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法国企业责任标志的几何构造

法国企业责任标志的几何构造
几何画板及绘图内容加载中，请稍等……
2019-12-22 05:51
多边形向量函数变换几何作图
该范例演示了如何利用几何变换与函数曲线构造一个企业责任标志图形，将抽象的品牌符号转化为精确的数学绘图。核心数学概念包括二维向量、旋转、平移、对称、三角形与菱形性质、中线、双曲线以及参数曲线。作图要点涉及GeoGebra中的Line、OrthogonalLine、LineBisector、Vector、OrthogonalVector、Mirror、Intersect、Rotate、Midpoint、Polygon、Circle、CurveCartesian、CircleArc等命令，通过构造点A、B、s、b、m、u、v、I、h、C、d、h'、N、B_1、O、E、C_1、E_1、O'、O''、O'''、G、G'、q_2、N'_1、p_2、V、W、a、R、Q、A_2、K、K'、K''、K'''、P、P'、T、S等对象，综合运用几何关系与代数曲线实现标志的对称与层次。适合高中及以上学段学习几何变换、向量运算与函数图像的综合应用，也可作为数学与设计结合的跨学科教学案例。

GeoGebra 命令及参数

  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. OrthogonalLine(I, b) → h
  7. LineBisector(A, C) → d
  8. Mirror(h, d) → h'
  9. Intersect(m, h') → N
  10. Intersect(m, d) → E
  11. Rotate(B_1, (-(20°)), E) → C_1
  12. Rotate(C_1, (-(20°)), E) → E_1
  13. Rotate(O, (-(15°)), E) → O'
  14. Rotate(O', (-(60°)), E) → O''
  15. Rotate(O'', (-(60°)), E) → O'''
  16. Rotate(O''', (-(60°)), E) → G
  17. Rotate(G, (-(60°)), E) → G'
  18. OrthogonalLine(G', b) → q_2
  19. Rotate(N, (-(60°)), E) → N'_1
  20. LineBisector(E_1, N'_1) → p_2
  21. OrthogonalLine(V, s) → a
  22. Rotate(A_2, (-(30°)), E) → K
  23. Rotate(K, (-(60°)), E) → K'
  24. Rotate(K', (-(60°)), E) → K''
  25. Rotate(K'', (-(60°)), E) → K'''
  26. Rotate(K''', (-(60°)), E) → P
  27. Rotate(P, (-(60°)), E) → P'
  28. Intersect(h, m) → S
  29. OrthogonalLine(C, v, xOyPlane) → f
  30. Intersect(f, m) → U
  31. Midpoint(C, A) → J
  32. OrthogonalLine(M, d) → i
  33. Mirror(i, m) → i'
  34. OrthogonalLine(B, u, xOyPlane) → g
  35. Intersect(g, f) → D
  36. Mirror(M, m) → M'
  37. Midpoint(E, M') → L
  38. Intersect(g, h') → A_1
  39. Polygon(A, B, D, C) → q11, a_3, b_2, d_2, c_3
  40. Circle(E, N) → c
  41. Circle(E, O) → k
  42. OrthogonalLine(F, b) → j
  43. OrthogonalLine(V, a) → e
  44. Rotate(N, 60°, E) → N'
  45. Rotate(N', 60°, E) → N''
  46. Rotate(N'', 60°, E) → N'''
  47. Rotate(N'_1, (-(60°)), E) → J_1
  48. Circle(E, A_2) → p
  49. Rotate(G', (-(60°)), E) → G''
  50. CurveCartesian(((1 - t)^(4) * N) + (((4 * (1 - t)^(3)) * t) * Q) + (((6 * (1 - t)^(2)) * t^(2)) * T) + (((4 * (1 - t)) * t^(3)) * R) + (t^(4) * W), t, 0, 1) → n
  51. Mirror(n, m) → n'
  52. Rotate(n, (-(60°)), E) → n'_1
  53. Rotate(n', (-(60°)), E) → n''
  54. Rotate(n'_1, (-(60°)), E) → l
  55. Rotate(n'', (-(60°)), E) → n'''
  56. Rotate(l, (-(60°)), E) → l'
  57. Rotate(n''', (-(60°)), E) → q
  58. Rotate(q, (-(60°)), E) → q'
  59. Rotate(l', (-(60°)), E) → l''
  60. Mirror(q', d) → q''
  61. Mirror(l'', d) → l'''
  62. CurveCartesian(((1 - t)^(4) * O') + (((4 * (1 - t)^(3)) * t) * Q') + (((6 * (1 - t)^(2)) * t^(2)) * T') + (((4 * (1 - t)) * t^(3)) * R') + (t^(4) * W), t, 0, 1) → r
