四维框架弹射器

四维框架弹射器
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2016-08-24 06:16
①本范例演示一个四维框架弹射器的数学模型,通过动态交互展示空间几何变换;②涉及核心数学概念包括圆、随机过程、矩阵运算、特殊点和导数;③构造过程中运用了点、线段、正交平面、正交线、圆、交点、向量、平移、旋转等GeoGebra命令与对象;④适合高中及以上数学学习者,用于理解空间几何与线性代数的结合应用。

GeoGebra 命令及参数

  1. Point(zAxis) → A
  2. Segment(O_1, PointIn[Sphere[O_1, 6]]) → b_5
  3. OrthogonalPlane(A, zAxis) → a_1
  4. OrthogonalLine(O_1, b_5, a_1) → c_5
  5. OrthogonalLine(O_1, a_1) → e_5
  6. Circle(A, (4 * a), e_5) → p_1
  7. Intersect(c_5, p_1) → U, V
  8. Point(Circle[A, (5 * a), a_1]) → P
  9. Segment(A, P) → k_1
  10. Circle(A, (3 * a), k_1) → e_1
  11. Intersect(e_5, e_1) → S, T
  12. Circle(A, (10 * a), a_1) → d_1
  13. Intersect(c_5, d_1) → Q, R
  14. OrthogonalPlane(B, zAxis) → b
  15. OrthogonalLine(N_1, b_5, a_1) → d_5
  16. Segment(P_1, O_1) → f_6
  17. OrthogonalLine(P_1, c_5, a_1) → g_6
  18. Intersect(d_5, g_6) → R_1
  19. Segment(R_1, P_1) → h_6
  20. Segment(R_1, N_1) → i_6
  21. OrthogonalLine(Q_1, c_5, a_1) → j_6
  22. Intersect(d_5, j_6) → S_1
  23. Intersect(e_5, b) → T_1
  24. Vector(O_1, T_1) → u_1
  25. Translate(R_1, u_1) → U_1
  26. Translate(N_1, u_1) → W_1
  27. Translate(P_1, u_1) → V_1
  28. Segment(W_1, T_1) → i_1
  29. Segment(U_1, W_1) → k_6
  30. Segment(U_1, V_1) → l_6
  31. Segment(V_1, T_1) → m_6
  32. Segment(V_1, P_1) → n_6
  33. Segment(U_1, R_1) → p_6
  34. Segment(O_1, Q_1) → q_6
  35. Segment(N_1, S_1) → r_6
  36. Segment(S_1, Q_1) → s_6
  37. Segment(T_1, Q_1) → h_2
  38. Segment(W_1, S_1) → l_2
  39. Circle(T_1, m_6, i_1) → e
  40. Intersect(e_5, e) → D, E
  41. Segment(V_1, D) → n
  42. Line(U_1, n) → p
  43. Line(D, l_6) → q
  44. Intersect(p, q) → K
  45. Segment(K, D) → r
  46. Segment(U_1, K) → s
  47. Segment(B, A) → t
  48. Midpoint(i_1) → L
  49. Segment(D, B) → f_1
  50. Segment(K, W_1) → g_1
  51. Segment(W_1, N_1) → f
  52. Circle(L, f_1, i_1) → c
  53. Circle(L, (3 * a), i_1) → d
  54. Midpoint(m_6) → F
  55. Circle(l_6, F) → h
  56. Intersect(n, h) → G,
  57. Line(G, l_6) → i
  58. Intersect(i, s) → H
  59. Segment(H, G) → j
  60. Midpoint(j) → I
  61. Segment(I, L) → k
  62. Rotate(I, (-(135°)), L, c) → I'
  63. Angle(I', L, I, c) → α
  64. Segment(L, I') → l
  65. Intersect(l, d, 1) → C
  66. Line(L, f_1) → g
  67. Intersect(g, d, 2) → J
  68. Rotate(J, (-(135°)), L, d) → J'
  69. Angle(J', L, J, d) → β
  70. CircleArc(L, J', C, d) → c_1
  71. Point(c_1) → M
  72. Segment(M, L) → m
  73. Rotate(M, 135°, L, d) → M'
  74. Angle(M, L, M', d) → γ
  75. Ray(L, M') → h_1
  76. Intersect(h_1, c) → N, O
  77. Segment(N, L) → j_1
  78. Line(N, j) → l_1
  79. Plane(h_1, l_1) → o
  80. Circle(N, (5 * a), o) → q_1
  81. Intersect(h_1, q_1) → Z, A_1
  82. OrthogonalLine(Z, o) → n_1
  83. Sphere(Z, (sqrt(2) * a / 2)) → u
  84. Intersect(n_1, u) → W, B_1
  85. Plane(B_1, o) → v
  86. Line(B_1, l_1) → m_1
  87. Line(B_1, h_1) → r_1
  88. Circle(B_1, (1.5 * a), v) → s_1
  89. Circle(B_1, (2.5 * a), v) → t_1
  90. Intersect(m_1, t_1) → C_1, D_1
  91. Intersect(r_1, s_1) → E_1, F_1
  92. Line(E_1, m_1) → b_1
  93. Line(F_1, m_1) → f_2
  94. Line(D_1, r_1) → g_2
  95. Line(C_1, r_1) → i_2
  96. Intersect(b_1, g_2) → H_1
  97. Intersect(b_1, i_2) → I_1
  98. Intersect(f_2, g_2) → J_1
  99. Intersect(i_2, f_2) → K_1
  100. Segment(H_1, I_1) → j_2
  101. Segment(I_1, K_1) → k_2
  102. Segment(K_1, J_1) → m_2
  103. Segment(J_1, H_1) → n_2
  104. Segment(H_1, Z) → p_2
  105. Segment(Z, K_1) → q_2
  106. Segment(Z, J_1) → r_2
  107. Segment(Z, I_1) → s_2
  108. Segment(J_1, N) → t_2
  109. Segment(Z, N) → a_2
  110. Segment(K_1, N) → b_2

AI 绘图提示语参考

绘制一个四维框架弹射器模型,包含一个中心点O1,围绕它构建一系列圆和直线,通过旋转和平移生成复杂的几何结构。首先创建一个垂直于Z轴的平面A,然后在此平面上构建一系列圆和直线,通过交点和旋转生成更多几何元素,最终形成一个复杂的四维框架结构。
以上提示语为根据原始绘图命令整理而来,仅供参考。