Description
Rescale coordinates for independently scaled basis vectors by dividing by each supplied basis scale.
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.
Rescale coordinates for independently scaled basis vectors by dividing by each supplied basis scale.
When to use this tool
Use Vector Basis Coordinate Unit Scale 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 coordinates, basisScales. 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 coordinates. Use the output convention below.
Require aligned coordinates and nonzero basisScales. Divide each coordinate by its corresponding scale.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| coordinates | Coordinates | Required. Array of Finite number.; maximum items 256. |
| basisScales | Basis Scales | Required. Array of Finite number.; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| coordinates | Coordinates | Required. Array of Finite number.; maximum items 256. |
{
"input": {
"coordinates": [
2,
6
],
"basisScales": [
2,
3
]
},
"output": {
"coordinates": [
1,
2
]
}
}Limitations and assumptions
- Negative scales reverse coordinate directions, and division assumes each new basis vector is its old counterpart times the supplied scale. No mixing or full change-of-basis matrix is applied.
- 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 3d Coordinate Cyclic Permutation
Cyclically reorder three coordinates by an integer shift modulo three.