Description
Calculate horizontal=hypot(x,y), label pole when horizontal is zero but z is not, and origin when all three vanish.
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.
Calculate horizontal=hypot(x,y), label pole when horizontal is zero but z is not, and origin when all three vanish.
When to use this tool
Use Vector Azimuth Elevation Pole Ambiguity 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 x, y, z. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read pole, origin, azimuthRadians, elevationRadians. Inspect pole, origin before interpreting the associated values.
Calculate horizontal=hypot(x,y), label pole when horizontal is zero but z is not, and origin when all three vanish. Return azimuthRadians=atan2(y,x) except zero at poles, and elevationRadians=atan2(z,horizontal) except zero at the origin.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| x | X | Required. Finite number. |
| y | Y | Required. Finite number. |
| z | Z | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| pole | Pole | Required. Boolean. |
| origin | Origin | Required. Boolean. |
| azimuthRadians | Radian azimuth; zero is a placeholder at a pole or the origin. | Required. Finite number. |
| elevationRadians | Radian elevation; zero is a placeholder at the origin. | Required. Finite number. |
{
"input": {
"x": 0,
"y": 0,
"z": 3
},
"output": {
"pole": true,
"origin": false,
"azimuthRadians": 0,
"elevationRadians": 1.5707963267948966
}
}Limitations and assumptions
- Azimuth zero at a pole and both zero angles at the origin are placeholders identified by the flags. The tool does not make those ambiguous directions unique or choose a geodetic coordinate system.
- 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 Cylindrical Basis Azimuth Term
Transform vector components in the local cylindrical basis to Cartesian components at an explicit azimuth.
- Vector: Vector Polar Elevation Convention
Crosswalk spherical polar angle from +z and elevation above the xy plane with explicit convention-specific domains.