Description
Select the requested endpoint tangent and divide by x1 - x0 only when tangentsAreParameterDerivatives; subtract suppliedSlope for residual.
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.
Select the requested endpoint tangent and divide by x1 - x0 only when tangentsAreParameterDerivatives; subtract suppliedSlope for residual.
When to use this tool
Use Hermite Endpoint Slope Residual when you need one Hermite basis, derivative, or endpoint-unit calculation.
How to use the tool and how it works
- Enter x0, x1, y0, y1, leftTangent, rightTangent, tangentsAreParameterDerivatives, rightEndpoint, suppliedSlope. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read segmentSlope, residual. Use the output convention below.
Require distinct x endpoints. Select the requested endpoint tangent and divide by x1 - x0 only when tangentsAreParameterDerivatives; subtract suppliedSlope for residual.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| x0 | X0 | Required. Finite number. |
| x1 | X1 | Required. Finite number. |
| y0 | Y0 | Required. Finite number. |
| y1 | Y1 | Required. Finite number. |
| leftTangent | Left Tangent | Required. Finite number. |
| rightTangent | Right Tangent | Required. Finite number. |
| tangentsAreParameterDerivatives | If true, divide the selected tangent by x1-x0 to obtain a physical-coordinate slope. | Required. Boolean. |
| rightEndpoint | Right Endpoint | Required. Boolean. |
| suppliedSlope | Supplied Slope | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| segmentSlope | Segment Slope | Required. Finite number. |
| residual | Signed residual using the convention in the calculation paragraph. | Required. Finite number. |
{
"input": {
"x0": 0,
"x1": 2,
"y0": 1,
"y1": 5,
"leftTangent": 4,
"rightTangent": 8,
"tangentsAreParameterDerivatives": true,
"rightEndpoint": true,
"suppliedSlope": 3
},
"output": {
"segmentSlope": 4,
"residual": 1
}
}Limitations and assumptions
- The tangent convention is explicit; the secant is checked for finite arithmetic but does not replace the endpoint tangent.
- 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 Data Continuity Gap
Return rightValue - leftValue and rightSlope - leftSlope as valueGap and slopeGap.
- Cubic Hermite Endpoint Tangent Units
Multiply slope by positive span for normalizedTangent.