Description
Bound separation of points within two error balls.
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.
Bound separation of points within two error balls.
When to use this tool
Use Distance Error Radius Pair Gap when checking a supplied interval gap or metric distance bound.
How to use the tool and how it works
- Enter centerDistance, firstErrorRadius, secondErrorRadius. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read minimumDistance, maximumDistance, separated. Inspect separated before interpreting the associated values.
Bound separation of points within two error balls. Require nonnegative centerDistance and error radii; minimumDistance = max(0,d-r1-r2), maximumDistance = d+r1+r2, separated uses strict d > r1+r2.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| centerDistance | Center Distance | Required. Finite number; minimum 0. |
| firstErrorRadius | First Error Radius | Required. Finite number; minimum 0. |
| secondErrorRadius | Second Error Radius | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| minimumDistance | Minimum Distance | Required. Finite number. |
| maximumDistance | Maximum Distance | Required. Finite number. |
| separated | Separated | Required. Boolean. |
{
"input": {
"centerDistance": 10,
"firstErrorRadius": 2,
"secondErrorRadius": 3
},
"output": {
"minimumDistance": 5,
"maximumDistance": 15,
"separated": true
}
}Limitations and assumptions
- Touching balls are not strictly separated; the radii are supplied deterministic bounds.
- 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
- Measured Distance Triangle Slack
Return the smallest triangle-inequality slack for three distances.
- Distance: Coordinate Uncertainty Gap Lower Bound
Return minimum possible gap between two bounded coordinate intervals.