Description
Enumerate six Cartesian regular-hex corners at an explicit center and circumradius; angle zero for flat, thirty degrees for pointy, mathematical positive-y coordinates.
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.
Enumerate six Cartesian regular-hex corners at an explicit center and circumradius; angle zero for flat, thirty degrees for pointy, mathematical positive-y coordinates.
When to use this tool
Use this tool to enumerate six Cartesian regular-hex corners at an explicit center and circumradius; angle zero for flat, thirty degrees for pointy, mathematical positive-y coordinates.
How to use the tool and how it works
- Enter center, size, pointy using the field definitions below.
- Run the operation. Correct input errors before interpreting an output.
- Read result.corners. Use the ordering, boundary rules and absence conditions described below.
For six angles separated by pi/3, starting at pi/6 for pointy or zero for flat-top, add size × [cos(angle), sin(angle)] to center.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| center | Hex center [x, y], in the same units as size. | Dense list of at most 128 finite numbers; integer/shape constraints above also apply. |
| size | Positive center-to-corner radius, not edge-to-edge diameter. | A finite number satisfying the operation’s stated comparisons. |
| pointy | True selects pointy-top formulas; false selects flat-top formulas. | A boolean true or false. |
| Output field | Interpretation |
|---|---|
| result | Object containing the named fields below. |
| result.corners | Six [x, y] corner points in the angular order stated above. |
{
"input": {
"center": [
0,
0
],
"size": 1,
"pointy": false
},
"output": {
"result": {
"corners": [
[
1,
0
],
[
0.5000000000000001,
0.8660254037844386
],
[
-0.4999999999999998,
0.8660254037844387
],
[
-1,
1.2246467991473532e-16
],
[
-0.5000000000000004,
-0.8660254037844384
],
[
0.5000000000000001,
-0.8660254037844386
]
]
}
}
}Limitations and assumptions
- Size is center-to-corner distance in the same units as center; tiny floating-point remnants may appear at nominally zero components.
- 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 Line Coordinate List
Enumerate a bounded shortest hex cube line by linear interpolation and deterministic zero-sum rounding, including both endpoints; no obstacles or tie-randomization.
- Hex Doubled Coordinate Axial Parser
Invert doubled hex coordinates only when column-row parity agrees; odd parity is invalid lattice evidence, not rounded silently.