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莫索博物馆：瓷砖图案4

莫索博物馆：瓷砖图案4
几何画板及绘图内容加载中，请稍等……
2023-03-22 21:40
向量立体几何几何作图函数图像
所属专题 geometriadinamica.es
①本范例演示三维空间中瓷砖图案的几何构造与变换；②涉及核心数学概念包括向量、三维几何、函数图像、几何变换等；③构造过程中运用了Line（线段）、Point（点）、OrthogonalLine（垂线）、Intersect（交点）、Midpoint（中点）、Mirror（镜像）、Rotate（旋转）、Vector（向量）、Translate（平移）等GeoGebra命令；④适合高中及以上学生用于学习立体几何、向量运算及几何作图的综合应用。

GeoGebra 命令及参数

  1. Line(A, B) → b
  2. Line(G, b) → e
  3. Point(e) → J
  4. OrthogonalLine(J, e) → h
  5. OrthogonalLine(G, e) → f
  6. Point(f) → H
  7. OrthogonalLine(H, f) → g
  8. Intersect(g, h) → E
  9. Midpoint(E, H) → I
  10. Midpoint(I, E) → B_1
  11. Midpoint(G, J) → D
  12. Midpoint(J, E) → F
  13. Midpoint(H, G) → K
  14. Midpoint(D, I) → L
  15. Midpoint(K, L) → M
  16. Midpoint(L, F) → N
  17. Midpoint(F, J) → O
  18. Midpoint(J, D) → P
  19. Midpoint(G, D) → Q
  20. Midpoint(K, G) → R
  21. Midpoint(Q, M) → S
  22. Midpoint(L, D) → T
  23. Midpoint(P, N) → U
  24. Midpoint(F, E) → V
  25. Midpoint(K, H) → W
  26. Midpoint(W, V) → Z
  27. Midpoint(H, I) → A_1
  28. Midpoint(N, B_1) → C_1
  29. Midpoint(Z, W) → D_1
  30. Midpoint(D, U) → E_1
  31. Midpoint(U, J) → F_1
  32. Midpoint(T, Q) → G_1
  33. Midpoint(S, G) → H_1
  34. Midpoint(S, K) → I_1
  35. Midpoint(M, T) → J_1
  36. Midpoint(T, N) → K_1
  37. Midpoint(N, O) → L_1
  38. Midpoint(F, C_1) → M_1
  39. Midpoint(C_1, L) → N_1
  40. Midpoint(L, D_1) → O_1
  41. Midpoint(D_1, K) → P_1
  42. Midpoint(H, D_1) → Q_1
  43. Midpoint(D_1, I) → R_1
  44. Midpoint(I, C_1) → S_1
  45. Midpoint(C_1, E) → T_1
  46. Mirror(F_1, h) → U_1
  47. Mirror(L_1, h) → V_1
  48. Mirror(M_1, h) → W_1
  49. Mirror(T_1, h) → Z_1
  50. Mirror(B_1, h) → A_2
  51. Mirror(L_1, h) → C_2
  52. Line(S, A_1) → t
  53. Line(I, T) → a_1
  54. Line(U, B_1) → b_1
  55. Line(E_1, N_1) → c_1
  56. Line(F_1, M_1) → d_1
  57. Line(G_1, R_1) → e_1
  58. Line(W_1, P_1) → g_1
  59. Line(Q_1, Z_1) → h_1
  60. Point(a_1) → F_2
  61. Point(b) → A1
  62. Min(90, ((a - 1) * 90)) → r1
  63. Rotate(F_2, ((-r1))°, T) → K_{11}
  64. Rotate(T, ((-r1))°, T) → T'_7
  65. Rotate(U, ((-r1))°, T) → U'_3
  66. Rotate(T, ((-r1))°, T) → T'_8
  67. Rotate(T, ((-r1))°, T'_8) → T'_9
  68. Rotate(F_2, ((-r1))°, T) → J_{13}
  69. Rotate(L, ((-r1))°, T) → L'_2
  70. Mirror(U'_3, b_1) → A_{14}
  71. Mirror(T'_8, b_1) → B_{14}
  72. Mirror(T'_9, b_1) → O_{15}
  73. Mirror(K_{11}, b_1) → G_{16}
  74. Mirror(T'_7, b_1) → H_{16}
  75. Mirror(J_{13}, b_1) → J_{17}
  76. Mirror(L'_2, b_1) → K_{17}
