Description
For suppliedReferenceGap within zero through 90 degrees reduce secondAxisDegrees-firstAxisDegrees modulo 180 and return unorientedGap=min(wrapped,180-wrapped) and residual=unorientedGap-suppliedReferenceGap.
Optical calculations distinguish lens power in diopters, prism notation, angular axes, geometric distances, and visual-acuity reporting scales. Sign conventions and length units are especially important when a formula combines power with decentration or vertex distance. A supplied model term is separate from a validated visual test or prescription.
For suppliedReferenceGap within zero through 90 degrees reduce secondAxisDegrees-firstAxisDegrees modulo 180 and return unorientedGap=min(wrapped,180-wrapped) and residual=unorientedGap-suppliedReferenceGap.
When to use this tool
Use Optical Axis Reference Gap when you need this explicit optical, chart, frame, axis, or reference conversion with compatible supplied units.
How to use the tool and how it works
- Enter firstAxisDegrees, secondAxisDegrees, suppliedReferenceGap. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read unorientedGap, residual. Use the output convention below.
For suppliedReferenceGap within zero through 90 degrees reduce secondAxisDegrees-firstAxisDegrees modulo 180 and return unorientedGap=min(wrapped,180-wrapped) and residual=unorientedGap-suppliedReferenceGap.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| firstAxisDegrees | First Axis Degrees | Required. Finite number. |
| secondAxisDegrees | Second Axis Degrees | Required. Finite number. |
| suppliedReferenceGap | Supplied Reference Gap | Required. Finite number; minimum 0; maximum 90. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| unorientedGap | Shortest unoriented axis difference in degrees, from zero through 90. | Required. Finite number. |
| residual | Signed supplied-minus-reconstructed discrepancy under the stated formula. | Required. Finite number. |
{
"input": {
"firstAxisDegrees": 170,
"secondAxisDegrees": 10,
"suppliedReferenceGap": 15
},
"output": {
"unorientedGap": 20,
"residual": 5
}
}Limitations and assumptions
- Axes are unoriented and use degrees. The result lies between zero and 90 under this convention; no anatomical axis detection, optical correction, or clinical significance is inferred.
- 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 the appropriate complete optical or measurement model when a scalar term is insufficient. Verify power, axis, length, notation, and reference conventions before applying the result within a broader assessment.
References
Similar or alternative tools
- Lens Axis Wrapped Angle
Wrap an explicitly supplied unoriented research axis to a half-turn coordinate; no prescription is generated.
- Lens Transposition Cylinder Axis Wrap
Algebraic sphero-cylinder transposition with axis normalized to [0,180), not a prescription recommendation.