Description
At the right endpoint use [6(left - right) + span(2leftSlope + 4rightSlope)]/span²; at the left use [6(right - left) - span(4leftSlope + 2rightSlope)]/span².
Cubic Hermite interpolation combines endpoint values with endpoint tangents. A slope per physical coordinate becomes a normalized-parameter tangent after multiplication by the interval span.
At the right endpoint use [6(left - right) + span(2leftSlope + 4rightSlope)]/span²; at the left use [6(right - left) - span(4leftSlope + 2rightSlope)]/span².
When to use this tool
Use Cubic Hermite Endpoint Curvature Term when you need one Hermite basis, derivative, or endpoint-unit calculation.
How to use the tool and how it works
- Enter left, right, leftSlope, rightSlope, span, atRight. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read curvature. Use the output convention below.
Require positive span. At the right endpoint use [6(left - right) + span(2leftSlope + 4rightSlope)]/span²; at the left use [6(right - left) - span(4leftSlope + 2rightSlope)]/span².1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| left | Left | Required. Finite number. |
| right | Right | Required. Finite number. |
| leftSlope | Left Slope | Required. Finite number. |
| rightSlope | Right Slope | Required. Finite number. |
| span | Coordinate interval width; its unit must match the derivative convention. | Required. Finite number; strictly above 0. |
| atRight | At Right | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| curvature | Curvature | Required. Finite number. |
{
"input": {
"left": 0,
"right": 1,
"leftSlope": 0,
"rightSlope": 0,
"span": 1,
"atRight": false
},
"output": {
"curvature": 6
}
}Limitations and assumptions
- This returns the second derivative with respect to the original coordinate; endpoint slopes must use that same coordinate rather than normalized tangents.
- 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
Track the derivative coordinate explicitly and evaluate the complete endpoint data on a validated interval.
References
Similar or alternative tools
- Hermite Endpoint Slope Residual
Select the requested endpoint tangent and divide by x1 - x0 only when tangentsAreParameterDerivatives; subtract suppliedSlope for residual.
- Interpolation: Cubic Hermite Basis Derivative
For t in [0, 1], return the four parameter derivatives: 6t² - 6t, 3t² - 4t + 1, -6t² + 6t, and 3t² - 2t.