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The (Pixel) Perfect Guide


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#1 Oliver666666

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Posted 22 July 2016 - 09:05 AM

The (Pixel) Perfect Guide 

 

PEZLBC9.gif

(Original animation by Poldi here: http://forum.kingoft...d-geffi-sprite/)

 

This guide will explain what pixel perfect jumps are and how they are different from other jumps. Hopefully a better understanding of pixel perfect jumps will help everyone. I will include a useful little trick that can mostly be used to help save saw jumps later in this guide. 

 

Special thanks to Fezzik, for his great arguements, (counter-) examples, videos, images (especially the non-blurry merged pictures), and setting up testing in his bases.
 
Contents

  • (5 images, 5 GIFs) Physics: Explains how the game works 
  • (0 images, 7 GIFsDefinitions: Explains and clears up what is what and why. 
  • (0 images, 8 GIFsPixel perfect jumps: Kind of trivial what this is about.
  • (0 images, 8 GIFsPath dependent jumps: Similar to the previous section.
  • (0 images, 7 GIFsThe inline saw saving guide: A little help to save those saw jumps. 
  • (1 images, 9 GIFs) Exceptions and special cases: Nifty cases, hopefully super interesting.
  • (1 images, 6 GIFs) Exceptions and special cases (part 2): More nifty cases and super interesting stuff.
  • (1 videos) Video guides: Skip to this section if you are interested in learning a variety of paths. 

All of the GIFs (moving images) are hidden in spoilers to help minimise data traffic. On average they are 4-8 Mb each. A Wi-Fi connection is recomended.
 
Physics
 
First, I will explain the current physics the game uses. Lets start from the beginning. Phones, tablets, and monitors have screens that are composed of pixels (little tiny squares that only colour a portion of the image). However there are many variations of the screen sizes, so the game physics cannot be based on pixels, otherwise there would be a lot of problems. 
 
This is how your thief looks if you take a closer look at the pixels it's built from:
3Ej52EF.jpg
 
However, to be fair for everyone, the game uses a higher level structure to form its physics. The game actually runs itself on a different model, and then projects itself into the form of pixels. So to understand the game, we must examine how exactly it is built up from basic elements. 
 
Any space where the thief can move (dungeon, maze, etc.) is made up of a grid. All the elements (square/location/position) of the grid can be defined with a set of coordinates. Here is an example of how that would look. (Obviously the game uses a denser grid, so it can draw smooth, small objects).
bUjDjny.jpg
 
This grid is the basis of the physics, everything is calculated here, and then projected onto your screen. That is why there are very few jumps where you are visually in the air, but you can still jump. 
 
Now that we have a grid, we can put objects in it. I wont really be talking about traps, since they are pretty straightforward and cannot be manipulated. So we can pass traps, platforms, and gravity switches and get right to the thief. The thief can move in two dimensions. Up/down and left/right. Any other visual effects (ie. a parabola of a jump) is just a combination of these two. 
 
Once the game is in a position, and has all the data (ie. did the player jump?), it will refresh. However, this does not happen once every second, or the game would be very laggy. Instead, it refreshes multiple times every second, and stays in that condition until next step. This condition is called a frame. Therefore, the game constantly goes from one frame to the next, calculating what to do in between. When I am talking about frames, I will assume all the information not stored in just the image, such as the speed and direction of objects, is available for ongoing calculations. (Therefore It will be more similar to states, than simple images.) 
 
(The short version: Frames will be used to describe the dimension of time in the game.) 
 
Movement on the X axis: The thief has a constant speed. Horizontally, it is always moving, unless there is an obstacle in its path. For demonstrative purposes, we could say the thiefs' X coordinate grows by 6 in every frame. The current existing models we have suggest there usually is no acceleration on the X axis.

 

Since we are talking about movement/frame ratios, this image will help demonstrate that the thief doesn't actually slide, but "teleports" continuously in a line. This is the root of all path dependent & pixel perfect jumps.

3J5thDx.jpg
 
However, when the thief jumps, it slows down horizontal movement a little (This probably happens during taking off from the ground and while landing on the ground). This means that there are exceptions like jumping or contact with objects (ie. walls) which may nudge the coordinates a little. Also, when the thiefs' head bumps into the ceiling at the peak of his jump, it will look like he gets a tiny "boost" in his X axis trajectory, while hitting the ceiling too early will make the thief start falling very fast (Example is given later). The jump when the theifs' head scrapes the ceiling can be called a max length jump. This name comes from the fact the thief jumps from the highest point on the wall that doesn't get effected drastically by the cieling, allowing the maximum distance to be travelled horizontally.
 
