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穆汗萨斯几何形体

穆汗萨斯几何形体
几何画板及绘图内容加载中，请稍等……
2023-01-20 16:11
向量立体几何几何作图
这个范例演示了穆汗萨斯（Muqarnas）的几何原理。穆汗萨斯是一种伊斯兰建筑装饰艺术，通过一系列几何形体的组合创造出独特的立体效果。核心数学概念包括立体几何、对称性和向量。通过使用GeoGebra命令如Rotate、Intersect、Segment等，可以构造出复杂的几何形体。适合高中或大学的立体几何和建筑艺术课程。

GeoGebra 命令及参数

  1. Rotate(A + (1 / sin(67.5°) * (B - A)), 22.5°, A) → BARB
  2. Rotate(B, 135°, A) → BBA
  3. Rotate(B, 45°, A) → ABR
  4. Rotate(B, 45°, A) → ABSM
  5. Rotate(A + (sin(45°) / sin(112.5°) * (B - A)), 22.5°, A) → ABT
  6. Rotate(A, -90°, B) → AB
  7. Rotate(B, -135°, A) → ABA
  8. Rotate(A + (sin(45°) / sin(22.5°) * (B - A)), 112.5°, A) → ABAB
  9. Intersect(Line[A, Rotate[B, 45°, A]], Line[B, Rotate[A, -45°, B]]) → ABH
  10. Intersect(Line[A, Rotate[B, 67.5°, A]], Line[B, Rotate[A, -67.5°, B]]) → ABHR
  11. Rotate(B, 90°, A) → BA
  12. Rotate(B, 135°, A) → BAR
  13. Intersect(OrthogonalLine[B, Line[A, B]], OrthogonalLine[BBA, Line[BBA, A]]) → BBAB
  14. Segment(A, ABT) → t9pijl1
  15. Segment(A, B) → t9pijl2
  16. Segment(A, ABR) → t9pijl3
  17. Segment(A, BBAB) → t3pijl1
  18. Segment(B, BBAB) → t3pijl2
  19. Segment(BBA, BBAB) → t3pijl3
  20. Segment(BBA, A) → t3vet1
  21. Segment(A, B) → t3vet2
  22. Intersect(Line[C, Rotate[DB, 45°, Line[C, C + (0, 0, 1)]]], Line[E, Rotate[DB, -45°, Line[E, E + (0, 0, 1)]]]) → CESB
  23. Intersect(Line[C, Rotate[DB, 22.5°, Line[C, C + (0, 0, 1)]]], Line[E, Rotate[DB, -22.5°, Line[E, E + (0, 0, 1)]]]) → CELB
  24. Intersect(Line[C, Rotate[DB, 90°, Line[C, C + (0, 0, 1)]]], Line[E, Rotate[DB, -90°, Line[E, E + (0, 0, 1)]]]) → CEA
  25. Polygon(A, B, ABT, ABR) → SmBiped9, smb92, smb91, smb94, smb93
  26. Dilate(A, 0.75, Centroid[SmBiped9]) → A'
  27. Dilate(B, 0.75, Centroid[SmBiped9]) → B'
  28. Dilate(ABT, 0.75, Centroid[SmBiped9]) → ABT'
  29. Dilate(ABR, 0.75, Centroid[SmBiped9]) → ABR'
  30. Polygon(A, B, BARB, BBA) → Almond3, alm31, alm32, alm33, alm34
  31. Polygon(A', B', ABT', ABR') → SmBiped9', a', b', abt', abr'
  32. Dilate(A, 0.75, Centroid[Almond3]) → A'_1
  33. Dilate(B, 0.75, Centroid[Almond3]) → B'_1
  34. Dilate(BBAB, 0.75, Centroid[Almond3]) → BBAB'
  35. Dilate(BBA, 0.75, Centroid[Almond3]) → BBA'
  36. Polygon(A'_1, B'_1, BBAB', BBA') → Almond3', a'_1, b'_1, bbab', bba'
  37. Polygon(D, E, EE, DD) → achter1, d, e, ee, dd
  38. Polygon(C, CC, DD, D) → achter2, c, cc, f, d_1
  39. Polygon(EE, ECA, DD) → EAlmond3boven1, g, i, eca
  40. Polygon(CC, ECA, DD) → EAlmond3boven2, j, k, l
  41. Rotate(A + (sin(22.5°) / sin(112.5°) * (B - A)), 45°, A) → ABL
  42. Polygon(A, B, AB, BA) → Square1, sq11, sq13, sq12, sq14
  43. Dilate(A, 0.75, Centroid[Square1]) → A'_2
