Description
Return tangent [2 × scale × parameter, 2 × scale] and a perpendicular normal [-2 × scale, 2 × scale × parameter].
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 tangent [2 × scale × parameter, 2 × scale] and a perpendicular normal [-2 × scale, 2 × scale × parameter].
When to use this tool
Use Parabola Parametric Tangent Normal Pair when you need a local conic-curve parameter or derivative calculation.
How to use the tool and how it works
- Enter parameter, scale. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read tangent, normal. Use the output convention below.
Require nonzero scale. Return tangent [2 × scale × parameter, 2 × scale] and a perpendicular normal [-2 × scale, 2 × scale × parameter].1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| parameter | Parameter | Required. Finite number. |
| scale | Nonzero parameter a for curve (a·t², 2a·t). | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| tangent | Tangent | Required. Array of finite number; maximum items 256. |
| normal | Normal | Required. Array of finite number; maximum items 256. |
{
"input": {
"parameter": 2,
"scale": 3
},
"output": {
"tangent": [
12,
6
],
"normal": [
-6,
12
]
}
}Limitations and assumptions
- The modeled parabola is (scale × parameter², 2 × scale × parameter); vectors are not normalized and no supplied curve, tangent orientation, or actual point 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
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 Latus Rectum Halfwidth
Return twice its absolute value as halfwidth and twice that again as fullWidth.
- Parabola Focus Directrix Distance Residual
Return Euclidean point-to-focus distance minus absolute line-expression value divided by the normal length.