Description
Rigid planar tilt of a supplied frame height about an explicit pivot.
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.
Rigid planar tilt of a supplied frame height about an explicit pivot.
When to use this tool
Use Spectacle Pantoscopic Height Projection Term 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 height, tiltRadians, pivotHeight. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read projectedHeight, forwardOffset, displacement. Use the output convention below.
Return projectedHeight=pivotHeight+(height-pivotHeight)*cos(tiltRadians), forwardOffset=(height-pivotHeight)*sin(tiltRadians), and displacement=(height-pivotHeight)*(cos(tiltRadians)-1).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| height | Height | Required. Finite number. |
| tiltRadians | Signed pivot tilt angle in radians. | Required. Finite number. |
| pivotHeight | Pivot Height | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| projectedHeight | Projected Height | Required. Finite number. |
| forwardOffset | Forward Offset | Required. Finite number. |
| displacement | Displacement | Required. Finite number. |
{
"input": {
"height": 20,
"tiltRadians": 0,
"pivotHeight": 5
},
"output": {
"projectedHeight": 20,
"forwardOffset": 0,
"displacement": 0
}
}Limitations and assumptions
- Heights need one length unit and tilt is radians. This ideal pivot geometry does not validate frame fit, lens orientation, optical power, comfort, or a clinical spectacle adjustment.
- 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
- Spectacle Bridge Fit Clearance Term
Audit explicit planar bridge/support dimensions without a fitting recommendation.
- Spectacle Asymmetric Frame Decentration Pair
Explicit planar model decentration and conservative circular-blank budget, without selecting spectacle fitting measurements.