Description
Rotate integer hex cube coordinates by signed multiples of sixty degrees via [x,y,z] -> [-z,-x,-y]; not a Cartesian pixel rotation.
Hexagonal grids can use axial, three-component cube or parity-based offset coordinates. Cube coordinates satisfy x + y + z = 0; axial coordinates use two components. Pixel layouts additionally need orientation, origin and center-to-corner size, which are separate from the integer coordinate convention.
Rotate integer hex cube coordinates by signed multiples of sixty degrees via [x,y,z] -> [-z,-x,-y]; not a Cartesian pixel rotation.
When to use this tool
Use this tool to rotate integer hex cube coordinates by signed multiples of sixty degrees via [x,y,z] -> [-z,-x,-y]; not a Cartesian pixel rotation.
How to use the tool and how it works
- Enter cube, turns using the field definitions below.
- Run the operation. Correct input errors before interpreting an output.
- Read result.cube. Use the ordering, boundary rules and absence conditions described below.
Require integer cube coordinates summing to zero and apply [x,y,z] → [−z,−x,−y] turns modulo six times.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| cube | Three cube components [x, y, z] summing to zero; fractional values are accepted only by the rounding operation. | Dense list of at most 128 finite numbers; integer/shape constraints above also apply. |
| turns | Signed integer count of the explicit sixty-degree cube mapping. | A finite safe integer within the operation’s stated bounds. |
| Output field | Interpretation |
|---|---|
| result | Object containing the named fields below. |
| result.cube | Resulting [x, y, z] cube coordinate with zero component sum. |
{
"input": {
"cube": [
1,
-1,
0
],
"turns": 1
},
"output": {
"result": {
"cube": [
0,
-1,
1
]
}
}
}Limitations and assumptions
- Turns are signed counts of this explicit sixty-degree mapping; clockwise interpretation depends on the drawing convention.
- Integer layout coordinates are bounded to ±1,000,000,000 where required. Cube components must sum to zero within 1e−8. Pixel coordinates, origin and size must use the same distance units; angular calculations use radians internally.
- Every declared top-level input field is required and unexpected fields are rejected. Ordinary strings are limited to 8,192 UTF-16 code units and lists to 128 entries, with tighter operation-specific bounds where stated. JSON text has bounded nesting and node counts.
- Numeric outputs must be finite and no larger in absolute magnitude than the safe-integer limit; operations returning exact large integers use decimal text. Positions are zero-based and spans end exclusively unless the operation explicitly states a different convention.
Alternative or Complementary methods
Keep coordinate layout, parity convention and drawing orientation consistent. Use an explicit rounding operation to choose an integer cell from fractional coordinates and a separate pathfinding model for obstacles or routes.
References
Similar or alternative tools
- Hex Cube Axis Reflection
Reflect integer hex cube coordinates across a named cube axis by swapping the other two components; preserves zero-sum coordinates.
- Hex Fractional Cube Rounding
Round zero-sum fractional hex cube coordinates and repair the largest rounding-error component to preserve zero sum; ties repair z then y under the documented strict comparisons.