How is rotation defined in a tetris game?

Question

I'm working on implementing the backend logic behind the classical tetris game, and I'm a bit confused on how a rotation is performed. I understand that you can apply a rotation matrix, but I still have some questions that are perhaps better explained with an example.

In my implementation, I use square matrices of 0s and 1s to represent the shape. e.g., I use a 4x4 matrix with a single row filled to represent the long horizontal block: $$ \begin{bmatrix} 1 & 1 & 1 & 1 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{bmatrix} $$

And for each block, I also keep track of the bottom right location of the 4x4 matrix relative to the location of the game board.

The question I have is, when you apply a rotation (in this case it would turn into a vertical block), do you have to fix some center? If so, how is this center of rotation defined?

e.g., I could define the center of rotation of the above as the top left element, so apply 90 degree clockwise rotation would yield:

$$ \begin{bmatrix} 1 & 0 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 1 & 0 & 0 & 0 \end{bmatrix} $$

But you could also make any of the other 15 elements the center of rotation, though it probably makes the most sense to make one of the 4 elements of the original block the center of rotation. I think the issue here is that for the other 3 elements, if you make any of them the center of rotation, part of the rotated block is going to lie outside the existing 4x4 window. So how is something like this prescribed in an implementation?

Alternatively you can swap the indices as in Tetris - Rotations using Linear Algebra (Rotation Matrices) without using a center of rotation, but I'm not sure which approach makes the most sense. Swapping indices is certainly much easier to implement.

Answer 1

It works however you (as he game designer) define it. Various implementations of Tetris have implemented rotations in different ways:

Super Rotation System is the current Tetris Guideline standard for how tetrominoes behave, defining where and how the tetrominoes spawn, how they rotate, and what wall kicks they may perform. Henk Rogers developed this system in order to unify all new Tetris games under the Tetris Guideline:

• When unobstructed, the tetrominoes all appear to rotate purely about a single point & is solely a mathematical rotation as opposed to the combination of rotation and translation found in some other systems.

The NES and SNES use a "right handed rotation system":

• O : no rotations.
• I : two rotations, favoring the lower half when horizontal, and the right half when vertical.
• J, L, and T : 4 rotations centered around the middle square of the three square edge.
• S and Z : four rotations, favoring the bottom and right sides.

The Game Boy Tetris is identical to the NES version it uses a left hand rotation for the S and Z pieces.

Sega rotation system is similar to the NES version, except that:

• The flat-side-down states of J, L, and T are pushed down by one space
• S and Z round in different directions
• I rounds differently from the other pieces.
• I requires more space under it to rotate to a vertical orientation.

The above mostly covers the 'basic' rotations - the various systems have varying rules for things like wall kicks and spawning orientations. More information can be found here.

Subjectively, I wouldn't expect the I rotation to behave as you've described in your question because it differs strongly from the precedents I'm familiar with, but that doesn't necessarily make it wrong. Test it out and focus on how it plays rather than how it's implemented. If it play tests well and meets your design goals, then it is a working design.