Description
Transform vector components in the local cylindrical basis to Cartesian components at an explicit azimuth.
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.
Transform vector components in the local cylindrical basis to Cartesian components at an explicit azimuth.
When to use this tool
Use Vector Cylindrical Basis Azimuth Term 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 radial, azimuthal, vertical, azimuthRadians. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read cartesian. Use the output convention below.
Convert supplied radial and azimuthal components to Cartesian x=radial*cos(azimuthRadians)-azimuthal*sin(azimuthRadians) and y=radial*sin(azimuthRadians)+azimuthal*cos(azimuthRadians), preserving vertical as z.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| radial | Radial vector component, not a point radius. | Required. Finite number. |
| azimuthal | Azimuthal vector component, not an angle or angular rate. | Required. Finite number. |
| vertical | Vertical | Required. Finite number. |
| azimuthRadians | Basis azimuth in radians. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| cartesian | Cartesian | Required. Array of Finite number.; maximum items 256. |
{
"input": {
"radial": 3,
"azimuthal": 4,
"vertical": 5,
"azimuthRadians": 0
},
"output": {
"cartesian": [
3,
4,
5
]
}
}Limitations and assumptions
- Azimuth is in radians and components share one vector unit. This transforms basis components rather than cylindrical point coordinates; no radius-dependent angular-rate factor is introduced.
- 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
- Basis Vector Determinant Sign
Inspect floating-point orientation of a supplied 3D basis after row scaling; no exact-predicate guarantee.
- Vector Azimuth Elevation Pole Ambiguity
Calculate horizontal=hypot(x,y), label pole when horizontal is zero but z is not, and origin when all three vanish.