I'm implementing ECC in my spare time project. I'm referencing RFC-6090 for point arithmetic algorithm over homogeneous coordinates.
In Appendix F subsection 2, there are 5 case labels when determining which formula to use depending on how many if any point-at-infinity exists in operands. For me, implementing these case labels in constant-time isn't too big a problem, but I'm not too sure about determining whether a point is at infinity.
When the point-at-infinity occurs within point arithmetic, it has the homogeneous coordinates $(0,y,0)$ where $y\ne 0$. So Q: is it sufficient to check $Z = 0$ for point at infinity, or all 3 dimensions has to be checked?