Half Open Interval Overlap Length
Compute Lebesgue overlap length of half-open finite intervals; touching and empty intervals have zero length.
Description
Compute Lebesgue overlap length of half-open finite intervals; touching and empty intervals have zero length.
Half-open spans include their start and exclude their end, a common convention for array slices and duration ranges. Their continuous overlap length is unaffected by isolated endpoint contact.
When to use this tool
Compute Lebesgue overlap length of half-open finite intervals; touching and empty intervals have zero length.
- Prepare the supplied aStart, aEnd, bStart, bEnd fields for this operation.
- Compare the complete example with the representation used by your own input before carrying the result into another step.
How to use the tool and how it works
- Enter aStart, aEnd, bStart, bEnd. Use the exact text syntax, units and index conventions explained below.
- Run the tool. If input validation fails, correct the supplied fields before interpreting any result.
- Read result.overlapLength. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.
Require ordered bounds and compute max(0,min(endA,endB)-max(startA,startB)). Allow zero-length inputs.1
| Input field | Meaning and representation | Accepted input |
|---|---|---|
| aStart | a start. | Finite number |
| aEnd | a end. | Finite number |
| bStart | b start. | Finite number |
| bEnd | b end. | Finite number |
| Output field | Interpretation |
|---|---|
| result | Object containing the named outputs below. |
| result.overlapLength | The overlap length value under the stated formula or text convention. |
{
"input": {
"aStart": 0,
"aEnd": 2,
"bStart": 1,
"bEnd": 3
},
"output": {
"result": {
"overlapLength": 1
}
}
}Limitations and assumptions
- Touching spans and empty spans both yield zero. The result is continuous length in the input unit, not the number of included integer indexes.
- Interval-array rows contain exactly two finite endpoints in start/end order, with at most 128 intervals per collection. Individual operations state when positive length, integer endpoints or explicit inclusion flags are required.
- Every declared top-level field is required and unexpected fields are rejected. Numeric inputs must be finite; ordinary text fields are bounded to 8,192 UTF-16 code units, with tighter operation-specific limits where stated.
- Ordinary string lists have at most 128 entries of at most 128 code units each; numeric lists and matrices have separate bounded size checks. Nonfinite results and excessively large serialized outputs are rejected.
- Indexes are zero-based and spans have an exclusive end unless explicitly stated otherwise. A valid false, null or empty-list result is distinct from malformed input.
Alternative or Complementary methods
Retain the endpoint convention with every result. Continuous length, integer point counts and open/closed membership differ; merge returned cells separately when a canonical minimal interval collection is required.
References
Similar or alternative tools
- Half Open Interval Distance
Compute infimum distance between nonempty half-open intervals and distinguish zero-distance touching from attained overlap.
- Closed Integer Interval Overlap Count
Count shared integers in closed integer endpoint intervals, including one-point contact.