Example: Thief speed vs. cannon bullet speed 

Spoiler

Movement on the Y axis: The thief has a constant speed of 0 on the Y axis. When the thief jumps, it starts with a speed going upwards. However, there is a form of gravity in the game, which behaves like real gravity. I'm not going to go into a physics lesson here. Another tip: while sliding on walls, the thief is locked into certain Y axis coordinates. That means walls can be used as great starting points for tight jumps.
 
Example: Ceiling effects
Spoiler

Corner physics will not be explained because superjumps are now impossible to save. Due to this, corner physics are quite simple now. Also explaining the rare bugs that can still happen would over complicate this thread.
 
Lets summarise all this with an example that shows how the coordinates of the thief are effected.
Example:
Lets assume the following rules are the physics (all of this is just representative)

  • The thief has a constant X axis speed of 5 squares per frame.
  • At the moment of jumping and landing, the thief gets -1 square on the X axis
  • A jump lasts 2 frames, and it has a max height of 5 squares

These imaginary rules and numbers are far from what really happens while jumping, but it will help understand sufficiently because it is very simple.
 
Situation 1: This is the path for passing a saw jump. 
D0K5L2O.png
 
Situation 2: And this is a path that fails on the saw jump. The thief would not survive the last jump here
T3DM1Se.png
 
Basically, there are a bunch of numbers. If you look really hard, you can even find a small inconsistency, but lets just leave that for the attentive. In the second picture, the thief ends up two squares left of the coordinates of the first picture. This is caused by the extra jump.
 
To summarise, every time the thief jumps, his X axis coordinates are moved a few squares out of sync. This tiny difference could be what makes or breaks any jump.
 
Now that we (hopefully) understand how the thief behaves in dungeons, lets define some expressions I will use in the guide. This is necessary, so that this thread can be clear, understandable, and arguable.


Edited by Oliver666666, 04 July 2017 - 11:01 AM.


#2 Oliver666666

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Posted 26 July 2016 - 11:32 AM

Definitions
 
I am defining these for the first time to my belief. Usually these definitions are not defined properly, only intuitively and are easily mixed up. I do not expect this thread to change that. However within this thread, whenever I use them, I am referring to these definitions.
 
Path: The path of the thief is the series of coordinates of its movement. The path of two thieves may differ even if visually they are almost identical (ie. just sliding in a simple line). Two paths are equivalent if both paths have a subsequence starting from any point in time, from where they are identical. (Example is provided just a little later.)
 
Path dependent: A jump or jump series is path dependent, if there exists a path for the thief of which the jump (series) is impossible to perform with correct timing. 
 
Example: Long jump

Spoiler

Pixel perfect: A jump or jump series is pixel perfect, if there exists only one path for the thief of which the jump (series) is possible to perform with correct timing. 
 
Pixel perfect jumps are all path dependent, but what's the difference? The only difference between pixel perfect and path dependent jumps are the number of speed and location (coordinate) combinations of which the jump can be performed. Path dependent jumps usually have very few of these pairs, but more than one. However, to perform a pixel perfect jump, there is only one coordinate from where the jump (series) can be started.
 
(Note): The name "pixel perfect" comes from the occurrence of two paths being so close to each other, that they are displayed in the same pixel if the screen is small enough. Hence they are completely equal to the naked eye, but still have different sets of coordinates. 
 
(Note): The name "pixel perfect" also comes from the grid coordinates being called pixels in another explanation. And if the grid coordinates were called pixels, then the name is formed such as "you have to be on the perfect set of pixels".
 
Example: Starfall jump with multiple equivalent paths
Spoiler

HItbox: All objects (thieves, traps, chests, platforms, gravity switches, etc...) in a dungeon that are meant to interact have a hitbox. A hitbox is the group of grid coordinates that count as solid, meaning the object is there. Sometimes to make things easier, a hitbox may be a circle or a square that contains the object. Lets assume that the hitboxes of all objects contain only grid coordinates of the object, and no extra points. 
 
This is the reason why there are jumps where you are so close to touching something (gravity/platform/chest/even a trap), that sometimes the pixels are visually touching, but it counts as a miss. Simply because the game cannot be based on the pixels of your screen.
 
Example: Red Guard jump & Corner saw jump, Boring gravity jump
Spoiler


Edited by Oliver666666, 04 July 2017 - 11:12 AM.


#3 Oliver666666

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Posted 26 July 2016 - 11:32 AM

Pixel perfect jumps
 
Because of the strict definition of these jumps, proving there is only one path can be extremely hard in some bases.
 
1) Corner glitch jumps
These jumps are very hard, and its' existences is based on two things:

  • Platforms, to be able to jump into a corner from underneath
  • A Phenomenon of corner physics. When you hit a corner from underneath..., lets just say things get complicated. What is important, is that the result depends on what point the thief hits the corner. (This may be unintended and may cause the jump to be removed.)

Corner glitch jumps are pixel perfect because of the second property.
Examples: 

Spoiler

2) The GR jump (Gem retrieval)
This jump is (currently) only possible one base. It is based on two things.

  • The complicated trajectory of a thief that jumps a long distance while scraping the ceiling.
  • The hitbox of the thief and the platform barely touching with a certain path.

This is indeed pixel perfect and currently there is no similar pixel perfect jump in the game.
Example:

Spoiler

3) Starfall Jump
This jump is based on

  • The hitbox of the thief barely missing the hitbox of the saw with a certain path.

There is only one path because jumps originating closer to the saw will be hit, and jumps originating from any coordinates further away will hit the top left corner of the middle column block.
Example: 

Spoiler

4) Inline saw jumps (april fools jump)
This is a very strong defence. Using saws in placements like these allow exactly one path past them, and hit the thieves on any failed attempts. 
This jump is based on

  • The hitbox of the thief and the saw barely missing each other on a certain path.

Example:

Spoiler

5) Long jump in specific base
This is (currently) only possible in this specific base, however, there could be similar pixel perfect setups of long jumps.
This jump is based on

  • The hitbox of the thief and the chest barely touching with a certain path.

It is different from the first long jump example in this guide because the object that needs to be reached with the jump is in a totally different location.
Example:

Spoiler

I Hope I got most of them, the point isn't to list all the jumps here. Hopefully new pixel perfect jumps will be discovered, old ones will probably be removed, etc. But when you see one of these bases, maybe a bell will ring saying that if you fail, maybe you can try another path!


Edited by Oliver666666, 04 July 2017 - 11:23 AM.


#4 Oliver666666

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Posted 26 July 2016 - 11:50 AM

Path dependent jumps
 
Instead of inserting gifs of random jumps that  may or may not be removed from the game, I will try to represent types of jumps. Also you may find jumps here that are even pixel perfect, but as I defined them, they are also path dependent.
 
1) Slide jumps
Most of these jumps end up in a chest (there is one exception). Its' existence is based on two things:

  • The hitbox of the thief being manipulated just enough to touch the chests' hitbox.
  • A Phenomenon of wall physics. When you jump onto a wall, and slide for one frame, that jump will have a slightly different path than if you have been sliding for 2 or more frames. (This may be unintended and may cause the jump to be removed.)

Slide jumps are path dependent because of the second property.
Examples:

Spoiler

2) Long jump into gravity or wall to totem
Yes, there is a long jump in the pixel perfect section, then why is this different? The difference is the target of the jump. Due to these hitboxes being easier to reach, they are less dependent on the coordinates of the thief. This jump is based on

  • The hitbox of the thief and the chest & gravity switch barely touching with a certain path.

Example:

Spoiler

3) Long jump in specific base
This is exactly the same case as the long jump in the pixel perfect section. However this one hasn't been confirmed as pixel perfect, and that doesnt really matter.
Example:
Spoiler

4) Gravity leap into totem in specific base
Another jump mostly possible in one base, however it takes little space and can be tested widely. Interestingly this is only based on

  • The calculation of new trajectories with multiple obstacles (2 corners, a wall, and a gravity switch in total.)

Example:

Spoiler


Edited by Oliver666666, 04 July 2017 - 11:33 AM.


#5 Oliver666666

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Posted 26 July 2016 - 12:45 PM

The inline saw saving guide
 
So OK, there are hard jumps, there are special paths that we must find to do them, but how can we use this to our advantage? Here's the answer: how about a way to find new paths instead of relying on watching videos to save hard jumps. For example, there are tons of saw jumps that can be made, and almost all of them have multiple different paths. But what if I said you don't have to rely on memorising them all?
 
Here is the idea: Inline saw jumps are always saved on corners. However, if you recall the corner glitch jumps, the physics get messy in the corner. The trick is to examine the animation when you die, and retrieve information on how to alter your path.
 