  44. Dilate(B, 0.75, Centroid[Square1]) → B'_2
  45. Dilate(AB, 0.75, Centroid[Square1]) → AB'
  46. Dilate(BA, 0.75, Centroid[Square1]) → BA'
  47. Polygon(A'_2, B'_2, AB', BA') → Square1', a'_2, b'_2, ab', ba'
  48. Rotate(A, -45°, B) → ABRH
  49. Polygon(A, B, ABRH, BAR) → Rhombus2, rh21, rh23, rh22, rh24
  50. Dilate(A, 0.75, Centroid[Rhombus2]) → A'_3
  51. Dilate(B, 0.75, Centroid[Rhombus2]) → B'_3
  52. Dilate(ABRH, 0.75, Centroid[Rhombus2]) → ABRH'
  53. Dilate(BAR, 0.75, Centroid[Rhombus2]) → BAR'
  54. Polygon(A'_3, B'_3, ABRH', BAR') → Rhombus2', a'_3, b'_3, abrh', bar'
  55. Rotate(A + (sin(67.5°) / sin(45°) * (B - A)), 67.5°, A) → BAJ
  56. Polygon(A, B, BAJ, BBA) → Jug4, jug41, jug42, jug43, jug44
  57. Dilate(A, 0.75, Centroid[Jug4]) → A'_4
  58. Dilate(B, 0.75, Centroid[Jug4]) → B'_4
  59. Dilate(BAJ, 0.75, Centroid[Jug4]) → BAJ'
  60. Dilate(BBA, 0.75, Centroid[Jug4]) → BBA'_1
  61. Polygon(A'_4, B'_4, BAJ', BBA'_1) → Jug4', a'_4, b'_4, baj', bba'_1
  62. Polygon(A, B, ABH) → HSquare5, hsq52, hsq51, hsq53
  63. Dilate(A, 0.75, Centroid[HSquare5]) → A'_5
  64. Dilate(B, 0.75, Centroid[HSquare5]) → B'_5
  65. Dilate(ABH, 0.75, Centroid[HSquare5]) → ABH'
  66. Polygon(A'_5, B'_5, ABH') → HSquare5', abh', a'_5, b'_5
  67. Polygon(A, B, ABHR) → HRhombus6, hrh62, hrh61, hrh63
  68. Dilate(A, 0.75, Centroid[HRhombus6]) → A'_6
  69. Dilate(B, 0.75, Centroid[HRhombus6]) → B'_6
  70. Dilate(ABHR, 0.75, Centroid[HRhombus6]) → ABHR'
  71. Polygon(A'_6, B'_6, ABHR') → HRhombus6', abhr', a'_6, b'_6
  72. Polygon(A, B, ABL, BA) → LBiped10, lb101, lb103, lb102, lb104
  73. Dilate(A, 0.75, Centroid[LBiped10]) → A'_7
  74. Dilate(B, 0.75, Centroid[LBiped10]) → B'_7
  75. Dilate(ABL, 0.75, Centroid[LBiped10]) → ABL'
  76. Dilate(BA, 0.75, Centroid[LBiped10]) → BA'_1
  77. Polygon(A'_7, B'_7, ABL', BA'_1) → LBiped10', a'_7, b'_7, abl', ba'_1
  78. Polygon(A, B, BA) → HSquare11, hsq113, hsq111, hsq112
  79. Dilate(A, 0.75, Centroid[HSquare11]) → A'_8
  80. Dilate(B, 0.75, Centroid[HSquare11]) → B'_8
  81. Dilate(BA, 0.75, Centroid[HSquare11]) → BA'_2
  82. Polygon(A'_8, B'_8, BA'_2) → HSquare11', ba'_2, a'_8, b'_8
  83. Polygon(A, B, ABR) → HRhombus12, hrh121, hrh123, hrh122
  84. Dilate(A, 0.75, Centroid[HRhombus12]) → A'_9
  85. Dilate(B, 0.75, Centroid[HRhombus12]) → B'_9
  86. Dilate(ABR, 0.75, Centroid[HRhombus12]) → ABR'_1
  87. Polygon(A'_9, B'_9, ABR'_1) → HRhombus12', abr'_1, a'_9, b'_9
  88. Polygon(ABA, A, B, ABAB) → SmBiped13, smb132, smb131, smb134, smb133
  89. Dilate(ABA, 0.75, Centroid[SmBiped13]) → ABA'
  90. Dilate(A, 0.75, Centroid[SmBiped13]) → A'_{10}
