I watched one of your earlier runs, so I'm not sure if you've taken this to mind yet: on the special stages, surely there's a part where you can take a shortcut by jumping over the endless field of red spheres to get to another part of the stage faster?
I watched one of your earlier runs, so I'm not sure if you've taken this to mind yet: on the special stages, surely there's a part where you can take a shortcut by jumping over the endless field of red spheres to get to another part of the stage faster?
Answer:
nifboy wrote:
The distance you jump is constant and consistent with your speed; the distance a tiny bit more than three squares; not enough to clear three red spheres, but just enough to make it so you can't cross a string of red spheres more than about 12 spheres long.
* Quietust, QMT Productions
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atro city wrote:
I watched one of your earlier runs, so I'm not sure if you've taken this to mind yet: on the special stages, surely there's a part where you can take a shortcut by jumping over the endless field of red spheres to get to another part of the stage faster?
I see no real use in this, as jumping does not make you go any faster. Yellow spheres DO make you go faster, so I'll have more thinking to do when I get to the S&K stages.
>I see no real use in this, as jumping does not make you go any faster.
Going above a field of red spheres is faster than going around it. The shortest distance between two points is a straight line.
Joined: 2/15/2005
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Truncated wrote:
>I see no real use in this, as jumping does not make you go any faster.
Going above a field of red spheres is faster than going around it. The shortest distance between two points is a straight line.
Most times I go in straight lines between groups of blue spheres anyway. I'll see if there is anywhere I could use jumping, but I'm not sure it would help at all...
EDIT: After watching it I noticed 11 mistakes. I'll fix them next time I start over, as at this point in time the special stages aren't my main concern.
Oh, for those curious, I've been messing around with maps of the special levels.
A fast reminder of the frame system: Turns are 12 frames, each square is at between 8 and 12 frames.
Maps taken from GameFAQs.
Good idea with maps but you have to consider that it wraps around and therefore it might sometimes be quicker to jump over the red spheres at the edges - are there really 2 at all sides making 4 in total?
You can jump trough it (well, anything) most of the time, I think.
There isn't always a wall. Some levels just loop. Some more or less require you to wrap around, but you'll never notice that you did so when you play.
Unless my memory is failing me.
Joined: 2/15/2005
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Truncated wrote:
Some more or less require you to wrap around, but you'll never notice that you did so when you play.
Special Stage 6 almost guarantees you will sometime.
By the way (even though this is a little off-topic), ever noticed that these stages defy the laws of physics? Only a torus will wrap in the way that these maps do, not a sphere, which the game makes it look like.
Space itself bends around the emeralds. Wait, that shape is still impossible... It is actually an infinite plain, but the blue spheres are linked every 32 squares... oh wait, the horizon...
I cut corners as a shortcut when flying around FFVI and StarFox 64. It's fun to sneak up on people in multiplayer like that.
By the way (even though this is a little off-topic), ever noticed that these stages defy the laws of physics? Only a torus will wrap in the way that these maps do, not a sphere, which the game makes it look like.
I'm fairly certain that since you can only travel along an orthogonal grid, there is an analytic map from the torus to the sphere, though such a mapping clearly wouldn't preserve distances. If there were any singularities, you could hide them inside bouncers. Anyways, even if I'm wrong, what's so bad about a torus? They certainly exist and can be constructed. If you are referring to the curvature of the horizon in the game, well, light can be bent.
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xebra wrote:
bobxp wrote:
By the way (even though this is a little off-topic), ever noticed that these stages defy the laws of physics? Only a torus will wrap in the way that these maps do, not a sphere, which the game makes it look like.
I'm fairly certain that since you can only travel along an orthogonal grid, there is an analytic map from the torus to the sphere, though such a mapping clearly wouldn't preserve distances. If there were any singularities, you could hide them inside bouncers. Anyways, even if I'm wrong, what's so bad about a torus? They certainly exist and can be constructed. If you are referring to the curvature of the horizon in the game, well, light can be bent.
In a torus or a sphere, going off the left or right of the map puts you on the other side of the map.
In a torus, going off the top or bottom of the map puts you on the other side of the map.
In a sphere, going off the top or bottom of the map moves your x position to (width of map)-x, and you reverse direction.
In the game it looks like a sphere, but acts like a torus, thus defying the laws of physics.
In a torus or a sphere, going off the left or right of the map puts you on the other side of the map.
In a torus, going off the top or bottom of the map puts you on the other side of the map.
In a sphere, going off the top or bottom of the map moves your x position to (width of map)-x, and you reverse direction.
Sorry for using unfamiliar mathematical terms. What I was saying is that the map is not a torus. It's a subset of the torus, specifically, a grid of lines at 90 degree angles to each other. I am fairly certain there is a way that you can lift this grid off of the torus, bend it smoothly, and transplant it to a sphere. It is even allowed (and probably necessary) that you bend the grid "not smoothly" at a finite number of points, as long as you can prevent Sonic from actually going to those problematic points. For example, if you needed to not-smoothly-bend the grid at any particular point, you could just put a bouncer there and not worry about ever encountering that point that ruins the transformation.
