SPG:Special Stages

Sonic Physics Guide
Basics Positions And Speeds Angles Variables Calculations (Technical) Pixel and Subpixel Hex Angles Characters Sonic Tails Knuckles
Collision
Solid Tiles (Terrain Part 1) Sensors Solid Terrain (Terrain Part 2) Layers Loops Slope Collision (Slopes Part 1) The Player's Sensors While Grounded 360 Degree Collision While Airborne Hitboxes The Player's Hitbox Trigger Areas Solid Objects Solid Objects Sloped Objects Jump Through Platforms Pushable Blocks Item Monitor
Physics
Slope Physics (Slopes Part 2) Moving Along Slopes 360 Degree Movement Falling and Slipping Down Slopes Landing On The Ground Air State Running Jumping Rolling Getting Hit Rebound Underwater Air Physics Super Speeds
Gameplay
Main Game Loop Game Objects Game Enemies Badniks Bosses Ring Loss Special Abilities Spindash Super Peel Out Drop Dash Insta-Shield Flying Gliding Climbing Elemental Shields Flame Shield Bubble Shield Lightning Shield Player 2 Player 2 CPU Respawning Special Stages Rotating Maze
Presentation
Camera Animations Animation System Variable Speed Animation Timings Normal Animation Timings Animation Rules
Special
Overlay Scripts Sonic 1 Overlay Sonic 2 Overlay

Notes:

• The research applies to all four of the Sega Mega Drive games.
• For 100% accuracy and retain the exact same movement from the original games, it is recommended you don't use degrees and rather follow the original game's 256 angle structure - though you'll have to also use the trigonometry functions from the original games. These can be found in Calculations.

Rotating Maze

The special stages in Sonic 1 have very unique physics, controls, and "feel". They do not share physics code with the normal gameplay at all.

Maze Blocks

the Maze is constructed out of a grid of tiles. The size of each grid tile is 24 x 24. Some tiles contain solid "Blocks" (which includes normal solid blocks and special blocks such as Bumpers and Up/Down Blocks), some contain non-solid tiles like Rings, while others are empty.

Maze Rotation

The handling of Special Stage rotation is more of an illusion than actual rotation.

While they appear to, these special stages don't actually rotate. The blocks don't even actually move at all. Instead, the Player's gravity, jump direction, and left/right input movement angle all change based on the stage's current angle. The actual Sonic object still moves relative to the static, unrotated, base layout.

So, because the Player is only ever truly colliding with flat sides of a block and not sloped angles of rotated blocks, this makes collision much easier.

Rotation Illusion

When Player motion and physics are processed in the Maze, it's always happening on a static un-rotated grid of the stage tiles/blocks.

While playing, the Player's gravity direction is being manipulated, and the stage is simply displayed as if it was rotated. When the game displays any given block, it gets rotated around Sonic (which is always centre of the screen) by the current Stage rotation angle. Thus completing the illusion.

How the game is actually processing the movement on the right (gravity direction shown as a white line).

A more general way to imagine this is: Instead of the stage itself rotating, it's as if the camera and gravity direction rotates while moving across the stage.

Maze Speeds and Angles

The special stage starts with a rotation speed of 0.25 in the original games. (In degrees, this would be -0.3515625)

Note:

• The stage_angle is always kept positive, the angle needs to be "wrapped" otherwise it will give weird results when snapping the angle when negative.

To get the snapped_stage_angle (used for physics and drawing the stage), just do

(stage_angle div 4) * 4 

A rough conversion for degrees:

floor(stage_angle / 5.625) * 5.625

Maze Player Object

Much of the Special stage Player object is the same as the normal Player object.

Variables & Constants

The Player object is like any other, it uses similar constants, and has X/Y Speed values, and a Ground Speed value. However, these values are applied differently as will be explain up ahead.

Constant	Value
acceleration_speed	0.046875 (12 subpixels)
deceleration_speed	0.25 (64 subpixels)
top_speed	8
gravity_force	0.1640625 (42 subpixels)

States

At any time the Player knows if they are touching a solid block at any side (up, down, left, right, any). This will be referred to as the "block_hitting flag" (true or false).

Player Physics

Note:

• All of the Player's motion that reacts to the stage's angle uses the snapped_stage_angle rather than stage_angle.

The Player is essentially always performing the same code, with only slight differences depending on the current situation. The following will describe the different functions/routines the Player can for their physics. How and when these routines are executed will be detailed in Player events.

Left/Right Movement Routine

The Movement routine checks for or input and updates Sonic's Ground Speed. Acceleration/deceleration works the same as normal, like when Sonic walks on normal ground. Friction (same as acceleration) is applied when no or input is detected.

After updating Ground Speed, a potential_x_speed and potential_y_speed are created using Sonic's current Ground Speed and the movement_angle.

 potential_x_speed = Ground Speed * cos(movement_angle);
 potential_y_speed = Ground Speed * -sin(movement_angle);

Movement Angle

What's the movement_angle? The movement_angle used here is not the real stage_angle or even the snapped_stage_angle. movement_angle is the snapped_stage_angle wrapped to a 90 degree slice.

movement_angle shown as a white line over Sonic.

