From Sonic Retro
|Sonic Physics Guide|
- The following only describes how the Player object collides and interacts with stage terrain. Solid objects, such as Monitors, Jump Through Platforms, and Pushable Blocks each have their own collision routines with the Player and don't necessarily behave exactly the same as the tiles do. For this, refer to Solid Objects.
- 1 Introduction
- 2 Solid Tiles
- 3 Sensors
- 4 The Player's Sensors
- 4.1 Sensor Activation
- 4.2 Floor Sensors (A and B)
- 4.3 Ceiling Sensors (C and D)
- 4.4 Wall Sensors (E and F)
- 4.5 Extra
- 4.6 Summary
- 5 Notes
What are solid tiles? While there are often solid objects in Sonic zones, the zone itself would require far too much object memory if the environment were constructed entirely of solid objects, each with their own 64 bytes of RAM. A clever short-cut is used - the zone is constructed out of tiles anyway, so all that needs be done is have each tile know whether or not it is solid.
You may know that zones are broken down into 128x128 pixel chunks (or 256x256 pixel chunks in Sonic 1 and Sonic CD), which are in turn broken into 16x16 pixel blocks, which are again in turn broken into even smaller 8x8 pixel tiles. All of the solidity magic happens with the 16x16 blocks, so those are the only ones we will be interested in throughout this guide.
the Player's collisions and interactions with these solid tiles are what make up their basic engine. They dictate how they handles floors, walls, ceilings, slopes, and loops.
First we will look at how the environment is constructed from tiles, and then the Player's method for detecting their environment.
Solid tiles are a grid of data blocks, which represent solid areas within each grid cell.
How is a solid tile set up? How is the shape of the terrain stored?
Each Solid Tile is simply an array of 16 height values that can range from 0px ($00) to 16px ($10) inclusive. Solid tiles also have a single angle value associated with then.
This tile's height array has the values 0 0 1 2 2 3 4 5 5 6 6 7 8 9 9 9, and has the angle 33.75° ($E8).
Solid Tiles also have another height array (or, well, a width array) for horizontal collisions. This other array represents the same data and creates the exact same shape within the tile.
You may rightly wonder how sloped ceilings are possible if the height array starts at one end only. The answer to this is that tiles can be flipped horizontally or vertically. The collision systems take this into account when reading the height data from tiles. The angles of flipped tiles are also adjusted when being checked.
Nearly all tiles have a specific angle value which is used to allow the Player to rotate with sloped ground. However, some tiles angle is used as a flag. In the original games, if the angle of the tile is 255 ($FF), it is a flagged tile. How this angle is reacted to is determined by the object's code. In the case of the Player, they will not set their Ground Angle to the tile's angle as normal, but will instead find a new Ground Angle which is the Player's current Ground Angle snapped to the nearest 90° increment.
This flag applies to all full block tiles, as it is a quick and easy way to allow the Player to walk on all sides of a full block without needing to flip it around or provide multiple angle values for each side. This is also used as a trick to effectively "flatten" the end of ramps. The ramps found in Emerald Hill Zone end with a diagonal slope - yet Spindashing up it sends you flying directly upwards into the air. How? The trick is that the last tile on that ramp has an angle of 255 ($FF), so is flagged despite not being a flat tile. This snaps the Player to 90° (aka, moving directly upwards) just as they leave the ramp.
Not all tiles behave the same. Some tiles are only solid from the top, some only from the sides, and some of course are solid from all sides. This solidity aspect affects which directions of sensors can detect them. For example, a "top only" tile will be ignored by sideways and upwards facing sensors, but downward facing sensors will detect them.
What are sensors? Well, that's up next.
"Sensors" are simply checks performed by objects which look for solid tiles around them.
An x/y position (anchor point) is checked, and if it finds a solid tile, they will gather information about the tile. Sensors can point down, right, up, and left, and all behave the same in their respective directions.
In this example, the sensor to the Player's mid right points right, and those at the Player's feet point down. Their direction dictates in which direction they are looking for a surface. A sensor pointing right is looking for the leftmost edge of solid terrain nearby, a sensor pointing down is looking for the topmost edge of solid terrain nearby.
Which value of the height array is used? Subtract the tile's X position from the sensor's X position. The result is the index of the height array to use.
So, now we know they are points which look for solid tiles they touch, and that they can check the height of tiles at specific positions to get the floor surface position.
However, this is not the whole picture. If a sensor finds an empty tile or the array value of the tile found by the sensor is 16 (a full block amount), then it's likely that the surface of the solid terrain is actually found within an adjacent tile instead.
Sensor Regression & Extension
So when a sensor check is performed at a sensor's anchor point it has either found a solid tile, or it hasn't. If it has, what if the height value found is 16 and isn't actually the surface of the terrain? Or if it hasn't, what if there's a solid tile nearby?
Well, this is easily solved by checking neighbouring tiles if certain conditions are met.
- The following is an example in the case of a sensor which is pointing down looking for solids below (like a floor sensor while standing upright).
- The current height array value of a tile at the sensor's X position will be referred to as the tile height.
When the anchor point finds a Solid Tile and the tile height of the first tile is between 1 and 15 (inclusive), the game can be sure the surface of the terrain has been found without needing to check extra tiles at all.
Otherwise, one of the following 2 things will happen.
When the anchor point finds a Solid Tile and the tile height of the first tile is 16 (meaning the tile is completely filled in that position), it will check up by 1 extra Solid Tile. We'll call this the "regression" since it goes back against the sensor direction.
If a regression occurs and tile height of the second tile is 0 (or the tile is empty), it will just default to processing the first tile, as the first tile must be the terrain surface.
When the anchor point just finds an empty tile (or the tile height of the first tile is 0), it will check down by 1 extra Solid Tile. We'll call this the "extension" because it goes outwards, in the direction of the sensor.
If an extension occurs and just finds an empty second tile (or the tile height of the second tile is 0), the game knows that no terrain or terrain surface has been found, and will return the distance to the end of the second tile checked.
If a solid tile was found to be processed, it will calculate the distance between that tile height and the sensor.
In the above example, a downward facing sensor moves down through 3 Solid Tiles. We can see the tiles it checks, and the distance it returns at each position. We can also see if it is performing extension or regression. You can see this means the sensor can effectively act as a line, it can regress or extend up to 32 pixels to find the nearest surface.
The regression & extension will occur in the direction of the sensor, be it horizontal or vertical. If the sensor is horizontal, it reads the other height array belonging to the tile, using the sensor's y position. Essentially rotating the entire setup. So a right facing sensor's regression would check an extra tile to the left, and extension would check an extra tile to the right. While an upward facing sensor's regression would check an extra tile below, and extension would check an extra tile above.
With all this, a sensor can always locate the nearest open surface (and the tile containing that surface) of the terrain within a range of 2 tiles (the tile the sensor anchor point is touching plus another).
Once a final suitable tile has been found, information about the tile is returned.
The information a sensor finds is as follows:
- The distance from the sensor pixel to the surface of the solid tile found (in the sensor's direction)
- The angle of the tile found
- The tile ID
The distance to the solid tile surface (found by the sensor) is the most important piece of information dictating how an object will react to solid tiles. It's not the distance to the tile, it's the distance to the edge of the solid area within the tile, precisely.
The distance can either be 0, negative, or positive.
When no Solid Tile is found by a sensor, the sensor will return a distance between 16 and 32 (inclusive), which is the distance to the end of the second tile checked. When casting sensors, objects check the returned distances it accepts for collision. For example, checking if a distance is > 14 and if it is, not colliding. This will effectively filter out these potentially no-tile-found distances. This avoids a need for the game to remember after the sensor was cast if a tile was found. In future, if the guide references a tile not being found, this means either the distance is out of the range the object wants, or the distance is between 16 and 31. Of course, most of the time an object will only react to negative distances which automatically rules these out anyway.
