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圣诞装饰的圆环舞

圣诞装饰的圆环舞
几何画板及绘图内容加载中，请稍等……
2020-12-14 16:48
圆变换几何作图
这是一个用于圣诞装饰的圆环舞图形。它展示了对称性和平移变换的概念。通过使用GeoGebra中的Circle, Line, Intersect, Mirror, Vector, CircleArc, Point, Translate, Segment, Polygon等命令，可以构造出一系列的圆环和三角形，形成一个动态的几何图案。适合初中及以上学生学习几何变换和对称性。

GeoGebra 命令及参数

  1. Circle(Départ, b) → e
  2. Line(Départ, xAxis) → d
  3. Line(Départ, yAxis) → b_1
  4. Intersect(e, b_1) → B_{2}, C
  5. Line(B_{2}, d) → g
  6. Circle(Départ, a) → c
  7. Intersect(c, d) → D, E
  8. Mirror(Départ, E) → A'
  9. Line(E, b_1) → f
  10. Intersect(g, f) → F
  11. Line(F, E) → i
  12. Vector(E, F) → u_2
  13. CircleArc(F, Départ, A') → h
  14. Point(h) → Move
  15. Translate(Move, u_2) → G'
  16. Segment(G', Move) → aa_1
  17. Polygon(G', F, E, Move) → poly1, g', f_1, e_1, g_1
  18. PointIn(poly1) → J
  19. Mirror(J, aa_1) → J'
  20. PointIn(poly1) → K
  21. Mirror(K, aa_1) → K'
  22. PointIn(poly1) → L
  23. Mirror(L, aa_1) → L'
  24. PointIn(poly1) → M
  25. Mirror(M, aa_1) → M'
  26. PointIn(poly1) → N
  27. Mirror(N, aa_1) → N'
  28. PointIn(poly1) → O
  29. Mirror(O, aa_1) → O'
  30. PointIn(poly1) → P
  31. Mirror(P, aa_1) → P'
  32. PointIn(poly1) → Q
  33. Mirror(Q, aa_1) → Q'
  34. PointIn(poly1) → R_{1}
  35. Mirror(R_{1}, aa_1) → R'
  36. PointIn(poly1) → S_{1}
  37. Mirror(S_{1}, aa_1) → S'
  38. PointIn(poly1) → U
  39. PointIn(poly1) → S
  40. PointIn(poly1) → R_{2}
  41. PointIn(poly1) → T
  42. PointIn(poly1) → W
  43. Midpoint(G', Move) → I
  44. Intersect(g_1, d) → H
  45. Mirror(E, H) → E'
  46. Translate(E', u_2) → E''
  47. Polygon(E'', E', Move, G') → poly2, e'', e', g_2, g'_1
  48. Angle(Départ, E, Move) → α
  49. Vector(Départ, E) → u
  50. Line(G', Move) → i_2
  51. Intersect(i_2, d) → I_2
  52. Vector(E, I_2) → v
  53. Vector(E, E') → w
  54. Sequence(Polygon[Translate[E'', Vector[(s * w)]], Translate[E', Vector[(s * w)]], Translate[Move, Vector[(s * w)]], Translate[G', Vector[(s * w)]]], s, 0, Nombre, 1) → liste2
  55. Sequence(Polygon[Translate[G', Vector[(s * w)]], Translate[F, Vector[(s * w)]], Translate[E, Vector[(s * w)]], Translate[Move, Vector[(s * w)]]], s, 0, Nombre) → liste7
  56. Polygon(J, K, R_{2}, S, T, U, W, M, O, P, S_{1}, R_{1}, Q, N, L) → poly3, j, i_1, j_1, k_1, l_1, m_1, n_1, k, l, m, n, p, q, r, s
  57. Sequence(Polygon[Translate[J, Vector[(s * w)]], Translate[K, Vector[(s * w)]], Translate[M, Vector[(s * w)]], Translate[O, Vector[(s * w)]], Translate[P, Vector[(s * w)]], Translate[S_{1}, Vector[(s * w)]], Translate[R_{1}, Vector[(s * w)]], Translate[Q, Vector[(s * w)]], Translate[N, Vector[(s * w)]], Translate[L, Vector[(s * w)]]], s, 0, Nombre) → liste1
  58. Sequence(Segment[Translate[Move, Vector[(s * w)]], Translate[G', Vector[(s * w)]]], s, 0, Nombre) → liste4
  59. Segment(F, E) → aa
