Description
Return distance to a closed axis-aligned slab.
Distances between intervals and bounds on metric distances describe geometric separation under declared assumptions. Touching intervals have zero gap; triangle bounds require distances that share a common endpoint in an actual metric.
Return distance to a closed axis-aligned slab.
When to use this tool
Use Distance: Point To Axis Aligned Slab Gap when checking a supplied interval gap or metric distance bound.
How to use the tool and how it works
- Enter coordinate, lower, upper. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read result. Expand result to inspect the returned fields.
Return distance to a closed axis-aligned slab. Require lower <= upper; gap = max(lower-coordinate,0,coordinate-upper), and insideInclusive includes both endpoints.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| coordinate | Coordinate | Required. Finite number. |
| lower | Lower | Required. Finite number. |
| upper | Upper | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Returned object; expand its named members below. | Required. Object. |
| result.gap | Gap | Calculated result member: number. |
| result.insideInclusive | Inside Inclusive | Calculated result member: boolean. |
{
"input": {
"coordinate": 7,
"lower": 2,
"upper": 5
},
"output": {
"result": {
"gap": 2,
"insideInclusive": false
}
}
}Limitations and assumptions
- This is one coordinate axis, without a full multi-axis region calculation.
- Outputs are nested inside result. Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use the full point or set geometry and a suitable metric when you need an actual distance rather than a bound or local term.
References
Similar or alternative tools
- Distance: Point To Open Interval Distance
Return distance infimum to an open interval and whether it is attained.
- Distance Interval Absolute Value Envelope
Map a real interval through absolute value.