Darboux 循环曲面上的圆系与切割演示

GeoGebra 命令及参数

1. Intersect(xAxis, yAxis) → o
2. Point(xAxis) → e
3. Circle(o, e) → c_E
4. Intersect(c_E, yAxis, 1) → i'
5. Intersect(c_E, yAxis, 2) → i
6. Line(i, i') → f_{1}
7. Intersect(c_E, xAxis, 2) → e'
8. Line(e, e') → g
9. Point(g) → f
10. LineBisector(f'', f) → n
11. Point(g) → s
12. Mirror(s, c_E) → s'''
13. Midpoint(s, s''') → A
14. Circle(A, s) → d
15. Mirror(f, d) → f'_{4}
16. Mirror(d, f_{1}) → d'
17. Mirror(f, d') → f'_{5}
18. Circle((1 / 2 * (f'_{4} + f'_{5})), f'_{4}) → cE_L
19. Point(cE_L) → qE_L
20. Circle(f', qE_L, f''') → e_1
21. Mirror(s, f_{1}) → s'
22. Mirror(s', c_E) → s''
23. Midpoint(s'', s) → B
24. Circle(B, s) → h
25. Mirror(f, h) → f'_{1}
26. Mirror(h, f_{1}) → h'
27. Mirror(f, h') → f'_{2}
28. Circle((1 / 2 * (f'_{1} + f'_{2})), f'_{1}) → c_L
29. Mirror(f, c_L) → f_{#}
30. Circle(qE_L, f, f_{#}) → g_1
31. Tangent(f, g_1) → h_1,
32. OrthogonalLine(f, h_1) → i_1
33. Intersect(n, i_1) → E
34. Circle(E, f) → k_1
35. Intersect(k_1, e_1) → p2_2, p2_1, ,
36. Mirror(p2_1, g_1) → z_{1}
37. Circle(z_{1}, p2_1, p2_2) → dbc2ell
38. MittelkreisKreisKreisHyperbolisch(k_1, e_1) → dbc2hyp
39. ImplicitCurve(darboux(x, y, 0)) → bizQu_{xy}
40. ImplicitCurve(darboux(0, y, x)) → bizQu_{yz}
41. ImplicitCurve(darboux(x, 0, y)) → bizQu_{xz}
42. Translate(ImplicitCurve[darboux(x, y, h_z)], Vector[(0, 0, h_z)]) → bizQuh_z
43. Circle(s, s'', S_z) → bizQu1_{xz}
44. Circle(s', s''', S'_z) → bizQu2_{xz}
45. Circle(o, s''') → k
46. Circle(o, s) → p
47. Point(c_L) → p_L
48. Circle(f', f'', p_L) → cb11
49. Circle(p_L, f, f_{#}) → r
50. Center(r) → C
51. Line(C, f) → j
52. LineBisector(f, f''') → l
53. Intersect(j, l) → D
54. Circle(D, f) → cb12
55. If(x(Intersect[cb12, cb11, 1]) > 0, Intersect[cb12, cb11, 1], Intersect[cb12, cb11, 2]) → p_1
56. Mirror(p_1, r) → F'
57. Mirror(p_1, c_E) → p_4
58. LineBisector(p_4, p_1) → b
59. Center(bizQu1_{xz}) → K
60. Sphere(o, S_z) → eKu
61. Center(e_1) → M
62. Center(k_1) → N
63. Point(g) → s2_x
64. ImplicitCurve(darboux2(x, y, 0)) → bizQu2_{xy}
65. Line(o, S_z) → f_2
66. If(x(Intersect[cb12, cb11, 1]) > 0, Intersect[cb12, cb11, 2], Intersect[cb12, cb11, 1]) → p_2
67. Mirror(p_1, r) → p'_{2}
68. Circle(p'_{2}, p_1, p_2) → dbc1
69. Center(dbc1) → mdb1
70. Sphere(mdb1, p_1) → dbKu1
71. Line(p_1, mdb1) → ldbc
72. Intersect(ldbc, f_{1}) → mdb3
73. Mirror(p_1, f_{1}) → p'_1
74. Circle(mdb3, p_1) → dbc3
75. Sphere(mdb3, p_1) → dbKu3
76. LineBisector(p_4, p_1) → m
77. Intersect(m, ldbc) → mdb4
78. Circle(mdb4, p_1) → dbc4
79. Sphere(mdb4, p_1) → dbKu4
80. Intersect(g, ldbc) → mdb2
81. Circle(mdb2, p_1) → dbc2
82. Sphere(mdb2, p_1) → dbKu2
83. CurveCartesian(T_{-1}((1 / (1 + sqrt(1 - (a_T^(2) * (cos(u))^(2)) - (b_T^(2) * (sin(u))^(2)))) * ((a_T * cos(u)) + ((b_T * sin(u)) * ί)))), u, (-π), π) → TBizQu_{+}
84. CurveCartesian(T_{-1}((1 / (1 - sqrt(1 - (a_T^(2) * (cos(u))^(2)) - (b_T^(2) * (sin(u))^(2)))) * ((a_T * cos(u)) + ((b_T * sin(u)) * ί)))), u, (-π), π) → TBizQu_{-}
85. Sequence(k, k, (-anz), anz) → L_{anz}
86. Zip(Circle[PP((k / anz * π)), S_z, S'_z], k, L_{anz}) → KreisGitter
87. Mirror(p2_2, g_1) → F
88. Circle(p2_1, p2_2, F) → cdb_E
89. MittelkreisKreisKreisHyperbolisch(e_1, k_1) → cdb_{ell}
90. If(Defined[cdb_E], cdb_E, cdb_{ell}) → dbc_E
91. Center(dbc_E) → mdbc_E
92. Center(cE_L) → G
93. Center(k_1) → mcb1_E
94. Line(mdbc_E, mcb1_E) → q
95. OrthogonalLine(o, q) → t
96. Intersect(dbc_E, q) → q2_E, q1_E
97. Sphere(mdbc_E, q2_E) → dbKu_E
98. Intersect(c_E, t) → H, I
99. Intersect(bizQu1_{xz}, dbKu_E) → J, L, ,
100. Intersect(bizQu2_{xz}, dbKu_E) → O, P, ,
101. Line(L, P) → a
102. Plane(o, I, L) → Esec
103. IntersectPath(Esec, dbKu_E) → csec
104. Line(o, J) → j_1
105. Plane(o, I, J) → Esec'
106. IntersectPath(Esec', dbKu_E) → csec'
107. Circle(S_z, S'_z, p_1) → dbcE4