  91. Dilate(B, 0.75, Centroid[SmBiped13]) → B'_{10}
  92. Dilate(ABAB, 0.75, Centroid[SmBiped13]) → ABAB'
  93. Polygon(ABA', A'_{10}, B'_{10}, ABAB') → SmBiped13', aba', a'_{10}, b'_{10}, abab'
  94. Polygon(A, B, BARB, ABR) → Almond14, m, n, p, q
  95. Dilate(A, 0.75, Centroid[Almond14]) → A'_{11}
  96. Dilate(B, 0.75, Centroid[Almond14]) → B'_{11}
  97. Dilate(BARB, 0.75, Centroid[Almond14]) → BARB'
  98. Dilate(BAR, 0.75, Centroid[Almond14]) → BAR'_1
  99. Segment(A, AB) → sq1pijl1
  100. Segment(B, AB) → sq1pijl2
  101. Segment(A, B) → sqvet1
  102. Segment(A, BA) → sqvet2
  103. Segment(BA, AB) → sq1pijl3
  104. Segment(A, B) → sq7pijl3
  105. Segment(A, BA) → sq7pijl2
  106. Segment(A, ABRH) → rh2pijl1
  107. Segment(B, ABRH) → rh2pijl2
  108. Segment(BAR, ABRH) → rh2pijl3
  109. Segment(A, B) → rh2vet1
  110. Segment(A, BAR) → rh2vet2
  111. Segment(A, B) → rh8pijl2
  112. Segment(A, BAR) → rh8pijl3
  113. Segment(A, BARB) → alm3pijl1
  114. Segment(B, BARB) → alm3pijl2
  115. Segment(BBA, BARB) → alm3pijl3
  116. Segment(A, B) → alm3vet1
  117. Segment(A, BBA) → alm3vet2
  118. Segment(A, BAJ) → jug4pijl1
  119. Segment(B, BAJ) → jug4pijl2
  120. Segment(BBA, BAJ) → jug4pijl3
  121. Segment(A, B) → jug4vet1
  122. Segment(A, BBA) → jug4vet2
  123. Segment(Midpoint[A, B], ABH) → hsq5pijl1
  124. Segment(A, ABH) → hsq5pijl2
  125. Segment(B, ABH) → hsq5pijl3
  126. Segment(A, B) → hsq5vet1
  127. Segment(Midpoint[A, B], ABHR) → hrh6pijl1
  128. Segment(A, ABHR) → hrh6pijl2
  129. Segment(B, ABHR) → hrh6pijl3
  130. Segment(A, B) → hrh6vet1
  131. Segment(A, ABT) → smb9pijl1
  132. Segment(A, B) → smb9pijl2
  133. Segment(A, ABR) → smb9pijl3
  134. Segment(A, ABL) → lb10pijl1
  135. Segment(A, B) → lb10pijl2
  136. Segment(A, BA) → lb10pijl3
  137. Segment(A, Midpoint[BA, B]) → hsq11pijl1
  138. Segment(A, B) → hsq11pijl2
  139. Segment(A, BA) → hsq11pijl3
  140. Segment(A, Midpoint[ABR, B]) → hrh12pijl1
  141. Segment(A, ABR) → hrh12pijl2
  142. Segment(A, B) → hrh12pijl3
  143. Segment(A, ABAB) → smb13pijl1
  144. Segment(B, ABAB) → smb13pijl2
  145. Segment(ABA, ABAB) → smb13pijl3
  146. Segment(A, B) → smb13vet1
  147. Segment(A, ABA) → smb13vet2
  148. Segment(A, BARB) → alm14pijl1
  149. Polygon(EE, EC, DD) → ESquare1boven1, i_1, j_1, ec
  150. Polygon(CC, EC, DD) → ESquare1boven2, k_1, l_1, m_1
  151. Intersect(Line[C, Line[DB, E]], Line[E, Line[DB, C]]) → CE
  152. Polygon(DO, E, CE) → ESquare7boven1, r, s, t
  153. Polygon(DO, CE, C) → ESquare7boven2, a, b, f_1
  154. Polygon(EE, ECJ, DD) → EJug4boven1, q_1, r_1, ecj
  155. Polygon(CC, ECJ, DD) → EJug4boven2, s_1, t_1, f_2
