Our work on Geometric Origin of Self-Intersection Points in Non-Hermitian Energy Spectra lead by the postdoc Jinghui Pi has been published by PRB. The non-Hermitian energy spectra of system with periodic boundary condition could be a spaghetti. This paper says that how exactly these spaghetti cross itself are related to the auxiliary generalized Brillouin zone (open chain) and the Brillouin zone (a concept for the periodic boundary condition, a unit circle). Note that auxiliary generalized Brillouin zone is a seemly purely mathematical concept, which could be think of the analytical continuation of the generalized Brillouin zone, a concept generalized to open quantum systems.