扇形与圆锥侧面展开 by Alfred Estberg

GeoGebra 命令及参数

1. Circle((0, 0, 0), CircleRad, zAxis) → c
2. Point(c) → B
3. Rotate(B, 0.1°, zAxis) → B'_1
4. Rotate(B, 359°, zAxis) → B'
5. CircumcircleArc(B, B'_1, B') → d
6. Point(d) → C
7. AngularBisector(C, A, B) → j
8. Sector(c, C, B) → g
9. Arc(c, C, B) → e
10. Circle(A, ConeRad, zAxis) → h
11. Intersect(j, h) → F, G
12. Circle(C, G, B) → r
13. Circle(C, F, B) → p
14. Segment(A, D) → i
15. Point(i) → E
16. Circle(A, ChangingRad, zAxis) → q
17. Intersect(r, q) → J, K, ,
18. Intersect(q, p) → H, I, ,
19. If(g < ((0.5 * π) * CircleRad^(2)), K, H) → L
20. Segment(A, L) → s
21. If(g < ((1 / 2 * π) * CircleRad^(2)), J, I) → M
22. Angle(M, A, L, zAxis) → α
23. Line((0, 0, 0), (0, 0, 1)) → f
24. Segment(L, E) → l
25. Segment(M, E) → m
26. Segment(M, A) → t
27. Line(L, E) → f_1
28. Surface((u * cos(v)), (u * sin(v)), w(u), u, 0, ChangingRad, v, If[Distance[C, M] < Distance[C, L], 360° - α, 0°], If[Distance[C, M] < Distance[C, L], 360°, 360° - α]) → b
29. Cone(A, D, ConeRad) → a, k, n
30. Rotate(b, (-Angle[L, A, (1, 0, 0), zAxis]), zAxis) → n'
31. Circle(A, ChangingRad, zAxis) → c_1
32. Intersect(j, c_1) → N, O
33. Angle(C, A, B, zAxis) → β
34. If(β < 180° ∧ α > 180°, CircleArc[A, L, M], If[β < 180° ∧ α < 180°, CircumcircleArc[L, N, M], CircumcircleArc[L, O, M]]) → d_1
35. Segment(A, E) → g_1