- A distance of 0 means the sensor is just touching the solid tile surface and the object will not need to move (but may still choose to collide).
- A negative distance means the surface found is closer to the object than the sensor position. Negative distances are almost always reacted to when colliding, because it indicates that the object is inside the solid and can be pushed out.
- Positive distances mean the surface found is further away from the object than the sensor position. Since this means the object isn't actually touching the tile, it's rarely used - but not never. A notable example of it's use is by floor sensors of various objects, including the Player, to keep them attached to the ground even if the ground has sloped away from them a bit as they move. Objects usually employ a limit to how far an object can be "pulled" down to a solid they aren't actually touching. This will be detailed further down for the Player.
If the object decides to snap itself to the terrain, it simply has to add the distance value to it's position. Or subtract, depending on the sensor's direction. A sensor pointing left may return a negative distance if it is inside a solid, but the object would have to subtract the distance in order to move to the right, out of it.
Of course, as stated, this distance can be representative of any 4 directions, depending on the sensor's own angle.
Here's a demonstrative animation showing a very simplified process of how the floor sensors detect a tile and be moved upwards. In this case, the Player will have a Ground Speed of 6.
Throughout this guide these sensors will be drawn as lines. But, they are not. Or well, they are, but not quite as shown ahead.
Sensors will be drawn from the sensor anchor, extending towards the centre of the object. You can imagine it like so - if the exact surface pixels of the ground is within these lines, the Player will be pushed out. It is of course not quite this simple in reality. As shown in the previous visualisation of a sensor, the "line" portion can extend up to 32 pixels in either direction, all depending on where the sensor anchor currently sits within it's tile... This would be impossible to accurately draw over the Player while keeping things understandable and clear. This visualisation is the most easy to visualise way to think about the solidity on a surface level.
Just be aware that the line based depictions are for simple illustration purposes only and the endpoints of the lines are the active sensor anchors (which always behave as described).
The Player's Sensors
Like any object which wants to collide with tiles, sensors surround the Player.
A and B - Floor collision C and D - Ceiling collision (only used mid-air) E and F - Wall collision (shifting by 8px depending on certain factors, which will be explained) XY - the Player's X Position and Y Position
Since the Player's collision setup is symmetrical, it makes sense for the game to set up widths and heights using radius values. The Player has separate radius values for their E and F sensor pair (their Push Radius) which always remains the same, and for their A, B, C and D sensors there is a Width Radius and Height Radius both of which will change depending on the Player's state. For these sizes see Characters.
Note on sprite alignment:
- The Player's sprite is 1 pixel offset to the left when they faces left, which can result in them appearing to be 1px inside a tile when pushing leftwards. Amusingly, this offset will appear corrected when pushing most objects thanks to their hitboxes sticking out 1px further on their right and bottom (due to their origins being off-centre by 1 in X and Y). So while tiles are collided with accuracy, it will appear the opposite in-game. More about object collision in Solid Objects.
Before jumping into exactly where these sensors are how these sensors make Sonic react to the floor, it's best to know when they are actually being used.
Floor Sensors A and B are always active while grounded, and will actively search for new floor below the Player's feet.
When grounded, Wall Sensors E and F only activate when the Player is walking in that direction. For example, while standing still the Player isn't checking with their wall sensors at all, but while Ground Speed is positive, the Player's E sensor is inactive, and while Ground Speed is negative, the Player's F sensor is inactive.
However this is not always the case, both wall sensors simply don't appear when the Player's Ground Angle is outside of a 0 to 90 and 270 to 360 (or simply -90 to 90) degree range, meaning when you running around a loop, the wall sensors will vanish for the top half of the loop. In S3K however these sensors will also appear when the Player's Ground Angle is a multiple of 90 in addition to the angle range.
While grounded Ceiling Sensors C and D are never active, and the Player won't check for collision with solid tiles above them while on the floor.
