莱昂纳多·达·芬奇与最后的晚餐

莱昂纳多·达·芬奇与最后的晚餐
几何画板及绘图内容加载中,请稍等……
2023-03-20 19:52
所属专题 geometriadinamica.es
①本范例通过动态演示几何图形构造,模拟莱昂纳多·达·芬奇名作《最后的晚餐》中的构图布局;②涉及核心数学概念包括几何作图、坐标几何、相似变换、分形几何;③构造过程中运用了Line(直线)、OrthogonalLine(垂线)、Point(点)、Dilate(缩放)、Circle(圆)、Intersect(交点)、Polygon(多边形)、Midpoint(中点)、Segment(线段)、CircleArc(圆弧)等GeoGebra命令与对象;④适合高中及以上数学爱好者、几何作图教学与艺术几何交叉研究。

GeoGebra 命令及参数

  1. Line(H1, H2) → a
  2. OrthogonalLine(A, a) → c
  3. Line(A, a) → b
  4. Point(b) → B
  5. OrthogonalLine(B, b) → f
  6. Dilate(B, pr, A) → Dil
  7. Circle(A, Dil) → d
  8. Intersect(d, c) → D5, C
  9. OrthogonalLine(C, c) → e
  10. Intersect(f, e) → D
  11. If(paso > 0 ∧ paso < 7, 1, 0) → t_1
  12. If(paso > 1 ∧ paso < 7, 1, 0) → t_2
  13. If(paso > 2 ∧ paso < 7, 1, 0) → t_3
  14. If(paso > 3 ∧ paso < 7, 1, 0) → t_4
  15. If(paso > 4 ∧ paso < 7, 1, 0) → t_5
  16. If(paso > 5 ∧ paso < 7, 1, 0) → t_6
  17. Polygon(A, B, D, C) → P, a_1, b_1, d_1, c_1
  18. Point(b_1) → W_2
  19. Midpoint(A, B) → F
  20. Circle(A, F) → g
  21. Circle(B, F) → h
  22. Intersect(g, c_1) → E,
  23. Intersect(h, b_1) → G,
  24. Segment(E, G) → i
  25. OrthogonalLine(B_1, a_1) → j
  26. Point(j) → H
  27. CircleArc(A, H, E) → k
  28. CircleArc(B, G, H) → p
  29. Intersect(j, i) → I
  30. Segment(H, I) → l
  31. OrthogonalLine(B_2, a_1) → m
  32. Point(m) → K
  33. Midpoint(A, K) → L
  34. Midpoint(K, B) → M
  35. OrthogonalLine(M, a_1) → n
  36. OrthogonalLine(L, a_1) → q
  37. Intersect(i, q) → N
  38. Intersect(n, i) → O
  39. Segment(N, L) → r
  40. Segment(O, M) → s
  41. Segment(K, E) → f_1
  42. Segment(K, G) → g_1
  43. Intersect(m, i) → Q
  44. Segment(Q, A) → t
  45. Segment(Q, B) → e_1
  46. Circle(N, N1) → h_1
  47. Circle(N, N2) → k_1
  48. Circle(N, N4) → q_1
  49. Circle(N, N5) → r_1
  50. OrthogonalLine(B_3, a_1) → i_1
  51. Point(i_1) → S
  52. Point(i_1) → T
  53. Point(i_1) → U
  54. Point(i_1) → V
  55. Point(i_1) → W
  56. Point(i_1) → Y
  57. OrthogonalLine(G, i_1) → j_1
  58. Point(j_1) → Z
  59. Point(j_1) → C_1
  60. Point(j_1) → D_1
  61. Point(j_1) → E_1
  62. Point(j_1) → F_1
  63. Circle(O, F_1) → p_1
  64. Circle(O, E_1) → s_1
  65. Circle(O, D_1) → c_2
  66. Circle(O, C_1) → d_2
  67. Circle(O, Z) → e_2
  68. Circle(L, V) → f_2
  69. Circle(L, U) → g_2
