Description
Use their ratio to compute center-to-focus distance and return suppliedFocusDistance minus the derived value.
A conic curve has parameters tied to a chosen axis system and parameterization. Parametric angle, polar angle, focus distance, tangent, and normal describe different relationships and cannot be interchanged without their definitions.
Use their ratio to compute center-to-focus distance and return suppliedFocusDistance minus the derived value.
When to use this tool
Use Ellipse Focal Distance Residual when you need a local conic-curve parameter or derivative calculation.
How to use the tool and how it works
- Enter semimajor, semiminor, suppliedFocusDistance. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read derivedFocusDistance, residual. Use the output convention below.
Require semimajor at least nonnegative semiminor. Use their ratio to compute center-to-focus distance and return suppliedFocusDistance minus the derived value.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| semimajor | Semimajor | Required. Finite number. |
| semiminor | Semiminor | Required. Finite number; minimum 0. |
| suppliedFocusDistance | Supplied Focus Distance | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| derivedFocusDistance | Derived Focus Distance | Required. Finite number. |
| residual | Residual | Required. Finite number. |
{
"input": {
"semimajor": 5,
"semiminor": 3,
"suppliedFocusDistance": 5
},
"output": {
"derivedFocusDistance": 4,
"residual": 1
}
}Limitations and assumptions
- Zero axes and flattened degenerate ellipses are accepted; all lengths share units and no actual ellipse, measurement tolerance, or focus-to-focus conversion is inferred.
- 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 the full conic equation and coordinate transform for rotated or translated curves. Check semiaxis ordering, parameter units, and degeneracy before interpreting a local tangent or focus identity.
References
Similar or alternative tools
- Ellipse Eccentric Angle Focal Distance
Compute c=sqrt(a²-b²) and return a-c cos(parameter) and a+c cos(parameter).
- Ellipse Focal Radius Derivative
Return sqrt(a²-b²), mark derivativeDefined only when a>b, and return a/c or -b/c accordingly, otherwise derivative zero.