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旋转芭蕾舞女音乐盒

旋转芭蕾舞女音乐盒
几何画板及绘图内容加载中，请稍等……
2022-06-30 23:35
立体几何变换几何作图
这个范例演示了一个旋转的芭蕾舞女音乐盒。它涉及旋转、立体几何和几何变换等核心数学概念。通过使用Polygon, Prism, Mirror, Line, Rotate, Centroid, OrthogonalLine, Point, Cylinder, Intersect, Cone, Sphere, Midpoint, Ray, Segment等GeoGebra命令，可以构造出一个动态的旋转芭蕾舞女模型。适合高中或大学的立体几何和几何变换课程。

GeoGebra 命令及参数

  1. Polygon(C, G, H, B) → q1, c, g, h, b
  2. Polygon(C, G, F, D) → q2, c_1, g_1, f, d
  3. Polygon(D, F, E, A) → q3, d_1, f_1, e, a
  4. Polygon(E, A, B, H) → q4, e_1, a_1, b_1, h_1
  5. Prism(q2, -2) → j, Q, edgeCQ, edgeGR, edgeFS, edgeDT, edgeQR, edgeRS, edgeST, edgeQT, R, S, T, faceCGRQ, faceFGRS, faceDFST, faceCDTQ, faceQRST
  6. Prism(q1, 2) → k, U, edgeCU, edgeGV, edgeHW, edgeBZ, edgeUV, edgeVW, edgeWZ, edgeUZ, V, W, Z, faceCGVU, faceGHWV, faceBHWZ, faceBCUZ, faceUVWZ
  7. Prism(q4, 2) → l, A_1, edge3, edge1, edge2, edge4, edge5, edge7, edge8, edge6, B_1, C_1, D_1, face2, face1, face3, face4, face5
  8. Prism(q3, -2) → m, E_1, edge10, edge12, edge11, edge9, edge13, edge15, edge16, edge14, F_1, G_1, H_1, face8, face9, face7, face6, face10
  9. Polygon(F, G, H, E) → q5, f_2, g_2, h_2, e_2
  10. Polygon(D, L, I, A) → q6, d_2, l_1, i, a_2
  11. Polygon(A, I, J, B) → q7, a_3, i_1, j_1, b_2
  12. Polygon(B, J, K, C) → q8, b_3, j_2, k_1, c_2
  13. Polygon(K, L, D, C) → q9, k_2, l_2, d_3, c_3
  14. Polygon(K, J, I, L) → q10, k_3, j_3, i_2, l_3
  15. Mirror(J, p) → J'
  16. Mirror(I, p) → I'
  17. Mirror(L, p) → L'
  18. Mirror(D, p) → D'
  19. Mirror(K, p) → K'
  20. Mirror(C, p) → C'
  21. Mirror(B, p) → B'
  22. Mirror(A, p) → A'
  23. Line(H_1, C_1) → n
  24. Rotate(D', ang, n) → D''
  25. Rotate(L', ang, n) → L''
  26. Rotate(C', ang, n) → C''
  27. Rotate(K', ang, n) → K''
  28. Rotate(A', ang, n) → A''
  29. Rotate(I', ang, n) → I''
  30. Rotate(B', ang, n) → B''
  31. Rotate(J', ang, n) → J''
  32. Polygon(K'', L'', I'', J'') → q11, k'', l'', i'', j''
  33. Polygon(L'', D'', A'', I'') → q12, q, d'', a'', r
  34. Polygon(K'', C'', D'', L'') → q13, s, c'', t, m_1
  35. Polygon(J'', B'', C'', K'') → q14, n_1, b'', p_1, q_1
  36. Polygon(I'', A'', B'', J'') → q15, r_1, s_1, t_1, m_2
  37. Rotate(E_1, ang, n) → M
  38. Rotate(U, ang, n) → U'
  39. Mirror(G, p) → G'
  40. Mirror(F, p) → F'
  41. Mirror(H, p) → H'
