Description
Return 8 × sagitta/(chord²+4 × sagitta²) and its derivative with respect to sagitta.
Circle calculations distinguish radius, diameter, chord, sagitta, tangent, and oriented offsets. Branch choices determine signs and which arc or segment is meant; a scalar identity does not always establish an actual geometric construction.
Return 8 × sagitta/(chord²+4 × sagitta²) and its derivative with respect to sagitta.
When to use this tool
Use Chord Sagitta Curvature Sensitivity when you need a local circle identity with explicit radius and branch conventions.
How to use the tool and how it works
- Enter chord, sagitta. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read curvature, sagittaDerivative. Use the output convention below.
Require positive chord and nonnegative sagitta. Return 8 × sagitta/(chord²+4 × sagitta²) and its derivative with respect to sagitta.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| chord | Chord | Required. Finite number; strictly above 0. |
| sagitta | Sagitta | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| curvature | Curvature | Required. Finite number. |
| sagittaDerivative | Sagitta Derivative | Required. Finite number. |
{
"input": {
"chord": 2,
"sagitta": 1
},
"output": {
"curvature": 1,
"sagittaDerivative": 0
}
}Limitations and assumptions
- Chord and sagitta share units, giving inverse-length curvature and inverse-squared-length sensitivity; zero sagitta is accepted and no measurement quality or chosen circular-segment branch is validated.
- 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
Construct the circles, chord, or segment in coordinates when existence or orientation matters. Use the complete geometry and an appropriate tolerance for intersection or tangency decisions.
References
Similar or alternative tools
- Chord Sagitta Residual
Compute the minor sagitta using its rationalized expression and return measuredSagitta minus expectedSagitta.
- Chord Apothem Sign Branch
Compute sqrt(radius²-(chord/2)²) using scaled alternatives where needed and apply the positiveBranch sign.