Given a hinged tetromino, give it a unique, consistent label independent of location, rotation, and reflection.

Tetrominoes

A tetromino is a connected subset of the square tiling, composed of 4 squares, where connection can only be edge connection.

Here are the 5 tetrominoes:

Hinged tetrominoes

A hinged tetromino is a connected subset of the square tiling, composed of 4 squares, where connection can be edge connection or corner connection.

Here are the 22 hinged tetrominoes:

Equivalence

The following 8 shapes are all considered to be the same hinged tetromino. They are equivalent because any one can be reached from any other by some combination of rotation, reflection, and translation:

All 8 of these rotated and reflected versions must have the same label. Translating, rotating, or reflecting a hinged tetromino must not change its label.

Input

• A 4 by 4 grid containing a hinged tetromino.
• Apart from the 4 squares of the hinged tetromino, all other squares are empty.
• You may take input in any convenient format that does not include full or partial precalculation. For example:
  • A string or sequence of strings.
  • A 1 or 2 dimensional list/array/vector.
  • A sequence of coordinates (even a sequence of X coordinates and a separate sequence of Y coordinates if you wish).
  • A 16 bit variable where each 1 bit represents part of the hinged tetromino and each 0 bit represents part of the background.
  • A variable with more than 16 bits where only 16 of the bits are used would also be acceptable.

Output

• A label for the hinged tetromino.
• The label for each hinged tetromino can be anything you choose, including nothing (no output).
• Each label must be unique (it must not be the label for any other hinged tetromino).
• Each label must be consistent (a given hinged tetromino must always result in the same label, regardless of rotation, reflection, or translation).

Scoring

This is a code golf challenge. Your score is the number of bytes in your code.

Explanations are optional, but I'm more likely to upvote answers that have one.

posted 11 months ago

CC BY-SA 4.0

10mo ago

trichoplax‭

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