While in the air, all sensors play a part to find ground to reattach the Player to. But rather than have all active at once and risk lag, only 4-5 will be active at any given time.
As you move, the game will check the angle of your motion (X Speed and Y Speed) through the air. It will then pick a quadrant by rounding to the nearest 90 degrees. (this is different to the Mode, this is simply a measurement of if you are going mostly left, right up or down). The quadrant can be more easily found by simply comparing the X Speed and Y Speed and finding which is larger or smaller.
if absolute X Speed is larger then or equal to absolute Y Speed then if X Speed is larger than 0 then the Player is going mostly right else the Player is going mostly left else if Y Speed is larger than 0 then the Player is going mostly down else the Player is going mostly up
Depending on the quadrant, different sensors will be active.
When going mostly right, the Player's F sensor will be active, along with both A and B floor sensors and the C and D ceiling sensors.
When going mostly left, it is the exact same as going right, but the E wall sensor instead.
When going mostly up, both the C and D ceiling sensors and the E and F wall sensors are active.
When going mostly down, it is the same as going up, but the A and B floor sensors are active instead of the ceiling sensors.
Floor Sensors (A and B)
A and B sit at their feet at Y Position + Height Radius.
A and B Movement
These sensors are A on the Player's left side, at X Position - Width Radius, Y Position + Y Radius. While B should be on their right, at X Position + Width Radius, Y Position + Height Radius.
These radius values change depending on the character and action (see Characters).
A and B Process
Floor sensors are a special case, there are 2 sensors and they effectively compete to find the nearest floor to the Player. Both sensors behave the same and search for a Solid Tile and the smaller distance is the sensor that wins. For example, -10 is a smaller distance than 5. The sensor that wins is is then the distance and tile angle used (and it's found tile is the one referenced).
Once the winning distance is found, it can be tested and used to reposition the player.
As we know, sensors return a distance to the nearest surface, up to an extreme maximum of 32 pixels. If the Player's floor sensors are within 32ish pixels of the floor, the game may know the floor is there but we might not just want them to snap down right away. The game will test the winning distance found and react appropriately.
In Sonic 1, if the winning distance value is less than -14 or greater than 14, the Player won't collide. In Sonic 2 onward however the positive limit depends on the Player's current speed - in this case, (for when the Player is on the floor) if the distance is greater than
minimum(absolute(X Speed)+4, 14)
then they won't collide. So the faster the Player moves, the greater the distance the Player can be from the floor while still being pulled back down to it. The -14 limit remains the same.
If the Player was in a sideways mode, such as on a wall, it would use Y Speed instead.
If the player does collide with the floor, the distance will be added to (or subtracted from, on ceilings or left walls) the Players position, and the Ground Angle will be set to the tile angle found by the winning sensor.
Well, the angle changing isn't quite so simple. Above it was mentioned that certain tiles are flagged, which changes how the game reacts to the angle. If the tile is flagged, (like a normal full block or certain other special tiles) rather than using the tile's angle, Ground Angle is simply set to the current Ground Angle, but snapped to the nearest 90 degrees.
In Sonic 2 onwards, this angle snapping also occurs with normal tiles if the absolute difference between your current Ground Angle and the tile's angle is greater than 45° (32) ($20).
While airborne, if the winning distance value is greater than or equal 0 (meaning the sensor isn't overlapping the floor yet) the Player won't collide.
If still colliding after that check, the game will then check the following:
When moving mostly down, both sensor's distances are larger than or equal to -(YSpeed + 8). If either of them are, the player will collide, if neither of them are, the Player will not collide.
However when moving mostly left or mostly right, the Player will simply collide if the Player's Y Speed is greater than or equal to 0.
Of course, upon successfully colliding with the floor, the the Player's grounded flag is set and Ground Speed is set according to the angle.
Jumping "Through" Floors
The above airborne behaviours are most noticeable with jump through (top solid) tiles when jumping from underneath. The solid tiles that make up these ledges are flagged by the engine as being a certain type that should only be detected by the Player's A and B sensors, so solid from the top only.
