Board Coordinate Quarter Turn
Apply signed clockwise quarter turns to zero-based board coordinates, retaining swapped rectangular dimensions; positive y points downward.
Description
Apply signed clockwise quarter turns to zero-based board coordinates, retaining swapped rectangular dimensions; positive y points downward.
Quarter-turning a rectangular grid rotates coordinates and swaps its dimensions for odd turns.
When to use this tool
Apply signed clockwise quarter turns to zero-based board coordinates, retaining swapped rectangular dimensions; positive y points downward.
- Prepare the supplied x, y, width, height, turns fields for this operation.
- Compare the complete example with the representation used by your own input before carrying the result into another step.
How to use the tool and how it works
- Enter x, y, width, height, turns. Use the exact text syntax, units and index conventions explained below.
- Run the tool. If input validation fails, correct the supplied fields before interpreting any result.
- Read result.x, result.y, result.width, result.height. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.
Validate the cell and dimensions, normalize signed turns modulo four and repeatedly map (x,y) to (height-1-y,x), swapping width and height each step. Return coordinate and resulting dimensions.1
| Input field | Meaning and representation | Accepted input |
|---|---|---|
| x | x. | Integer from 0 to width - 1 inclusive |
| y | y. | Integer from 0 to height - 1 inclusive |
| width | width. | Integer from 1 to 1e6 inclusive |
| height | height. | Integer from 1 to 1e6 inclusive |
| turns | turns. | Integer from -1e9 to 1e9 inclusive |
| Output field | Interpretation |
|---|---|
| result | Object containing the named outputs below. |
| result.x | The x value under the stated formula or text convention. |
| result.y | The y value under the stated formula or text convention. |
| result.width | The width value under the stated formula or text convention. |
| result.height | The height value under the stated formula or text convention. |
{
"input": {
"x": 1,
"y": 2,
"width": 5,
"height": 4,
"turns": 1
},
"output": {
"result": {
"x": 1,
"y": 1,
"width": 4,
"height": 5
}
}
}Limitations and assumptions
- This formula is clockwise in an x-right/y-down display convention. No board content is moved or game state interpreted.
- Every declared top-level field is required and unexpected fields are rejected. Numeric inputs must be finite; ordinary text fields are bounded to 8,192 UTF-16 code units, with tighter operation-specific limits where stated.
- Lists are limited to 128 entries. JSON text must meet bounded size and depth checks, and numeric outputs beyond the safe finite magnitude are rejected. Exact large integers use decimal strings.
- Indexes are zero-based and spans have an exclusive end unless explicitly stated otherwise. A valid false, null or empty-list result is distinct from malformed input.
Alternative or Complementary methods
Use a game-state-aware rules engine when occupancy, legal moves or scoring rules matter. These operations calculate coordinates, local geometry or supplied ledger totals without inferring a complete position.
References
Similar or alternative tools
- Board Coordinate Mirror Tool
Mirror zero-based rectangular board cell coordinates across explicitly selected board centerlines; no piece-state transformation.
- Board Captured Piece Ledger
Aggregate explicit captured-piece events by side and piece name; no inferred moves, scoring or game legality.