Cube Mirror Transformation Animation

Cube Mirror Transformation Animation
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2017-01-26 03:24
This example demonstrates the mirror transformation of a cube in 3D space. Key mathematical concepts include mirror transformations in solid geometry and geometric construction. Using GeoGebra commands such as Mirror, Intersect, and Dilate, a mirror transformation animation of the cube is constructed. Suitable for high school or university solid geometry courses.

GeoGebra Commands & Parameters

  1. Mirror(G, f) → G'
  2. Mirror(F, f) → F'
  3. Mirror(E, g) → E'
  4. Mirror(F, g) → F'_1
  5. Mirror(G, g) → G'_1
  6. Mirror(F', g) → F''
  7. Mirror(G', g) → G''
  8. Mirror(E, f) → E'_1
  9. Mirror(E'_1, g) → H
  10. Intersect(g, j) → I
  11. Intersect(g, i) → J
  12. Intersect(g, h) → K
  13. Dilate(L, If[0 < a ≤ 1, 1 - a, 0], J) → L'
  14. Segment(L, L') → k
  15. Dilate(J, If[1 < a ≤ 2, 2 - a, 0], F) → K'
  16. Polygon(L, J, F) → poly1, n, e, k_1
  17. Dilate(F, If[2 < a ≤ 3, 3 - a, 0], L) → E'_2
  18. Rotate(K, If[4 < a < 5, ((-(a - 4)) * π / 3), ((-π)) / 3], E) → K'_1
  19. Rotate(K', If[4 < a < 5, ((-(a - 4)) * π / 3), ((-π)) / 3], E) → K''
  20. Rotate(L, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → L'_1
  21. Rotate(K, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → K'_2
  22. Rotate(E, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → E'_3
  23. Rotate(K, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → K'_3
  24. Rotate(K', If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → K''_1
  25. Rotate(L, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → L'_2
  26. Rotate(L', If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → L''
  27. Rotate(K'', If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → K'''_1
  28. Rotate(L'_1, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → Q
  29. Rotate(K'_2, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → R
  30. Rotate(E'_3, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → S
  31. Rotate(K'_3, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → T
  32. Rotate(K''_1, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → U
  33. Rotate(L'_2, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → V
  34. Rotate(L'', If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → L'''
  35. Rotate(K'''_1, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → W
  36. Rotate(Q, If[8 < a < 9, ((a - 8) * π / 2), π / 2], L) → Q'
  37. Rotate(R, If[8 < a < 9, ((a - 8) * π / 2), π / 2], L) → R'
  38. Rotate(S, If[8 < a < 9, ((a - 8) * π / 2), π / 2], L) → S'
  39. Rotate(V, If[8 < a < 9, ((a - 8) * π / 2), π / 2], L) → V'
  40. Rotate(L''', If[8 < a < 9, ((a - 8) * π / 2), π / 2], L) → Z
  41. Rotate(W, If[8 < a < 9, ((a - 8) * π / 2), π / 2], L) → W'
  42. Rotate(T, If[8 < a < 9, ((a - 8) * π / 2), π / 2], L) → T'
  43. Rotate(U, If[8 < a < 9, ((a - 8) * π / 2), π / 2], L) → U'
  44. Rotate(K'_1, If[11 < a < 12, ((a - 11) * π / 6), π / 6], L) → E_1
  45. Rotate(K'', If[11 < a < 12, ((a - 11) * π / 6), π / 6], L) → K'''_2
  46. Dilate(K, If[9 < a ≤ 10, 10 - a, 0], E') → K'_4
  47. Rotate(E_1, π / 2, L) → T_1
  48. Rotate(K'''_2, π / 2, L) → U_1
  49. Rotate(K'''_2, π, L) → W_1
  50. Rotate(E_1, (3 * π / 2), L) → Z_1
  51. Rotate(K'''_2, (3 * π / 2), L) → A_2
  52. Segment(J, K') → l
  53. Segment(F, E'_2) → m
  54. Rotate(L, If[3.5 < a ≤ 4.5, ((-(a - 3.5)) * π / 2), ((-π)) / 2], J) → L'_3
