Description
Cyclically reorder three coordinates by an integer shift modulo three.
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.
Cyclically reorder three coordinates by an integer shift modulo three.
When to use this tool
Use Vector 3d Coordinate Cyclic Permutation 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, shift. 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 and integer shift. Reduce shift modulo three and return components starting at that offset, wrapping cyclically.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| vector | Vector | Required. Array of Finite number.; maximum items 256. |
| shift | Shift | Required. Safe integer. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| vector | Vector | Required. Array of Finite number.; maximum items 256. |
{
"input": {
"vector": [
1,
2,
3
],
"shift": 1
},
"output": {
"vector": [
2,
3,
1
]
}
}Limitations and assumptions
- Positive shift one maps (x,y,z) to (y,z,x), and negative shifts wrap in the opposite direction. No sign change, arbitrary permutation, or inferred physical rotation is performed.
- 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 Basis Coordinate Unit Scale
Rescale coordinates for independently scaled basis vectors by dividing by each supplied basis scale.
- Vector Bivector Single Coordinate
Calculate one ordered antisymmetric bivector coordinate from two supplied vectors.