三维填充曲线交互构型与变换

GeoGebra 命令及参数

1. Line(B, yAxis) → ff
2. Point(a) → C1
3. Point(c_1) → C21
4. Point(b_1) → C20
5. Point(a_1) → C19
6. Point(t) → C18
7. Point(r) → C17
8. Point(q) → C16
9. Point(p) → C15
10. Point(n) → C14
11. Point(m) → C13
12. Point(l) → C12
13. Point(k) → C11
14. Point(j) → C10
15. Point(i) → C9
16. Point(h_1) → C8
17. Point(g) → C7
18. Point(f) → C6
19. Point(e) → C5
20. Point(d) → C4
21. Point(c) → C3
22. Point(b) → C2
23. Mirror(C2, ff) → D2
24. Mirror(C3, ff) → D3
25. Mirror(C4, ff) → D4
26. Mirror(C5, ff) → D5
27. Mirror(C6, ff) → D6
28. Mirror(C7, ff) → D7
29. Mirror(C8, ff) → D8
30. Mirror(C9, ff) → D9
31. Mirror(C10, ff) → D10
32. Mirror(C11, ff) → D11
33. Mirror(C12, ff) → D12
34. Mirror(C13, ff) → D13
35. Mirror(C14, ff) → D14
36. Mirror(C15, ff) → D15
37. Mirror(C16, ff) → D16
38. Mirror(C17, ff) → D17
39. Sequence(abs(x(Object["C" + (t)]) - x(B)), t, 1, 21) → rayon
40. PolyLine(liste1) → s
41. Sequence(Element[rayon, k]^(2) + Element[rayon, k + 1]^(2) + (Element[rayon, k] * Element[rayon, k + 1]), k, 1, 20) → volumes
42. Sum(volumes) → volumenT
43. Sequence(Sum[First[volumeB, k]], k, 1, 21) → volumeA
44. Mirror(C18, ff) → D18
45. Mirror(C19, ff) → D19
46. Mirror(C20, ff) → D20
47. Mirror(C21, ff) → D21
48. Sequence(((20 * Element[volumeA, k]), k), k, 1, 21) → points
49. Mirror(C1, ff) → D1
50. PolyLine(liste2) → d_1
51. Midpoint(C1, D1) → A
52. Sequence(Segment[Element[points, k], Element[points, k + 1]], k, 1, 19) → liste3
53. Segment(D1, (10, 0)) → e_1
54. Sequence(Segment[(k, 0), (k, 20)], k, 0, 20) → traitverti
55. Sequence(Segment[(0, k), (20, k)], k, 1, 20) → traith
56. Sequence(Segment[Object["D" + (t)], (0, t - 1)], t, 1, 21) → liste4
57. Ellipse(D1, C1, C) → f_1
58. Midpoint(C21, D21) → D
59. Ellipse(C21, D21, E) → g_1
60. Sequence(Segment[Element[points, t], (0, t)], t, 1, 21) → liste5
61. Segment((0, 0), Element[points, 1]) → i_1
62. Take(liste5, 1, h - 1) → liste7
63. Take(liste4, 1, h) → liste6
64. Take(points, 1, h - 1) → haut1
65. Take(liste1, 1, h) → rec1
66. Take(liste2, 1, h) → rec2
67. Union(rec1, rec2) → rec
68. Sequence(Polygon[Element[liste1, i], Element[liste1, i + 1], Element[liste2, i + 1], Element[liste2, i]], i, 1, Length[liste7]) → liste8
69. Ellipse(D1, C1, C) → k_1
70. Ellipse(C21, D21, E) → p_1
71. Segment(Element[liste1, h], Element[points, h - 1]) → haut
72. Sequence(G + ((i * AxisStepX[]), 0), i, 0, 20) → liste9
73. Sequence(G + (0, (i * AxisStepY[])), i, 0, 20) → liste10
74. Vector(G, H) → u
75. Vector(G, I) → v
76. Sequence(Text["" + (i), Element[liste9, i + 1] - (0.2, 0.75)], i, 0, 20) → liste11
77. Take(volumes, 1, h - 1) → volhaut
78. Sum(volhaut) → Vol
79. Take(liste3, 1, h - 2) → liste12
80. Translate(s, Vector[C1, J]) → s'
81. Translate(D1, Vector[C1, J]) → D1'
82. Line(J, D1') → j_1
83. Midpoint(D1', J) → K
84. Rotate(s', 90°, j_1) → s''
85. Line(K, zAxis) → l_1
86. Surface(s'', (2 * π), l_1) → o
87. Circle(K, Distance[K, J], l_1) → q_1
88. Take(liste1, 1, h) → liste1b
89. PolyLine(liste1b) → m_1
90. Translate(m_1, Vector[C1, J]) → n_1
91. Rotate(n_1, 90°, j_1) → r_1
92. Surface(r_1, (2 * π), l_1) → w
93. Translate(C21, Vector[C1, J]) → C21'
94. Rotate(C21', 90°, j_1) → C21''
95. Translate(D21, Vector[C1, J]) → D1'_{1}
96. Rotate(D1'_{1}, 90°, j_1) → L
97. Midpoint(C21'', L) → M
98. Circle(M, Distance[M, L], l_1) → s_1
99. Element(liste1, h) → l1
100. Translate(l1, Vector[C1, J]) → l1'
101. Rotate(l1', 90°, j_1) → l1''
102. Mirror(l1'', l_1) → l1'''
103. Midpoint(l1'', l1''') → N
104. Circle(N, Distance[N, l1''], l_1) → t_1
105. Circle(N, Distance[N, l1''], l_1) → c_2