The movement_angle keeps to a cardinal direction of the stage. As the stage rotates snapped_stage_angle, so does the movement_angle. But when the stage rotation means the movement_angle would pass a 45 degree mark, the movement_angle snaps back (or forward) 90 degrees. Essentially always pointing within a 90 degree slice towards the right of the screen, wrapped.

 movement_angle = ((angle + 45) div 90) * 90;

This is the angle used for the Player's left/right movement, even when in the air. Because this occurs in the air too, it makes the special stage feel all the more disorienting, which is by design.

Checks

The game performs a tile check at the Player's X Position + potential_x_speed, and the Player's Y Position + potential_y_speed.

Note:

• Tile checking is explained up ahead in Tile Checks.

If a solid block is found, Ground Speed is set to 0, otherwise, the potential_x_speed and potential_y_speed are simply directly added to the Player's X/Y Position. Neither the Player's block_hitting flag nor the Player's actual speeds are changed/used in this routine.

Fall Routine

The fall routine is where the Player's real X Speed and Y Speed come into play.

Firstly, the Player's block_hitting flag is reset to false.

Falling Speeds

Directional gravity speeds x_gravity and y_gravity are calculated based on the snapped_stage_angle.

 x_gravity = gravity_force * sin(-snapped_stage_angle);
 y_gravity = gravity_force * cos(-snapped_stage_angle);

Then, a potential_x_speed and potential_y_speed are calculated using that new gravity:

potential_x_speed = X Speed + x_gravity
potential_y_speed = Y Speed + y_gravity

Checks

The game then performs a tile check at the Player's X Position + potential_x_speed, and the Player's Y Position.

If a solid block is found, potential_x_speed is set to 0, and Sonic's block_hitting flag is set to true.

Then the game performs a tile check at the Player's X Position + potential_x_speed, and the Player's Y Position + potential_y_speed.

Note:

• Here, potential_x_speed could potentially be 0 if something was found in the previous tile check.

If a solid block is found, potential_y_speed is set to 0, and the Player's block_hitting flag is set to true.

Then, X Speed is set to potential_x_speed, and Y Speed is set to potential_y_speed.

Jump Routine

The jump routine simply checks if a jump button is pressed, if it is, set's the Player's X Speed and Y Speed based on the snapped_stage_angle, and sets the Player's block_hitting flag to false.

Collision

Judging by the complexity presented ingame, you may think collision in a rotating special stage will be extremely complicated, but it's not at all as complicated as it first appears. As previously stated, the stage doesn't really rotate, which simplifies things incredibly.

Collision is purely based on what tiles are nearby Sonic's position.

Tile Checks

Whenever a tile check occurs, it accepts an x and y position as parameters and will check the 4 closest tiles to this location.

To locate the tiles to check based on this position, it will do the following

check_x = (X Position - 12) div 24;
check_y = (Y Position - 12) div 24;

So this essentially rounds the position and gets the grid coordinates of the top left tile of what will be a 2 x 2 check area.

The game then goes through and checks the top left, top right, bottom left, and bottom right tile in that square, in that order. It will always check all 4 tiles.

Note:

• No matter the stage rotation, this always happens the same way. Stage rotation is not accounted for.
• If any of these 4 tiles contains a solid Block, a solid Block was found and a collision will occur as stated in the physics routines previously.

The last tile checked which had a Block in it (no matter the Stage orientation or layout of the Blocks) will become the current_block, and will be the one focused on for any unique reaction (if it is a Bumper for example).

Reaction To Blocks

Because of how collision is processed, the Player can only be "focused" on one block at any given time (the current_block), and will only react to that block. The Player will only react to the current_block if the block_hitting flag is currently true.

Some blocks that change the special stage state have a global 48 frame cooldown timer (per block type) so the Player can only interact with them once even if they are touching them for more than 1 frame. These include the Up/Down blocks and the R block.

Up/Down Blocks

Up blocks double the speed of the stage, Down blocks divide it by 2 (if it's > 0.25) This Block turns into the opposite type each time it activates.

R Blocks

R blocks multiply the stage rotation speed by -1.

Bumper Blocks

Bumper blocks act exactly like a normal Bumper does (aside from the fact that the initial collision condition is completely different) The game measures the angle from the centre of the Bumper tile to Sonic's position, with a repulsion force of 7.

Order of events

Each frame, the special stage works in the same order:

1: Player Events

Firstly, the Player's code is executed.

• If the Player's block_hitting flag is true, run Jump Routine.
• After this, regardless of the block_hitting flag state, the Player will then perform the Movement routine and lastly the Falling routine.

After the movement routines, the current_block will be reacted to (only when the block_hitting flag is true).

Then lastly, the Player's X Speed and Y Speed are added to his X/Y Position.

2: Other Events

After the Player's events, the game will update the stage_angle, by adding the rotation speed, and then calculating the snapped_stage_angle.

Notes

• For 100% accuracy and retain the exact same movement from the original games, it is recommended you don't use degrees and rather follow the original game's 256 angle structure - though you'll have to also use the trigonometry functions from the original games. These can be found in Calculations.
• As you can tell, the Player's speeds and motion are simply halted when a block is detected at his next move. The only reason he nicely smoothly falls onto surfaces and doesn't stop short is thanks to the gravity softly nestling him in each frame.