Description
Return normalized anatomical-axis dot product and orthogonality residual.
Anatomical diagrams and idealized models require explicit coordinate origins, axes, dimensions and indexing conventions. Translations, vector projections and simple shape formulas describe supplied geometry rather than identifying actual anatomy or determining a medical finding. A scaled drawing or ideal branching tree needs separate anatomical verification.
Return normalized anatomical-axis dot product and orthogonality residual.
When to use this tool
Use Anatomical Axis Orthogonality Residual when checking the stated diagram, coordinate, vector or ideal-shape convention.
How to use the tool and how it works
- Enter firstAxis, secondAxis. Follow any array-alignment requirements below. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read cosine, absoluteResidual. Use the output convention below.
Return normalized anatomical-axis dot product and orthogonality residual. Require both three-component vectors and use the shared normalized-dot calculation; cosine is the normalized inner product, absoluteResidual = abs(cosine).1
The normalized dot-product calculation is shared with Vector Normalized Dot Residual. It rescales each nonzero vector before normalizing; this tool restricts both axes to three components and returns the absolute cosine.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| firstAxis | First Axis | Required. Array of finite number; maximum items 256. |
| secondAxis | Second Axis | Required. Array of finite number; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| cosine | Cosine | Required. Finite number. |
| absoluteResidual | Absolute normalized dot product; zero means orthogonality under the supplied floating-point coordinates. | Required. Finite number. |
{
"input": {
"firstAxis": [
1,
0,
0
],
"secondAxis": [
0,
2,
0
]
},
"output": {
"cosine": 0,
"absoluteResidual": 0
}
}Limitations and assumptions
- Zero-length vectors are rejected by the shared calculation; no tolerance, actual frame calibration or clinical plane identification is established.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- 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. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use verified anatomical measurements and an appropriate complete spatial model; consult qualified health professionals for actual medical interpretation.
References
Similar or alternative tools
- Section Plane Normal Reference Token
Compare nonzero three-component plane normals.
- Anatomical Angle Three Landmark Term
Return angle at a supplied three-landmark vertex.