  77. Midpoint(C_1, E) → K_{20}
  78. Line(G_1, O_1) → l_1
  79. Point(a_1) → C
  80. Min(180, ((a - 1) * 180)) → r2
  81. Min(270, ((a - 1) * 270)) → r3
  82. Rotate(T, r1°, T) → T'_4
  83. Rotate(F_2, r1°, T) → G_2
  84. Rotate(T, r2°, T) → T'_5
  85. Rotate(F_2, r2°, T) → J_2
  86. Rotate(T, r3°, T) → T'_6
  87. Rotate(F_2, r3°, T) → N_2
  88. Rotate(F_2, r1°, T) → Q_2
  89. Rotate(C, r1°, T) → C'
  90. Rotate(F_2, r2°, T) → Z_2
  91. Rotate(C, r2°, T) → C'_1
  92. Rotate(F_2, r3°, T) → H_3
  93. Rotate(C, r3°, T) → C'_2
  94. Rotate(C, r1°, T) → C'_3
  95. Rotate(L, r1°, T) → L'_1
  96. Rotate(K_1, r1°, T) → Q_3
  97. Rotate(C, r2°, T) → C'_4
  98. Rotate(L, r2°, T) → L'_3
  99. Rotate(K_1, r2°, T) → Z_3
  100. Rotate(C, r3°, T) → C'_5
  101. Rotate(L, r3°, T) → L'_4
  102. Rotate(K_1, r3°, T) → H_4
  103. Mirror(C'_4, a_1) → F_5
  104. Mirror(L'_3, a_1) → G_5
  105. Mirror(Z_3, a_1) → J_5
  106. Mirror(Z_2, a_1) → O_5
  107. Mirror(C'_1, a_1) → P_5
  108. Mirror(T'_5, a_1) → W_5
  109. Mirror(J_2, a_1) → Z_5
  110. Mirror(C, a_1) → C'_6
  111. Mirror(L, a_1) → L'_5
  112. Mirror(K_1, a_1) → R_6
  113. Mirror(F_2, a_1) → T_6
  114. Mirror(C, a_1) → C'_7
  115. Mirror(T, a_1) → T'_{10}
  116. Mirror(F_2, a_1) → W_6
  117. Min(180, ((a - 5.5) * 180)) → r4
  118. Line(S, O) → q
  119. Line(F, M) → r
  120. Line(D_1, V) → s
  121. Mirror(pic1, t) → pic1'
  122. Mirror(pic1', a_1) → pic1''
  123. Mirror(pic1'', b_1) → pic1'''
  124. Mirror(pic1''', h) → pic2
  125. Vector(C_1, V) → u_1
  126. Line(E_1, l_1) → f_1
  127. Line(F_1, f_1) → k_1
  128. Vector(V, F) → u
  129. Translate(pic1, u) → pic1'_1
  130. Translate(pic1', u) → pic1''_1
  131. Translate(pic1'', u) → pic1'''_1
  132. Translate(pic1''', u) → pic3
  133. Translate(pic2, u) → pic2'
  134. Translate(pic2', u) → pic2''
  135. Translate(pic3, u) → pic3'
  136. Translate(pic2'', u) → pic2'''
  137. Translate(pic2''', u) → pic4
  138. Translate(pic3', u) → pic3''
  139. Translate(pic3'', u) → pic3'''
  140. Translate(pic1'''_1, u) → pic5
  141. Translate(pic5, u) → pic5'
  142. Translate(pic5', u) → pic5''
  143. Translate(pic1''_1, u) → pic6
  144. Translate(pic6, u) → pic6'
  145. Translate(pic6', u) → pic6''
  146. Translate(pic1'_1, u) → pic7
  147. Translate(pic7, u) → pic7'
  148. Translate(h, u) → h'
  149. Translate(pic7', u) → pic7''
  150. Vector(C_1, N) → w

AI 绘图提示语参考

绘制一个三维空间中的瓷砖图案，包含多个点和线段，通过镜像和中点构造方法，形成复杂的几何图形。首先定义两条线段b和e，然后通过交点、中点和镜像操作，逐步构建出一系列点和线段，最终形成一个对称的三维图案。
以上提示语为根据原始绘图命令整理而来，仅供参考。