Description
Encode a 2D/3D affine point or free direction into homogeneous coordinates with explicit final weight one or zero; no projective division.
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.
Encode a 2D/3D affine point or free direction into homogeneous coordinates with explicit final weight one or zero; no projective division.
When to use this tool
Use Vector: Vector Affine Point Direction 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, kind. 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 result. Expand result to inspect the returned fields.
Require two or three coordinates and kind point or direction. Append one for a point or zero for a direction and return homogeneous inside result.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| coordinates | Coordinates | Required. Array of Finite number.. |
| kind | Kind | Required. Text; one of "point", "direction". |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Result | Required. Object. |
{
"input": {
"coordinates": [
1,
2,
3
],
"kind": "direction"
},
"output": {
"result": {
"homogeneous": [
1,
2,
3,
0
]
}
}
}Limitations and assumptions
- This tags the supplied coordinates without transforming them. A zero direction is accepted even though its homogeneous all-zero tuple does not define a projective direction; no projective validity check is implied.
- Outputs are nested inside result. 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 Homogeneous Weight Zero Tag
Divide homogeneous coordinates by a nonzero final weight or flag the zero-weight branch.
- Homogeneous Point Weight Flag
Classify a supplied homogeneous weight; other coordinates must separately define a nonzero projective tuple.