Description
Validate degree 0-64, index within degree, and t in [0, 1].
Bernstein basis weights describe how Bézier control points contribute to a curve at a normalized parameter. Endpoint weights and interior sensitivities are different evaluations of the same basis.
Validate degree 0-64, index within degree, and t in [0, 1].
When to use this tool
Use Interpolation: Bernstein Basis Single Index when you need one Bernstein or control-point weight.
How to use the tool and how it works
- Enter degree, index, 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.
Validate degree 0-64, index within degree, and t in [0, 1]. Form the exact integer binomial coefficient before numeric conversion and multiply by t^index × (1-t)^(degree-index).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| degree | Nonnegative polynomial degree, with the implemented upper limit. | Required. Safe integer. |
| index | Zero-based position or diagnostic index under the calculation above; inspect any sentinel policy. | Required. Safe integer. |
| t | Normalized interpolation coordinate under the stated domain. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Result | Required. Object. |
| result.basisValue | Basis Value | Calculated result member: number. |
{
"input": {
"degree": 3,
"index": 1,
"t": 0.5
},
"output": {
"result": {
"basisValue": 0.375
}
}
}Limitations and assumptions
- The weight is floating point even though the coefficient is formed exactly; no curve values or error bound are calculated.
- 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
Use all basis weights and aligned control coordinates to evaluate a complete curve or its derivatives.
References
Similar or alternative tools
- Cubic Bezier Control Point Sensitivity
For parameter t in [0, 1], choose the cubic Bernstein weight (1-t)³, 3(1-t)²t, 3(1-t)t², or t³ for control 0-3.
- Spline Control Point Endpoint Weight
Validate controlIndex from zero through degree.