Description
Return radius times angular step divided by two as latitudeHalfwidth and multiply it by cosine latitude for longitudeHalfwidth.
Coordinate uncertainty can be expressed as angular halfwidths, linear components, or variances. A local spherical conversion and a covariance projection use different conventions; neither alone defines a complete confidence region.
Return radius times angular step divided by two as latitudeHalfwidth and multiply it by cosine latitude for longitudeHalfwidth.
When to use this tool
Use Coordinate Rounding Ground Error Bound when you need a local uncertainty or rounding term with supplied geometry and statistics.
How to use the tool and how it works
- Enter angularStepRadians, radius, latitudeRadians. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read latitudeHalfwidth, longitudeHalfwidth. Use the output convention below.
Require nonnegative angularStepRadians, positive radius, and latitudeRadians within ±π/2. Return radius times angular step divided by two as latitudeHalfwidth and multiply it by cosine latitude for longitudeHalfwidth.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| angularStepRadians | Angular Step Radians | Required. Finite number; minimum 0. |
| radius | Radius in the common length unit, with its geometric role defined above. | Required. Finite number; strictly above 0. |
| latitudeRadians | Latitude Radians | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| latitudeHalfwidth | Latitude Halfwidth | Required. Finite number. |
| longitudeHalfwidth | Longitude Halfwidth | Required. Finite number. |
{
"input": {
"angularStepRadians": 0.001,
"radius": 6000000,
"latitudeRadians": 0
},
"output": {
"latitudeHalfwidth": 3000,
"longitudeHalfwidth": 3000
}
}Limitations and assumptions
- This is a local spherical rounding model for nearest-step coordinate rounding, in the radius length unit. It does not include measurement error, ellipsoid effects, or a combined radial confidence bound.
- 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 error-propagation model with known coordinate reference and covariance. Distinguish resolution from measurement uncertainty and variance from standard deviation or confidence limits.
References
Similar or alternative tools
- Coordinate Uncertainty Angular Halfwidth
Divide halfwidth by radius for radians and multiply by 180/π for degrees.
- Geographic Axis Uncertainty Projection
Return eastSigma² cos²(angle) plus northSigma² sin²(angle) plus twice correlation times both sigmas times cosine and sine.