Description
Enumerate one axial hex ring in a fixed six-direction walk; radius zero is the center and positive rings are bounded to 126 cells.
Hexagonal grids can store cells as axial [q,r], parity-based offset or doubled coordinates. Those integer layouts describe the same lattice with different row/column conventions. Drawing cell centers also needs an orientation, origin and center-to-corner radius; those drawing units are separate from lattice coordinates.
Enumerate one axial hex ring in a fixed six-direction walk; radius zero is the center and positive rings are bounded to 126 cells.
When to use this tool
Use this tool to enumerate one axial hex ring in a fixed six-direction walk; radius zero is the center and positive rings are bounded to 126 cells.
How to use the tool and how it works
- Enter q, r, radius using the input definitions below.
- Run the operation. Resolve malformed-input errors before interpreting the result.
- Read result.coordinates. Interpret signs, units, ordering and null values using the rules below.
At radius zero return the center alone. Otherwise start at [q−radius,r+radius] and walk radius steps in each direction [1,0], [1,−1], [0,−1], [−1,0], [−1,1], [0,1], recording each position before its step.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| q | Axial q coordinate, integer except for pixel-center mapping. | Finite safe integer satisfying the stated bounds. |
| r | Axial r coordinate, integer except for pixel-center mapping. | Finite safe integer satisfying the stated bounds. |
| radius | Nonnegative integer ring/disk radius in hex-cell steps; its operation-specific upper bound is stated above. | Finite safe integer satisfying the stated bounds. |
| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.coordinates | Ordered axial [q,r] cells in the explicit ring/disk traversal. |
{
"input": {
"q": 0,
"r": 0,
"radius": 1
},
"output": {
"result": {
"coordinates": [
[
-1,
1
],
[
0,
1
],
[
1,
0
],
[
1,
-1
],
[
0,
-1
],
[
-1,
0
]
]
}
}
}Limitations and assumptions
- Radius is an integer 0–21; a positive ring has exactly 6×radius coordinates and does not include its center.
- Integer lattice inputs are bounded to ±1,000,000,000; the pixel-center operation accepts fractional axial values. Ring/disk radius bounds are stated above. No geographic projection, physical scale or board boundary is inferred.
- Every declared top-level input is required and unknown 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 within the absolute safe-integer magnitude; exact larger integers use decimal text. Source positions are zero-based UTF-16 offsets and span ends are exclusive unless a different convention is explicitly stated.
Alternative or Complementary methods
Keep grid layout, parity convention and drawing orientation consistent. Use coordinate conversion for an existing cell and a separate pathfinding model for obstacles or routes.
References
Similar or alternative tools
- Hex Axial Disk Coordinate List
Enumerate axial hex disk cells center-first then increasing fixed-order rings; radius 0–6 yields at most 127 distinct cells.
- Hex Axial Doubled Coordinate Formatter
Convert integer axial hex coordinates to horizontal- or vertical-doubled coordinates, preserving parity-constrained lattice spacing.