A question of Fixed Stars

1
Hello,

I think I know how to determine whether a fixed star is permanently hidden or circumpolar (having permanent curtailed passage) using the declination of the star and geographical latitude.

I wonder if there is a simple way to know whether a star that are neither circumpolar nor permanently hidden is either curtailed passage or arising but lying hidden in some part of the year.

Thank you!

2
declinations and geo lats have signs associated with them as used below:

south: -
north: +

This is open to correction, but I believe a point is circumpolar if for the northern hemisphere:

decl >= 90 - geo lat

for the southern hemisphere:

decl <= -90 - geo lat


Similarly for curtailed:

northern hemisphere:

decl <90>= 90 + geo lat