Description
Test whether the sum of two supplied unit vectors is large enough to normalize under a 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.
Test whether the sum of two supplied unit vectors is large enough to normalize under a tolerance.
When to use this tool
Use Vector Normalized Sum Antipodal Domain 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 first, second, tolerance. 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 defined, sumNorm. Inspect defined before interpreting the associated values.
Require aligned vectors whose norms each lie within 1e-12 of one and nonnegative tolerance. Calculate sumNorm=norm(first+second) and return defined only when sumNorm>tolerance.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| first | First | Required. Array of Finite number.; maximum items 256. |
| second | Second | Required. Array of Finite number.; maximum items 256. |
| 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 |
|---|---|---|
| defined | Whether sumNorm strictly exceeds tolerance; normalized direction itself is not returned. | Required. Boolean. |
| sumNorm | Sum Norm | Required. Finite number. |
{
"input": {
"first": [
1,
0
],
"second": [
-1,
0
],
"tolerance": 0
},
"output": {
"defined": false,
"sumNorm": 0
}
}Limitations and assumptions
- Exact antipodes have zero sum and equality with tolerance is undefined. The tool checks the domain for a normalized sum without returning a bisector or establishing a stable direction near cancellation.
- 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 Cross Product Normalized Area Term
Return sine=crossMagnitude/(firstNorm*secondNorm), requiring positive norms and crossMagnitude within zero and their product.
- Vector Normalized Dot Residual
Calculate a scaled normalized dot product and its residual from a supplied cosine.