Keep in mind that walls reset coordinates, and allow less freedom than anywhere else. For this reason, a wall is the perfect point of origin for creating your path, as you can always start from exactly the same coordinates.
 
Take a look at the following images:

Spoiler

Luckily, when starting a path for a saw jump in any base, and performing it from a correct point of origin, without any extra jumping, then the results will usually be the same: Wiggle animation when you start above, and the casual animation underneath it. Secondly, that strange animation that happens in the third image, is very rare, so rare in fact, that you can assume you started just above the point of origin for the correct path.
 
Even if the correct point of origin is not directly under the one of the wiggly animations, or you run out of walls, then you can spice things up creatively with what we have learned. I will show you how I found another path in this same base on my own (I actually used a ghost potion for the first path :P )
Spoiler

In this example I was obviously lucky, but that's part of the process too. Here's the global version of how to do this:
 
Step 1) Select a point of origin and start testing any paths. Try to keep them simple if there's space. Look for strange animations (or a success)
Step 2) Keep moving the point of origin in one direction on the wall, little by little (if you run out of space go the other way). Systematically search for that wiggly animation (but don't get stuck anywhere, a solution is not 100% guaranteed to exist near a wiggly)
Step 3) Add extra variations to your path if you feel you are very close to a solution or running out of space.
 
Keep in mind there are impossible positions for some jumps in the game, and no matter how thorough you are, you might not find a solution. However in the remaining cases, I really hope these tips help.


Edited by Oliver666666, 04 July 2017 - 11:40 AM.


#6 Oliver666666

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Posted 02 August 2016 - 10:14 AM

Exceptions and special cases
 
Well the title says it all, here there will be special cases. You could even call this the bug section. Since a global model is given, and then elements are introduced, it is more than likely that strange things happen once in a while. 

1) Steep entry saw jumps
I will explain why these exceptions occur after the examples. These were new to me until Fezzik pointed them out, so thank you!
 
Example: One block difference inline saw jump
First let's start from the case where the jump starts one block higher than the saw. In these cases, the jump may become more forgiving, allowing one or two more paths to also pass the saw jump. This means that some of these inline saw jumps are not pixel perfect, only path dependent. Keep in mind this does not automatically mean all similar jumps are only path dependent! I just mean to show that these cases exist.

Spoiler

Example: Two block difference inline saw jump
This is a very extreme case possible in very few bases. Inline saw jumps starting 2 blocks higher than the destination are neither path dependent, nor pixel perfect. On first hearing, I didn't believe this myself, so lets jump straight to the GIF.
Spoiler

 

Explanation

Let's see what happened here. In both cases the explanation is the same. Because of gravity simulation, the thiefs' path starts to become very steep. While in the air, this doesn't have any effect. However, there is one frame where the thief starts in the air, and ends up on the ground. Luckily, we don't have to know exactly how the game calculates the point where it sticks the thief. (Distance approximations can be very complex). With a closer look, we can see what happens. The super slow motion animations are in the next spoiler.

Spoiler

In the 5th frame of the GIFs, the thieves all have the same animation. They all start on different paths, however, when they land, they are all nudged into similar coordinates. From that point they are on a correct path that passes the inline saw jump. In the first three images, the thieves land further away from the saw than in the other cases. Because of the steep fall, a new landing zone is available. This allows safe passage through the saw. In the case of the one block difference inline saw jump, the path is much less steep, so the previously mentioned new landing zone can still only rarely be reached, which is why there are much less correct paths for that jump. 

 

2) Inline saw jumps from ceiling-high platforms

Platforms aren't available in many bases. And even less contain saws in their trap sets. And just one base allows this special setup (with a decent variety though).

 

What makes up this jump are: an inline saw jump, a (wooden) platform one half block higher, and the ceiling being another half block above. These saw jumps are only path dependent, not pixel perfect. This is a similar case to the one block difference inline saw jump, but here the roof provides the steep fall, not the extra height the thief has to travel.

Example:

Spoiler


Edited by Oliver666666, 04 July 2017 - 11:49 AM.


#7 Oliver666666

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Posted 04 August 2016 - 10:59 AM

Exceptions and special cases (part 2)
 
3) Inline saw jumps with mid-air gravity switches
Looks like the jumps names are getting a bit carried away. Lets dig right in. 
 
Example: Weird Inline saw jump with mid-air gravity in specific base
A picture says more than 1000 words. This saw jump is neither path dependentnor pixel perfect. It is really hard to explain. The most possible reason could be due to

  • The gravity switch activating while the thief is in the air.
  • The thief spending a lot of time in the air.
  • The thiefs landing coordinates being forgiving for this special jump (similar to the two block height inline saw jump).

