Description
Return Euclidean point-to-focus distance minus absolute line-expression value divided by the normal length.
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.
Return Euclidean point-to-focus distance minus absolute line-expression value divided by the normal length.
When to use this tool
Use Parabola Focus Directrix Distance Residual when you need a local conic-curve parameter or derivative calculation.
How to use the tool and how it works
- Enter point, focus, line. Keep parallel arrays aligned. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read residual. Use the output convention below.
Require two-dimensional point and focus and three directrix coefficients with nonzero normal. Return Euclidean point-to-focus distance minus absolute line-expression value divided by the normal length.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| point | Point | Required. Array of finite number; maximum items 256. |
| focus | Focus | Required. Array of finite number; maximum items 256. |
| line | Line | Required. Array of finite number; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| residual | Residual | Required. Finite number. |
{
"input": {
"point": [
0,
0
],
"focus": [
0,
1
],
"line": [
0,
1,
1
]
},
"output": {
"residual": 0
}
}Limitations and assumptions
- The directrix is a·x+b·y+c=0 and lengths share units; zero residual is an exact algebraic check without a geometric tolerance, curve fit, or validation of an entire parabola.
- 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 Focal Distance Residual
Use their ratio to compute center-to-focus distance and return suppliedFocusDistance minus the derived value.
- Geometry: Ellipse Focus Directrix Gap
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.