Description
Rotate an ECEF displacement into local east, north and up at a supplied origin direction.
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.
Rotate an ECEF displacement into local east, north and up at a supplied origin direction.
When to use this tool
Use this tool when you need to rotate an ECEF displacement into local east, north and up at a supplied origin direction.
How to use the tool and how it works
- Enter latitudeDegrees, longitudeDegrees, ecefDeltaMeters using the definitions below.
- Run the operation. Resolve input-format errors before interpreting an output.
- Read result.enuMeters, using the stated boundary, ordering, sign and absence conventions.
Rotate the supplied ECEF displacement [dX,dY,dZ] into local east, north and up at the given geodetic latitude/longitude, using the orthonormal tangent-frame matrix.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| latitudeDegrees | Geodetic latitude in degrees, north positive; the operation’s pole restrictions apply. | Finite numeric value satisfying the stated comparisons. |
| longitudeDegrees | East-positive longitude in degrees from −180 through 180. | Finite numeric value satisfying the stated comparisons. |
| ecefDeltaMeters | Three Cartesian displacement components [dX,dY,dZ] in meters, each magnitude≤10⁹. | Dense list of at most 128 finite numbers, under the stated integer/range rules. |
| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.enuMeters | Rotated displacement [east,north,up] in meters. |
{
"input": {
"latitudeDegrees": 0,
"longitudeDegrees": 0,
"ecefDeltaMeters": [
1,
2,
3
]
},
"output": {
"result": {
"enuMeters": [
2,
3,
1
]
}
}
}Limitations and assumptions
- The vector is already a displacement in meters, with three entries within ±10⁹. Absolute ECEF positions require subtracting an origin first; the tool performs no origin translation or geodetic datum conversion.
- 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
- ECEF X-Y-Z from Geodetic Coordinates Calculator
Convert ellipsoidal geodetic coordinates to right-handed ECEF meter coordinates.
- Geodetic from ECEF XYZ Iterative Converter
Convert ECEF coordinates to geodetic latitude, longitude and ellipsoidal height with bounded iteration and a reconstruction residual.