto, 1]), B') → B3Popa
  33. If(tB < tImpacto, B3Popa, B3Proa) → B3''
  34. If(t < tImpacto, B4', If[t - tImpacto < tGiro, B4'', If[y(B') - y(B4''') < 200, B4''', B' - (0, 200)]]) → BB4Popa
  35. If(t < tImpacto, B3', If[t - tImpacto < tGiro, B3'', If[y(B3') - y(B3''') < 200, B3''', B' - (0, 200)]]) → BB3Proa
  36. If(t < tImpacto, B3', If[t - tImpacto < tGiro, B3'', If[y(B') - y(B3''') < 200 - Ship_B / 2, B3''', B' - (0, 200 - Ship_B / 2)]]) → BB3Popa
  37. Rotate(B5', ((180° - βB3) * If[t - tImpacto < tGiro, t - tImpacto, 1]), B') → B5Popa
  38. Rotate(B5', ((-βB3) * If[t - tImpacto < tGiro, t - tImpacto, 1]), B') → B5Proa
  39. If(tB < tImpacto, B5Popa, B5Proa) → B5''
  40. If(t < tImpacto, B5', If[t - tImpacto < tGiro, B5'', If[y(B5') - y(B5''') < 200, B5''', B' - (40, 200)]]) → BB5Popa
  41. If(t < tImpacto, B5', If[t - tImpacto < tGiro, B5'', If[y(B5') - y(B5''') < 200 - Ship_B / 2, B5''', B' - (-40, 200 - Ship_B / 2)]]) → BB5Proa
  42. If(t < tImpacto, A0, A_1 + (tImpacto * u)) → A
  43. CircleSector(C0, Zcenit, Zang0) → g
  44. Sequence(Segment[((s * cos(α)), (s * sin(α)) + k), ((s * cos(α)) + 1200, (s * sin(α)) + k)], s, 0, 1200, 100) → LowerGridHorizontal
  45. Sequence(Segment[(s, k), (s + (1200 * cos(α)), (1200 * sin(α)) + k)], s, 0, 1200, 100) → LowerGridVertical
  46. Sequence(Segment[(0, s), (1200, s)], s, 100, 1200, 100) → UpperGridHorizontal
  47. Sequence(Segment[(s, 0), (s, 1200)], s, 100, 1200, 100) → UpperGridVeritical
  48. Ray(B'_1, B') → h
  49. Ray(A'_1, A') → i
  50. Segment(B'_1, C') → j
  51. Segment(A'_1, C') → l
  52. Segment(B3, B4) → m
  53. Segment(A3, A4) → n
  54. Intersect(m, n) → D
  55. Vector(A', A' - (0, 200)) → wA
  56. Vector(A_1, C) → u1
  57. Vector(A'_1, A') → uA
  58. Angle(wA, uA) → βA3
  59. If(t < tImpacto, A3', If[y(A3') - y(A3'') < 200, A3'', A3' - (0, 200)]) → AA3
  60. If(t < tImpacto, A4', If[y(A4') - y(A4'') < 200, A4'', A4' - (0, 200)]) → AA4
  61. If(t < tImpacto, A5', If[y(A5') - y(A5'') < 200, A5'', A5' - (0, 200)]) → AA5
  62. If(tB < tImpacto, BB5Popa, BB5Proa) → BB5
  63. If(tB < tImpacto, BB3Popa, BB3Proa) → BB3
  64. If(tB < tImpacto, BB4Popa, BB4Proa) → BB4
  65. Polygon(E, F, H, G) → p1, p11, p12, p13, p14
  66. Polygon(E, G, G - (0, 200), E - (0, 200)) → p2, p21, p22, p23, p24
  67. Polygon(G, H, H - (0, 200), G - (0, 200)) → p3, p33, p34, p31, p32

AI 绘图提示语参考

绘制一个在网格中移动的船的动画。首先画出中心点和网格线，然后创建一个圆弧表示船的路径。接着定义船的初始位置和方向，通过旋转和移动创建船的各个部分。最后，使用参数方程动态显示船在网格中的移动路径，包括船头和船尾的旋转，以及船在碰撞后的转向。整个过程包括圆弧、圆、旋转、向量、角度和参数方程等几何元素。
以上提示语为根据原始绘图命令整理而来，仅供参考。