Description
Normalize the sum of equal-norm vectors to obtain a bisector direction, rejecting a zero sum.
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.
Normalize the sum of equal-norm vectors to obtain a bisector direction, rejecting a zero sum.
When to use this tool
Use Vector Angle Bisector Equal Norm Case 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. 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 direction. Use the output convention below.
Require aligned nonzero vectors whose norms agree within 1e-12 times the larger norm. Add them, require the sum norm positive, and return its normalized direction.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. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| direction | Direction | Required. Array of Finite number.; maximum items 256. |
{
"input": {
"first": [
3,
0
],
"second": [
0,
3
]
},
"output": {
"direction": [
0.7071067811865475,
0.7071067811865475
]
}
}Limitations and assumptions
- Antiparallel vectors are rejected because their sum vanishes. Near-antiparallel inputs can be sensitive to cancellation, and unequal-norm vectors outside the stated tolerance are not reweighted into a bisector.
- 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 Axis Angle Infinitesimal Step
Return the first-order active Rodrigues rotation v+angle*(unitAxis cross v), with angle in radians.
- Vector Rejection Norm Roundoff Gap
Subtract squaredProjection from squaredNorm for raw.