Description
Multiply (y1 - y0)/(x1 - x0)² by x - x1 for leftSensitivity and by -(x - x0) for rightSensitivity.
Linear interpolation blends endpoint values by a normalized coordinate. Its value weights, inverse slope, and sensitivities to moving nodes answer different questions and use different units.
Multiply (y1 - y0)/(x1 - x0)² by x - x1 for leftSensitivity and by -(x - x0) for rightSensitivity.
When to use this tool
Use Linear Interpolant Node Position Sensitivity when you need one explicitly defined linear interpolation term.
How to use the tool and how it works
- Enter x, x0, x1, y0, y1. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read leftSensitivity, rightSensitivity. Use the output convention below.
Require x0 different from x1. Multiply (y1 - y0)/(x1 - x0)² by x - x1 for leftSensitivity and by -(x - x0) for rightSensitivity.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| x | X | Required. Finite number. |
| x0 | X0 | Required. Finite number. |
| x1 | X1 | Required. Finite number. |
| y0 | Y0 | Required. Finite number. |
| y1 | Y1 | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| leftSensitivity | Left Sensitivity | Required. Finite number. |
| rightSensitivity | Right Sensitivity | Required. Finite number. |
{
"input": {
"x": 1,
"x0": 0,
"x1": 2,
"y0": 0,
"y1": 4
},
"output": {
"leftSensitivity": -1,
"rightSensitivity": -1
}
}Limitations and assumptions
- These derivatives vary node positions while holding x and node values fixed; they are not value weights or a full uncertainty propagation.
- 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
Validate endpoints and units and use a complete evaluator when clamping, extrapolation, or uncertainty propagation is required.
References
Similar or alternative tools
- Linear Interpolant Node Value Sensitivity
Return 1 - t and t as sensitivities to the left and right node values.
- Linear Interpolant Inverse Sensitivity
Return (rightX - leftX)/(rightY - leftY) as derivative of inverse position with respect to value.