Description
Validate controlIndex from zero through degree.
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 controlIndex from zero through degree.
When to use this tool
Use Spline Control Point Endpoint Weight when you need one Bernstein or control-point weight.
How to use the tool and how it works
- Enter degree, atEnd, controlIndex. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read weight. Use the output convention below.
Validate controlIndex from zero through degree. Return weight one only for the first control at the start or final control at the end; other controls get zero.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| degree | Nonnegative polynomial degree, with the implemented upper limit. | Required. Safe integer; minimum 0; maximum 255. |
| atEnd | At End | Required. Boolean. |
| controlIndex | Control Index | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| weight | Weight | Required. Safe integer. |
{
"input": {
"degree": 3,
"atEnd": true,
"controlIndex": 3
},
"output": {
"weight": 1
}
}Limitations and assumptions
- This is an endpoint Bernstein-weight identity, not a general spline evaluator or arbitrary knot-vector endpoint rule.
- 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
- Interpolation: Bernstein Basis Single Index
Validate degree 0-64, index within degree, and t in [0, 1].
- 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.