I think the difference between split point drills and the 4 facet grind is that the 4 facet method is just 4 flat grinds, there isn't and crown in the cutting face relief, and without split points, there is still the small chisel edge at the web.
In all the years/decades of developing drill sharpeners, the tooling companies haven't come up with a decent drill sharpener that's affordable for the part-time tinkerer/home workshop users. Some Drill Doctor owners will probably argue that, but I've read the complaints of many stating it works OK some of the time, on certain sizes.
I don't like the little General fixture mentioned earlier, because the little twist indexing finger isn't a good feature. That's the little pointy adjustment located under the V (only the worst place for it). The little General fixture makes a great relief grind as it swings, but it will make it anywhere on the end of the drill. So ya play and adjust and try a few grinds, then play and adjust some more until it's leaving the narrowest chisel point, but ya start over as soon as you try another size drill. Besides that problem, the only sensible way to mount the General fixture is on a slide or a mount that allows it to be moved toward/away from the grinding wheel and held in place. Bolting it to a fixed point as suggested in the instruction sheet, sucks.
I'm fairly certain that you already realize the basis of these comments DoN, but I'll add them FWIW.
As the point is ground, the angular rotation of a drill needs to follow a fixed point on the fixture that has a relationship to the twist spiral. Just moving a drill toward the grinding wheel without following the twist will change the orientation of the chisel point.
If the fixed point on the General fixture was on top where it could be adjusted easily, that would be t*ts. With a conventional grind on a drill, maintaining the narrowest chisel point (at the web) is the key to having a drill that cuts and feeds easily, and a drill that may only rub a hole in something if enough pressure can be put on it. The key to attaining the narrowest web/chisel point width is a fixed point that causes the advancement of the drill to follow the twist.
A while ago, someone was looking for the identity/maker of a drill grinding fixture that was made by Delta (Rockwell/Delta, maybe). It was a couple of arms and a few adjustments with scales which takes up quite a bit of space just to mount the fixture.. considerably more than a sqare foot of space, not including the bench grinder it gets mounted to. You probably need a workspace about 24" square to operate it.
I have one that's similar to the Delta that was made by Kalamazoo, but I haven't used it yet, since all my stuff is waiting for me to locate a new shop. It's got a long sweeping arm and a scale or two, but I suspect that it's performance will depend upon some futzing around too.
It's beyond me why some tool maker hasn't developed a drill sharpener that is as easy to use as zing, rotate, zing for the trailing side grinds, then insert, rotate, lift, rotate and it produces a resharpened drill that as good as factory fresh new.
Beyond me, besides the fact that there aren't many small tool manufacturers left, today.
That's all the motion that the machine shop drill grinder needed to produce perfect split point grinds. I realize that a single drill holder won't suffice for all the sizes up to
3/4", it's just not realistic, and a large portion of the value of a real drill sharpener would be in the precision drill holders.
I've pondered how to make a round drill holder resembling a drill chuck for quite a while, and haven't come up with anything better than modifying a drill chuck. Snugging the chuck jaws against the drill flutes could cause chipping, so gripping the shank would likely be a better approach. Supporting the drill near the point presents another challenge, since bushings for every drill size would be problematic as far as time consuming to make and/or expensive to buy. Something like a camera lens iris might be a possibility. If large drills are to be resharpened, then a small drill chuck would need to be adapted/adaptable upward in size to fit in the same place as the big drill chuck.