Description
Reflect a vector across the origin plane normal to a supplied normal and report normal-sign invariance.
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.
Reflect a vector across the origin plane normal to a supplied normal and report normal-sign invariance.
When to use this tool
Use Vector Reflection Normal Sign Invariance 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 reflected, reversedNormalResult. Use the output convention below.
Require matching vector and nonzero normal dimensions. Calculate reflected=vector-2*dot(vector,normal)/dot(normal,normal)*normal, and return the same vector as reversedNormalResult.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 |
|---|---|---|
| reflected | Reflected | Required. Array of Finite number.; maximum items 256. |
| reversedNormalResult | Reversed Normal Result | Required. Array of Finite number.; maximum items 256. |
{
"input": {
"vector": [
2,
3
],
"normal": [
1,
0
]
},
"output": {
"reflected": [
-2,
3
],
"reversedNormalResult": [
-2,
3
]
}
}Limitations and assumptions
- The normal need not have unit length. ReversedNormalResult expresses the formula's invariance without independently recomputing with a second normal; no reflection plane offset or point translation is modeled.
- 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 Normal Projection Sign Flip
Normal reversal flips the scalar coefficient but preserves the projected vector.
- Vector Reflection Axis Component Sign
Preserve the supplied parallel scalar and negate perpendicular.