I only use two types of drill points in my tool room. One is the standard 135* split point drill type & the other is the four faceted type drill point. I use the four faceted point on difficult to drill materials. C-2 carbide drills that can easily drill Rc 65 tool steels are also four faceted. I never use standard point drills that "auger" the metal out of the middle & need center drilling to prevent drill walking when starting. These type drills also generate very high heat when drilling. The other two drill points cut from the middle & do not require center drilling when starting. The four faceted drill point generates very low heat & therefore can be used in very difficult to drill alloys.
Split point drills can be sharpened in the surface grinder with a simple indexing fixture. Faceted drills can easily be ground by hand. Things to watch for include uneven lands, different land angles, overheating & clearance angles when re-sharpening.
There is also a six faceted point drill type that is even more durable than the four faceted drill point type. All of this information is available on the internet.
I posted a photo of a four faceted drill point & a 135* split drill point.
JA