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Generator Figure Construction

Generator Figure Construction
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2022-04-04 02:19
VectorTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the construction of a complex geometric figure using GeoGebra commands, involving points, lines, circles, and Voronoi diagrams. Key math concepts include geometric construction, transformation, trigonometry, and analytical geometry. Construction highlights: utilized commands like Line, Translate, Circle, Voronoi, and objects A1-A15 for precise creation. Suitable for high school and above learners to understand geometric constructions and algorithmic applications.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

On a plane, choose several reference points and connect them pairwise to form three main lines. Translate each main line in the direction orthogonal to itself to create two parallel copies (a pair above and below). Next, form several additional lines using other reference points as the outer boundary, and for each of these lines create corresponding two translated parallel copies in the same orthogonal direction. Finally, draw three circles centered at three of the reference points using the same given radius, so the circles intersect and interact with the line network, producing a structured geometric construction with translations, parallel lines, and line–circle overlaps.
The prompt above was compiled from the original drawing commands and is for reference only.