Description
Measure deviation from perpendicularity to a plane by reusing normalized-dot arithmetic on its supplied normal.
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.
Measure deviation from perpendicularity to a plane by reusing normalized-dot arithmetic on its supplied normal.
When to use this tool
Use Vector Plane Orthogonality 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 vector, planeNormal. 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 normalCosine, absoluteParallelResidual. Use the output convention below.
Require nonzero three-component vector and planeNormal. Delegate the scaled normalized-dot calculation for normalCosine, then return absoluteParallelResidual=max(0,1-abs(normalCosine)).1
The normalized dot product is calculated by the linked vector operation, using its scaled normalization of nonzero inputs.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| vector | Vector | Required. Array of Finite number.; maximum items 256. |
| planeNormal | Plane Normal | Required. Array of Finite number.; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| normalCosine | Normal Cosine | Required. Finite number. |
| absoluteParallelResidual | One minus absolute cosine to the normal, floored at zero; zero means perpendicular to the plane. | Required. Finite number. |
{
"input": {
"vector": [
1,
0,
0
],
"planeNormal": [
2,
0,
0
]
},
"output": {
"normalCosine": 1,
"absoluteParallelResidual": 0
}
}Limitations and assumptions
- A zero residual means the vector is parallel or antiparallel to the normal, hence perpendicular to the plane. It does not mean parallel to the plane; no angle tolerance, plane offset, or geometric fitting is applied.
- 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/projection
Project one numeric vector onto a nonzero basis vector.
- Vector Nullspace Single Constraint Residual
Check one homogeneous dot-product constraint against a supplied absolute tolerance.