圆柱体交集研究

GeoGebra 命令及参数

1. Point(xAxis) → X
2. Circle(X, c, xAxis) → r
3. Point(yAxis) → Y
4. Intersect(n, r) → D, E
5. Vector(X, D) → u
6. If(Defined[D], Angle[u, v], If[y(Y) > c, 0, π]) → β
7. Circle(Y, b, yAxis) → q
8. Surface((b * cos(u)), t, (b * sin(u)), u, 0, (2 * π), t, y(Y), y(Y) + 10) → c_y
9. Point(f) → A
10. Locus(A', A) → LlocGeomètric1
11. CurveCartesian(c_y(acos((a * cos(t) / b)), (a * sin(t))), t, -10, 10) → g
12. Surface(t, (c * cos(u)), (c * sin(u)), u, 0, (2 * π), t, x(X), x(X) + 10) → c_x
13. Mirror(g, xOyPlane) → g'
14. CurveCartesian(c_x(acos((a * cos(t) / c)), (a * sin(t))), t, -10, 10) → h
15. Mirror(h, xOyPlane) → h'
16. Circle(xAxis, C) → k
17. Point(k) → B
18. CurveCartesian(c_y(asin((c * sin(t) / b)), (c * cos(t))), t, (-β), β) → j
19. Mirror(j, l) → j'
20. Surface((b * cos(u)), (t * cos(α)) - ((b * sin(u)) * sin(α)), (t * sin(α)) + ((b * sin(u)) * cos(α)), u, 0, (2 * π), t, -5, 5) → m
21. Point(zAxis) → Z
22. Surface((a * cos(u)), (a * sin(u)), t, u, 0, (2 * π), t, z(Z), z(Z) + 10) → c_z
23. Circle(Z, a, zAxis) → p
24. Translate(p, Vector[(0, 0, 10)]) → p'
25. Translate(q, Vector[(0, 10, 0)]) → q'
26. Translate(r, Vector[(10, 0, 0)]) → r'
27. Intersect(o, q) → F, G
28. Segment(F, G) → s
29. Mirror(F, xOyPlane) → F'
30. Mirror(G, xOyPlane) → G'
31. Segment(F', G') → s'
32. Intersect(n', r) → D', H
33. Intersect(o', q') → F_1, G_1
34. Mirror(F_1, xOyPlane) → F_1'
35. Mirror(G_1, xOyPlane) → G_1'
36. Segment(F_1, G_1) → s_1
37. Segment(F_1', G_1') → s_1'
38. Line(Y, (0, 1, 0)) → e_y
39. Line(X, (1, 0, 0)) → e_x
40. Line(Z, (0, 0, 1)) → f_1