Description
Classify a supplied homogeneous weight; other coordinates must separately define a nonzero projective tuple.
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.
Classify a supplied homogeneous weight; other coordinates must separately define a nonzero projective tuple.
When to use this tool
Use Homogeneous Point Weight Flag 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 weight. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read finitePoint, pointAtInfinity. Inspect finitePoint, pointAtInfinity before interpreting the associated values.
Set finitePoint when weight is nonzero and pointAtInfinity when it is exactly zero.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| weight | Weight | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| finitePoint | Finite Point | Required. Boolean. |
| pointAtInfinity | Point At Infinity | Required. Boolean. |
{
"input": {
"weight": 2
},
"output": {
"finitePoint": true,
"pointAtInfinity": false
}
}Limitations and assumptions
- This classifies a supplied homogeneous weight only. Without the remaining coordinates it cannot establish projective validity, and no tolerance or Euclidean coordinate division 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
- Vector Homogeneous Weight Zero Tag
Divide homogeneous coordinates by a nonzero final weight or flag the zero-weight branch.
- Vector Projective Point Horizon Denominator Gap
Return distanceFromHorizon=abs(homogeneousWeight) and atHorizon when that magnitude is no greater than nonnegative tolerance.