Description
Return (value - lowerKnot)/span and distance outside either endpoint divided by span, or zero outsideDistance within the interval.
An interpolation weight, geometric extrapolation distance, and mathematical error bound describe different quantities. A curvature-based bound needs assumptions about the underlying function, not just a computed coordinate.
Return (value - lowerKnot)/span and distance outside either endpoint divided by span, or zero outsideDistance within the interval.
When to use this tool
Use Extrapolation Distance In Knot Units when you need one explicit interpolation error or amplification component.
How to use the tool and how it works
- Enter value, lowerKnot, upperKnot. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read signedParameter, outsideDistance. Use the output convention below.
Require lowerKnot < upperKnot. Return (value - lowerKnot)/span and distance outside either endpoint divided by span, or zero outsideDistance within the interval.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| value | Value | Required. Finite number. |
| lowerKnot | Lower Knot | Required. Finite number. |
| upperKnot | Upper Knot | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| signedParameter | Signed Parameter | Required. Finite number. |
| outsideDistance | Outside Distance | Required. Finite number. |
{
"input": {
"value": 7,
"lowerKnot": 1,
"upperKnot": 5
},
"output": {
"signedParameter": 1.5,
"outsideDistance": 0.5
}
}Limitations and assumptions
- The signed parameter is not clamped; outsideDistance is a dimensionless geometric measure, not prediction error.
- 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
Establish valid derivative bounds and compare methods or measurements before claiming a prediction-error guarantee.
References
Similar or alternative tools
- Linear Extrapolation Horizon Amplification
Return leftWeight = 1 - parameter, rightWeight = parameter, and the sum of their absolute values as amplification.
- Interpolant Extrapolated Weight Sign
Mark leftNegative for t > 1, rightNegative for t < 0, and extrapolated outside [0, 1].