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3D彩虹形成模拟

3D彩虹形成模拟
几何画板及绘图内容加载中，请稍等……
2015-03-05 01:39
向量立体几何几何作图
①本范例通过模拟演示了彩虹的形成过程；②涉及的核心数学概念包括反射、面积、二次函数、微分方程、二维向量；③作图要点——从下方『构造摘要』提炼用到了Circle（圆）、Point（点）、Angle（角）、Rotate（旋转）、Ray（射线）、Intersect（相交）、Sphere（球体）、Line（直线）、Plane（平面）、Segment（线段）、Vector（向量）、Mirror（镜像）等GeoGebra命令/对象；④适合高中及以上学段学习光学、几何及数学建模的学生使用。

GeoGebra 命令及参数

  1. Circle(Q, R) → c
  2. Point(c) → U
  3. Point(xAxis) → C
  4. Angle(C, Viewer, S) → α
  5. Rotate(U, (-α), Q) → T
  6. Rotate(I_1, (-α), T) → J_1
  7. Ray(Q, T) → r
  8. Ray(T, J_1) → d
  9. Angle(r, d) → δ
  10. Rotate(Q, asin(sin(δ) / 1.33), T) → Q'
  11. Ray(T, Q') → s
  12. Intersect(c, s) → V, W
  13. Angle(Q, T, Q') → ε
  14. Rotate(Q', (2 * ε), W) → Q''
  15. Ray(W, Q'') → a_1
  16. Intersect(c, a_1) → Z, A_1
  17. Ray(Q, A_1) → c_1
  18. Sphere(Viewer, 5.55) → l
  19. Line(S, Viewer) → a
  20. Intersect(a, l) → K, L
  21. Circle(L, B2, a) → C1
  22. Point(xAxis) → F
  23. Point(yAxis) → G
  24. Plane(F, E, G) → b
  25. Point(C1) → A
  26. Line(A, a) → f
  27. Point(f) → B
  28. Ray(A, B) → e
  29. Segment(A, Viewer) → g
  30. Point(e) → D
  31. Point(e) → I
  32. Angle(e, g) → β
  33. Circle(L, B3, a) → C2
  34. Circle(L, B4, a) → C3
  35. Circle(L, B5, a) → C4
  36. Circle(L, B6, a) → C5
  37. Circle(L, B7, a) → C6
  38. Circle(L, B8, a) → C7
  39. Circle(L, B9, a) → C8
  40. Circle(L, B10, a) → C9
  41. Circle(L, B11, a) → C10
  42. Circle(L, B12, a) → C11
  43. Circle(L, B13, a) → C12
  44. Circle(L, B14, a) → C13
  45. Circle(L, B15, a) → C14
  46. Circle(L, B16, a) → C15
  47. Circle(L, B17, a) → C16
  48. Circle(L, B18, a) → C17
  49. Circle(L, B19, a) → C18
  50. Circle(L, B20, a) → C19
  51. Circle(L, B21, a) → C20
  52. Circle(L, B22, a) → C21
  53. Circle(L, B23, a) → C22
  54. Circle(L, B24, a) → C23
  55. Circle(L, B25, a) → C24
  56. Circle(L, B26, a) → C25
  57. Circle(L, B27, a) → C26
  58. Circle(L, B28, a) → C27
  59. Circle(L, B29, a) → C28
  60. Circle(L, B30, a) → C29
  61. Circle(L, B31, a) → C30
  62. Circle(L, B32, a) → C31
  63. Circle(L, B33, a) → C32
  64. Circle(L, B34, a) → C33
  65. Circle(L, B35, a) → C34
  66. Circle(L, B36, a) → C35
  67. Circle(L, B37, a) → C36
  68. Circle(L, B38, a) → C37
  69. Circle(L, B39, a) → C38
  70. Circle(L, B40, a) → C39
  71. Circle(L, B41, a) → C40
  72. Circle(L, B42, a) → C41
  73. Circle(L, B43, a) → C42
  74. Circle(L, B44, a) → C43
  75. Circle(L, B45, a) → C44
  76. Circle(L, B46, a) → C45
  77. Circle(L, B47, a) → C46
  78. Circle(L, B48, a) → C47
  79. Circle(L, B49, a) → C48
  80. Circle(L, B50, a) → C49
  81. Circle(L, B51, a) → C50
  82. Circle(L, B52, a) → C51
  83. Circle(L, B53, a) → C52
  84. Circle(L, B54, a) → C53
  85. Circle(L, B55, a) → C54
  86. Circle(L, B56, a) → C55
  87. Circle(L, B57, a) → C56
  88. Circle(L, B58, a) → C57
  89. Circle(L, B59, a) → C58
  90. Circle(L, B60, a) → C59
  91. Circle(L, B61, a) → C60
  92. Circle(L, B62, a) → C61
  93. Circle(L, B63, a) → C62
  94. Circle(L, B64, a) → C63
  95. Circle(L, B65, a) → C64
  96. Circle(L, B66, a) → C65
  97. Circle(L, B67, a) → C66
  98. Circle(L, B68, a) → C67
  99. Circle(L, B69, a) → C68
  100. Circle(L, B70, a) → C69
  101. Circle(L, B71, a) → C70
  102. Circle(L, B72, a) → C71
  103. Circle(L, B73, a) → C72
  104. Circle(L, B74, a) → C73
  105. Circle(L, B75, a) → C74
  106. Circle(L, B76, a) → C75
  107. Circle(L, B77, a) → C76
  108. Circle(L, B78, a) → C77
  109. Angle(Viewer, A, M) → γ
  110. Point(C77) → O
  111. Segment(O, Viewer) → m
  112. Line(O, e) → p
  113. Point(p) → P
  114. Ray(O, P) → q
  115. Vector(O, N) → n
  116. Vector(A, M) → k
  117. Ray(Q, W) → t
  118. Point(c_1) → B_1
  119. Rotate(B_1, (-δ), A_1) → C_1
  120. Angle(C_1, A_1, B_1) → ζ
  121. Segment(W, A_1) → d_1
  122. Segment(T, Z) → e_1
  123. Rotate(Q, asin(sin(δ) / 1.345), T) → Q'_1
  124. Ray(T, Q'_1) → f_1
  125. Intersect(c, f_1) → D_1, E_1
  126. Segment(T, E_1) → g_1
  127. Ray(Q, E_1) → h_1
  128. Mirror(T, h_1) → T'
  129. Mirror(E_1, h_1) → F_1
  130. Segment(T', F_1) → i_1
  131. Angle(Q, T, E_1) → η
  132. Ray(Q, T') → j_1
  133. Point(j_1) → G_1
  134. Rotate(G_1, (-δ), T') → H_1
  135. Vector(T', H_1) → k_1
  136. Vector(A_1, C_1) → b_1
  137. Point(q) → K_1
  138. Vector(L_1, M_1) → u
  139. Vector((0.3, 0, -0.4), Viewer) → v

AI 绘图提示语参考

创建一个三维彩虹形成模拟图，展示光线通过水滴形成彩虹的过程。首先绘制一个圆和圆上的点，然后利用角度和旋转构造反射光线和向量，通过球体和圆的交点确定彩虹的位置，最后用多个同心圆模拟彩虹的色带分布，整体呈现光线在水滴中反射和折射的动态效果。
以上提示语为根据原始绘图命令整理而来，仅供参考。