Description
At an exact node hit return one for that selected node and zero for others; otherwise normalize selected weight/(x-node) by the sum of all such terms.
Barycentric interpolation expresses a polynomial as a quotient of weighted sums. Standard weights depend on node differences; common nonzero scaling cancels only when applied consistently to the full quotient.
At an exact node hit return one for that selected node and zero for others; otherwise normalize selected weight/(x-node) by the sum of all such terms.
When to use this tool
Use Barycentric Single Node Influence Ratio when you need one barycentric weight, sign, or influence component.
How to use the tool and how it works
- Enter weights, nodes, x, index. Keep parallel arrays aligned. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read influence. Use the output convention below.
Require aligned nonempty weights and distinct nodes. At an exact node hit return one for that selected node and zero for others; otherwise normalize selected weight/(x-node) by the sum of all such terms.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| weights | Weights | Required. Array of finite number; maximum items 256. |
| nodes | Nodes | Required. Array of finite number; maximum items 256. |
| x | X | Required. Finite number. |
| index | Zero-based position or diagnostic index under the calculation above; inspect any sentinel policy. | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| influence | Influence | Required. Finite number. |
{
"input": {
"weights": [
1,
-1
],
"nodes": [
0,
2
],
"x": 1,
"index": 0
},
"output": {
"influence": 0.5
}
}Limitations and assumptions
- Supplied weights need not be valid polynomial weights; a zero normalizing sum is rejected and no values are interpolated.
- 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 a complete barycentric evaluator with exact-node handling and appropriate weight scaling for actual interpolation.
References
Similar or alternative tools
- Quadratic Barycentric Pole Residue
For poleIndex, compute the reciprocal product of its two node differences; return that denominator residue, its product with the node value, and the removable limit.
- Barycentric Node Weight Common Scale Invariance
Require nonzero commonScale, multiply one weight by it, and return invariant true.