Description
Return distanceFromHorizon=abs(homogeneousWeight) and atHorizon when that magnitude is no greater than nonnegative tolerance.
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.
Return distanceFromHorizon=abs(homogeneousWeight) and atHorizon when that magnitude is no greater than nonnegative tolerance.
When to use this tool
Use Vector Projective Point Horizon Denominator Gap 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 homogeneousWeight, tolerance. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read atHorizon, distanceFromHorizon. Inspect atHorizon before interpreting the associated values.
Return distanceFromHorizon=abs(homogeneousWeight) and atHorizon when that magnitude is no greater than nonnegative tolerance.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| homogeneousWeight | Homogeneous Weight | Required. Finite number. |
| tolerance | Nonnegative absolute tolerance in the quantity tested; see the stated units and boundary rule. | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| atHorizon | At Horizon | Required. Boolean. |
| distanceFromHorizon | Absolute homogeneous weight, not Euclidean distance to a horizon. | Required. Finite number. |
{
"input": {
"homogeneousWeight": 0.001,
"tolerance": 0.01
},
"output": {
"atHorizon": true,
"distanceFromHorizon": 0.001
}
}Limitations and assumptions
- This is a tolerance test on the supplied homogeneous weight, not Euclidean distance to a geometric horizon. Scaling homogeneous coordinates changes this numeric test unless tolerance is scaled consistently.
- 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
- Homogeneous Point Weight Flag
Classify a supplied homogeneous weight; other coordinates must separately define a nonzero projective tuple.
- 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.