  70. Circle(L, T) → h_2
  71. Circle(L, S) → k_2
  72. Circle(L, Y) → p_2
  73. Intersect(i_1, j_1) → H_1
  74. Circle(L, H_1) → q_2
  75. Intersect(g_2, a_1) → I_1, J_1
  76. Intersect(f_2, a_1) → K_1, L_1
  77. Intersect(h_2, a_1) → M_1,
  78. Intersect(k_2, a_1) → N_1,
  79. Intersect(p_2, a_1) → O_1,
  80. Intersect(q_2, a_1) → P_1,
  81. Intersect(p_1, s) → Q_1,
  82. Intersect(s_1, s) → R_1,
  83. Intersect(c_2, s) → S_1,
  84. Intersect(d_2, s) → T_1,
  85. Intersect(e_2, s) → U_1,
  86. Segment(Z, L_1) → l_1
  87. Segment(C_1, J_1) → m_1
  88. Segment(M_1, D_1) → n_1
  89. Segment(E_1, N_1) → a_2
  90. Segment(O_1, F_1) → b_2
  91. Segment(Q_1, Y) → i_2
  92. Segment(S, R_1) → j_2
  93. Segment(S_1, T) → l_2
  94. Segment(U, T_1) → m_2
  95. Segment(V, U_1) → n_2
  96. OrthogonalLine(B_4, a_1) → r_2
  97. Line(W_1, r_2) → s_2
  98. Line(Y_1, r_2) → a_3
  99. Line(Z_1, r_2) → b_3
  100. Point(s_2) → C_2
  101. Point(s_2) → D_2
  102. Point(r_2) → E_2
  103. Point(r_2) → F_2
  104. Point(a_3) → G_2
  105. Point(a_3) → H_2
  106. Point(b_3) → I_2
  107. Point(b_3) → J_2
  108. Polygon(C_2, I_2, J_2, D_2) → P_2, c_3, i_3, j_3, d_3
  109. Polygon(E_2, G_2, H_2, F_2) → Q_2, e_3, g_3, h_3, f_3
  110. Line(B_5, a_1) → k_3
  111. Point(k_3) → K_2
  112. Segment(K_2, E) → l_3
  113. Segment(K_2, N) → m_3
  114. Segment(K_2, N1) → n_3
  115. Segment(K_2, N2) → p_3
  116. Segment(K_2, D_1) → q_3
  117. Segment(K_2, N4) → r_3
  118. Segment(K_2, N5) → s_3
  119. Segment(K_2, O) → a_4
  120. Segment(K_2, G) → b_4
  121. Line(B_6, a_1) → c_4
  122. Point(c_4) → L_2
  123. Point(c_4) → M_2
  124. Point(c_4) → N_2
  125. Point(c_4) → O_2
  126. Circle(M_2, ra) → d_4
  127. Circle(L_2, ra) → e_4
  128. Circle(N_2, ra) → f_4
  129. Circle(O_2, ra) → g_4
  130. Midpoint(N, L) → R_2
  131. OrthogonalLine(R_2, c_1) → h_4
  132. Intersect(c_1, h_4) → S_2
  133. Intersect(b_1, h_4) → T_2
  134. Segment(S_2, T_2) → i_4
  135. Point(c_1) → U_2
  136. Segment(K_2, U_2) → j_4
  137. Segment(K_2, W_2) → k_4

AI 绘图提示语参考

绘制一幅受达芬奇《最后的晚餐》启发的几何构图作品。先在画面中确定一条水平基准线,在其上方设定消失点位置。通过消失点向画面底部两个角点绘制辐射线,形成透视框架。以两个底角为端点绘制弧线交于上方一点,围合成梯形人物布局区域。在梯形内绘制中垂线和平行线形成网格结构,再以关键节点为圆心绘制多个同心圆和圆弧,形成具有放射对称性的装饰图案。整体构图强调水平垂直线条与圆弧曲线的对比,体现文艺复兴时期绘画的透视原理和几何美感。
以上提示语为根据原始绘图命令整理而来,仅供参考。