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八角星环旋转动画

八角星环旋转动画
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2020-07-17 00:23
多边形立体几何变换
所属专题 Action Modular Origami
①本范例演示了一个由纸折叠而成的八角星环模型的旋转动画；②涉及的核心数学概念包括多边形构造、几何变换（旋转、平移等）、向量运算；③作图要点提炼自构造摘要，使用了Intersect, PolyLine, If, Plane, Line, Midpoint, Rotate, Vector, Dilate, Circle, OrthogonalLine, Polygon, AngularBisector, Point, Translate, LineBisector, Mirror, Distance等GeoGebra命令和对象；④适合高中及以上学生学习几何作图、变换以及参数化模型，也可用于数学教学演示。

GeoGebra 命令及参数

  1. Intersect(yAxis, zAxis) → K
  2. PolyLine(C_2, E_3, O_3, F_3, H_3, I_3, J_3, K_3, L_3, M_3, N_3) → j_3
  3. Intersect(g_3, j_3) → offsetCurve
  4. If(clock0 < 2.75, clock0, 2.75 - (clock0 - 2.75)) → clockuse
  5. If(clock < 1 ∨ clock > 3, 0°, (-((((clock - 1) * 90))°))) → β
  6. If(clock < 1 ∨ clock > 3, 0°, ((((clock - 1) * 90)) / 2)°) → γ
  7. Plane(E, F, C) → a
  8. Line(E, C) → p
  9. Midpoint(C, D) → H
  10. Intersect(xAxis, yAxis) → A
  11. Rotate(C, If[α ≥ 0°, (-α), (-2 * α)], A, a) → C'
  12. Vector((0, 0, (-z(C')))) → vShift
  13. Dilate(C, 0.5^(0.5), A) → C'_1
  14. Midpoint(C'_1, A) → O
  15. Circle(O, C'_1, a) → r
  16. OrthogonalLine(O, p, a) → q
  17. Intersect(q, r) → P, Q
  18. Polygon(C'_1, Q, A) → poly5, a_2, c'_1, q_1
  19. AngularBisector(p, c'_1) → s, t
  20. Intersect(a_2, t) → R
  21. OrthogonalLine(A, xOyPlane) → l
  22. OrthogonalLine(R, l, a) → f_1
  23. Intersect(f_1, l) → S
  24. Polygon(R, S, 4, a) → poly6, g_1, h_1, i_1, j_1, T, U
  25. Rotate(K, (-β), T, a) → K'
  26. Polygon(R, S, T) → poly7, t_1, r_1, s_1
  27. AngularBisector(s_1, r_1) → l_1, m_1
  28. Intersect(f_1, m_1) → W
  29. Rotate(W, (-β), T, a) → W'
  30. Line(W', K') → b_1
  31. Rotate(R, If[clock < 2, (-γ), 45° - (2 * γ)], T, a) → R'
  32. OrthogonalLine(R', b_1, a) → p_1
  33. Intersect(b_1, p_1) → A_1
  34. Line(R', T) → f_2
  35. Point(zAxis) → C_1
  36. Midpoint(E, B) → J
  37. Plane(H, C_1, J) → o
  38. Rotate(S, If[clock < 2, (-β), 45° + ((-β)) / 2], T, o) → S'_1
  39. Polygon(S', T, R') → poly8, r', s', t_2
  40. Plane(R', T, S') → u
  41. Line(T, S'_1) → g_2
  42. AngularBisector(f_2, g_2) → h_2, i_2
  43. Intersect(i_2, t_2) → D_1
  44. Line(D_1, f_2) → j_2
  45. Intersect(g_2, j_2) → E_1
  46. OrthogonalLine(E_1, g_2, u) → k_2
  47. Intersect(k_2, f_2) → F_1
  48. OrthogonalLine(F_1, a) → k_3
  49. Point(k_3) → P_3
  50. Dilate(F_1, offsetCurveValue, P_3) → Q_3
  51. Polygon(R', Q_3, S') → poly16, q_3, r_3, s_3
  52. Polygon(T, Q_3, S') → poly15, a_3, b_3, c_3
  53. PolyLine(Q_2, R_2, C_3, D_3, S_2, T_2, U_2, V_2, W_2, Z_2, A_3, B_3) → i_3
  54. PolyLine(D_2, E_2, N_2, O_2, P_2, F_2, G_2, H_2, I_2, J_2, K_2, L_2, M_2) → h_3
  55. PolyLine(O_1, P_1, A_2, B_2, Q_1, R_1, S_1, T_1, U_1, V_1, W_1, Z_1) → f_3
  56. Intersect(g_3, i_3) → offsetZ
  57. Intersect(g_3, h_3) → offsetY
  58. Intersect(g_3, f_3) → offsetX
  59. Vector((offsetXX, offsetYY, offsetZZ)) → vOffset
  60. Polygon(R', F_1, 4, a) → poly10, n_2, p_2, q_2, r_2, I_1, J_1
  61. Translate(Polygon[R', Q_3, E_1], vOffset) → poly12
