球体与椭圆/双曲圆柱相交的几何构造

GeoGebra 命令及参数

1. Intersect(xAxis, yAxis) → o
2. Point(xAxis) → e_{1}
3. Circle(o, e_{1}) → c_E
4. Intersect(c_E, yAxis, 2) → i
5. Intersect(c_E, yAxis, 1) → i'
6. Line(i, i') → g_y
7. Intersect(c_E, xAxis, 2) → e'
8. Line(e', e_{1}) → g_x
9. Sphere(o, 1) → eku
10. Point(zAxis) → N
11. Point(g_x) → f
12. Point(g_x) → f'
13. Point(g_x) → s_x
14. If(abs((1 / 2 * (f + f')) - s_x) > (1 / 2 * abs(f - f')), Ellipse[f, f', s_x], Hyperbola[f, f', s_x]) → ccon
15. CurveCartesian(m + (a * cos(t)) + ((b * ί) * sin(t)), t, (-π), π) → eelli
16. CurveCartesian(x(m + (a * cos(t)) + ((b * ί) * sin(t))), y(m + (a * cos(t)) + ((b * ί) * sin(t))), oProj_{+}(x(m + (a * cos(t)) + ((b * ί) * sin(t))), y(m + (a * cos(t)) + ((b * ί) * sin(t)))), t, (-π), π) → qq_{+}
17. CurveCartesian(x(m + (a * cos(t)) + ((b * ί) * sin(t))), y(m + (a * cos(t)) + ((b * ί) * sin(t))), oProj_{-}(x(m + (a * cos(t)) + ((b * ί) * sin(t))), y(m + (a * cos(t)) + ((b * ί) * sin(t)))), t, (-π), π) → qq_{-}
18. CurveCartesian(projSt_{+}(m + (a * cos(t)) + ((b * ί) * sin(t))), t, (-π), π) → stqq_{+}
19. CurveCartesian(projSt_{-}(m + (a * cos(t)) + ((b * ί) * sin(t))), t, (-π), π) → stqq_{-}
20. CurveCartesian(T(projSt_{+}(m + (a * cos(t)) + ((b * ί) * sin(t)))), t, (-π), π) → bizQu_{+}
21. CurveCartesian(T(projSt_{-}(m + (a * cos(t)) + ((b * ί) * sin(t)))), t, (-π), π) → bizQu_{-}
22. Line(P_{u+}, N) → g
23. Line(N, P_{u-}) → h