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2D Vectors and Geometric Construction

2D Vectors and Geometric Construction
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2020-01-05 03:31
PolygonVectorTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates how to draw the iconic Louis Vuitton logo using 2D vectors and geometric constructions. The core mathematical concepts involved include vectors, line segments, linear functions, ratios, equilateral triangles, cones, and trigonometric functions. The construction highlights GeoGebra commands such as Line, OrthogonalLine, LineBisector, Vector, OrthogonalVector, Intersect, Midpoint, Mirror, Polygon, and CircleArc. It is suitable for high school and above, focusing on vector operations, geometric transformations, and the application of analytical geometry.

GeoGebra Commands & Parameters

  1. Line(A, B) → s
  2. OrthogonalLine(A, s) → b
  3. LineBisector(A, B) → m
  4. Vector(A, B) → u
  5. OrthogonalVector(u) → v
  6. LineBisector(A, C) → d
  7. Intersect(m, d) → I
  8. OrthogonalLine(V, m) → f_1
  9. OrthogonalLine(A_1, m) → h_1
  10. OrthogonalLine(B_1, m) → i_1
  11. Midpoint(C, A) → J
  12. OrthogonalLine(L, d) → j
  13. Intersect(j, f_1) → F_1
  14. OrthogonalLine(C_1, d) → l_1
  15. Intersect(l_1, f_1) → J_1
  16. OrthogonalLine(D_1, d) → n_1
  17. Intersect(n_1, f_1) → L_1
  18. Intersect(n_1, h_1) → K_1
  19. OrthogonalLine(G_1, d) → j_1
  20. OrthogonalLine(K, d) → i
  21. Mirror(N_1, m) → Q_1
  22. OrthogonalLine(V_1, i_1) → s_1
  23. Intersect(s_1, i_1) → W_1
  24. Mirror(i, m) → i'
  25. Intersect(i, s) → G
  26. OrthogonalLine(T, b) → t
  27. OrthogonalLine(H, b) → r
  28. Intersect(j_1, r) → I_1
  29. Line(F_1, I_1) → k_1
  30. Line(J_1, k_1) → m_1
  31. Intersect(m_1, t) → P_1
  32. Line(P_1, U_1) → p_1
  33. Line(T_1, p_1) → r_1
  34. Intersect(r, r_1) → M_2
  35. Line(C, B) → h
  36. Intersect(i, h) → H_1
  37. Intersect(m, d) → E
  38. OrthogonalLine(C, v, xOyPlane) → f
  39. Intersect(f, m) → U
  40. OrthogonalLine(B, u, xOyPlane) → g
  41. Intersect(g, f) → D
  42. Polygon(A, B, D, C) → q11, a_3, b_2, d_2, c_3
  43. OrthogonalLine(M, d) → k
  44. OrthogonalLine(R, b) → l
  45. OrthogonalLine(S, b) → p
  46. OrthogonalLine(O, m) → c
  47. OrthogonalLine(W, m) → e
  48. Intersect(k, p) → F
  49. Intersect(k, l) → Z
  50. OrthogonalLine(N, b) → n
  51. Intersect(h, n) → Q
  52. Mirror(Q, m) → Q'
  53. Mirror(Q'', m) → Q'_1
  54. Polygon(Q'', Q'_1, Q, Q') → q2, q'', q'_1, q_2, q'
  55. Polygon(Q'_1, D, B, A, Q', Q) → poly2, q, d_1, b_1, a_1, g_1, q_1
  56. OrthogonalLine(P, m) → a
  57. Line(R_1, r_1) → t_1
  58. Intersect(t_1, l) → Z_1
  59. Intersect(m_1, e) → B_2
  60. Line(F, B_2) → c_1
  61. Intersect(p, n_1) → D_2
  62. Line(D_2, c_1) → e_1
  63. Intersect(c, c_1) → E_2
  64. Intersect(c, e_1) → F_2
  65. Line(G_2, c_1) → f_2
  66. Intersect(c_1, f_2) → H_2
  67. Intersect(f_2, a) → I_2
  68. Line(K_2, e_1) → g_2
  69. Polygon(N_1, M_1, U_1, P_1, J_1, L_1, K_1, F_1, I_1, M_2, T_1, Q_1, S_1, W_1, V_1) → poly1, h_2, s_2, t_2, a_2, c_2, e_2, f_3, i_2, j_2, k_2, l_2, m_2, n_2, p_2, r_2
  70. Intersect(g_2, a) → L_2
  71. Polygon(I_2, L_2, S, F, E_2, G_2, K_2, F_2, D_2, C_2, A_2, R_1, Z_1, R) → poly3, g_3, r_3, s_3, f_4, p_3, q_3, h_3, i_3, j_3, k_3, l_3, m_3, n_3, z_1
  72. LineBisector(A_2, C_2) → t_3
  73. Intersect(r_1, t_3) → O_1
  74. CircleArc(O_1, C_2, A_2) → d_3
  75. Polygon(Q', A, C, D, Q'_1, Q'') → poly4, b_3, a_4, c_4, d_4, e_3, g_4
  76. Vector(F, E_2) → w
  77. Vector(I_1, F_1) → u_1
  78. LineBisector(S, N_2) → h_4
  79. Intersect(t, h_4) → S_2
  80. CircleArc(S_2, S, N_2) → e_4
  81. Polygon(S, N_2, F) → t1, f_5, s_4, i_4
  82. Intersect(b, c) → T_2
  83. Mirror(T_2, m) → U_2
  84. Polygon(T_2, U_2, D, C) → q1, j_4, u_2, d_5, c_5
  85. LineBisector(O_2, M_1) → k_4
  86. Intersect(i, k_4) → V_2
  87. CircleArc(V_2, O_2, M_1) → p_4
  88. Polygon(O_2, F_1, M_1) → t2, l_4, o_2, m_4
  89. LineBisector(P_2, K_2) → n_4
  90. Intersect(g_2, n_4) → W_2
  91. LineBisector(Q_2, Q_1) → r_4
  92. Intersect(r_4, i') → Z_2
  93. CircleArc(Z_2, Q_1, Q_2) → t_4
  94. LineBisector(V_1, R_2) → b_4
  95. Intersect(b_4, a) → A_3
  96. CircleArc(A_3, R_2, V_1) → e_5
  97. Polygon(P_2, K_2, F_2) → t3, g_5, h_5, i_5
  98. Polygon(V_1, R_2, U_1) → t4, j_5, v_1, k_5
  99. Polygon(Q_1, Q_2, T_1) → t5, l_5, m_5, n_5
  100. Intersect(n_4, p_1) → J_2
  101. Midpoint(W_2, J_2) → B_3
  102. CircleArc(B_3, K_2, P_2) → q_4
  103. Intersect(c, b) → C_3
  104. Mirror(J, m) → J'
  105. Mirror(C_3, m) → D_3
  106. Polygon(J, C_3, D_3, J') → q3, j_6, p_5, q_5, j'

AI Drawing Prompt Reference

Draw the Louis Vuitton logo using 2D vectors and geometric constructions. Start by drawing line segment AB, then construct the perpendicular bisector m of AB, draw vector u and its perpendicular vector v, and use these to construct a series of intersections and line segments to form the logo's outline.
The prompt above was compiled from the original drawing commands and is for reference only.