These are often in the hilly, green zones such as Green Hill Zone, Emerald Hill Zone, Palmtree Panic Zone, and so on. They are ignored entirely by C and D as well as the wall sensors E and F. Finally, sensor A and B (mostly) are only active in the air when the player is not moving mostly upwards. So with a slightly shorter jump, you will see the Player 'pop' upwards onto a jump through surface once they begin to fall.
As discussed above there are conditions to be met aside from just the sensors being active and finding the floor related to both the distances found and the current Y Speed of the Player. So you may also see the Player pop upwards onto a Jump through ledge if you start moving to the side at the peak of a straight jump thanks to those more relaxed rules for landing when moving mostly left or mostly right.
The Player has to be able to run off of ledges. It would not do to just keep walking like Wile E. Coyote, not noticing that there is nothing beneath them.
If both sensor A and B detect no solid tiles, the Player will "fall" - a flag will be set telling the engine they is now in the air.
Balancing On Edges
One nice touch is that the Player goes into a balancing animation when near to the edge of a ledge. This only happens when they is stopped (their Ground Speed is 0).
How does the engine know? It is simple - any time only one of the ground sensors is activated, the Player must be near a ledge. If A is active and B is not the ledge is to their right and vice versa.
But if the Player began balancing the instant one of the sensors found nothing, they would do it too "early", and it would look silly. So it only happens when only one sensor is active, and X Position is greater than the edge of the solid tile. This is checked with an extra downward sensor at the Player's X Position and Y Position + Height Radius when Ground Speed is 0. All this extra sensor does is check if there is floor at their X Position, is it not related to collision or physics.
Assuming the right edge of the ledge to be an X position of 2655 ($0A5F), the Player will only start to balance at an X Position of 2656 ($0A60) (edge pixel+1). they'll fall off at an X Position of 2665 ($0A69) (edge pixel+10) when both sensors find nothing.
In Sonic 2, Sonic 3, and Sonic & Knuckles, the Player has yet a third balancing animation, for when they are even further out on the ledge. Assuming the same values as above, this would start when they is at an X Position of 2662 ($0A66).
Note: While balancing, certain abilities are not allowed (ducking, looking up, spindash, etc). In the Player 3 & Knuckles, the player is still allowed to duck and spindash (not to look up, though) when balancing on the ground but not when balancing on an object.
Ceiling Sensors (C and D)
the Player's C and D sensors are always an exact mirror image of the Player's floor sensors, they have the same X positions but are flipped upside down and face upwards. They perform in the exact same way, competing against eachother, simply up instead of down.
However, they aren't active at the same times as the floor sensors, only while airborne.
C and D Process
When these sensors find a ceiling, much like the floor sensors the sensor which finds the smallest distance will win. The sensor that wins is the distance and angle used (and it's found tile is the one referenced). This winning distance can then be subtracted from the Player's position.
The distances are processed here in the same way as the floor sensors while airborne, mainly being that a winning distance of greater than 0 is not reacted to.
Wall Sensors (E and F)
E sits at their left at X Position-Push Radius, while F sits at their right at X Position+Push Radius.
E and F Movement
Push Radius is always 10, placing E to the Player's left side, at X Position - 10. While F is to their right, at X Position + 10, giving the Player a total width of 21 pixels when pushing.
Sensors E and F Spend most of their time at the Player's Y Position however while the Player's Ground Angle is 0 (on totally flat ground) both wall sensors will move to their Y Position + 8 so that they can push against low steps and not just snap up ontop of them.
The horizontal sensors are always positioned at Y Position while airborne.
You may remember that sensors A and B are only 19 pixels apart but the Player is 21 pixels wide when pushing into walls. This means that the Player is skinnier by 2 pixels when running off of ledges than when bumping into walls.
