Board Hex Axial Cube Converter
Convert integer axial hex coordinates q,r to cube x=q,z=r,y=-q-r, preserving the zero-sum invariant.
Description
Convert integer axial hex coordinates q,r to cube x=q,z=r,y=-q-r, preserving the zero-sum invariant.
Axial coordinates can reconstruct cube coordinates once the axis convention is fixed.
When to use this tool
Convert integer axial hex coordinates q,r to cube x=q,z=r,y=-q-r, preserving the zero-sum invariant.
- Prepare the supplied q, r 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 q, r. 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.z. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.
Require q and r as bounded integers. Return x=q, z=r and y=-q-r.1
| Input field | Meaning and representation | Accepted input |
|---|---|---|
| q | q. | Integer from -1e9 to 1e9 inclusive |
| r | r. | 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.z | The z value under the stated formula or text convention. |
{
"input": {
"q": 2,
"r": -1
},
"output": {
"result": {
"x": 2,
"y": -1,
"z": -1
}
}
}Limitations and assumptions
- No board extent or pixel coordinate mapping is applied. The derived y can exceed the per-input axis bound even though inputs are valid.
- 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 Hex Cube Axial Converter
Convert validated zero-sum integer hex cube coordinates to axial q=x,r=z; invalid cube coordinates are rejected.
- Board Hex Axial Neighborhood
Enumerate six infinite axial hex-grid neighbors in a fixed direction order; no board clipping or geographic coordinates.