Description
Differentiate (a cos t, b sin t), returning the tangent vector and its normalized unitTangent 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.
Differentiate (a cos t, b sin t), returning the tangent vector and its normalized unitTangent inside result.
When to use this tool
Use Geometry: Ellipse Parametric Tangent Direction when you need a local conic-curve parameter or derivative calculation.
How to use the tool and how it works
- Enter semiAxisX, semiAxisY, parameterDegrees. 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 positive semiAxisX and semiAxisY and parameterDegrees within [-360, 360]. Differentiate (a cos t, b sin t), returning the tangent vector and its normalized unitTangent inside result.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| semiAxisX | Semi Axis X | Required. Finite number. |
| semiAxisY | Semi Axis Y | Required. Finite number. |
| parameterDegrees | Parameter Degrees Unit: deg. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Object containing the calculated members; expand to inspect the fields below. | Required. Object. |
| result.tangentVector | Tangent Vector | Calculated result member: array. |
| result.unitTangent | Unit Tangent | Calculated result member: array. |
{
"input": {
"semiAxisX": 2,
"semiAxisY": 3,
"parameterDegrees": 0
},
"output": {
"result": {
"tangentVector": [
0,
3
],
"unitTangent": [
0,
1
]
}
}
}Limitations and assumptions
- The parameter is an ellipse parameter, not generally the polar bearing of the point; axes are aligned and centered, without arbitrary rotation, point validation, or a supplied curve fit.
- 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
- Ellipse Normal Tangent Orthogonality Residual
Return tangent [-a sin t, b cos t], normal [cos t/a, sin t/b], and their dot product as residual.
- Ellipse Parametric Normal Unit Vector
Form [cos/a, sin/b] and normalize it for the outward normal.