MathPlotAI Logo MathPlotAI

Logo Carrefour (Bézier Curve)

Logo Carrefour (Bézier Curve)
Loading the math board and drawing, please wait…
2019-06-03 19:14
VectorFunctionCoordinate Geometry
This example demonstrates how to use Bézier curves to draw the Carrefour logo. Key mathematical concepts include Bézier curves, vectors, and geometric transformations. Using commands like Polygon, LineBisector, Vector, Line, Mirror, and Intersect in GeoGebra, the various parts of the logo are constructed. Suitable for high school and above students or teachers for teaching and learning geometric transformations and curve drawing.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 8) → polígono1, f, D, E, F, G, H, g, h, i, j, k, l, m, C
  2. LineBisector(C, D) → p
  3. Vector(H, G) → u
  4. Line(M, p) → f_1
  5. Mirror(F, f_1) → F'
  6. Mirror(F', f_1) → F''
  7. Line(J, p) → r
  8. LineBisector(A, B) → n
  9. Vector(A, B) → v
  10. Line(N, n) → h_1
  11. Intersect(h_1, r) → P
  12. Line(O, n) → g_1
  13. Line(F, p) → a
  14. Intersect(g_1, a) → Q
  15. Intersect(g_1, r) → S_1
  16. Line(H, W) → r_3
  17. Mirror(P, r_3) → P'_1
  18. Midpoint(S_1, P'_1) → A_2
  19. Intersect(n, p) → I
  20. CircleArc(I, F, G) → c
  21. Mirror(c, p) → c'
  22. Mirror(c', n) → c''
  23. Mirror(G, n) → G'
  24. Mirror(H, n) → H'
  25. LineBisector(J, D) → t
  26. LineBisector(F, K) → q
  27. Intersect(q, t) → L
  28. CircleArc(L, F, K) → e
  29. Mirror(P, f_1) → P'
  30. Mirror(Q, f_1) → Q'
  31. CircleArc(R, Q, Q') → c_1
  32. LineBisector(P, Q) → i_1
  33. Intersect(i_1, a) → S
  34. CircleArc(I, A, B) → e_1
  35. Rotate(e_1, 90°, I) → k_1
  36. LineBisector(H, K) → s
  37. OrthogonalLine(R, f_1) → b
  38. Intersect(b, s) → T
  39. CircleArc(U, K, H) → p_1
  40. Mirror(W, h_1) → W'
  41. LineBisector(Q, W) → j_1
  42. Intersect(j_1, n) → Z
  43. Intersect(j_1, a) → A_1
  44. Midpoint(A_1, Z) → B_1
  45. LineBisector(W', F) → l_1
  46. Intersect(l_1, j_1) → C_1
  47. CircleArc(C_1, F, W') → r_1
  48. Intersect(t, g_1) → E_1
  49. CircleArc(E_1, D, J) → d
  50. Intersect(h_1, f_1) → D_1
  51. Segment(J, F_1) → m_1
  52. Translate(W, Vector[(-2 * v)]) → W'_1
  53. Mirror(F_1, h_1) → I_1
  54. Segment(I_1, W'_1) → n_1
  55. Mirror(I_1, f_1) → G_1
  56. Mirror(W'_1, f_1) → J_1
  57. Segment(G_1, J_1) → a_1
  58. Mirror(c', f_1) → c''_1
  59. Mirror(c'', f_1) → c'''
  60. Mirror(r_1, f_1) → d_2
  61. Mirror(p_1, f_1) → e_2
  62. Mirror(J, f_1) → J'
  63. Mirror(F_1, f_1) → K_1
  64. Segment(J', K_1) → b_1
  65. Mirror(d, f_1) → d'
  66. Mirror(e, f_1) → e'
  67. Mirror(e_1, f_1) → h_2
  68. Mirror(k_1, f_1) → k_2
  69. Polygon(W, W', F, Q) → c1, w, w', f_3, q_2
  70. Mirror(W, f_1) → W'_2
  71. Mirror(W', f_1) → W''
  72. Mirror(Q, f_1) → Q'_1
  73. Polygon(W'_2, W'', F', Q'_1) → c1', w'_2, w'', f', q'_1
  74. Polygon(J, K_1, J') → t1, j', j_2, l_2
  75. Polygon(W'_1, J_1, G_1) → t2, m_2, w'_1, n_2
  76. Intersect(a, m_1) → L_1
  77. Mirror(L_1, f_1) → M_1
  78. Polygon(Q, L_1, M_1, Q') → c3, q_4, p_2, r_2, s_2
  79. Polygon(B, C, D, J) → c4, b_2, c_3, d_3, j_3
  80. Polygon(F, K, H, A) → c5, f_5, k_3, h_3, a_2
  81. Mirror(D, f_1) → D'
  82. Mirror(D, f_1) → D'_1
  83. Mirror(B, f_1) → B'_2
  84. Mirror(C, f_1) → C'_2
  85. Mirror(D, f_1) → D'_2
  86. Mirror(J, f_1) → J'_3
  87. Polygon(B'_2, C'_2, D'_2, J'_3) → c4', b'_2, c'_2, d'_2, j'_3
  88. Mirror(F, f_1) → F'_1
  89. Mirror(H, f_1) → H'_1
  90. Mirror(H, f_1) → H'_2
  91. Mirror(H, f_1) → H'_3
  92. Mirror(F, f_1) → F'_2
  93. Mirror(F, f_1) → F'_3
  94. Mirror(K, f_1) → K'_3
  95. Mirror(H, f_1) → H'_4
  96. Mirror(A, f_1) → A'_2
  97. Polygon(F'_3, K'_3, H'_4, A'_2) → c5', f'_3, k'_3, h'_4, a'_2
  98. Polygon(F', A'_2, B'_2, J') → c2, i_2, t_2, g_3, i_3
  99. Mirror(A'_2, f_1) → N_1
  100. Mirror(B'_2, f_1) → O_1
  101. Mirror(J', f_1) → J''
  102. Polygon(F'', N_1, O_1, J'') → c2', f'', l_3, o_1, j''
  103. Mirror(H_1, f_1) → P_1
  104. Intersect(h_1, r_3) → Q_1
  105. Vector(H, Q_1) → u_1
  106. Mirror(W, f_1) → W'_3
  107. Mirror(Q, f_1) → Q'_2
  108. Mirror(W', f_1) → W''_1
  109. Mirror(H_1, f_1) → U_1
  110. Mirror(F'', f_1) → F'''
  111. Mirror(K, f_1) → K'
  112. Mirror(A, f_1) → A'
  113. Mirror(B, f_1) → B'
  114. CurveCartesian(((1 - t)^(2) * F'') + (((2 * (1 - t)) * t) * B_2) + (t^(2) * W), t, 0, 1) → d_1
  115. Mirror(d_1, f_1) → t_1
  116. CurveCartesian(((1 - t)^(2) * W) + (((2 * (1 - t)) * t) * A_2) + (t^(2) * Q), t, 0, 1) → q_1
  117. Mirror(q_1, f_1) → v_1
  118. CurveCartesian(((1 - t)^(2) * W'_1) + (((2 * (1 - t)) * t) * W_1) + (t^(2) * J_1), t, 0, 1) → s_1
  119. Intersect(n, r) → Z_1

AI Drawing Prompt Reference

Draw the Carrefour logo using Bézier curves and geometric transformations. Start by drawing a polygon, then use mirroring, rotation, and midpoints to construct key points and curves. Finally, determine the logo's components using the perpendicular bisectors of line segments and their intersections.
The prompt above was compiled from the original drawing commands and is for reference only.