  156. Polygon(CC, DD, CDHS) → EHSquare5boven, cdhs, g_2, h_2
  157. Polygon(CC, DD, CDHR) → EHRhombus6boven, cdhr, i_2, j_2
  158. Polygon(DO, E, CESB) → ESmBiped9boven1, g_1, h_1, n_1
  159. Polygon(DO, CESB, C) → ESmBiped9boven2, p_1, a_1, b_1
  160. Polygon(DO, E, CELB) → ELBiped10boven1, c_1, e_1, k_2
  161. Polygon(DO, CELB, C) → ELBiped10boven2, l_2, m_2, n_2
  162. Polygon(C, DO, E) → EHSquare11boven11, p_2, q_2, r_2
  163. Polygon(EE, ECSB, DD) → ESmbiped13boven1, s_2, t_2, ecsb
  164. Polygon(DD, ECSB, CC) → ESmbiped13boven2, d_2, f_3, g_3
  165. Polygon(DO, E, CEA) → EAlmond14onder1, a_2, b_2, c_2
  166. Polygon(DO, CEA, C) → EAlmond14onder2, e_2, h_3, i_3
  167. Dilate(A, 0.75, Centroid[Almond14]) → A'_{12}
  168. Dilate(B, 0.75, Centroid[Almond14]) → B'_{12}
  169. Dilate(BARB, 0.75, Centroid[Almond14]) → BARB'_1
  170. Dilate(ABR, 0.75, Centroid[Almond14]) → ABR'_2
  171. Polygon(A'_{12}, B'_{12}, BARB'_1, ABR'_2) → Almond14', a'_{12}, b'_{12}, barb'_1, abr'_2
  172. Segment(A, B) → alm14pijl2
  173. Segment(A, ABR) → alm14pijl3
  174. Point(xAxis) → F
  175. Point(xAxis) → G
  176. HSquare5(F, G) → H, driehoek1, driehoek2, j_3, k_3, l_3, m_3
  177. HSquare5(G, I) → J, driehoek3, driehoek4, n_3, p_3, q_3, r_3
  178. Point(xAxis) → K
  179. HSquare5(K, F) → L, driehoek5, driehoek6, s_3, t_3, a_3, b_3
  180. TSquare1(F, H) → M, N, vierhoek1, vierhoek2, c_3, d_3, e_3, f_4, g_4
  181. TSquare1(G, J) → O, P, vierhoek3, vierhoek4, h_4, i_4, j_4, k_4, l_4
  182. TSquare1(H, O) → Q, R, vierhoek5, vierhoek6, m_4, n_4, p_4, q_4, r_4
  183. HSquare5(K, F) → S, driehoek7, driehoek8, s_4, t_4, a_4, b_4
  184. EHSquare5(K, F) → T, U, V, vierhoek7, driehoek9
  185. EHSquare5(F, G) → W, Z, A_1, vierhoek8, driehoek10
  186. EHSquare5(G, I) → C_1, D_1, E_1, vierhoek9, driehoek11
  187. Polygon(E_1, C_1, F_1) → driehoek12, c_4, d_4, e_4
  188. Polygon(F_1, C_1, A_1) → driehoek13, f_5, g_5, h_5
  189. Polygon(A_1, W, B_1) → driehoek14, i_5, j_5, w
  190. Polygon(B_1, W, V) → driehoek15, v_1, k_5, w_1
  191. ESquare1(V, B_1, A_1) → G_1, H_1, I_1, vierhoek10, vierhoek11, driehoek16, driehoek17
  192. ESquare1(A_1, F_1, E_1) → J_1, K_1, L_1, vierhoek12, vierhoek13, driehoek18, driehoek19
  193. Polygon(L_1, J_1, M_1) → driehoek20, l_5, m_5, n_5
  194. Polygon(M_1, J_1, I_1) → driehoek21, p_5, q_5, r_5
  195. ESquare1(I_1, M_1, L_1) → N_1, O_1, P_1, vierhoek14, vierhoek15, driehoek22, driehoek23

AI 绘图提示语参考

请绘制一个具有几何美感的穆斯林建筑装饰图案。图案由多个旋转的三角形和四边形组成，形成复杂的立体结构。关键对象包括一个中心点、多个旋转后的三角形和四边形，以及它们之间的相交线。构造顺序是先确定中心点，然后旋转三角形和四边形，最后通过相交线连接这些对象，形成对称且富有层次感的图形。
以上提示语为根据原始绘图命令整理而来，仅供参考。