Description
Return +1 when the number of nodes to its right is even and -1 when odd.
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.
Return +1 when the number of nodes to its right is even and -1 when odd.
When to use this tool
Use Interpolation: Barycentric Node Weight Sign when you need one barycentric weight, sign, or influence component.
How to use the tool and how it works
- Enter nodes, nodeIndex. 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.
Require nonempty strictly increasing nodes and valid nodeIndex. Return +1 when the number of nodes to its right is even and -1 when odd.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| nodes | Nodes | Required. Array of finite number. Implementation limit: 128 items. |
| nodeIndex | Node Index | Required. Safe integer. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Result | Required. Object. |
| result.weightSign | Weight Sign | Calculated result member: number. |
{
"input": {
"nodes": [
1,
2,
4
],
"nodeIndex": 1
},
"output": {
"result": {
"weightSign": -1
}
}
}Limitations and assumptions
- This is the sign of standard reciprocal-product weights, not an arbitrary scaled set; magnitudes are not computed.
- 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 a complete barycentric evaluator with exact-node handling and appropriate weight scaling for actual interpolation.
References
Similar or alternative tools
- Lagrange Basis Leading Coefficient
Return the reciprocal product of selected-node minus every other node.
- Barycentric Weight Node Deletion Factor
Require node different from deletedNode and multiply weight by node - deletedNode for newWeight.