Description
Subtract squaredProjection from squaredNorm for raw.
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.
Subtract squaredProjection from squaredNorm for raw.
When to use this tool
Use Vector Rejection Norm Roundoff 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 squaredNorm, squaredProjection, tolerance. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read squaredRejection, raw, clamped. Inspect clamped before interpreting the associated values.
Subtract squaredProjection from squaredNorm for raw. Require nonnegative supplied squared quantities and tolerance and raw>=-tolerance, then return squaredRejection=max(0,raw) and clamped when raw is negative.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| squaredNorm | Squared Norm | Required. Finite number; minimum 0. |
| squaredProjection | Squared Projection | Required. Finite number; minimum 0. |
| tolerance | Maximum permitted negative discrepancy in squared-vector units. | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| squaredRejection | Squared Rejection | Required. Finite number. |
| raw | Raw | Required. Finite number. |
| clamped | Clamped | Required. Boolean. |
{
"input": {
"squaredNorm": 25,
"squaredProjection": 9,
"tolerance": 0
},
"output": {
"squaredRejection": 16,
"raw": 16,
"clamped": false
}
}Limitations and assumptions
- Tolerance uses squared-vector units. This accepts a small supplied negative residual by policy rather than proving the input quantities come from a valid projection; larger violations are rejected.
- 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 Angle Bisector Equal Norm Case
Normalize the sum of equal-norm vectors to obtain a bisector direction, rejecting a zero sum.
- Vector Axis Rejection Length
Return only the perpendicular component magnitude relative to a supplied nonzero axis.