So, these sensors remain rather steady, especially considering that Push Radius never changes. That's not to say these sensors don't relative to this starting position though. They do, and a lot. As noted in Main Game Loop wall collision (while grounded) actually takes place before the Player's position physically moves anywhere, so they wont actually be in a wall when they tries to collide with it. The game accounts for this by actually adding their X Speed and Y Speed to the sensor's default position each frame, this is where the sensor would be if the Player had moved yet.
E and F Process
Assuming the wall's left side to be at an X position of 704 ($02C0), the Player cannot get closer than an X Position of 693 ($02B5). Assuming the wall's right side to be at an X position of 831 ($033F), the Player cannot get closer than an X Position of 842 ($034A). Thus the distance between both sensors inclusive should be 21 pixels, stretching from the Player's X Position-10 to X Position+10.
When the Player collides with a wall, this will set their Ground Speed to 0 if they is moving in the direction of the wall, not away from it.
The distance value found by the sensor in it's given direction is used to stop the Player at a wall.
The distances found by the wall sensors are used slightly differently while grounded.
Naturally, the game will ignore a positive distance because they will not collide. If the sensor's distance is negative, this means that when the Player's position actually does change, they will be inside the wall.
In this case, because the sensor is actually out in front of the Player (where they will be after they moves) instead of using the distance to reposition the Player by directly changing their position, the game smartly uses the fact that the Player has still yet to move within the current frame. All it has to do is add the distance to the Player's X Speed (if moving right, or subtract the distance from the Player's X Speed if moving left. This would be done to Y Speed if in wall mode). This results in the Player moving when their position changes, right up to the wall, but no further. In the next frame, because Ground Speed has been set to 0 the Player will have stopped just like in any other situation.
Thanks to this process and the sensor's movement, this effectively results in no difference between this and if the sensor was simply checked after movevment had occured like all other sensors.
Like normal, if the distance is negative and the sensor is inside the wall, they will collide. The game will ignore a positive distance.
The Player cannot jump when there is a low ceiling above them. When the Player initally tries jumping, C and D sensors are activated for one frame to check if their is ceiling too close. If there is a collision detected with upwards C and D sensors at the Player's X Position - Width Radius and X Position + Width Radius, and if the closest distance found is less than 6 (meaning for a character the same size as Sonic the ceiling would be 25 pixels above the Player's Y Position or closer while standing), the Player won't bother jumping at all.
Here's a handmade visualisation of how sensors interact with solid tiles (here highlighted in bright blue, green, and cyan). You can notice how the sensors are pushing the Player from the ground tiles, and is overall rather simple. The E and F sensors lower when on flat ground. You can also notice the sensors snap in 90 degree rotations resulting in four modes, this is covered in Slope Physics.
Keep in mind, while on the ground the upper C and D sensors would not exist, and while gsp is positive the left wall sensor would also not appear. These sensors are only included for illustration purposes.
Bugs Using This Method
Unfortunately, there are a couple of annoying bugs in the original engine because of this method.
If the Player stands on a slanted ledge, one sensor will find no tile and return a height of foot level. This causes the Player to be set to the wrong position.
The Player raises up with sensor B sensor as they moves right. When B drops off the ledge, the Player defaults to the level of sensor A. Then they raises up with sensor A as they moves further right. So they will move up, drop down, and move up again as they runs off the ledge.
There are only a few areas where this is noticeable, but it applies to all Mega Drive titles and is pretty tacky.
Sensor B starts climbing down the ramp on the right, but the Player still defaults to the level of the previous ramp found by sensor A. Because these ramps are usually shallow, this only causes them to dip down in the middle by about 1 pixel.
But that is not all. Because the highest sensor is the one the Player gets the angle from, even though it looks like they should be considered to be at the angle of the ramp on the right (because they is closer to it), they will still have the angle of the ramp on the left. When you jump, they will jump at that angle, moving backward, not forward like you would expect.
- Find information on how the Player's momentum and slope handling work, and about how sensors adjust when walking on walls and ceilings in the Slope Physics guide.