Description
Divide homogeneous coordinates by a nonzero final weight or flag the zero-weight branch.
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.
Divide homogeneous coordinates by a nonzero final weight or flag the zero-weight branch.
When to use this tool
Use Vector Homogeneous Weight Zero Tag 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. 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 atInfinity, euclidean. Inspect atInfinity before interpreting the associated values.
Require at least two homogeneous coordinates and take the final value as weight. If it is zero return atInfinity true and empty euclidean; otherwise divide every preceding coordinate by weight.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| coordinates | Coordinates | Required. Array of Finite number.; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| atInfinity | At Infinity | Required. Boolean. |
| euclidean | Weight-divided coordinates, or an empty list when weight is zero. | Required. Array of Finite number.; maximum items 256. |
{
"input": {
"coordinates": [
4,
6,
2
]
},
"output": {
"atInfinity": false,
"euclidean": [
2,
3
]
}
}Limitations and assumptions
- The empty list is a zero-weight branch marker. An all-zero homogeneous tuple is also labeled atInfinity even though it does not define a valid projective point; projective validity is not fully checked.
- 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: 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.
- Homogeneous Point Weight Flag
Classify a supplied homogeneous weight; other coordinates must separately define a nonzero projective tuple.