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生成器图形构造

生成器图形构造
几何画板及绘图内容加载中，请稍等……
2022-04-04 02:19
向量三角函数解析几何几何作图
①本范例演示如何通过 GeoGebra 命令构造一个复杂的几何图形，涉及点、线、圆和 Voronoi 图的生成；②核心数学概念包括几何作图、变换、三角函数和解析几何；③作图要点：使用了 Line（直线）、Translate（平移）、Circle（圆）、Voronoi（Voronoi 图）等 GeoGebra 命令，以及 A1 至 A15 等对象进行精确构造；④适合高中及以上数学学习者，用于理解几何构造和算法应用。

GeoGebra 命令及参数

  1. Line(A12, A13) → r
  2. Line(A12, A14) → s
  3. Line(A13, A14) → t
  4. Translate(s, Vector[(offset * UnitOrthogonalVector[s])]) → s1
  5. Translate(s, Vector[((-offset) * UnitOrthogonalVector[s])]) → s2
  6. Translate(r, Vector[(offset * UnitOrthogonalVector[r])]) → r1
  7. Translate(r, Vector[((-offset) * UnitOrthogonalVector[r])]) → r2
  8. Translate(t, Vector[((-offset) * UnitOrthogonalVector[t])]) → t2
  9. Translate(t, Vector[(offset * UnitOrthogonalVector[t])]) → t1
  10. Line(A15, A1) → f
  11. Translate(f, Vector[((-offset) * UnitOrthogonalVector[f])]) → f2
  12. Line(A4, A5) → g
  13. Translate(f, Vector[(offset * UnitOrthogonalVector[f])]) → f1
  14. Translate(g, Vector[(offset * UnitOrthogonalVector[g])]) → g1
  15. Line(A9, A6) → h
  16. Translate(g, Vector[((-offset) * UnitOrthogonalVector[g])]) → g2
  17. Translate(h, Vector[(offset * UnitOrthogonalVector[h])]) → h1
  18. Translate(h, Vector[((-offset) * UnitOrthogonalVector[h])]) → h2
  19. Line(A15, A2) → i
  20. Line(A4, A7) → k
  21. Line(A9, A2) → j
  22. Line(A6, A7) → l
  23. Translate(i, Vector[(offset * UnitOrthogonalVector[i])]) → i1
  24. Translate(i, Vector[((-offset) * UnitOrthogonalVector[i])]) → i2
  25. Translate(j, Vector[(offset * UnitOrthogonalVector[j])]) → j1
  26. Translate(j, Vector[((-offset) * UnitOrthogonalVector[j])]) → j2
  27. Translate(k, Vector[(offset * UnitOrthogonalVector[k])]) → k1
  28. Translate(k, Vector[((-offset) * UnitOrthogonalVector[k])]) → k2
  29. Translate(l, Vector[(offset * UnitOrthogonalVector[l])]) → l1
  30. Translate(l, Vector[((-offset) * UnitOrthogonalVector[l])]) → l2
  31. Line(A8, A10) → n
  32. Line(A10, A11) → p
  33. Line(A5, A3) → m
  34. Line(A8, A11) → q
  35. Line(A1, A3) → a
  36. Translate(m, Vector[(offset * UnitOrthogonalVector[m])]) → m1
  37. Translate(m, Vector[((-offset) * UnitOrthogonalVector[m])]) → m2
  38. Translate(n, Vector[(offset * UnitOrthogonalVector[n])]) → n1
  39. Translate(n, Vector[((-offset) * UnitOrthogonalVector[n])]) → n2
  40. Translate(p, Vector[(offset * UnitOrthogonalVector[p])]) → p1
  41. Translate(p, Vector[((-offset) * UnitOrthogonalVector[p])]) → p2
  42. Translate(q, Vector[(offset * UnitOrthogonalVector[q])]) → q1
  43. Translate(q, Vector[((-offset) * UnitOrthogonalVector[q])]) → q2
  44. Translate(a, Vector[(offset * UnitOrthogonalVector[a])]) → a1
  45. Translate(a, Vector[((-offset) * UnitOrthogonalVector[a])]) → a2
  46. Circle(A1, offset) → B1
  47. Circle(A2, offset) → B2
  48. Circle(A3, offset) → B3
  49. Circle(A4, offset) → B4
  50. Circle(A5, offset) → B5
  51. Circle(A6, offset) → B6
  52. Circle(A7, offset) → B7
  53. Circle(A8, offset) → B8
  54. Circle(A9, offset) → B9
  55. Circle(A10, offset) → B10
  56. Circle(A11, offset) → B11
  57. Circle(A12, offset) → B12
  58. Circle(A13, offset) → B13
  59. Circle(A14, offset) → B14
  60. Circle(A15, offset) → B15
  61. Voronoi(A1:A15) → grafo1
  62. Circle(A1, C1) → D1
  63. Circle(A2, C2) → D2
  64. Circle(A3, C3) → D3
  65. Circle(A4, C4) → D4
  66. Circle(A5, C5) → D5
  67. Circle(A6, C6) → D6
  68. Circle(A7, C7) → D7
  69. Circle(A8, C8) → D8
  70. Circle(A9, C9) → D9
  71. Circle(A10, C10) → D10
  72. Circle(A11, C11) → D11
  73. Circle(A12, C12) → D12
  74. Circle(A13, C13) → D13
  75. Circle(A14, C14) → D14
  76. Circle(A15, C15) → D15
  77. Circle(A1, C1 + offset) → E1
  78. Circle(A2, C2 + offset) → E2
  79. Circle(A3, C3 + offset) → E3
  80. Circle(A4, C4 + offset) → E4
  81. Circle(A5, C5 + offset) → E5
  82. Circle(A6, C6 + offset) → E6
  83. Circle(A7, C7 + offset) → E7
  84. Circle(A8, C8 + offset) → E8
  85. Circle(A9, C9 + offset) → E9
  86. Circle(A10, C10 + offset) → E10
  87. Circle(A11, C11 + offset) → E11
  88. Circle(A12, C12 + offset) → E12
  89. Circle(A13, C13 + offset) → E13
  90. Circle(A14, C14 + offset) → E14
  91. Circle(A15, C15 + offset) → E15
  92. Circle(A1, C1 - offset) → F1
  93. Circle(A2, C2 - offset) → F2
  94. Circle(A3, C3 - offset) → F3
  95. Circle(A4, C4 - offset) → F4
  96. Circle(A5, C5 - offset) → F5
  97. Circle(A6, C6 - offset) → F6
  98. Circle(A7, C7 - offset) → F7
  99. Circle(A8, C8 - offset) → F8
  100. Circle(A9, C9 - offset) → F9
  101. Circle(A10, C10 - offset) → F10
  102. Circle(A11, C11 - offset) → F11
  103. Circle(A12, C12 - offset) → F12
  104. Circle(A13, C13 - offset) → F13
  105. Circle(A14, C14 - offset) → F14
  106. Circle(A15, C15 - offset) → F15

AI 绘图提示语参考

在平面内先取若干基准点，分别用它们两两连线得到三条核心线，并对每条核心线作垂直方向的平移得到上下成对的平行线；再用不同基准点对形成另外几条线段（作为外围边），同样把这些外围线整体向法向平移生成对应的成对平行线。随后以三组基准点为圆心、给定同一半径画三条圆，形成与前述线网交叠的几何构造；整体体现向量平移与线-圆相交的结构。
以上提示语为根据原始绘图命令整理而来，仅供参考。