Description
Scale coordinates by their largest absolute magnitude and normalize the scaled vector with a Euclidean norm.
A vector has ordered coordinates. Its length and direction are different properties: scaling changes length, while normalization retains direction when the vector is nonzero. Coordinate order and the chosen axes determine the interpretation.
Scale coordinates by their largest absolute magnitude and normalize the scaled vector with a Euclidean norm.
When to use this tool
Use Vector Unit Direction Zero Policy when you need a small coordinate transformation or a direction calculation under an explicit axis convention.
How to use the tool and how it works
- Enter coordinates. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read defined, direction. Inspect defined before interpreting the associated values.
Scale coordinates by their largest absolute magnitude and normalize the scaled vector with a Euclidean norm. For an empty or all-zero vector return matching zero direction and defined false.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| coordinates | Finite vector coordinates in one common coordinate system; an empty or zero vector has no direction. | Required. Array of finite number; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| defined | Whether the accompanying value has an available denominator; inspect before using placeholders. | Required. Boolean. |
| direction | Direction or sign convention stated above. | Required. Array of finite number; maximum items 256. |
{
"input": {
"coordinates": [
3,
4
]
},
"output": {
"defined": true,
"direction": [
0.6,
0.8
]
}
}Limitations and assumptions
- The zero vector has no unit direction; output zeros are placeholders and no coordinate frame or measurement tolerance is inferred.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- 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. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Verify the coordinate system and use a complete transformation matrix when several transformations must be composed.
References
Similar or alternative tools
- Unit L2 Coordinate Contribution
Divide coordinate by norm and square it for squaredNormShare.
- Cosine Coordinate Term
Multiply firstCoordinate/firstNorm by secondCoordinate/secondNorm.