透视椭圆演示

透视椭圆演示
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2018-05-08 00:07
①本范例演示了透视投影下椭圆的形成与性质;②涉及核心数学概念包括椭圆、透视几何、几何平均、正弦函数、参数方程、菱形及概率统计;③作图要点提炼自构造摘要,使用了Intersect(交点)、Line(直线)、OrthogonalLine(垂线)、Point(点)、Circle(圆)、Segment(线段)、Midpoint(中点)、Conic(圆锥曲线)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解析几何的结合应用。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Line(A, B) → a
  3. OrthogonalLine(B, a) → b
  4. Intersect(b, xAxis) → C
  5. Line(A, C) → c
  6. OrthogonalLine(B, c) → d
  7. Point(d) → D
  8. Line(A, D) → e
  9. Line(D, C) → f
  10. Circle(C, B) → g
  11. Circle(A, B) → h
  12. Intersect(g, c, 1) → E
  13. Intersect(h, c, 2) → F
  14. Point(d) → G
  15. OrthogonalLine(D, d) → i
  16. Circle(D, G) → k
  17. Intersect(k, i, 2) → H
  18. Intersect(k, i, 1) → I
  19. Line(I, E) → j
  20. Line(H, F) → l
  21. Intersect(e, l) → J
  22. Intersect(f, j) → K
  23. Line(J, d) → m
  24. Line(K, d) → n
  25. Line(A, G) → p
  26. Line(G, C) → q
  27. Intersect(m, p) → L
  28. Intersect(n, q) → M
  29. Line(M, A) → r
  30. Line(L, C) → s
  31. Intersect(r, s) → N
  32. Line(K, A) → t
  33. Line(J, C) → a_1
  34. Intersect(t, a_1) → O
  35. Line(D, L) → b_1
  36. Line(J, G) → c_1
  37. Intersect(b_1, c_1) → P
  38. Line(K, N) → d_1
  39. Line(O, M) → e_1
  40. Intersect(d_1, e_1) → Q
  41. Line(P, A) → f_1
  42. Intersect(m, f_1) → R
  43. Intersect(d, f_1) → S
  44. Line(P, m) → g_1
  45. Line(Q, d) → h_1
  46. Intersect(t, h_1) → T
  47. Intersect(e, g_1) → U
  48. Intersect(p, g_1) → V
  49. Intersect(r, h_1) → W
  50. Line(O, N) → i_1
  51. Line(Q, A) → j_1
  52. Intersect(i_1, j_1) → Z
  53. Intersect(n, j_1) → A_1
  54. Segment(L, J) → k_1
  55. Segment(J, D) → l_1
  56. Segment(G, L) → m_1
  57. Segment(N, L) → n_1
  58. Segment(M, G) → p_1
  59. Segment(K, M) → q_1
  60. Segment(D, K) → r_1
  61. Segment(G, D) → s_1
  62. Segment(M, N) → t_1
  63. Segment(O, N) → a_2
  64. Segment(J, O) → b_2
  65. Segment(K, O) → c_2
  66. Segment(P, Q) → d_2
  67. Midpoint(S, V) → B_1
  68. Midpoint(R, U) → C_1
  69. Line(G, B_1) → e_2
  70. Line(J, C_1) → f_2
  71. Intersect(e_2, f_2) → D_1
  72. Point(l_1) → E_1
  73. Line(P, E_1) → g_2
  74. Line(U, S) → h_2
  75. Intersect(g_2, h_2) → F_1
  76. Line(V, F_1) → i_2
  77. Line(R, E_1) → j_2
  78. Intersect(i_2, j_2) → G_1
  79. Conic(R, U, G_1, S, V) → k_2
  80. Circle(J, D_1) → p_2
  81. Line(G, D_1) → l_2
  82. Line(J, D_1) → m_2
  83. Intersect(p_2, m_2, 2) → H_1
  84. Intersect(p_2, l_2, 2) → I_1
  85. Line(V, S) → n_2
  86. Line(R, U) → q_2
  87. Line(D_1, n_2) → r_2
  88. Line(D_1, q_2) → s_2
  89. Intersect(p_2, r_2, 2) → J_1
  90. Intersect(p_2, s_2, 2) → K_1
  91. Line(H_1, K_1) → t_2
  92. Line(J_1, I_1) → a_3
  93. Intersect(t_2, a_3) → L_1
  94. Line(L_1, J) → b_3
  95. Intersect(p_2, b_3, 2) → M_1
  96. Line(M_1, D_1) → c_3
  97. OrthogonalLine(D_1, c_3) → d_3
  98. Intersect(k_2, d_3, 1) → N_1
  99. Intersect(k_2, c_3, 2) → O_1
  100. Intersect(k_2, c_3, 1) → P_1
  101. Intersect(k_2, d_3, 2) → Q_1
  102. Segment(N_1, Q_1) → e_3
  103. Segment(O_1, P_1) → f_3
  104. Segment(D_1, C) → g_3
  105. OrthogonalLine(P, d_2) → h_3

AI 绘图提示语参考

画一个椭圆透视投影的演示图,包含两条互相垂直的线段,它们分别与坐标轴相交形成四个点,再通过这些点构造出两条互相垂直的线段,并以此为基础绘制两个圆。接着,找到这些圆与线段的交点,并利用这些交点绘制两条线段,再找到它们的交点。最后,通过这些交点绘制两条线段,并找到它们的交点,从而形成一个闭合的椭圆。
以上提示语为根据原始绘图命令整理而来,仅供参考。