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泰森多边形生成范例

泰森多边形生成范例
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2015-11-20 22:17
多边形解析几何几何作图
①本范例演示如何根据一组样本点生成泰森多边形；②涉及的核心数学概念包括多边形构造、向量、二维解析几何；③作图要点：使用 GeoGebra 命令 Polygon（多边形）、Segment（线段）、LineBisector（角平分线）、Intersect（交点）、Point（点）；④适合高中数学教学或几何作图学习。

GeoGebra 命令及参数

  1. Polygon(C, B, I) → poly1, i, c, b
  2. Polygon(A, B, G) → poly2, g, a_1, b_1
  3. Polygon(I, G, B) → poly3, b_2, i_1, g_1
  4. Polygon(G, H, A) → poly4, a_2, g_2, h
  5. Polygon(E, I, G) → poly5, g_3, e, i_2
  6. Polygon(E, H, G) → poly6, g_4, e_1, h_1
  7. Polygon(F, E, H) → poly7, h_2, f, e_2
  8. Polygon(D, F, E) → poly8, e_3, d, f_1
  9. Polygon(I, D, E) → poly9, e_4, i_3, d_1
  10. Polygon(C, D, I) → poly10, i_4, c_1, d_2
  11. Segment(L, M) → j
  12. Segment(K, L) → k
  13. Segment(K, J) → l
  14. Segment(N, J) → m
  15. Segment(M, N) → n
  16. LineBisector(D, F) → p
  17. LineBisector(D, E) → q
  18. LineBisector(F, E) → r
  19. LineBisector(D, I) → s
  20. LineBisector(E, I) → t
  21. LineBisector(A, H) → j_1
  22. LineBisector(A, G) → k_1
  23. LineBisector(G, H) → l_1
  24. Intersect(j_1, k_1) → O
  25. Intersect(p, q) → P
  26. Intersect(q, s) → Q
  27. LineBisector(F, H) → m_1
  28. LineBisector(H, E) → n_1
  29. Intersect(r, m_1) → R
  30. LineBisector(H, E) → p_1
  31. LineBisector(E, G) → q_1
  32. LineBisector(G, H) → r_1
  33. Intersect(l_1, n_1) → S
  34. LineBisector(H, G) → s_1
  35. LineBisector(H, A) → t_1
  36. LineBisector(A, G) → c_2
  37. LineBisector(B, G) → f_2
  38. LineBisector(G, A) → j_2
  39. LineBisector(A, B) → k_2
  40. Point(m) → T
  41. LineBisector(H, G) → l_2
  42. Segment(R, S) → m_2
  43. Segment(S, O) → n_2
  44. LineBisector(C, B) → p_2
  45. LineBisector(C, I) → q_2
  46. LineBisector(I, B) → r_2
  47. Intersect(p_2, q_2) → U
  48. Segment(P, Q) → s_2
  49. Segment(Q, U) → t_2
  50. LineBisector(G, I) → a_3
  51. Intersect(f_2, r_2) → V
  52. Segment(U, V) → b_3
  53. Segment(R, P) → c_3
  54. LineBisector(E, G) → d_3
  55. LineBisector(G, I) → f_3
  56. LineBisector(I, E) → h_3
  57. Intersect(t, m_1) → W
  58. Segment(R, W) → j_3
  59. Segment(Q, W) → k_3
  60. Segment(W, V) → l_3
  61. LineBisector(H, G) → m_3
  62. LineBisector(G, A) → n_3
  63. Segment(V, O) → p_3
  64. Segment(V, W) → q_3
  65. Segment(V, U) → r_3
  66. Point(i_4) → Z
  67. Segment(Q, Z) → s_3
  68. Intersect(p_2, l) → A_1
  69. Segment(U, A_1) → t_3
  70. Intersect(m_1, e_2) → B_1
  71. Segment(R, B_1) → a_4
  72. Intersect(p, e_3) → C_1
  73. Segment(P, C_1) → b_4
  74. Polygon(M, N, J, K, L) → poly11, m_4, n_4, j_4, k_4, l_4
  75. Polygon(K, A_1, U, Q) → poly12, k_5, a_5, u, q_4
  76. Intersect(k_2, r_2) → D_1
  77. Polygon(D_1, J, A_1, U, V) → poly13, d_4, j_5, a_6, u_1, v
  78. Intersect(t, l_1) → E_1
  79. Polygon(D_1, N, E_1, S, R, W, V) → poly14, d_5, n_5, e_5, s_4, r_4, w, v_1
  80. Polygon(E_1, M, R, S) → poly15, e_6, m_5, r_5, s_5
  81. Polygon(R, W, Q, L) → poly16, r_6, w_1, q_5, l_5
  82. Polygon(W, V, U, Q) → poly17, w_2, v_2, u_2, q_6