Description
Normal reversal flips the scalar coefficient but preserves the projected vector.
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.
Normal reversal flips the scalar coefficient but preserves the projected vector.
When to use this tool
Use Vector Normal Projection Sign Flip 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 vector, normal. 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 coefficient, reversedCoefficient, projected. Use the output convention below.
Require aligned vectors and a normal with at least one nonzero component. Return coefficient=dot(vector,normal)/dot(normal,normal), reversedCoefficient as its negative, and projected=coefficient*normal.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| vector | Vector | Required. Array of Finite number.; maximum items 256. |
| normal | Normal | Required. Array of Finite number.; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| coefficient | Coefficient | Required. Finite number. |
| reversedCoefficient | Reversed Coefficient | Required. Finite number. |
| projected | Projected | Required. Array of Finite number.; maximum items 256. |
{
"input": {
"vector": [
3,
4
],
"normal": [
0,
2
]
},
"output": {
"coefficient": 2,
"reversedCoefficient": -2,
"projected": [
0,
4
]
}
}Limitations and assumptions
- The normal need not have unit length. Reversing its sign changes the scalar coefficient but leaves the geometric projection unchanged; no plane origin, point distance, or robust extreme-scale normalization is supplied.
- 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 Reflection Normal Sign Invariance
Reflect a vector across the origin plane normal to a supplied normal and report normal-sign invariance.
- Vector Two Axis Sign Flip
Negate two distinct explicitly selected vector coordinates.