Description
Apply a signed parts-per-million scale increment and expose its additive coordinate correction.
Geodesy distinguishes a mathematical reference ellipsoid, a realized coordinate datum and the physical gravity field. Geodetic latitude follows the ellipsoid normal; geocentric latitude follows a radius from the center. Ellipsoidal height, orthometric height and geoid undulation are separate signed quantities. Keep the declared ellipsoid, coordinate axes, angular units and time scale with a result.
Apply a signed parts-per-million scale increment and expose its additive coordinate correction.
When to use this tool
Use this tool when you need to apply a signed parts-per-million scale increment and expose its additive coordinate correction.
How to use the tool and how it works
- Enter coordinateMeters, scalePpm using the definitions below.
- Run the operation. Resolve input-format errors before interpreting an output.
- Read result.scaleFactor, result.scaledMeters, result.correctionMeters, using the stated boundary, ordering, sign and absence conventions.
Calculate scaleFactor=1+scalePpm×10⁻⁶, scaledMeters=coordinateMeters×scaleFactor, and correctionMeters=coordinateMeters×scalePpm×10⁻⁶.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| coordinateMeters | Signed Cartesian coordinate in meters with magnitude≤10⁹. | Finite numeric value satisfying the stated comparisons. |
| scalePpm | Signed scale increment in parts per million, magnitude≤1000; factor is 1+ppm×10⁻⁶. | Finite numeric value satisfying the stated comparisons. |
| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.scaleFactor | Dimensionless multiplicative factor 1+scalePpm×10⁻⁶. |
| result.scaledMeters | Signed coordinate after multiplication by scaleFactor, in meters. |
| result.correctionMeters | Signed additive scale change, in meters. |
{
"input": {
"coordinateMeters": 1000,
"scalePpm": 2
},
"output": {
"result": {
"scaleFactor": 1.000002,
"scaledMeters": 1000.0020000000001,
"correctionMeters": 0.002
}
}
}Limitations and assumptions
- Coordinate magnitude is at most 10⁹ m and scale magnitude at most 1000 ppm. The correction retains the signs of coordinate and scale; ppm is not a percent value.
- All quantities are finite and retain the units stated for this operation. Ellipsoid-parameter tools use semi-major axis 1–10⁸ m and dimensionless flattening 0–0.02; explicit-axis tools use 0.9a≤b≤a unless a tighter bound is stated. These tools do not fetch datums, geoid grids, satellite observations or Earth-orientation updates.
- Every declared outer field is required and unknown outer fields are rejected. Strings and JSON text have size limits, lists are bounded to 128 entries, and JSON nesting/node counts are bounded. Tighter operation-specific bounds stated above take precedence.
- Numeric results must be finite. Large physical magnitudes are allowed by the output evidence checks, while integer fields and source schemas retain their exactness rules. Source indexes are zero-based. Floating-point residues can remain even where an ideal formula gives an exact zero.
Alternative or Complementary methods
Use a coordinate transform for a change of representation and explicit datum parameters for a change of reference frame. Preserve model and convergence metadata, and use observation and datum information appropriate to a real survey before interpreting a computed tolerance as accuracy.
References
Similar or alternative tools
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