Description
Compute c=sqrt(a²-b²), e=c/a, point distance to focus (+c, 0), distance to directrix x=a/e, and focus distance minus e times directrix distance inside result.
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.
Compute c=sqrt(a²-b²), e=c/a, point distance to focus (+c, 0), distance to directrix x=a/e, and focus distance minus e times directrix distance inside result.
When to use this tool
Use Geometry: Ellipse Focus Directrix Gap when you need a local conic-curve parameter or derivative calculation.
How to use the tool and how it works
- Enter semiMajor, semiMinor, point. 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 a two-dimensional point and positive semiMinor strictly below semiMajor. Compute c=sqrt(a²-b²), e=c/a, point distance to focus (+c, 0), distance to directrix x=a/e, and focus distance minus e times directrix distance inside result.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| semiMajor | Semi Major | Required. Finite number. |
| semiMinor | Semi Minor | Required. Finite number. |
| point | Point | Required. Array of finite number. Implementation limit: 128 items. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Object containing the calculated members; expand to inspect the fields below. | Required. Object. |
| result.focusDistance | Focus Distance | Calculated result member: number. |
| result.directrixDistance | Directrix Distance | Calculated result member: number. |
| result.eccentricity | Eccentricity | Calculated result member: number. |
| result.residual | Residual | Calculated result member: number. |
{
"input": {
"semiMajor": 5,
"semiMinor": 3,
"point": [
5,
0
]
},
"output": {
"result": {
"focusDistance": 1,
"directrixDistance": 1.25,
"eccentricity": 0.8,
"residual": 0
}
}
}Limitations and assumptions
- This assumes an origin-centered x-major ellipse and excludes a circle; residual is not clamped or checked against a tolerance and the supplied point need not lie on the ellipse.
- 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 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
- Parabola Focus Directrix Distance Residual
Return Euclidean point-to-focus distance minus absolute line-expression value divided by the normal length.
- Ellipse Eccentric Angle Focal Distance
Compute c=sqrt(a²-b²) and return a-c cos(parameter) and a+c cos(parameter).