Description
Return rightValue - leftValue and rightSlope - leftSlope as valueGap and slopeGap.
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.
Return rightValue - leftValue and rightSlope - leftSlope as valueGap and slopeGap.
When to use this tool
Use Hermite Endpoint Data Continuity Gap when you need one Hermite basis, derivative, or endpoint-unit calculation.
How to use the tool and how it works
- Enter leftValue, rightValue, leftSlope, rightSlope. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read valueGap, slopeGap. Use the output convention below.
Return rightValue - leftValue and rightSlope - leftSlope as valueGap and slopeGap.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| leftValue | Left Value | Required. Finite number. |
| rightValue | Right Value | Required. Finite number. |
| leftSlope | Left Slope | Required. Finite number. |
| rightSlope | Right Slope | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| valueGap | Value Gap | Required. Finite number. |
| slopeGap | Slope Gap | Required. Finite number. |
{
"input": {
"leftValue": 2,
"rightValue": 3,
"leftSlope": 4,
"rightSlope": 6
},
"output": {
"valueGap": 1,
"slopeGap": 2
}
}Limitations and assumptions
- The two sides must refer to the same join and derivative coordinate; no continuity tolerance or curve reconstruction is applied.
- 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.
- 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.