I'm not suggesting that the game designers thought about any of this stuff when making the game. I'm just saying that I don't think the bonus levels are a priori incorrect.
In the game it looks like a sphere, but acts like a torus, thus defying the laws of physics.
The only hint that you are on a sphere is the curvature of the horizon, and like I said before, light can be bent. Bizarre optical effects are no excuse for crying wolf. Additionally, there are directions you can look on the surface of a torus and see the same kind of horizon you see every on a sphere.
Joined: 2/15/2005
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xebra wrote:
In a torus or a sphere, going off the left or right of the map puts you on the other side of the map.
In a torus, going off the top or bottom of the map puts you on the other side of the map.
In a sphere, going off the top or bottom of the map moves your x position to (width of map)-x, and you reverse direction.
Sorry for using unfamiliar mathematical terms. What I was saying is that the map is not a torus. It's a subset of the torus, specifically, a grid of lines at 90 degree angles to each other. I am fairly certain there is a way that you can lift this grid off of the torus, bend it smoothly, and transplant it to a sphere. It is even allowed (and probably necessary) that you bend the grid "not smoothly" at a finite number of points, as long as you can prevent Sonic from actually going to those problematic points. For example, if you needed to not-smoothly-bend the grid at any particular point, you could just put a bouncer there and not worry about ever encountering that point that ruins the transformation.
What if Sonic jumped over the bouncer then?
In the game it looks like a sphere, but acts like a torus, thus defying the laws of physics.
The only hint that you are on a sphere is the curvature of the horizon, and like I said before, light can be bent. Bizarre optical effects are no excuse for crying wolf. Additionally, there are directions you can look on the surface of a torus and see the same kind of horizon you see every on a sphere.
If you take the geometry seriously, then the surface Sonic is running over is obviously a horosphere. A horosphere can have a curved-down horizon while simultaneously being smoothly covered with square pattern. The catch here is that the horosphere is a surface that requires a hyperbolic (i.e. negatively curved) universe to exist. In hyperbolic world, a zero-curvature surface (with Euclidean geometry) appears as curved.
The repetiveness of the horosphere can be explained by some simple topological wizardry (for example, the horosphere can be actually covered with infinite amount of identical copies of the level, each with its own Sonic moving in unisono, so there is no way to distinguish one from other).
So it's an infinite array of Sonics, running across an infinite array of grids of spheres, to take the Chaos Emerald from a negatively curved universe (with more space above the flat surface than below, causing the appearance of a curved horison), which only exists because of the emerald's chaos magic. I guess those are the same curved universes with a bit of an interior decoration in Sonic Advanced 2. And that Chaos was sealed in a similar universe made by the Master Emerald for Sonic Adventure.
Well, I'm glad that's cleared up. Math is fun.
Interesting movie so far. I can see a few places in the Special Stages that you can improve. For example, when you go for the first emerald, you take a longer route around a set of bumpers you could easily jump over. It's possible to jump two objects in a special stage at once.
Also, the second special stage, there are the 3*4 sets of blue spheres. There's an area with two of those in a row. Instead of making 2 turns to get the sphere set, you should move forward past the 4 for the first row and grab the 4 for the second set before turning around. Don't understand? Here's a pic. http://img.photobucket.com/albums/v299/Blackbelt/SSthingy.bmp
Edit: *smacks face* ...That last arrow. Move it up a row.
Anyway, now that I'm done watching the movie, I see possible fixes in the Special Stages. Mainly turning a little too late or something like that, but there could possibly be a few things like jumping in the right places. Timing some jumps right, you could probably get Sonic to successfully wade through an entire sea of red spheres unscathed, but that's just a possibiltiy. Might as well try it, right :)
(Bing-Bong)
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Joined: 2/15/2005
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IMPblackbelt wrote:
Interesting movie so far. I can see a few places in the Special Stages that you can improve. For example, when you go for the first emerald, you take a longer route around a set of bumpers you could easily jump over. It's possible to jump two objects in a special stage at once.
Yes, I know, and I've said that at least once before, and I'm not improving it until the next time I start over, and I'm not working on the movie whatsoever until I feel like it, and that's not going to happen for quite a long time now that I've discovered Forth. If I have to repeat this again I WILL use caps.
Also, the second special stage, there are the 3*4 sets of blue spheres. There's an area with two of those in a row. Instead of making 2 turns to get the sphere set, you should move forward past the 4 for the first row and grab the 4 for the second set before turning around. Don't understand? Here's a pic. http://img.photobucket.com/albums/v299/Blackbelt/SSthingy.bmp
Edit: *smacks face* ...That last arrow. Move it up a row.
Good idea, as I said before I'll do that when I restart the movie.
Anyway, now that I'm done watching the movie, I see possible fixes in the Special Stages. Mainly turning a little too late or something like that, but there could possibly be a few things like jumping in the right places. Timing some jumps right, you could probably get Sonic to successfully wade through an entire sea of red spheres unscathed, but that's just a possibiltiy. Might as well try it, right :)
bobxp, I printed out the maps and tried to find the optimal routes. I can show you later if you like. :)
Oh, and the surface that Sonic runs on is topologically equivalent to a torus. The surface is a square with both sides wrapped around without twisting.
