Description
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.
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.
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.
When to use this tool
Use Cubic Bezier Control Point Sensitivity when you need one Bernstein or control-point weight.
How to use the tool and how it works
- Enter parameter, control. 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.
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 0-3.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| parameter | Normalized interpolation coordinate under the stated domain; may permit extrapolation. | Required. Finite number; minimum 0; maximum 1. |
| control | Control | Required. Safe integer; minimum 0; maximum 3. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| weight | Weight | Required. Finite number. |
{
"input": {
"parameter": 0.5,
"control": 1
},
"output": {
"weight": 0.375
}
}Limitations and assumptions
- This is one control-point sensitivity, not a complete curve, tangent, or control-point fit.
- 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].
- Spline Control Point Endpoint Weight
Validate controlIndex from zero through degree.