  55. Rotate(L', If[3.5 < a ≤ 4.5, ((-(a - 3.5)) * π / 2), ((-π)) / 2], J) → L''_1
  56. Segment(L'_3, L''_1) → k'_1
  57. Circle(L, 0.5) → d_1
  58. Rotate(L, If[5 < a < 6, ((a - 5) * π / 2), π / 2], L) → L'_4
  59. Rotate(J, If[5 < a < 6, ((a - 5) * π / 2), π / 2], L) → J'
  60. Rotate(F, If[5 < a < 6, ((a - 5) * π / 2), π / 2], L) → F'_2
  61. Polygon(L'_4, J', F'_2) → poly1'_1, f'_2, l'_4, j'
  62. Rotate(L'_3, If[5 < a < 6, ((a - 5) * π / 2), π / 2], L) → M
  63. Rotate(L''_1, If[5 < a < 6, ((a - 5) * π / 2), π / 2], L) → N
  64. Segment(M, N) → b
  65. Rotate(L, If[5 < a < 6, ((a - 5) * π / 2), π / 2], L) → L'_5
  66. Rotate(L', If[5 < a < 6, ((a - 5) * π / 2), π / 2], L) → L''_2
  67. Segment(L'_5, L''_2) → k'_3
  68. Rotate(F, If[5 < a < 6, ((a - 5) * π / 2), π / 2], L) → F'_3
  69. Rotate(E'_2, If[5 < a < 6, ((a - 5) * π / 2), π / 2], L) → P
  70. Segment(F'_3, P) → m'
  71. Rotate(L'_4, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → O
  72. Rotate(J', If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → J''
  73. Rotate(F'_2, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → F_1
  74. Polygon(O, J'', F_1) → poly3, f_2, o, j''
  75. Rotate(M, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → M'
  76. Rotate(N, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → N'
  77. Segment(M', N') → b'
  78. Rotate(L'_5, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → G_1
  79. Rotate(L''_2, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → H_1
  80. Segment(G_1, H_1) → p
  81. Rotate(F'_3, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → I_1
  82. Rotate(P, If[6 < a < 7, ((a - 6) * π / 2), π / 2], L) → P'
  83. Segment(I_1, P') → m''
  84. Rotate(O, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → O'
  85. Rotate(J'', If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → J'''
  86. Rotate(F_1, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → J_1
  87. Polygon(O', J''', J_1) → poly3', j_2, o', j'''
  88. Rotate(M', If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → M''
  89. Rotate(N', If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → N''
  90. Segment(M'', N'') → b''
  91. Rotate(G_1, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → Q_1
  92. Rotate(H_1, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → R_1
  93. Segment(Q_1, R_1) → p'
  94. Rotate(I_1, If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → S_1
  95. Rotate(P', If[7 < a < 8, ((a - 7) * π / 2), π / 2], L) → P''
  96. Segment(S_1, P'') → m'''
  97. Intersect(d_1, x = 0) → B_2, C_2
  98. Line(L, F) → q
  99. Intersect(d_1, q) → D_2, E_2
  100. CircleSector(L, E_2, B_2) → r
  101. Rotate(r, If[9 < a < 10, ((-(a - 9)) * π / 4), ((-π)) / 4], L) → r'
  102. Segment(L''_2, B) → s
  103. Segment(L', A) → t
  104. Segment(D, N'') → f_1
  105. Segment(H_1, C) → g_1

AI Drawing Prompt Reference

Draw a cube in 3D space and animate its mirror transformations across two planes. Start with the original cube, then create mirrored copies about each plane. Use a slider to sequentially show rotations, dilations, and mirroring of the cube and its parts, including vertices, edges, and faces. The scene includes multiple cubes, their mirrors, and auxiliary planes and intersection points, demonstrating symmetry and geometric transformations.
The prompt above was compiled from the original drawing commands and is for reference only.