  63. Line(O', W) → t
  64. Mirror(r, t) → r'
  65. Rotate(r, (-(60°)), E) → r'_1
  66. Rotate(r', (-(60°)), E) → r''
  67. Rotate(r'_1, (-(60°)), E) → w
  68. Rotate(r'', (-(60°)), E) → r'''
  69. Rotate(r''', (-(60°)), E) → a_1
  70. Rotate(w, (-(60°)), E) → w'
  71. Rotate(a_1, (-(60°)), E) → b_1
  72. Rotate(w', (-(60°)), E) → w''
  73. Rotate(w'', (-(60°)), E) → w'''
  74. Rotate(b_1, (-(60°)), E) → c_1
  75. CurveCartesian(((1 - t)^(4) * K) + (((4 * (1 - t)^(3)) * t) * Q'_1) + (((6 * (1 - t)^(2)) * t^(2)) * T'_1) + (((4 * (1 - t)) * t^(3)) * R'_1) + (t^(4) * W), t, 0, 1) → d_1
  76. Line(K, W) → f_1
  77. Mirror(d_1, f_1) → e_1
  78. Rotate(d_1, (-(60°)), E) → g_1
  79. Rotate(g_1, (-(60°)), E) → h_1
  80. Rotate(h_1, (-(60°)), E) → i_1
  81. Rotate(i_1, (-(60°)), E) → j_1
  82. Rotate(j_1, (-(60°)), E) → k_1
  83. Rotate(e_1, (-(60°)), E) → l_1
  84. Rotate(l_1, (-(60°)), E) → m_1
  85. Rotate(m_1, (-(60°)), E) → n_1
  86. Rotate(n_1, (-(60°)), E) → o_1
  87. Rotate(o_1, (-(60°)), E) → p_1
  88. Intersect(h', b) → Z
  89. Mirror(I, m) → I'
  90. Polygon(Z, I, I', A_1) → q1, z_1, i_2, q_1, r_1
  91. Circle(E, B_1) → s_1
  92. Rotate(E_1, (-(40°)), E) → F_1
  93. Rotate(F_1, (-(20°)), E) → G_1
  94. Rotate(G_1, (-(40°)), E) → H_1
  95. Rotate(H_1, (-(60°)), E) → I_1
  96. Rotate(I_1, (-(60°)), E) → K_1
  97. Rotate(K_1, (-(60°)), E) → L_1
  98. Rotate(G_1, (-(60°)), E) → M_1
  99. Rotate(M_1, (-(60°)), E) → N_1
  100. Rotate(N_1, (-(60°)), E) → O_1
  101. Rotate(O_1, (-(60°)), E) → P_1
  102. Polygon(N', O_1, L_1) → t1, t_1, f_2, g_2
  103. Mirror(N', E) → N''_1
  104. Mirror(O_1, E) → Q_1
  105. Mirror(L_1, E) → R_1
  106. Polygon(N''_1, Q_1, R_1) → t1', h_2, n''_1, j_2
  107. Rotate(W, (-(60°)), E) → W'
  108. Rotate(W, (-(120°)), E) → W'_1
  109. Rotate(W', (-(120°)), E) → W''
  110. Rotate(W', (-(180°)), E) → W''_1
  111. Rotate(W''_1, (-(60°)), E) → S_1
  112. Polygon(E_1, F_1, N'_1) → t2, k_2, l_2, m_2
  113. Mirror(E_1, E) → T_1
  114. Mirror(F_1, E) → U_1
  115. Mirror(N'_1, E) → V_1
  116. Intersect(p_2, q_2) → W_1
  117. Polygon(T_1, U_1, V_1) → t2', v_1, n_2, u_1
  118. CircleArc(W_1, N'_1, E_1) → c_2
  119. LineBisector(E_1, F_1) → r_2
  120. Mirror(c_2, r_2) → e_2
  121. Mirror(c_2, E) → s_2
  122. Mirror(e_2, E) → t_2
  123. Mirror(c_2, m) → d_3
  124. Mirror(e_2, m) → e_3
  125. Mirror(d_3, E) → f_3
  126. Mirror(e_3, E) → g_3
  127. Polygon(I_1, M_1, S) → t3, s_3, a_2, h_3
  128. Rotate(g_3, (-(60°)), E) → k_3
  129. Mirror(k_3, m) → p_3

AI 绘图提示语参考

绘制一个对称的几何标志：先画一条水平基准线，过其左端点作垂线，再作两端点的中垂线。以中垂线与垂线的交点为旋转中心，将若干点按逆时针方向依次旋转20度、60度等角度，形成多层对称结构。连接关键点构成一个菱形，并以其中心为圆心画两个同心圆。从菱形顶点向基准线作垂线，与另一条斜线相交，得到交点。再通过旋转复制这些交点，形成环绕中心的多组对称点。最后用曲线连接部分点，形成双曲线状的弧线，整体呈现对称、层叠的几何图案。
以上提示语为根据原始绘图命令整理而来，仅供参考。