What are the best algorithms (and explanations) for representing and rotating the pieces of a tetris game? I always find the piece rotation and representation schemes confusing.

Most tetris games seem to use a naive "remake the array of blocks" at each rotation:

http://www.codeplex.com/Project/ProjectDirectory.aspx?ProjectSearchText=tetris

However, some use pre-built encoded numbers and bit shifting to represent each piece:

http://www.codeplex.com/wintris

Is there a method to do this using mathematics (not sure that would work on a cell based board)?

## Best Solution

There is a limited amount of shapes, so I would use a fixed table and no calculation. That saves time.

But there are rotation algorithms.

Chose a centerpoint and rotate pi/2.

If a block of a piece starts at (1,2) it moves clockwise to (2,-1) and (-1,-2) and (-1, 2). Apply this for each block and the piece is rotated.

Each x is the previous y and each y - the previous x. Which gives the following matrix:

For counterclockwise rotation, use: