Description
Validate node and basis indices within count 1-256.
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.
Validate node and basis indices within count 1-256.
When to use this tool
Use Impulse Basis Node Exactvalue Label when you need one polynomial basis weight or residual.
How to use the tool and how it works
- Enter node, basis, count. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read value. Use the output convention below.
Validate node and basis indices within count 1-256. Return one when they coincide and zero otherwise.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| node | Node | Required. Safe integer; minimum 0. |
| basis | Basis | Required. Safe integer; minimum 0. |
| count | Count | Required. Safe integer; minimum 1; maximum 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| value | Value | Required. Safe integer. |
{
"input": {
"node": 2,
"basis": 2,
"count": 4
},
"output": {
"value": 1
}
}Limitations and assumptions
- This is the cardinal-basis value at an exact node, not an interpolant at an arbitrary coordinate.
- 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
- Interpolation: Quadratic Lagrange Basis At Point
Multiply (x - otherNode) / (selectedNode - otherNode) across the two other nodes for basisValue.
- Spline Control Point Endpoint Weight
Validate controlIndex from zero through degree.