正方体的投影

GeoGebra 命令及参数

1. Sphere((0, 0, 0), r) → s
2. PointIn(s) → P
3. Vector(P) → u
4. OrthogonalPlane(P, u) → a
5. Angle(Vector[Z], Vector[P]) → φ
6. Angle(Vector[X], Vector[(x(P), y(P), 0)]) → θ
7. Angle(Vector[X], Vector[(x(P), y(P), 0)]) → θ'
8. If(y(P) ≥ 0, (((r * sin(φ + π / 2)) * cos(θ)), ((r * sin(φ + π / 2)) * sin(θ)), (r * cos(φ + π / 2))), (((r * sin(φ + π / 2)) * cos(θ')), ((r * sin(φ + π / 2)) * sin(θ')), (r * cos(φ + π / 2)))) → Q
9. Vector(Q) → v
10. OrthogonalPlane(Q, v) → b
11. IntersectPath(a, b) → j
12. Line(O, d) → f
13. Intersect(f, s) → A, R
14. Vector(R) → w
15. OrthogonalPlane(R, w) → c
16. IntersectPath(a, c) → k
17. Intersect(j, k) → B
18. IntersectPath(b, c) → g
19. Cube(C, B, D) → e, E, face5, face6, edge1, edge2, edge3, edge4, edge5, edge6, edge7, edge8, G, edge9, edge10, edge11, edge12, H, I, J, face1, face2, face3, face4
20. Segment(C', G') → h
21. Segment(G', H') → i
22. Segment(C', B') → l
23. Segment(B', H') → m
24. Segment(B', D') → n
25. Segment(C', E') → p
26. Segment(E', D') → q
27. Segment(G', J') → t
28. Segment(J', E') → f_1
29. Segment(I', H') → g_1
30. Segment(J', I') → h_1
31. Intersect(F, Line[S, B]) → B''
32. Intersect(F, Line[S, C]) → C''
33. Intersect(F, Line[S, D]) → D''
34. Intersect(F, Line[S, E]) → E''
35. Intersect(F, Line[S, G]) → G''
36. Intersect(F, Line[S, H]) → H''
37. Intersect(F, Line[S, I]) → I''
38. Intersect(F, Line[S, J]) → J''
39. Segment(C'', G'') → i_1
40. Segment(G'', H'') → j_1
41. Segment(C'', B'') → k_1
42. Segment(B'', H'') → l_1
43. Segment(E'', D'') → m_1
44. Segment(E'', J'') → n_1
45. Segment(J'', I'') → p_1
46. Segment(I'', D'') → q_1
47. Segment(C'', E'') → r_1
48. Segment(D'', B'') → s_1
49. Segment(J'', G'') → t_1
50. Segment(I'', H'') → a_1
51. Segment(S, B'') → b_1
52. Segment(S, C'') → c_1
53. Segment(S, D'') → d_1
54. Segment(S, E'') → e_1
55. Segment(S, H'') → f_2
56. Segment(S, G'') → g_2
57. Segment(S, J'') → h_2
58. Segment(S, E'') → i_2
59. Segment(S, I'') → j_2