Description
For positive span, return -span × (2 × leftSecond + rightSecond) / 6 and span × (leftSecond + 2 × rightSecond) / 6 as endpoint slope contributions.
A spline joins polynomial pieces under continuity and endpoint conditions. A local slope or curvature contribution is only part of the system needed to define the complete spline.
For positive span, return -span × (2 × leftSecond + rightSecond) / 6 and span × (leftSecond + 2 × rightSecond) / 6 as endpoint slope contributions.
When to use this tool
Use Spline Endpoint Clamped Weight Pair when you need a supplied spline endpoint component.
How to use the tool and how it works
- Enter leftSecond, rightSecond, span. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read leftSlopeContribution, rightSlopeContribution. Use the output convention below.
For positive span, return -span × (2 × leftSecond + rightSecond) / 6 and span × (leftSecond + 2 × rightSecond) / 6 as endpoint slope contributions.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| leftSecond | Left Second | Required. Finite number. |
| rightSecond | Right Second | 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 |
|---|---|---|
| leftSlopeContribution | Left Slope Contribution | Required. Finite number. |
| rightSlopeContribution | Right Slope Contribution | Required. Finite number. |
{
"input": {
"leftSecond": 3,
"rightSecond": 6,
"span": 2
},
"output": {
"leftSlopeContribution": -4,
"rightSlopeContribution": 5
}
}Limitations and assumptions
- Second derivatives must refer to the same interval coordinate; these are corrections to secant slopes, not complete endpoint slopes or solved boundary conditions.
- 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 a complete spline solver with explicit boundary conditions to construct and validate the curve.
References
Similar or alternative tools
- Cubic Hermite Endpoint Curvature Term
At the right endpoint use [6(left - right) + span(2leftSlope + 4rightSlope)]/span²; at the left use [6(right - left) - span(4leftSlope + 2rightSlope)]/span².
- Hermite Endpoint Slope Residual
Select the requested endpoint tangent and divide by x1 - x0 only when tangentsAreParameterDerivatives; subtract suppliedSlope for residual.