Description
Invoke the linked cubic Hermite evaluator through the shared helper with each unit endpoint basis.
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.
Invoke the linked cubic Hermite evaluator through the shared helper with each unit endpoint basis.
When to use this tool
Use Interpolation: Cubic Hermite Four Basis Values 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.
Invoke the linked cubic Hermite evaluator through the shared helper with each unit endpoint basis. Return h00 = 2t³ - 3t² + 1, h10 = t³ - 2t² + t, h01 = -2t³ + 3t², and h11 = t³ - t² for t in [0, 1].1
The linked cubic Hermite calculator is invoked four times through the shared helper, once for each unit endpoint datum, to obtain the basis values.2
| 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.h00 | Weight on the left endpoint value. | Calculated result member: number. |
| result.h10 | Weight on the left normalized tangent. | Calculated result member: number. |
| result.h01 | Weight on the right endpoint value. | Calculated result member: number. |
| result.h11 | Weight on the right normalized tangent. | Calculated result member: number. |
{
"input": {
"t": 0.5
},
"output": {
"result": {
"h00": 0.5,
"h10": 0.125,
"h01": 0.5,
"h11": -0.125
}
}
}Limitations and assumptions
- The tangent basis multiplies derivatives with respect to the normalized parameter; physical-coordinate slopes need interval scaling.
- 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 Basis Derivative
For t in [0, 1], return the four parameter derivatives: 6t² - 6t, 3t² - 4t + 1, -6t² + 6t, and 3t² - 2t.
- Cubic Hermite Endpoint Tangent Units
Multiply slope by positive span for normalizedTangent.