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Distance: Coordinate Uncertainty Gap Lower Bound Tool

Compute sharp one-axis separation lower bound for two explicit closed uncertainty intervals; no probability distribution or coverage claim.

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Description

Return minimum possible gap between two bounded coordinate intervals.

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 minimum possible gap between two bounded coordinate intervals.

When to use this tool

Use Distance: Coordinate Uncertainty Gap Lower Bound when checking a supplied interval gap or metric distance bound.

How to use the tool and how it works

  1. Enter firstCenter, firstHalfwidth, secondCenter, secondHalfwidth. Use the units and conventions below.
  2. Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
  3. Read result. Expand result to inspect the returned fields.

Return minimum possible gap between two bounded coordinate intervals. Require nonnegative halfwidths; minimumPossibleGap = max(0,abs(center1-center2)-halfwidth1-halfwidth2), and intervalsOverlap includes touching.1

Input fieldMeaning and unitsAccepted input
firstCenterFirst CenterRequired. Finite number.
firstHalfwidthFirst HalfwidthRequired. Finite number.
secondCenterSecond CenterRequired. Finite number.
secondHalfwidthSecond HalfwidthRequired. Finite number.
Output fieldInterpretationReturned shape
resultReturned object; expand its named members below.Required. Object.
result.minimumPossibleGapMinimum Possible GapCalculated result member: number.
result.intervalsOverlapIntervals OverlapCalculated result member: boolean.
json
{
  "input": {
    "firstCenter": 0,
    "firstHalfwidth": 1,
    "secondCenter": 5,
    "secondHalfwidth": 2
  },
  "output": {
    "result": {
      "minimumPossibleGap": 2,
      "intervalsOverlap": false
    }
  }
}

Limitations and assumptions

  • Halfwidths are supplied bounds, not inferred measurement errors or confidence levels.
  • 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

  1. Calculation and input contract: distance/coordinate-uncertainty-gap-lower-bound — tool.io

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