Description
Passive coordinate change to a new origin displaced by a supplied vector.
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.
Passive coordinate change to a new origin displaced by a supplied vector.
When to use this tool
Use Vector Affine Origin Shift Budget 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, originShift. 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 shifted, displacementNorm. Use the output convention below.
Require aligned nonempty coordinates and originShift arrays. Return shifted=coordinates-originShift and displacementNorm=norm(originShift).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| coordinates | Coordinates | Required. Array of Finite number.; maximum items 256. |
| originShift | Origin Shift | Required. Array of Finite number.; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| shifted | Shifted | Required. Array of Finite number.; maximum items 256. |
| displacementNorm | Displacement Norm | Required. Finite number. |
{
"input": {
"coordinates": [
3,
4
],
"originShift": [
1,
2
]
},
"output": {
"shifted": [
2,
2
],
"displacementNorm": 2.23606797749979
}
}Limitations and assumptions
- DisplacementNorm describes the supplied origin shift, not the original or shifted point's norm. Units and frame conventions must match; no rotation or physical reference-frame conversion is inferred.
- 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 Affine Combination Weight Residual
Sum weights and return residual=sum-1.
- Vector: Vector Affine Point Direction Tag
Encode a 2D/3D affine point or free direction into homogeneous coordinates with explicit final weight one or zero; no projective division.