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You know... appearing in a barrel like that makes it more likely that the warp is a programming error, the way I see it.
Each time you change screens - from the map screen to a level, or from a bonus to somewhere in a level - the game needs to know where to put you. So, let's say each of the places where you can do this has a value marking where you go, and the game looks up where to put you based on that value. The map point for the first level might be marked 01, which would lead you to the beginning of the first level... the exit for bonus #34 might be marked 7C, which would lead you to wherever that bonus exits. And so on.
Now, mostly, the map has levels connected by straight lines. Why are there bent lines in the first world? Perhaps they were going to add levels there, but decided not to, and didn't want to redraw the map. Perhaps the artists just drew a map with bent lines for no reason. It seems likely that the map was programmed to be composed of straight lines running between two endpoints... and when they had to add bent lines, they just made a special type of point that pushed you onto the next level instead of letting you stop there.
Of course, aside from this point automatically pushing you further along the path, it wasn't supposed to let you enter it, unlike every other point on the map. But, somehow, you can enter it under certain conditions. Now, where would you go if you did enter it? To the place named by the value associated with the point, of course! Except, that point isn't supposed to be entered, so they wouldn't pay any attention to what value is associated with it... meaning you'd go somewhere unusual, but probably somewhere you'd normally appear from a different point. Which, as I understand it, is exactly what happens.
I have no idea if this is how the warp works, or not. But it seems reasonable. Same general principle as Metroid's secret worlds; finding a way to make the game access and use data that's not supposed to be used...
Each time you change screens - from the map screen to a level, or from a bonus to somewhere in a level - the game needs to know where to put you. So, let's say each of the places where you can do this has a value marking where you go, and the game looks up where to put you based on that value. The map point for the first level might be marked 01, which would lead you to the beginning of the first level... the exit for bonus #34 might be marked 7C, which would lead you to wherever that bonus exits. And so on.
Now, mostly, the map has levels connected by straight lines. Why are there bent lines in the first world? Perhaps they were going to add levels there, but decided not to, and didn't want to redraw the map. Perhaps the artists just drew a map with bent lines for no reason. It seems likely that the map was programmed to be composed of straight lines running between two endpoints... and when they had to add bent lines, they just made a special type of point that pushed you onto the next level instead of letting you stop there.
Of course, aside from this point automatically pushing you further along the path, it wasn't supposed to let you enter it, unlike every other point on the map. But, somehow, you can enter it under certain conditions. Now, where would you go if you did enter it? To the place named by the value associated with the point, of course! Except, that point isn't supposed to be entered, so they wouldn't pay any attention to what value is associated with it... meaning you'd go somewhere unusual, but probably somewhere you'd normally appear from a different point. Which, as I understand it, is exactly what happens.
I have no idea if this is how the warp works, or not. But it seems reasonable. Same general principle as Metroid's secret worlds; finding a way to make the game access and use data that's not supposed to be used...
Sorry for bump. This is almost exactly what I was going to say... put a bit more eloquently perhaps. Your specific theory is even more likely because the warp can only be activated during one frame. It is on the frame that said point is reached when the walking-between-levels loop ends and input is checked for a moment. the programming error here, besides an accidental dangling pointer, is that in certain instances, on this special type of point on the map, the standard input for entering a level is still checked. moreover, because it does not work with two sprites on the map, it seems like someone attempted to fix it (only one line would be required), but misplaced the fix inside a conditional statement that is not executed with a single character. Should this indeed be how the glitch works, that more or less would prove it was never discovered. If this was actually found to be a bug, the fix would have been tested well. This was a programmer who thought about an exception but put the necessary fix in the wrong spot.
Even though that's only a theory, just the circumstances around this glitch, the conditions that prevent it from working, etc, make me think it's a glitch, not an intended element (and believe me, this game's intended elements are as mysterious as they come... I love it). I've been programming in various languages for 6 years so I would say I'm qualified to throw in my 2 cents :p. I've definitely made my share of bug fixes and almost-forgot-something-major moments, and I can tell you that you almost never get it perfectly right on the first try when you revisit code you've written in the past and add something in as a quick fix or change.
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The part of the rules I find most intriguing is that anything is banned that doesn't make sense from the character's point of view.
Everything on here makes sense according to those rules. Even savewarping can be thought of as your intervention to take a break and return to the game later, and it being a hassle to resume in the exact spot you were in... you'll be disoriented if you forgot exactly what you were doing at the time. The warp occurs during a time when play has ceased so our character is not presented with anything crazy... it may be assumed he returned to the point of the savewarp without incident.
Following the makes-sense rule you see why this warp cannot be allowed... the legit DK warps involve either entering doorways or launching out of barrels, which, however ridiculous it sounds, is normal in the DK game world. Entering a level, from the world map, at a point other than the start or the mid-way barrel, is mysterious in the DK world. There's a OoT run that was recently rejected because of a boundary violation in the Deku Tree, and it follows the same concept... something that makes no sense to the game character.
Having said that, it seems like anything that is intentionally put in the game is typically allowed, but subject to a seperate catagory. Cheats are allowed provided they do something constructive to a challenge we'd like to see (make the game harder). Furthermore, some glitches that do not involve leaving the game world or mysteriously teleporting are allowed (sequence breaking in OoT through various means, including glitches like superslide, seems to be acceptable here). It's SDA... we're concerned primarily about major atypical modes of travel through a game world and less about individual glitchy moves. If you found a glitch to walk faster or jump over things, great, you're still walking and jumping. If you suddenly appear on the other side of the map with no explaination other than you happened to glitch the game, well good for you, that's the stuff of TAS's.
When you analyze it properly, there is no run on this site that is truly an exception to the rules. You have to make a case for how a particular trick fits or doesn't fit into the declared rules. I think the supreme court does something like this.
Having said that, I think Mario 64's glitched 16 star run is very borderline on breaking the rules. I understand intimately how the glitch to BLJ works, but it is still a glitch, and it transports mario a very large distance in a single frame. It is used to go through doors, but TAS's have demonstrated that the game does not discriminate and will allow mario to travel through walls and beyond... anywhere that is currently loaded. What exactly you are using the glitch to do, go through a door or blast around a level quickly, is then irrelevant, because it's still a mysterious teleport via programming error... at a certain point you cease to be in one place and are suddenly in an entirely different one.
Nate himself said here that any run there is a lot of interest in will be captured for SDA. But perhaps it should be clarified that that is what the 16 star run is: a rule violation hosted due to popularity / awesomeness of appearance. Otherwise, then will come the issue of why not allow DK teleport too, why not allow OoT boundary violation... there's more or less already been one exception allowed to start everyone asking for one more :|