  62. OrthogonalLine(R', s', a) → m_2
  63. LineBisector(J_1, T, a) → c_1
  64. Mirror(R', c_1) → R''
  65. OrthogonalLine(R'', m_2, a) → d_1
  66. Intersect(m_2, d_1) → N_1
  67. Translate(Polygon[J_1, Q_3, R'], vOffset) → poly11
  68. Polygon(J_1, F_1, N_1) → poly14, s_2, b_2, e_2
  69. Circle(R', J_1, a) → d_2
  70. Intersect(m_2, d_2) → K_1, L_1
  71. Translate(Polygon[R', N_1, E_1], vOffset) → poly9
  72. OrthogonalLine(R', j_2, u) → l_2
  73. Intersect(j_2, l_2) → H_1
  74. Intersect(k_2, l_2) → G_1
  75. Intersect(s_1, p) → Z
  76. Rotate(Z, (-β), T, a) → Z'
  77. Line(Z', K') → n_1
  78. Intersect(p_1, n_1) → B_1
  79. Midpoint(C, B) → G
  80. Plane(A, G, F) → g
  81. Rotate(G, If[α < 0°, α, (2 * α)], A, g) → G'
  82. Polygon(A, G', C') → poly2, c', a_1, g'
  83. Point(g') → L
  84. Polygon(L, C', G') → poly3, i, j, k
  85. Midpoint(D, E) → I
  86. Circle(A, C, a) → f
  87. Circle(A, G, g) → h
  88. Translate(Sequence[Rotate[{poly3, Mirror[poly3, a]}, (n * 90°), zAxis], n, 0, 3, 1], vShift) → pos0r
  89. Translate(pos0r, vOffset) → list1'
  90. Rotate(list1', 45°, l) → list1''
  91. Rotate(poly3, 45°, l) → poly3'
  92. Plane(G', xOyPlane) → m
  93. Intersect(l, m) → M
  94. Midpoint(A, M) → N
  95. Plane(N, xOyPlane) → n
  96. Mirror(pos0r, n) → list1'_1
  97. Dilate(C', sqrt(2) - 1, L) → L'_1
  98. Dilate(G', sqrt(0.5), A) → L'
  99. Dilate(G', sqrt(2), A) → G''
  100. Polygon(L', L'_1, G'') → poly4, g'', l', l'_1
  101. Translate(poly4, vOffset) → poly4'
  102. Translate(Sequence[Rotate[{poly4', Mirror[poly4', a]}, (n * 90°), zAxis], n, 0, 3, 1], vShift) → pos0b
  103. Rotate(Q, γ, K, a) → Q'
  104. Rotate(C'_1, γ, K, a) → V
  105. Distance(R', S') → distanceR'S'
  106. Distance(G'', L'_1) → distanceG''L'1
  107. Circle(T, R, a) → e_1
  108. Circle(T, S'_1, o) → c_2
  109. If(clock < 1 ∨ clock > 3, 0°, (-((((clock - 1) * 90))°))) → β_3
  110. If(clock < 1 ∨ clock > 4, 0°, ((((clock - 3) * 90)) / 2)°) → γ_3
  111. Point(zAxis) → M_1
  112. Translate(Sequence[Rotate[{poly9, poly12, poly11, Mirror[{poly9, poly11, poly12}, a]}, (n * 90°), zAxis], n, 0, 3, 1], Vector[(0 * vShift)]) → pos2r
  113. Translate(Sequence[Rotate[{poly15, poly16, Mirror[{poly15, poly16}, a]}, (n * 90°), zAxis], n, 0, 3, 1], Vector[(0 * vShift)]) → pos2b
  114. Plane(M_1, xOyPlane) → v
  115. Rotate(Mirror[pos2b, v], 45°, l) → pos3b
  116. Rotate(Mirror[pos2r, v], 45°, l) → pos3r
  117. Vector((0, 0, If[clock0 ≥ 2.75, fall - (((clock0 - 3.5) * z(T) / 2) * 3.5) + If[clock0 ≥ 2.75, ((clock0 - 2.75) * z(T) / 1.75), 0], (-fall) - z(T)] / 2)) → vFall
  118. Translate(pos2r, vFall) → pos2r'
  119. Translate(pos2b, vFall) → pos2b'
  120. Translate(pos3b, vFall) → pos3b'
  121. Translate(pos3r, vFall) → pos3r'
  122. Dilate(S', 2, T) → S''
  123. Rotate(S'', (-(90°)), l) → S'''
  124. Polygon(S'', T, S''') → poly13, s''', s'', t_3
  125. Line(J_1, F_1) → k_1
  126. Intersect(k_2, f_2) → F_0
  127. Point(zAxis) → G_3

AI 绘图提示语参考

绘制一个八角星环动画，首先构造一个八边形，然后围绕中心点旋转和缩放该八边形，形成环状结构。接着，通过旋转、平移和镜像等操作，构建多个多边形，最终形成一个复杂的旋转动画效果。
以上提示语为根据原始绘图命令整理而来，仅供参考。