For fixture-held drill sharpening, there are numerous devices which can be added/bolted/clamped to most common grinders.
Look into 4-facet resharpening.. the only 2 facets that are important are the 2 primary facets (one on each flute), which assure centering and proper relief, while the secondary facets only determine the width/thickness of the cutting faces.
Generally, all holders require adjustment (or anticipation of) the proper finished location(s) of the final grinds. That means when material is removed from the tip, the orientation of the twist needs to follow. As more material is removed without rotating the drill, the cutting edges are established at the wrong place in the rotational relationship to the flutes.
Only a couple of resharpening machines are designed to follow the twist as the material is removed.. other more common (add-on) fixtures require a fixed setting of the twist for a specific amount of material removal, and after that much is removed, the drill needs to be rotated. For more material removal (chipped flute for example) the operator may freehand the rough shape to remove the damage, then rely on the accurate fixture settings to apply the proper centering and relief.
Some handy machines and add-ons:
Black Diamond Darex General/Craftsman copy Kaindl Kalamazoo Viel
Many precision resharpeners don't require using the side of a grinding wheel, in that the geometry of the fixture utilizes it's precisely-placed motion axes to use the dressed/flat edge of a wheel (or even a belt sander's abrasive path, such as the Viel for HSS drills).
As I've stated numerous times in the past, it's relatively easy to make center cutting split-points on common twist drills. The back side of the flute material is removed first, followed by any of the common methods used for point finishing. Split-point grinding isn't a delicate gashing operation which most folks think it is.
The benefit of split points are numerous.. they begin cutting as soon as they contact a surface and continue to cut for the entire operation. Conventionally ground common points require continuously applied power and pressure to displace the workpiece material in the area of the chisel edge present in the web area.
Split-point drills are widely accepted as being much less prone to wandering upon contact with the work surface, but they also make much more efficient use of time and energy.