旋转曲面：由两函数区域旋转而成

GeoGebra 命令及参数

1. Surface(u, c + ((f(u) - c) * cos(v)), ((f(u) - c) * sin(v)), u, a, b, v, 0, n) → OuterH
2. Textfield(c) → InputBox1
3. Surface(u, c + ((h(u) - c) * cos(v)), ((h(u) - c) * sin(v)), u, a, b, v, 0, n) → InnerH
4. IntegralBetween(f, h, a, b) → r
5. Surface(o + ((u - o) * cos(v)), f(u), ((u - o) * sin(v)), u, a, b, v, 0, n) → VerticalOuter
6. Surface(o + ((u - o) * cos(v)), h(u), ((u - o) * sin(v)), u, a, b, v, 0, n) → VerticalInner
7. Segment((a, 0), (a, h(a))) → g_1
8. Segment((b, h(b), 0), (b, f(b), 0)) → h_1
9. Rotate(h_1, (-n), (b, c, 0), k) → i_1
10. Rotate(g, (-n), k) → g_2
11. Rotate(p, (-n), k) → p_1
12. Segment((a, h(a), 0), (a, f(a), 0)) → j_1
13. Rotate(j_1, (-n), k) → k_1
14. CurveCartesian(a, (f(a) * t) + (h(a) * (1 - t)), 0, t, 0, 1) → w
15. CurveCartesian(b, (f(b) * t) + (h(b) * (1 - t)), 0, t, 0, 1) → b_1
16. Surface(w, n, k) → c_1
17. Mirror(c_1, z = 0) → LeftH
18. Surface(b_1, n, k) → e_1
19. Mirror(e_1, z = 0) → RightH
20. Surface(w, n, f_1) → d
21. Surface(b_1, n, f_1) → e
22. Mirror(d, z = 0) → LesserBoundaryV
23. Mirror(e, z = 0) → GreaterBoundaryV
24. Rotate(p, (-n), f_1) → p_2
25. Rotate(b_1, (-n), f_1) → u
26. Rotate(g, (-n), f_1) → g_3
27. Rotate(w, (-n), f_1) → w'
28. Rotate(D, If[0 < n ≤ pi, (-n), -3.14], k) → D'
29. Rotate(E, If[0 < n ≤ pi, (-n), -3.14], k) → E'
30. CircleArc((b, c, 0), E, E') → q
31. CircleArc((b, c, 0), D, D') → t
32. Mirror(E, k) → E'_1
33. CircleArc(F, E, E'_1) → d_1
34. CircleArc(F, E, E'_1) → q_1
35. Mirror(D, k) → D'_1
36. Rotate(D'_1, If[pi < n ≤ (2 * pi), (-(n - pi)), 6.28], k) → G
37. CircleArc(F, D', G) → r_1
38. Rotate(E'_1, If[pi < n ≤ (2 * pi), (-(n - pi)), 6.28], k) → H
39. CircleArc(F, E', H) → s_1
40. Rotate(E, If[0 < n ≤ pi, (-n), -3.14], f_1) → E'_2
41. Rotate(D, If[0 < n ≤ pi, (-n), -3.14], f_1) → D'_2
42. Mirror(E, f_1) → E'_3
43. Mirror(D, f_1) → D'_3
44. CircleArc(I, E, E'_2) → t_1
45. CircleArc(J, D, D'_2) → c_2
46. Rotate(D'_3, If[pi < n < (2 * pi), (-(n - pi)), -3.14], f_1) → K
47. Rotate(E'_3, If[pi < n < (2 * pi), (-(n - pi)), -3.14], f_1) → L
48. CircleArc(J, D'_3, K) → d_2
49. CircleArc(I, E'_3, L) → e_2
50. Rotate(N, If[0 < n ≤ pi, (-n), -3.14], M, k) → N'
51. Rotate(O, If[0 < n ≤ pi, (-n), -3.14], M, k) → A'
52. CircleArc(M, N, N') → f_2
53. CircleArc(M, O, A') → h_2
54. Mirror(N, k) → N'_1
55. Mirror(O, k) → O'
56. Rotate(N'_1, If[pi < n < (2 * pi), (-(n - pi)), -3.14], k) → P
57. Rotate(O', If[pi < n < (2 * pi), (-(n - pi)), -3.14], k) → O''
58. CircleArc(M, O', O'') → k_2
59. CircleArc(M, N'_1, P) → q_2
60. Rotate(N, If[0 < n ≤ pi, (-n), -3.14], I, f_1) → N'_2
61. Rotate(O, If[0 < n ≤ pi, (-n), -3.14], I, f_1) → O'_1
62. CircleArc(Q, N, N'_2) → r_2
63. CircleArc(R, O, O'_1) → s_2
64. Mirror(N, f_1) → N'_3
65. Mirror(O, f_1) → O'_2
66. Rotate(N'_3, If[pi < n ≤ (2 * pi), (-(n - pi)), -3.14], Q, f_1) → S
67. Rotate(O'_2, If[pi < n ≤ (2 * pi), (-(n - pi)), -3.14], Q, f_1) → T
68. CircleArc(Q, N'_3, S) → t_2
69. CircleArc(R, O'_2, T) → c_3
70. Textfield(o) → InputBox2
71. Textfield(a) → InputBox3
72. Textfield(b) → InputBox4
73. Textfield(f) → InputBox5
74. Textfield(h) → InputBox6