Description
For t in [0, 1], return the four parameter derivatives: 6t² - 6t, 3t² - 4t + 1, -6t² + 6t, and 3t² - 2t.
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.
For t in [0, 1], return the four parameter derivatives: 6t² - 6t, 3t² - 4t + 1, -6t² + 6t, and 3t² - 2t.
When to use this tool
Use Interpolation: Cubic Hermite Basis Derivative when you need one Hermite basis, derivative, or endpoint-unit calculation.
How to use the tool and how it works
- Enter t. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read result. Expand result to inspect the returned fields.
For t in [0, 1], return the four parameter derivatives: 6t² - 6t, 3t² - 4t + 1, -6t² + 6t, and 3t² - 2t.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| t | Normalized interpolation coordinate under the stated domain. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Result | Required. Object. |
| result.h00Derivative | H00 Derivative | Calculated result member: number. |
| result.h10Derivative | H10 Derivative | Calculated result member: number. |
| result.h01Derivative | H01 Derivative | Calculated result member: number. |
| result.h11Derivative | H11 Derivative | Calculated result member: number. |
{
"input": {
"t": 0.5
},
"output": {
"result": {
"h00Derivative": -1.5,
"h10Derivative": -0.25,
"h01Derivative": 1.5,
"h11Derivative": -0.25
}
}
}Limitations and assumptions
- Derivatives are with respect to normalized t; convert to physical-coordinate derivatives using the interval length.
- Outputs are nested inside result. 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
- Interpolation: Cubic Hermite Four Basis Values
Invoke the linked cubic Hermite evaluator through the shared helper with each unit endpoint basis.
- Cubic Hermite Endpoint Tangent Units
Multiply slope by positive span for normalizedTangent.