Description
Map supplied fractional axial hex coordinates to Cartesian pixel centers for explicit pointy/flat orientation, circumradius and origin; no geographic units.
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.
Map supplied fractional axial hex coordinates to Cartesian pixel centers for explicit pointy/flat orientation, circumradius and origin; no geographic units.
When to use this tool
Use this tool to map supplied fractional axial hex coordinates to Cartesian pixel centers for explicit pointy/flat orientation, circumradius and origin; no geographic units.
How to use the tool and how it works
- Enter q, r, size, pointy, origin using the input definitions below.
- Run the operation. Resolve malformed-input errors before interpreting the result.
- Read result.point. Interpret signs, units, ordering and null values using the rules below.
For pointy tops, x = originX + size×√3×(q+r/2) and y = originY + size×3r/2. For flat tops, x = originX + size×3q/2 and y = originY + size×√3×(r+q/2). Fractional axial coordinates remain fractional positions.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| q | Axial q coordinate, integer except for pixel-center mapping. | Finite number satisfying the stated comparisons. |
| r | Axial r coordinate, integer except for pixel-center mapping. | Finite number satisfying the stated comparisons. |
| size | Positive center-to-corner hex radius, in the same units as origin and output. | Finite number satisfying the stated comparisons. |
| pointy | True selects pointy tops; false selects flat tops. | Boolean true or false. |
| origin | Cartesian [x,y] origin in output coordinate units. | Dense list of at most 128 finite numbers, subject to the stated integer/shape rules. |
| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.point | Cartesian [x,y] center in the size/origin units. |
{
"input": {
"q": 0,
"r": 0,
"size": 2,
"pointy": true,
"origin": [
3,
4
]
},
"output": {
"result": {
"point": [
3,
4
]
}
}
}Limitations and assumptions
- size is a positive center-to-corner radius in the same units as origin and output; this operation does not round to a cell.
- 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 Direction Step Record
Advance axial hex coordinates by an explicit signed count along one of six documented direction vectors; no board-boundary or path legality model.
- 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.