Description
Check a necessary metric-ball separation bound.
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.
Check a necessary metric-ball separation bound.
When to use this tool
Use Metric Ball Diameter Bound when checking a supplied interval gap or metric distance bound.
How to use the tool and how it works
- Enter radius, measuredSeparation. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read upperBound, compatible. Inspect compatible before interpreting the associated values.
Check a necessary metric-ball separation bound. Require nonnegative radius and measuredSeparation; upperBound = 2*radius and compatible uses separation <= upperBound.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| radius | Radius | Required. Finite number; minimum 0. |
| measuredSeparation | Measured Separation | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| upperBound | Upper Bound | Required. Finite number. |
| compatible | Compatible | Required. Boolean. |
{
"input": {
"radius": 3,
"measuredSeparation": 5
},
"output": {
"upperBound": 6,
"compatible": true
}
}Limitations and assumptions
- Passing this necessary bound does not locate points or establish ball membership.
- 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: Coordinate Uncertainty Gap Lower Bound
Return minimum possible gap between two bounded coordinate intervals.
- Measured Distance Triangle Slack
Return the smallest triangle-inequality slack for three distances.