Description
Rotate a three-component vector around x, y, or z by an integer number of quarter turns using signed swaps.
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.
Rotate a three-component vector around x, y, or z by an integer number of quarter turns using signed swaps.
When to use this tool
Use Vector Fixed Axis Rotation Quarter Turn 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, axis, turns. 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 vector. Use the output convention below.
Require a three-component vector, axis x, y, or z, and integer turns from minus one million through one million. Reduce turns modulo four and apply signed coordinate swaps for each positive quarter turn.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| vector | Vector | Required. Array of Finite number.; maximum items 256. |
| axis | Axis | Required. Text; one of "x", "y", "z"; maximum UTF-16 length 8192. |
| turns | Turns | Required. Safe integer; minimum -1000000; maximum 1000000. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| vector | Vector | Required. Array of Finite number.; maximum items 256. |
{
"input": {
"vector": [
1,
2,
3
],
"axis": "z",
"turns": 1
},
"output": {
"vector": [
-2,
1,
3
]
}
}Limitations and assumptions
- Positive turns follow the implemented right-handed Cartesian rotation convention. Multiples of four preserve the vector, and the calculation avoids trigonometric approximation but does not infer screen or physical-axis conventions.
- 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 Axis Angle Infinitesimal Step
Return the first-order active Rodrigues rotation v+angle*(unitAxis cross v), with angle in radians.
- Vector Axis Rejection Length
Return only the perpendicular component magnitude relative to a supplied nonzero axis.