With the combination of these reasons, an explanation could be mixed up. However exact saw jump mechanics are extremely difficult to observe using only replay data even in just the normal cases.

Spoiler

 

Counter example: Vertical runway Inline saw jump with mid-air gravity in specific base

Spoiler

 

4) Corner saw jump
I was debating (with Fezzik again), that if corner saw jumps have only one path because of the walls, then they would technically be pixel perfect with the definitions I used. However, I realized that corner saw jumps fall out of this category, simply because they have more than one path.

Spoiler

 

For illustrative purposes, here is the overlay image of two thieves' starting point on the wall for a corner saw jump. One of them jumps instantly, while the other one is a thief that slides a little.
ojQdLIt.jpg


Edited by Oliver666666, 04 July 2017 - 11:56 AM.


#8 Oliver666666

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Posted 04 August 2016 - 03:09 PM

Video Guides

 

Here I will link in some of the most useful videos that contain solutions to the hardest jumps in the game. Since I did not create these videos, it is possible that a link may go down, and I will not be able to fix those problems myself. Still, please to contact me if any of the videos are not working.

 

1) Ultimate King of Thieves Saw Path Collection by Ash KOT

If you are looking for a way to pass a jump with a saw, I am 99% confident that you will find a way to pass it in this epic collection of saw related jumps. 

 

 

2) Bryan Berndt videos on Youtube

Known for making videos some of the most hardcore bases ever created. Definitely worth a look if you are interested.

 

https://www.youtube....QoHUpIaG4pWXhwA

 

More coming soon!


Edited by Oliver666666, 04 July 2017 - 11:59 AM.


#9 Oliver666666

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Posted 12 August 2016 - 10:40 AM

Reserved



#10 DanFariasM

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Posted 12 August 2016 - 03:12 PM

Awesome :wub:



#11 Chaos

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Posted 12 August 2016 - 03:34 PM

It is finally here! Gee, you are really good at these guides, it looks great, is easy to follow, understandable and of course, very useful.
My only question at the moment is why haven't I already noticed this, it says Posted 22 July 2016.
Apart from that, amazing work and thank you for the awesome guide : )

And this Gif is amazing

Spoiler


Edited by Oliver666666, 04 July 2017 - 11:50 AM.
updated image link


#12 Ryblik

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Posted 12 August 2016 - 03:41 PM

Amazing work! Thank You! It's very helpful!



#13 Oliver666666

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Posted 12 August 2016 - 03:44 PM

My only question at the moment is why haven't I already noticed this, it says Posted 22 July 2016.


I used watcher hax to write this without it being public. It took about that long to get into its current state. I didnt realise it took almost 3 weeks, but it was worth it :)

#14 Skydancer

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Posted 12 August 2016 - 06:13 PM

Amazing work ! Gotta read everything, a lot of interesting informations ;)

 

Btw, dunno if it's a loading problem on my side, but the GIFs in the last post are kinda fucked up. First one is a link and the two other ones don't load up.


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#15 Fezzik

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Posted 12 August 2016 - 06:41 PM

Excellent guide, Oliver.  And thanks for all the mentions.  It was fun working this stuff out.



#16 JohnDoe

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Posted 12 August 2016 - 10:09 PM

Many thanks for the work you did and this helpfull Guide !

Very cool infos and new things i dont know, so i can now practise them :)

Love you man  :wub:



#17 OnProch97

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Posted 13 August 2016 - 06:24 AM

Three words: PIN IT PLEASE...
Seriously, great work Oliver...

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#18 MrKukurykpl

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Posted 14 August 2016 - 06:24 PM

Finally remembered to look at this topic on my PC instead of mobile that can't handle so many gifs at one page. And I officially can say that this is the best and most complete jump guide ever, despite still being not completed (reserved posts). All I can say is thanks for hard work in researching information, writing, editing and everything else. That surely took you a long time, and you worked for others and for free. #respect

 

Oh, and this is my #555 post, gonna celebrate xD

edit again: enjoy my likes


Edited by MrKukurykpl, 14 August 2016 - 06:27 PM.

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#19 Gem Cultivator of Titans

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Posted 18 August 2016 - 11:42 PM

Wooow

This is awesome man, alot of thanks! 



#20 Michael

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Posted 19 August 2016 - 08:04 PM

Nice job Oliver, going to read through more thoroughly while I get locked out for 3 hours tonight   :P






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