Exit Points: Fast Travel: Time Warp Points:
So I think overall we are really close to the general story and game play loop. I have had a working theory based on what others are posting and I believe it is the inter connectivity of the Shrines, Green Spiral Stones and Glyphs that are being overlooked as it relates directly to the story of TotK.
In BotW the shrines were set up by the Ancient Sheikah Monks as a way to test the Hero and prepare Link for the battle ahead. While we can't say for certain what their purpose will be in TotK, I think it is a pretty safe bet they will center around Links healing from Malice, his Spiritual quest, which may or may not be related to his vials and energy, and the Tears themselves.
Link is going to have to remove the Malice from his body in order to wield the Master Sword again, so I think the beginning portion of the game will center around the Sky Islands and healing, all the while learning new abilities and getting stronger again. I like what
@NabiscoFelt said regarding the Green Spiral Stones because I think it represents pretty well what the majority of people think, and that they will be directly related to entering the Shrines exactly how the Shrines were utilized in BotW.
But there are few problems with this theory and they are backed up by what we see in the Art Book. We have talked extensively in this thread on the Spiritual Nature of the Sky Islands from the Ginkgo Trees, the Tori Gates, Alters etc, so they are going to be a big part of the overall story arc. The only other location we have seen a Tori gate other than the Sky Islands is in this shot from the Art Book, which shows a Tori gate at what I believe is the entrance to the beginning of the shrine. This implies that we will enter the Shrines from the Sky through the Tori Gates and not from the Green Spiral Stones, at the very least for the Spiritual Shrines only from the Sky.
The next 2 shots are what I believe show the exit point of the this particular Shrine. It is locked just like a normal Shrine in BotW. On the other side we see an alter where we will probably collect a Heart/Stamina or however TotK portrays the version of the Spiritual Orbs or if that is even a thing now.
So if this is the case that we enter the Shrines from the Sky via Tori Gates/Alters then where do we go when we return via the ending Alter in the Shrine. I think we re-emerge close to the Tori gate we entered from via a nearby Green Spiral Stone. So Green Spiral Stones are exit points at least the ones in the Sky. And once we exit through one of them after completing the Shrine, the Green Swirl will go away and it will simply now become a fast travel location that we can access at anytime.
And this is isn't to say this is exactly how they will function, but I'm offering a different solution to a complicated problem presented by what we see in the Art Book and one that ties into the overall narrative of TotK and provides another solution for the ones on the Surface' depending on how ambitious you think this game will be.
The Hyrule surface Green Spiral Stones are much more debatable in their overall function however. The next set of images seem to back up either my claim they are exit points or you could make a case they function the same as the Shrines in the BotW IMO.
First the Green Spiral is absent which from my previous speculation is what we should see if Link just transported here and is exiting the Green Spiral Stone. From the Circle ceiling motif we can also tell this is most likely a Shrine type location, we just don't have any evidence of where Link started from to get here. But I do think there will be a few different types of shrines other than the Spiritual ones for healing and there could be a reason on why we would need to return to a previous shrine type location, where as in BotW you were pretty much one and done with each Shrine unless you had trouble completing it and then you could always comeback later to it.
One reason you would need a fast travel location to this spot is that in the Art book later on we see this photo. I think we are able to make this energy stone, via Smithing as seen on some of the other Art Book pictures, and it might be more related to the vials or energy swirls.
I think the box on the right is the Mold for this energy stone and then we place it in the Alter to either create a Swirl for transporting or it will act as a more substantial energy source powering up what ever we are trying to accomplish in that area.
But overall I think the Surface Green Spiral Stones are all inactive and we won't have anyway to interact with them at first. They could be exit points from nearby underground caves or have a different purpose which I think might be more likely and that is more related to time travel and the Glyphs.
I think our first major objective related to time travel will involve repairing the time alter calendar we see Zelda standing in front of in the past in the last trailer. I also think it is located on the very first island we start from, because it would have to be in a place that all players would see it and know exactly where it is located.
I think we will solely be dealing with Muffydorf for the first 1/3 of the game as we gain our strength and help out the locals and Races etc. Once we repair the time machine we will then use it to travel to the past for the first time. And at that point, I think we will be dealing with Re-hydrated Gannondorf. It would be kind of cool if Mummydorf was a pretty easy fight early on and we think the game is basically over, then we get Re-Hydrated coming alive and getting even stronger in the past, that completely destroys the past which then effects the present time so we end up being basically back to square one again. So at this point it really depends on how ambitious you think this game will be, I think we will have a second map for the past. But as I pointed out awhile back it could be much smaller than the current Hyrule, it won't include any Sky islands either and will contain a lot more water on its surface and the water will be completely surrounding Hyrule.
Back to the Green Spiral Stones. Once we are in the past for the first time, we can now activate all the Green Spiral Stones on Surface and be able to freely travel back and forth through time at all these locations. They could act as fast travel points as well. This idea occurred to me from
@maidhhc with their last post regarding the new Sheikah slate. So I have thought that we will be able to transfer objects back and forth through time because Zelda has the broken Master Sword as well, but in the case of the Sheikah slate it could just be a matter of completing that particular Glyph, Zelda could leave it in spot where we could find it in the future, or she could even hand it to us if we are able to Travel to the past.
It would be strange that if we can actually travel to the past and play through that map that Zleda wouldn't accompany us at some point during that portion. But it could also be that the plan is to have her handle other things once Gannondorf eliminates Basket and Zeldas role could change.
I really like
@Selarmor reasoning that the Glyphs will be directly associated with fixing the Master Sword so I think Zelda will play a part in that portion of the game or we will travel to the past and do it ourselves. That's about as far as I have gotten so far so I can partially sleep at night until launch, story wise, Please add or subtract anything from this as you please.