  60. Sequence(Segment[Translate[E'', Vector[(s * w)]], Translate[E', Vector[(s * w)]]], s, 0, Nombre) → liste5
  61. Mirror(G', f_1) → G''
  62. Mirror(F, f_1) → F'
  63. Mirror(E, f_1) → E'_1
  64. Mirror(G', f_1) → G''_1
  65. Mirror(F, f_1) → F'_1
  66. Mirror(E, f_1) → E'_2
  67. Mirror(G', i) → G''_2
  68. Mirror(F, i) → F'_2
  69. Mirror(E, i) → E'_3
  70. Mirror(Move, i) → G'_1
  71. Polygon(G''_2, F'_2, E'_3, G'_1) → poly1', g''_2, f'_2, e'_3, g'_2
  72. Mirror(J, i) → J'_1
  73. Mirror(K, i) → K'_1
  74. Mirror(M, i) → M'_1
  75. Mirror(O, i) → O'_1
  76. Mirror(P, i) → P'_1
  77. Mirror(R_{1}, i) → R'_1
  78. Mirror(Q, i) → Q'_1
  79. Mirror(N, i) → N'_1
  80. Mirror(L, i) → L'_1
  81. Ellipse(C_1, D_1, E_1) → c_1
  82. Circle(F_1, G_1) → d_1
  83. Circle(H_1, I_1) → h_1
  84. Mirror(J, i) → J'_{2}
  85. Mirror(K, i) → K'_{2}
  86. Mirror(M, i) → M'_{2}
  87. Mirror(O, i) → O'_{2}
  88. Mirror(P, i) → P'_{2}
  89. Mirror(S_{1}, i) → J_1
  90. Mirror(R_{1}, i) → K_1
  91. Mirror(Q, i) → Q'_{2}
  92. Mirror(N, i) → N'_{2}
  93. Mirror(L, i) → L'_{2}
  94. Mirror(R_{2}, i) → R'_{2}
  95. Mirror(S, i) → S'_{1}
  96. Mirror(T, i) → T'
  97. Mirror(U, i) → U'
  98. Mirror(W, i) → W'
  99. Polygon(J'_{2}, K'_{2}, R'_{2}, S'_{1}, T', U', W', M'_{2}, O'_{2}, P'_{2}, J_1, K_1, Q'_{2}, N'_{2}, L'_{2}) → poly3', j'_{2}, l'_{2}, r'_{2}, s'_{1}, t', u', w', k'_{2}, m'_{2}, o'_{2}, p'_{2}, p_1, q_1, q'_{2}, n'_{2}
  100. Sequence(Polygon[Translate[J, Vector[(s * w)]], Translate[K, Vector[(s * w)]], Translate[M, Vector[(s * w)]], Translate[O, Vector[(s * w)]], Translate[P, Vector[(s * w)]], Translate[S_{1}, Vector[(s * w)]], Translate[R_{1}, Vector[(s * w)]], Translate[Q, Vector[(s * w)]], Translate[N, Vector[(s * w)]], Translate[L, Vector[(s * w)]], Translate[R_{2}, Vector[(s * w)]], Translate[S, Vector[(s * w)]], Translate[T, Vector[(s * w)]], Translate[U, Vector[(s * w)]], Translate[W, Vector[(s * w)]]], s, 0, Nombre) → l1
  101. Sequence(Polygon[Translate[J'_{2}, Vector[(s * w)]], Translate[K'_{2}, Vector[(s * w)]], Translate[M'_{2}, Vector[(s * w)]], Translate[O'_{2}, Vector[(s * w)]], Translate[P'_{2}, Vector[(s * w)]], Translate[J_1, Vector[(s * w)]], Translate[K_1, Vector[(s * w)]], Translate[Q'_{2}, Vector[(s * w)]], Translate[N'_{2}, Vector[(s * w)]], Translate[L'_{2}, Vector[(s * w)]], Translate[R'_{2}, Vector[(s * w)]], Translate[S'_{1}, Vector[(s * w)]], Translate[T', Vector[(s * w)]], Translate[U', Vector[(s * w)]], Translate[W', Vector[(s * w)]]], s, 0, Nombre) → l2

AI 绘图提示语参考

在平面直角坐标系中选定原点为出发点，同时给定一条水平和一条竖直轴。以原点为圆心画两圆：一个对应得到与竖直轴的交点，另一个与水平轴的交线相交形成两个交点。用这两个交点与轴构成边与角度位置，再以原点为对称中心把其中一个关键点关于原点镜像得到对应点。取原点到这组点之间的向量方向，将镜像后的位置按该向量平移得到另一组点，并用若干线段与三角形/多边形把原始图形与平移后的图形拼接成一条对称的“farandole”装饰链；在装饰链的边界线上取多组点并分别关于中心折线对称，形成连续的重复花纹，同时标出由出发点连到两点的夹角。
以上提示语为根据原始绘图命令整理而来，仅供参考。