Description
Return distance infimum to an open interval and whether it is attained.
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 infimum to an open interval and whether it is attained.
When to use this tool
Use Distance: Point To Open Interval Distance when checking a supplied interval gap or metric distance bound.
How to use the tool and how it works
- Enter point, 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 infimum to an open interval and whether it is attained. Require lower < upper; infimumDistance = max(lower-point,0,point-upper); attained requires point strictly inside.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| point | Point | 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.infimumDistance | Infimum Distance | Calculated result member: number. |
| result.attained | True only strictly inside the open interval; false at excluded endpoints even when distance is zero. | Calculated result member: boolean. |
{
"input": {
"point": 0,
"lower": 0,
"upper": 2
},
"output": {
"result": {
"infimumDistance": 0,
"attained": false
}
}
}Limitations and assumptions
- An excluded endpoint has zero infimum but attained = false.
- 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 Axis Aligned Slab Gap
Return distance to a closed axis-aligned slab.
- Distance Interval Absolute Value Envelope
Map a real interval through absolute value.