Hi @tungtwister, I am afraid the specific details of how the head tracking algorithm is implemented is not something open for public dissemination however I can inform you that the detection of the eyes is not required for successful head tracking.
Regarding minimum distance/rotation this is not a metric we analyse, however, the values are provided to one tenth of a radian within the Core SDK. I will however try to find out more information on your behalf. If you could describe your motivations, it would be helpful.. thanks!