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缓动函数动画演示

缓动函数动画演示
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2020-05-01 19:50
函数三角函数微积分滑块动画函数图像
①本范例通过动态演示展示缓动函数在动画中的应用效果；②涉及核心数学概念包括函数图像、分段函数、多项式函数、指数函数、三角函数等；③作图要点运用了Vector（向量）、Translate（平移）、Rotate（旋转）、Intersect（交点）、Root（根）、Point（点）、Segment（线段）、Circle（圆）、Sequence（数列）等GeoGebra命令与对象；④适合高中及以上数学学习者理解动画效果与函数变换的关联，可用于函数图像绘制与变换教学。

GeoGebra 命令及参数

  1. Vector(K, Z_1) → b_1
  2. Translate(K, b_1) → K'
  3. Rotate(K' + (0.5, 0), (F5(a) * 360°), K') → V_2
  4. Intersect(xAxis, yAxis) → A
  5. Root(q, 0.62) → G
  6. Rotate(C + (0.5, 0), (F1(a) * 360°), C) → D
  7. Point(yAxis) → E
  8. Vector(A, E) → u
  9. Point(xAxis) → F
  10. Vector(A, F) → v
  11. Point(yAxis) → H
  12. Point(yAxis) → I
  13. Vector(H, I) → w
  14. Vector(H, J) → b
  15. Rotate(K + (0.5, 0), (F2(a) * 360°), K) → L
  16. Point(xAxis) → M
  17. Point(xAxis) → N
  18. Vector(M, N) → c
  19. Vector(M, O) → d
  20. Vector(P, Q) → e
  21. Vector(P, R) → i
  22. Rotate(S + (0.5, 0), (F3(a) * 360°), S) → U
  23. Rotate(T + (0.5, 0), (F4(a) * 360°), T) → V
  24. Segment(C, D) → j
  25. Segment(K, L) → k
  26. Segment(S, U) → l
  27. Segment(T, V) → m
  28. Circle(C, D) → c_1
  29. Circle(S, U) → d_1
  30. Circle(T, V) → e_1
  31. Circle(K, L) → k_1
  32. Point(xAxis) → C_1
  33. Segment(C_1, D_1) → n
  34. Sequence(C_1 + (F1(k) * (D_1 - C_1)), k, 0, a, 0.05) → l1
  35. Sequence(Rotate[C + (0.5, 0), (F1(k) * 360°), C], k, 0, a, 0.025) → l2
  36. Sequence(Rotate[K + (0.5, 0), (F2(k) * 360°), K], k, 0, a, 0.025) → l3
  37. Segment(F_1, G_1) → i_1
  38. Sequence(F_1 + (F2(k) * (G_1 - F_1)), k, 0, a, 0.05) → l4
  39. Sequence(Rotate[S + (0.5, 0), (F3(k) * 360°), S], k, 0, a, 0.025) → l5
  40. Segment(I_1, J_1) → j_1
  41. Sequence(I_1 + (F3(k) * (J_1 - I_1)), k, 0, a, 0.05) → l6
  42. Sequence(Rotate[Segment[S, S + (0.5, 0)], (F3(k) * 360°), S], k, 0, a, 0.025) → l7
  43. Sequence(Rotate[T + (0.5, 0), (F4(k) * 360°), T], k, 0, a, 0.025) → l8
  44. Sequence(CircleSector[S, S + (0.5, 0), Rotate[S + (0.5, 0), (F3(k) * 360°), S]], k, 0, a, 0.025) → l9
  45. Point(yAxis) → L_1
  46. Point(yAxis) → M_1
  47. Vector(L_1, M_1) → u_1
  48. Vector(L_1, N_1) → v_1
  49. Vector(O_1, P_1) → w_1
  50. Vector(O_1, Q_1) → a_1
  51. Translate(k_1, b_1) → c_2
  52. Translate(F_1, b_1) → T_1
  53. Translate(G_1, b_1) → U_1
  54. Segment(T_1, U_1) → l_1
  55. Translate(K, b_1) → K'_1
  56. Segment(K'_1, V_1) → k'
  57. Sequence(T_1 + (F5(k) * (U_1 - T_1)), k, 0, a, 0.05) → l10
  58. Translate(k_1, m_1) → d_2
  59. Translate(K, m_1) → K'_2
  60. Rotate(K'_2 + (0.5, 0), (F6(a) * 360°), K'_2) → L'
  61. Segment(K'_2, L') → k'_1
  62. Translate(F_1, m_1) → B_2
  63. Translate(G_1, m_1) → C_2
  64. Segment(B_2, C_2) → n_1
  65. Sequence(B_2 + (F6(k) * (C_2 - B_2)), k, 0, a, 0.05) → l4'
  66. Sequence(Rotate[K'_2 + (0.5, 0), (F6(k) * 360°), K'_2], k, 0, a, 0.025) → l3'_1
  67. Sequence(Rotate[K' + (0.5, 0), (F5(k) * 360°), K'], k, 0, a, 0.025) → l3'
  68. Translate(I_1, u_2) → G_2
  69. Translate(J_1, u_2) → H_2
  70. Segment(G_2, H_2) → i_2
  71. Sequence(G_2 + (F4(k) * (H_2 - G_2)), k, 0, a, 0.05) → l6'
  72. Sequence(Polygon[(0, 0), (0.3, 0), (0.3, (Element[LF, k] * a)), (0, (Element[LF, k] * a))], k, 1, Length[LF]) → l11
  73. Translate(Polygon[(0, 0), (0.3, 0), (0.3, F1(a)), (0, F1(a))], (3, 0)) → q1
  74. Translate(Polygon[(0, 0), (0.3, 0), (0.3, F2(a)), (0, F2(a))], (3, -2)) → q2
  75. Translate(Polygon[(0, 0), (0.3, 0), (0.3, F3(a)), (0, F3(a))], (7, 0)) → q3
  76. Translate(Polygon[(0, 0), (0.3, 0), (0.3, F4(a)), (0, F4(a))], (7, -2)) → q4
  77. Translate(Polygon[(0, 0), (0.3, 0), (0.3, F5(a)), (0, F5(a))], (7, -4)) → q5
  78. Translate(Polygon[(0, 0), (0.3, 0), (0.3, F6(a)), (0, F6(a))], (3, -4)) → q6
  79. Translate(Polygon[(0, 0), (0.3, 0), (0.3, 1), (0, 1)], (3, 0)) → q7
  80. Translate(Polygon[(0, 0), (0.3, 0), (0.3, 1), (0, 1)], (7, 0)) → q8
  81. Translate(Polygon[(0, 0), (0.3, 0), (0.3, 1), (0, 1)], (7, -2)) → q9
  82. Translate(Polygon[(0, 0), (0.3, 0), (0.3, 1), (0, 1)], (7, -4)) → q10
  83. Translate(Polygon[(0, 0), (0.3, 0), (0.3, 1), (0, 1)], (3, -2)) → q11
  84. Translate(Polygon[(0, 0), (0.3, 0), (0.3, 1), (0, 1)], (3, -4)) → q12