凸球面镜反射：点光源成像与笛卡尔公式

GeoGebra 命令及参数

1. Point(xAxis) → C
2. Point(yAxis) → B
3. Semicircle(B, C_1) → MirrorConvex
4. Point(xAxis) → F
5. Line(F, yAxis) → b
6. Point(xAxis) → Directriz
7. Line(Directriz, yAxis) → a
8. Point(xAxis) → P
9. Point(MirrorConvex) → A
10. Line(P, A) → f_1
11. Tangent(A, MirrorConvex) → h_1,
12. OrthogonalLine(A, h_1) → i
13. Point(i) → G
14. Angle(P, A, G) → θ_i
15. Rotate(G, θ_i, A) → G'
16. Angle(G, A, G') → θ_ir
17. Line(A, G') → d
18. Intersect(d, xAxis) → Q
19. OrthogonalLine(A, xAxis) → e
20. Intersect(e, xAxis) → A_1
21. Vector(A_1, A) → h
22. OrthogonalLine(Q, xAxis) → g
23. Intersect(MirrorConvex, xAxis, 1) → O
24. Vector(P, A) → u
25. Point(d) → D
26. Vector(A, D) → v
27. Vector(P, F) → w
28. Vector(P, C) → c
29. Parabola(F, a) → k
30. Point(k) → J
31. Line(J, xAxis) → j
32. Tangent(J, k) → l,
33. OrthogonalLine(J, l) → m
34. Vector(J, F) → q_1
35. Line(O, e) → f_2
36. Point(f_2) → E
37. Point(f_2) → K
38. Point(f_2) → L
39. Line(E, c) → n
40. Line(K, xAxis) → p
41. Line(L, xAxis) → q_2
42. Intersect(g, n) → M
43. Intersect(b, p) → N
44. Intersect(q_2, yAxis) → R
45. Vector(E, M) → q
46. Vector(K, N) → f
47. Vector(L, R) → r