Description
Return arctangent of tan(longitude difference) times sin(latitude).
Map-grid directions and lengths depend on a projection and its local distortion. A supplied convergence or scale term can transform one local quantity, but does not define or execute the entire map projection.
Return arctangent of tan(longitude difference) times sin(latitude).
When to use this tool
Use Meridian Convergence Local Input Term when you need one projection-related local term under an explicit convention.
How to use the tool and how it works
- Enter longitudeDifferenceRadians, latitudeRadians. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read convergenceRadians. Use the output convention below.
Require latitudeRadians and longitudeDifferenceRadians within ±π/2. Return arctangent of tan(longitude difference) times sin(latitude).1
The spherical convergence term is atan(tan(longitude difference) times sin(latitude)). Ellipsoidal projection requires additional latitude transformations and corrections.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| longitudeDifferenceRadians | Signed offset from the central meridian in radians within ±π/2. | Required. Finite number. |
| latitudeRadians | Latitude Radians | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| convergenceRadians | Spherical transverse-Mercator convergence term, not a full ellipsoidal projection. | Required. Finite number. |
{
"input": {
"longitudeDifferenceRadians": 0.7853981633974483,
"latitudeRadians": 1.5707963267948966
},
"output": {
"convergenceRadians": 0.7853981633974483
}
}Limitations and assumptions
- This is a spherical transverse-Mercator convergence term in radians using the supplied central-meridian difference. It does not select a zone, compute a full projection, or model ellipsoidal corrections; tangent behavior near ±π/2 is numerically delicate.
- 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 a complete coordinate-reference transformation with known parameters for mapping. Derive local convergence and scale from the chosen projection rather than assuming they apply uniformly.
References
Similar or alternative tools
- Geographic Azimuth Meridian Reference Pair
Add convergence to gridAzimuth and wrap the sum modulo 360 for trueAzimuth; separately normalize gridAzimuth modulo 360.
- Cartographic Ground Grid Scale Term
Return grid equal to ground times scale and correction equal to grid minus ground.