无枢轴的“转折翻转”几何变换：旋转与镜像合成

GeoGebra 命令及参数

1. Point(Circle[A, 1.2851459061133876]) → B
2. Polygon(A, B, C, D, E, F) → preimage, a, b, c, d, e, f
3. Vector(G, H) → Vector
4. Line(I, J) → lineOfReflection
5. Translate(A, Vector) → A'_{5}
6. Translate(B, Vector) → B'_{5}
7. Translate(C, Vector) → C'_{5}
8. Translate(D, Vector) → D'_{5}
9. Translate(E, Vector) → E'_{5}
10. Translate(F, Vector) → F'_{5}
11. Polygon(A'_{5}, B'_{5}, C'_{5}, D'_{5}, E'_{5}, F'_{5}) → translated, a', b', c', d', e', f'
12. Mirror(A, lineOfReflection) → A'_{1}
13. Mirror(B, lineOfReflection) → B'_{1}
14. Mirror(C, lineOfReflection) → C'_{1}
15. Mirror(D, lineOfReflection) → D'_{1}
16. Mirror(E, lineOfReflection) → E'_{1}
17. Mirror(F, lineOfReflection) → F'_{1}
18. Polygon(A'_{1}, B'_{1}, C'_{1}, D'_{1}, E'_{1}, F'_{1}) → reflected, a'_{1}, b'_{1}, c'_{1}, d'_{1}, e'_{1}, f'_{1}
19. Rotate(A, α, Center) → A'_{2}
20. Rotate(B, α, Center) → B'_{2}
21. Rotate(C, α, Center) → C'_{2}
22. Rotate(D, α, Center) → D'_{2}
23. Rotate(E, α, Center) → E'_{2}
24. Rotate(F, α, Center) → F'_{2}
25. Polygon(A'_{2}, B'_{2}, C'_{2}, D'_{2}, E'_{2}, F'_{2}) → rotated, a'_{2}, b'_{2}, c'_{2}, d'_{2}, e'_{2}, f'_{2}
26. Line(K, lineOfReflection) → h
27. Point(h) → L
28. Vector(K, L) → Vector2
29. Mirror(A, lineOfReflection) → A'_{3}
30. Mirror(B, lineOfReflection) → B'_{3}
31. Mirror(C, lineOfReflection) → C'_{3}
32. Mirror(D, lineOfReflection) → D'_{3}
33. Mirror(E, lineOfReflection) → E'_{3}
34. Mirror(F, lineOfReflection) → F'_{3}
35. Polygon(A'_{3}, B'_{3}, C'_{3}, D'_{3}, E'_{3}, F'_{3}) → intermediary, a'_{3}, b'_{3}, c'_{3}, d'_{3}, e'_{3}, f'_{3}
36. Translate(A'_{3}, Vector2) → M
37. Translate(B'_{3}, Vector2) → N
38. Translate(C'_{3}, Vector2) → O
39. Translate(D'_{3}, Vector2) → P
40. Translate(E'_{3}, Vector2) → Q
41. Translate(F'_{3}, Vector2) → R
42. Polygon(M, N, O, P, Q, R) → image_{1}, m, n, o, p, q, r
43. Line(S, T) → g
44. Rotate(preimageList, angleAnimator, rotationCenter) → RFanimRotList
45. Rotate(A, rotationAngle) → A'_{4}
46. Rotate(C, rotationAngle) → C'_{4}
47. Rotate(D, rotationAngle) → D'_{4}
48. Rotate(E, rotationAngle) → E'_{4}
49. Rotate(F, rotationAngle) → F'_{4}
50. Rotate(A, rotationAngle, rotationCenter) → A'_{6}
51. Rotate(C, rotationAngle, rotationCenter) → C'_{6}
52. Rotate(D, rotationAngle, rotationCenter) → D'_{6}
53. Rotate(E, rotationAngle, rotationCenter) → E'_{6}
54. Rotate(F, rotationAngle, rotationCenter) → F'_{6}
55. Mirror(A'_{6}, g) → W
56. Mirror(C'_{6}, g) → F_1
57. Mirror(D'_{6}, g) → G_1
58. Mirror(E'_{6}, g) → H_1
59. Mirror(F'_{6}, g) → I_1
60. Rotate(preimageList, rotationAngle, rotationCenter) → RFintermList
61. Mirror(RFintermList, g) → RFfinalList
62. Mirror(preimageList, g) → FRintermList
63. Rotate(FRintermList, rotationAngle, rotationCenter) → FRfinalList
64. Rotate(FRintermList, angleAnimator, rotationCenter) → FRanimRotList
65. Polygon(FRanimFlipList) → FRanimFlip
66. Polygon(FRanimRotList) → FRanimRot
67. Polygon(FRintermList) → FRinterm
68. Polygon(RFanimRotList) → RFanimRot
69. Polygon(RFintermList) → RFinterm
70. Polygon(RFanimFlipList) → RFanimFlip
71. Polygon(RFfinalList) → RFfinal
72. Polygon(FRfinalList) → image
73. Segment(rotationCenter, FRanimRotList(2)) → FRrotationSegment
74. Segment(rotationCenter, RFanimRotList(2)) → RFrotSegment
75. Line(rotationCenter, V) → i
76. Rotate(V, rotationAngle / 2, rotationCenter) → V'
77. Angle(V, rotationCenter, V') → β
78. Line(rotationCenter, V') → line2