Description
Algebraic sphero-cylinder transposition with axis normalized to [0,180), not a prescription recommendation.
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.
Algebraic sphero-cylinder transposition with axis normalized to [0,180), not a prescription recommendation.
When to use this tool
Use Lens Transposition Cylinder Axis Wrap 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 sphere, cylinder, axisDegrees. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read sphere, cylinder, axisDegrees. Use the output convention below.
Return sphere'=sphere+cylinder, cylinder'=-cylinder, and axisDegrees=(normalizedInputAxis+90) modulo 180, where input axis is first normalized to [0,180).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| sphere | Sphere | Required. Finite number. |
| cylinder | Cylinder | Required. Finite number. |
| axisDegrees | Output axis wrapped into [0,180); zero represents the half-turn endpoint. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| sphere | Sphere | Required. Finite number. |
| cylinder | Cylinder | Required. Finite number. |
| axisDegrees | Output axis wrapped into [0,180); zero represents the half-turn endpoint. | Required. Finite number. |
{
"input": {
"sphere": -2,
"cylinder": -1,
"axisDegrees": 20
},
"output": {
"sphere": -3,
"cylinder": 1,
"axisDegrees": 110
}
}Limitations and assumptions
- Sphere and cylinder use one power unit and axes degrees. Output zero is the half-turn representation of 180 degrees; this algebraic transposition does not validate a prescription, choose a notation clinically, or model complex lenses.
- 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 Prescription Plusminus Axis Token
Parse an explicit signed sphere/cylinder and integer axis token without selecting a prescription.
- Lens Cylinder Axis Unit Flag
Convert a supplied axis unit and optionally normalize a 180-degree orientation; no prescription calculation.