  42. Mirror(E, p) → E'
  43. Rotate(H', ang, n) → H''
  44. Rotate(E', ang, n) → E''
  45. Rotate(G', ang, n) → G''
  46. Rotate(F', ang, n) → F''
  47. Polygon(C'', G'', H'', B'') → q16, n_2, g'', h'', p_2
  48. Prism(q16, -2) → u, J_1, edge20, edge23, edge22, edge21, edge24, edge26, edge27, edge25, K_1, L_1, M_1, face15, face17, face16, face14, face18
  49. Polygon(B'', H'', E'', A'') → q17, q_2, r_2, e'', s_2
  50. Polygon(F'', E'', A'', D'') → q18, f'', t_2, f_3, g_3
  51. Polygon(G'', F'', D'', C'') → q19, h_3, i_3, m_3, n_3
  52. Prism(q18, 2) → w, R_1, edge39, edge38, edge37, edge36, edge40, edge42, edge43, edge41, S_1, T_1, U_1, face27, face26, face24, face25, face28
  53. Prism(q17, -2) → o_1, V_1, edge45, edge46, edge47, edge44, edge48, edge50, edge51, edge49, W_1, Z_1, A_2, face31, face32, face30, face29, face33
  54. Polygon(B, J, K, C) → q20, b_4, j_4, k_4, c_4
  55. Polygon(C, K, L, D) → q21, c_5, k_5, l_4, d_4
  56. Polygon(D, L, I, A) → q22, d_5, l_5, i_4, a_4
  57. Polygon(A, I, J, B) → q23, a_5, i_5, j_5, b_5
  58. Polygon(L'', D'', A'', I'') → q24, p_3, q_3, r_3, s_3
  59. Polygon(I'', A'', B'', J'') → q25, t_3, e_3, f_4, g_4
  60. Polygon(J'', B'', C'', K'') → q26, h_4, m_4, n_4, p_4
  61. Polygon(L'', D'', C'', K'') → q27, q_4, r_4, s_4, t_4
  62. Centroid(q5) → N
  63. OrthogonalLine(N, q5) → e_4
  64. Point(e_4) → O
  65. Cylinder(N, O, 1) → o, e_5, f_5, u_1
  66. Point(e_4) → P
  67. Intersect(e_4, f_5) → I_1,
  68. Point(e_4) → B_2
  69. Cylinder(B_2, P, 0.06) → v_1, g_5, h_5, w_1
  70. Point(e_4) → C_2
  71. Cone(P, C_2, 0.5) → o_2, p_5, u_2
  72. Point(e_4) → D_2
  73. Point(e_4) → E_2
  74. OrthogonalLine(E_2, faceGHWV) → m_5
  75. OrthogonalLine(D_2, faceGHWV) → n_5
  76. OrthogonalLine(E_2, face4) → q_5
  77. OrthogonalLine(D_2, face4) → r_5
  78. Point(m_5) → F_2
  79. Mirror(F_2, E_2) → G_2
  80. OrthogonalLine(F_2, q5) → s_5
  81. OrthogonalLine(G_2, q5) → t_5
  82. Intersect(n_5, s_5) → H_2
  83. Intersect(n_5, t_5) → I_2
  84. Polygon(F_2, H_2, I_2, G_2) → q28, f_6, g_6, h_6, i_6
  85. Prism(q28, 0.16308498706014124) → w_2, N_2, edge57, edge59, edge60, edge58, edge61, edge63, edge64, edge62, O_2, P_2, Q_2, face37, face39, face38, face36, face40
  86. Prism(q28, -0.12477514781668185) → o_3, R_2, edge65, edge67, edge68, edge66, edge69, edge71, edge72, edge70, S_2, T_2, U_2, face42, face44, face43, face41, face45
