How to request a trajectory on the surface of the spherical segment

There is scope (x, y, z). I'm disconnecting the segment I need. The swelling of this segment requires moving the camera and the trajectory is necessary. Make an idea or formula that will help me achieve the challenge.
P.S. I'm asking a question as someone might have encountered it. How do you think to build a vector from the centre of the sphere to the centre of the segment (length = r(s)) and to build a vector of the same length with an angle between the vectors?

“Parametrical equation of sphere with centre at point”
https://ru.wikipedia.org/wiki/%D0%A1%D1%84%D0%B5%D1%80%D0%B0
Put your limits on the part where the area was cut off. Get the coordinates of camera A0 from two parameters. Make a vector A1 of A0 to point 0.0.0. Make a vector.
A2 (x(A0),y(A0),z(A0)+1)
♪ A3=Crossing product A1 on A2 will give the enclosure axle. A4=Crossing product A3 on A1 will give another axle. Get three axles for the A1 A3 A4 vector cell, providing orientation to the camera and camera centre A0. Need to normalize.