Description
Return curvature × span² / 8 for interpolantMinusFunction with positive span.
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 curvature × span² / 8 for interpolantMinusFunction with positive span.
When to use this tool
Use Quadratic Midpoint Error From Curvature when you need one explicit interpolation error or amplification component.
How to use the tool and how it works
- Enter curvature, span. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read interpolantMinusFunction. Use the output convention below.
Return curvature × span² / 8 for interpolantMinusFunction with positive span.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| curvature | Supplied second derivative in value per squared-coordinate units. | Required. Finite number. |
| span | Coordinate interval width; its unit must match the derivative convention. | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| interpolantMinusFunction | Signed midpoint linear-interpolation error in value units under the supplied curvature model. | Required. Finite number. |
{
"input": {
"curvature": 2,
"span": 4
},
"output": {
"interpolantMinusFunction": 4
}
}Limitations and assumptions
- The sign is linear-interpolant minus function at the midpoint for the supplied curvature convention; arbitrary-function error needs a valid curvature model or bound.
- 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.
- Linear Interpolant Midpoint Symmetry Gap
Average left and right using half terms for expectedMidpoint and return observedMidpoint minus that average as gap.