Description
Classify the orientation of a supplied planar tangent/normal pair from its determinant sign.
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.
Classify the orientation of a supplied planar tangent/normal pair from its determinant sign.
When to use this tool
Use Vector Tangent Normal Basis Orientation 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 tangent, normal. 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 determinant, orientation. Use the output convention below.
Require two-component tangent and normal vectors and calculate determinant=tangent.x*normal.y-tangent.y*normal.x. Label its sign counterclockwise, clockwise, or degenerate.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| tangent | Tangent | Required. Array of Finite number.; maximum items 256. |
| normal | Normal | Required. Array of Finite number.; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| determinant | Determinant | Required. Finite number. |
| orientation | Orientation | Required. Text; maximum UTF-16 length 8192. |
{
"input": {
"tangent": [
1,
0
],
"normal": [
0,
2
]
},
"output": {
"determinant": 2,
"orientation": "counterclockwise"
}
}Limitations and assumptions
- The inputs need not be unit vectors or perpendicular. This reports oriented area sign only; naming one vector normal does not validate a tangent-normal frame.
- 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.
- Basis Vector Determinant Sign
Inspect floating-point orientation of a supplied 3D basis after row scaling; no exact-predicate guarantee.