双光锥与丹德林球生成的圆锥曲线

GeoGebra 命令及参数

1. Plane((0, 0, -1), (1, 0, -1), (0, 1, -1)) → projectivePlane
2. Circle((1, 0, 0), (0, 0, 1), (-1, 0, 0)) → gimbalRing
3. Point(gimbalRing) → P
4. Rotate(P, (-(αAperture / 2)), yAxis) → Pn
5. Intersect(Line[Pn, O], projectivePlane) → VMn
6. AngularBisector(VMn + Vector[((x(VMn) * x(Pn)), 0, 0)], VMn, Pn) → bisectN
7. Line(O, P) → lightLine
8. Intersect(bisectN, lightLine) → On
9. Rotate(P, αAperture / 2, yAxis) → Pp
10. Intersect(Line[Pp, O], projectivePlane) → VMp
11. AngularBisector(VMp + Vector[((x(VMp) * x(Pp)), 0, 0)], VMp, Pp) → bisectP
12. Intersect(bisectP, lightLine) → Op
13. Intersect(lightLine, projectivePlane) → F_{0}
14. ConeInfinite(O, Vector[(0, 0, 1)], pi / 2) → f
15. Sphere(O, 1) → unitSphere
16. ConeInfinite(O, Vector[P], αAperture / 2) → lightCone
17. IntersectPath(projectivePlane, lightCone) → conics
18. If(αLight ≟ 0, "Circle", If[α < 90°, "Ellipse", If[α ≟ 90°, "Parabola", If[αLight ≟ 90° ∧ αAperture ≟ 90°, "Rectangular Hyperbola", "Hyperbola"]]]) → txtConicType
19. Point(O, Vector[(P * cos(αAperture / 2))]) → Pcos
20. Sphere(Op, Fp) → FpSphere
21. Point(O, Vector[(Vector[Pp] * dP)]) → FpTouch
22. Circle(lightLine, FpTouch) → FpTouchCircle
23. Sphere(On, Fn) → FnSphere
24. Point(O, Vector[(Vector[Pn] * dN)]) → FnTouch
25. Circle(lightLine, FnTouch) → FnTouchCircle