Description
Multiply (x - otherNode) / (selectedNode - otherNode) across the two other nodes for basisValue.
Lagrange basis functions equal one at their own node and zero at the other distinct nodes. Their weighted sum interpolates node values, but closely spaced nodes can create numerical sensitivity.
Multiply (x - otherNode) / (selectedNode - otherNode) across the two other nodes for basisValue.
When to use this tool
Use Interpolation: Quadratic Lagrange Basis At Point when you need one polynomial basis weight or residual.
How to use the tool and how it works
- Enter nodes, basisIndex, x. 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 exactly three distinct nodes and a valid basisIndex. Multiply (x - otherNode) / (selectedNode - otherNode) across the two other nodes for basisValue.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| nodes | Nodes | Required. Array of finite number. Implementation limit: 128 items. |
| basisIndex | Basis Index | Required. Safe integer. |
| x | X | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Result | Required. Object. |
| result.basisValue | Basis Value | Calculated result member: number. |
{
"input": {
"nodes": [
0,
1,
2
],
"basisIndex": 1,
"x": 0.5
},
"output": {
"result": {
"basisValue": 0.75
}
}
}Limitations and assumptions
- This evaluates one quadratic basis weight, allowing extrapolation; no y values, fitted curve, or stability estimate are supplied.
- 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 stable full interpolation evaluator and inspect node conditioning before relying on high-order or extrapolated values.
References
Similar or alternative tools
- Quadratic Interpolation One Abscissa Difference
Return ((x - second)/(first - second)) × ((x - third)/(first - third)).
- Quadratic Interpolant One Node Residual
Sum their quadratic Lagrange contributions at x and return observed minus that interpolant.