圆反射：度量空间

GeoGebra 命令及参数

1. Segment(A, B) → AB
2. Point(AB) → C
3. Segment(A, C) → AC
4. Vector(A, B) → u
5. Circle(A, A + v) → c
6. Midpoint(B, C') → D
7. Segment(B, D) → r
8. Vector(B, D) → w
9. UnitOrthogonalVector(u) → v'
10. Line(C', v') → g
11. Line(B, z) → l
12. UnitVector(u) → u'
13. Line(B + prm * v', u') → g_2
14. Point(Segment[Intersect[g_2, l], Intersect[g_2, g]]) → V
15. DynamicCoordinates(O, x(V), y(V)) → W
16. Line(W, u') → k
17. Intersect(k, l) → T
18. Segment(T, T + 2 * w) → t
19. UnitVector(t) → t'
20. Vector(A, L1) → a
21. UnitVector(a) → l'
22. Vector(H - L1) → v_1
23. Vector(L1, L2) → w_1
24. UnitVector(w_1) → z_1
25. Line(O, u') → e_1
26. Intersect(e_1, l) → T_1
27. Sequence(k / n4, k, -n4, n4) → list5
28. Midpoint(A, B) → M2
29. Circle(M2, A) → k_1
30. Point(k_1) → R
31. Intersect(Ray[A, R], l) → S
32. Line(D, v') → d
33. Sequence(m, m, -2 * n + 1, 2 * n - 1, 2) → n_j
34. Sequence(k, k, n0, n - 1) → n_i
35. Midpoint(A, C) → M1
36. Circle(M1, A) → f
37. Mirror(W, c) → L'_1
38. Mirror(T_1, c) → P'
39. Segment(A, C') → e_2
40. Mirror(Z, c) → Z'
41. Midpoint(A, Z') → G
42. Mirror(H, c) → H'
43. Sequence(L1 - k / n3 * v_1, k, 1, n3) → RingA2
44. Mirror(RingA2, c) → RingA1'
45. Sequence(L1 + k / n3 * v_1, k, 1, n3) → RingA1
46. Mirror(RingA1, c) → RingA2'
47. Zip(Circle[Midpoint[a, b], a], a, RingA1, b, RingA2) → plrArcs
48. Zip(Circle[Midpoint[a, b], a], a, RingA1', b, RingA2') → plrArcs'
49. Zip(S - z + (k + 1) * w, k, list5) → GridPtsw
50. Zip(S + k * z, k, list5) → GridPtsz
51. Zip(Midpoint[A, a], a, Mirror[Zip[S - u + k * z, k, list5], c]) → ringCen
52. Mirror(Grid1, c) → Grid1'
53. Translate(Dilate[Grid1, EH / r, S - z], S' - S + z) → list1
54. Mirror(list1, c) → list1'
55. Mirror(GridPtsz, c) → GridPtsw'
56. Zip(CircleArc[a, If[sgn((b - B) * v) ≥ 0, A, b], If[sgn((b - B) * v) ≥ 0, b, A]], a, ringCen, b, GridPtsw') → ringPart
57. Zip(Circle[a, A], a, ringCen) → ringFull
58. Line(W, v') → h_1
59. Mirror(h_1, c) → p_1
60. Mirror(t, c) → t'_1
61. Sequence(Rotate[H, k * 30 * ° / b_1, L1], k, 1, 12 * b_1) → plrPts
62. Zip(Segment[L1, k], k, plrPts) → plrRad2
63. Ray(L1, L2) → sdf
64. Mirror(L1, c) → L1'
65. Segment(A, L1) → l_1
66. Segment(A, B_1) → m_1
67. Angle(L1, B_1, A) → α
68. Line(A, v') → lineV
69. Line(A, B) → lineU
70. Mirror(B_1, c) → F
71. If(v' ⊗ (L1 - B) ≥ 0, Intersect[l, sdf], L1) → L
72. Intersect(g, sdf) → P
73. Segment(L, P) → q_1
74. Mirror(q_1, c) → s_1
75. Midpoint(A, F) → Q
76. Mirror(L2, c) → L2'
77. Segment(A, L2) → t_1
78. CircumcircleArc(L1', L2', A) → sdf'
79. Circle(Q, L1') → c_2
80. Segment(L1, B_1 - 0.25 * z_1) → r_1
81. Segment(A, F) → a_2
82. Ray(A, l') → b_2
83. Angle(A, Z, W) → γ
84. Segment(A, Z) → f_2
85. Mirror(Z, c) → Z'_1
86. Intersect(Line[V, v'], lineU) → C_1
87. Segment(A, T) → d_2
88. Segment(A, T + 2 * w) → f_1
89. Circle(Midpoint[A, Z'_1], A) → d_1
90. Sequence(Rotate[H, (k * 30)°, L1], k, 1, 12) → plrPts2
91. Zip(Segment[L1, k], k, plrPts2) → plrRad1
92. Mirror(plrRad2, c) → plrRad2'
93. Mirror(plrRad1, c) → plrRad1'
94. Ray(L1, Vector[-z_1]) → i_2
95. Zip(Ray[a + 2 * w, u'], a, GridPtsz) → list2
96. Zip(Line[a + 2 * w, u'], a, GridPtsz) → list4
97. Intersect(l, b_2) → U
98. Intersect(b_2, g) → A_1
99. Segment(U, A_1) → j_1
100. Point(Ray[L1, l']) → D_1
101. Mirror(k_2, c) → list6
102. Segment(Mirror[E_1, c], Mirror[D_1, c]) → j_2
103. Segment(Mirror[H, c], Mirror[2 * L1 - H, c]) → h_2
104. Midpoint(t) → N
105. Zip(A + (1 - ε) / (1 + ((m + k2)^(2) - 1) * ε^(2)) * (u + (m + k2) * ε * v), m, n_j + 1) → CyclCen
106. Zip(A + (1 - ε) / (1 + (m + k2)^(2) * ε^(2)) * (u + (m + k2) * ε * v), m, n_j) → CyclPts
107. Zip(Circle[a, b], a, CyclCen, b, CyclPts) → list3
108. Segment(A, T_1) → c_1
109. Point(CyclCen) → E
110. Segment(E, Intersect[Ray[E, u'], d]) → e
111. Segment(D - r / 2 * v', D + r / 2 * v') → p