Description
minimum = abs(left-right); maximum = left+right.
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.
minimum = abs(left-right); maximum = left+right.
When to use this tool
Use Triangle Reverse Inequality Distance Bound when checking a supplied interval gap or metric distance bound.
How to use the tool and how it works
- Enter left, right. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read minimum, maximum. Use the output convention below.
Require nonnegative left and right distances. minimum = abs(left-right); maximum = left+right.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| left | Left | Required. Finite number. |
| right | Right | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| minimum | Minimum | Required. Finite number. |
| maximum | Maximum | Required. Finite number. |
{
"input": {
"left": 3,
"right": 5
},
"output": {
"minimum": 2,
"maximum": 8
}
}Limitations and assumptions
- These bounds apply to a third metric distance when left and right share a common endpoint. The tool does not validate a metric or construct points attaining the endpoints.
- 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
- Weighted Interval Gap
gap = max(0,firstLower-secondUpper,secondLower-firstUpper); weightedGap = gap*weight.
- Distance: Spherical Arc Chord Ratio
Return arcToChordRatio = angle/(2*sin(angle/2)), using the continuous limit one at zero.