  87. Point(e_4) → J_2
  88. Cylinder(J_2, E_2, 0.05) → v_2, c_6, d_6, u_3
  89. Sphere(J_2, 0.15) → v_3
  90. Midpoint(P, B_2) → K_2
  91. OrthogonalLine(P, h_5) → j_6
  92. Midpoint(P, K_2) → L_2
  93. Midpoint(L_2, B_2) → M_2
  94. OrthogonalLine(L_2, face9) → k_6
  95. Point(k_6) → V_2
  96. Cylinder(P, V_2, 0.06) → w_3, e_6, p_6, o_4
  97. Cylinder(M_2, V_2, 0.06) → u_4, q_6, r_6, v_4
  98. Point(j_6) → W_2
  99. Ray(W_2, G_2) → l_6
  100. Ray(W_2, F_2) → m_6
  101. Point(t_5) → Z_2
  102. Point(l_6) → A_3
  103. Segment(A_3, Z_2) → n_6
  104. Segment(A_3, G_2) → s_6
  105. Rotate(R_2, (-rtt), zAxis) → B_3
  106. Rotate(U_2, (-rtt), zAxis) → C_3
  107. Rotate(U_2, (-rtt), zAxis) → D_3
  108. Rotate(Q_2, (-rtt), zAxis) → E_3
  109. Rotate(Q_2, (-rtt), zAxis) → F_3
  110. Rotate(N_2, (-rtt), zAxis) → G_3
  111. Rotate(S_2, (-rtt), zAxis) → H_3
  112. Rotate(S_2, (-rtt), zAxis) → I_3
  113. Rotate(T_2, (-rtt), zAxis) → J_3
  114. Rotate(T_2, (-rtt), zAxis) → K_3
  115. Rotate(P_2, (-rtt), zAxis) → L_3
  116. Rotate(O_2, (-rtt), zAxis) → M_3
  117. Rotate(A_3, (-rtt), zAxis) → N_3
  118. Rotate(G_2, (-rtt), zAxis) → O_3
  119. Segment(N_3, O_3) → a_6
  120. Rotate(A_3, (-rtt), zAxis) → P_3
  121. Rotate(A_3, (-rtt), zAxis) → Q_3
  122. Rotate(Z_2, (-rtt), zAxis) → R_3
  123. Segment(Q_3, R_3) → b_6
  124. Rotate(o_4, (-rtt), zAxis) → o_5
  125. Rotate(V_2, (-rtt), zAxis) → S_3
  126. Rotate(v_4, (-rtt), zAxis) → w_4
  127. Polygon(L_3, J_3, I_3, M_3) → q29, f_7, g_7, h_7, i_7
  128. Prism(q29, 0.61) → v_5, Z_3, edge75, edge74, edge73, edge76, edge77, edge79, edge80, edge78, A_4, B_4, C_4, face48, face46, face47, face49, face50
  129. Rotate(N_3, 180°, zAxis) → T_3
  130. Rotate(O_3, 180°, zAxis) → U_3
  131. Segment(T_3, U_3) → j_7
  132. Rotate(Q_3, 180°, zAxis) → V_3
  133. Rotate(Q_3, 180°, zAxis) → W_3
  134. Rotate(R_3, 180°, zAxis) → D_4
  135. Segment(W_3, D_4) → k_7
  136. Polygon(C'', J_1, U_1, D'') → q30, l_7, m_7, n_7, p_7
  137. Prism(q19, 2) → u_5, F_4, edge35, edge52, edge33, edge34, edge53, edge55, edge56, edge54, G_4, H_4, I_4, face34, face22, face21, face23, face35

AI 绘图提示语参考

绘制一个旋转的芭蕾舞女音乐盒。首先绘制四个矩形，然后将它们组合成两个长方体。接着绘制四个三角形，形成另一个长方体。使用镜像和旋转命令，创建旋转效果。最后，通过镜像和旋转，生成旋转的芭蕾舞女形象。
以上提示语为根据原始绘图命令整理而来，仅供参考。