Description
Project spherical Robinson coordinates using linear interpolation of a five-degree coefficient table.
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.
Project spherical Robinson coordinates using linear interpolation of a five-degree coefficient table.
Robinson is a global spherical pseudocylindrical projection. Keep its sphere radius and central meridian with the coordinates; this tool specifically declares its own linear coefficient-table interpolation.1
When to use this tool
Use this tool when you need to project spherical Robinson coordinates using linear interpolation of a five-degree coefficient table.
How to use the tool and how it works
- Enter latitudeDegrees, longitudeDegrees, centralMeridianDegrees, radiusMeters using the definitions below.
- Run the operation. Resolve input-format errors before interpreting an output.
- Read result.xMeters, result.yMeters, result.xMultiplier, result.yMultiplier, result.interpolation, using the stated boundary, ordering, sign and absence conventions.
Linearly interpolate the stored five-degree Robinson X/Y table at absolute latitude, restore the north/south Y sign, and wrap longitude relative to the central meridian into [−180,180). Calculate x=0.8487R deltaLambda X and y=1.3523R Y.2
| 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. |
| centralMeridianDegrees | East-positive central-meridian longitude in degrees, within ±180°. | Finite numeric value satisfying the stated comparisons. |
| radiusMeters | Explicit positive sphere radius in meters, from one through 10⁸. | Finite numeric value satisfying the stated comparisons. |
| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.xMeters | Projected east-like x coordinate in meters under the stated table convention. |
| result.yMeters | Projected north-like y coordinate in meters under the stated table convention. |
| result.xMultiplier | Interpolated dimensionless Robinson X multiplier. |
| result.yMultiplier | Signed interpolated dimensionless Robinson Y multiplier. |
| result.interpolation | Description of the actual linear five-degree-table interpolation. |
{
"input": {
"latitudeDegrees": 0,
"longitudeDegrees": 0,
"centralMeridianDegrees": 0,
"radiusMeters": 1
},
"output": {
"result": {
"xMeters": 0,
"yMeters": 0,
"xMultiplier": 1,
"yMultiplier": 0,
"interpolation": "linear interpolation of the published 5-degree Robinson table"
}
}
}Limitations and assumptions
- Latitude is within ±90°, both longitudes within ±180°, and radius 1–10⁸ m. The table interpolation is explicitly linear, so it can differ from implementations using fitted interpolation. Robinson is neither equal-area nor conformal.
- 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
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