Description
Return both oriented unit planar normals of a nonzero two-component vector under a Cartesian y-up convention.
A vector is an ordered set of components in a chosen basis. Its norm measures magnitude, while dot products, projections, and coordinate transformations describe different relationships. Component order, angle units, normalization, and numerical tolerances determine the meaning of a computed result.
Return both oriented unit planar normals of a nonzero two-component vector under a Cartesian y-up convention.
When to use this tool
Use Vector: Vector Two Component Normal Pair when you need the particular coordinate operation, derivative, residual, or domain check under a known basis convention.
How to use the tool and how it works
- Enter vector. 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 result. Expand result to inspect the returned fields.
Require exactly two vector components and positive Euclidean norm. Return leftUnitNormal=(-y/norm,x/norm) and rightUnitNormal=(y/norm,-x/norm) inside result.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| vector | Vector | Required. Array of Finite number.. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Result | Required. Object. |
{
"input": {
"vector": [
3,
4
]
},
"output": {
"result": {
"leftUnitNormal": [
-0.8,
0.6
],
"rightUnitNormal": [
0.8,
-0.6
]
}
}
}Limitations and assumptions
- Left and right use the usual upward-positive Cartesian orientation. No origin, tangent direction, surface geometry, or coordinate-system handedness is inferred.
- Outputs are nested inside result. The field tables state structural bounds; the mechanics also specify cross-field constraints. Malformed inputs and unsupported domains cause errors. A successful false flag, empty branch value, or zero placeholder has the meaning stated above and is distinct from an input error.
- 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. Signed zero is exported as zero.
Alternative or Complementary methods
Choose a complete vector or matrix operation when a single component or residual is insufficient. For sensitive near-zero or near-singular cases, inspect numerical conditioning and use an appropriate precision and tolerance.
References
Similar or alternative tools
- Vector Normal Tangent Component Pair
Separate a vector into normal and tangent components under a supplied unit-normal convention.
- Signed Component Ratio
Calculate a signed scalar component ratio and report whether both nonzero components share a sign.