Struct TransverseMercator

Prepared bounded Transverse Mercator projection.

struct TransverseMercator(T)
  
if (isGeodesyScalar!T);

Parameters follow the conventional EPSG Transverse Mercator model: ellipsoid, latitude/longitude of natural origin, natural-origin scale factor, false easting, and false northing.

The supported ellipsoid domain is spherical/oblate with 0 <= flattening <= 0.01. Non-polar forward inputs are bounded to abs(delta longitude) <= 60 degrees from the central meridian. Linear projected coordinates use the same unit as the ellipsoid axes and false offsets.

.init is invalid. Prepared objects are intended for reuse.

Properties

NameTypeDescription
ellipsoid[get] Ellipsoid!TProjection ellipsoid.
falseEasting[get] TEPSG 8806 false easting.
falseNorthing[get] TEPSG 8807 false northing.
isValid[get] boolTrue when the prepared operation contains valid supported parameters.
latitudeOfNaturalOrigin[get] Latitude!TEPSG 8801 latitude of natural origin.
longitudeOfNaturalOrigin[get] Longitude!TEPSG 8802 longitude of natural origin.
scaleFactorAtNaturalOrigin[get] TEPSG 8805 scale factor at natural origin.

Methods

NameDescription
forward (source) Project a geographic coordinate.
forwardFactors (source) Compute conformal factors at a geographic source coordinate or throw on projection/domain failure.
fromParameters (ellipsoid, latitudeOfNaturalOrigin, longitudeOfNaturalOrigin, scaleFactorAtNaturalOrigin, falseEasting, falseNorthing) Prepare a bounded Transverse Mercator operation.
reverse (source) Reverse a projected coordinate.
reverseFactors (source) Compute conformal factors for a represented projected coordinate or throw on projection/domain failure.
tryForward (source, result) Project a geographic coordinate.
tryForwardFactors (source, result) Compute conformal factors at a geographic source coordinate.
tryFromParameters (ellipsoid, latitudeOfNaturalOrigin, longitudeOfNaturalOrigin, scaleFactorAtNaturalOrigin, falseEasting, falseNorthing, result) Prepare a bounded Transverse Mercator operation without throwing.
tryReverse (source, result) Reverse a projected coordinate.
tryReverseFactors (source, result) Compute conformal factors for a represented projected coordinate.

Example

Example using struct TransverseMercator(T) if (isGeodesyScalar!T). 

import geodesy;

const tm = TransverseMercator!double.fromParameters(
    wgs84!double(),
    Latitude!double.fromDegrees(0.0),
    Longitude!double.fromDegrees(15.0),
    0.9996,
    500_000.0,
    0.0);

const source = GeographicCoordinate!double.fromComponents(
    Latitude!double.fromDegrees(48.0),
    Longitude!double.fromDegrees(16.0));

const projected = tm.forward(source);
const factors = tm.forwardFactors(source);
assert(projected.easting > 500_000.0);
assert(factors.pointScale > 0.0);

Example

Unit-invariance regression for the represented +60 degree TM boundary.

The same WGS 84 operation expressed in metres and kilometres must make the same reverse-domain acceptance decisions for coordinates produced by its own forward operation. 

import geodesy.ellipsoid : Ellipsoid;
import geodesy.geographic : GeographicCoordinate;
import geodesy.angle : Latitude, Longitude;

foreach (unit; [1.0, 0.001])
{
    const ellipsoid =
        Ellipsoid!double.fromInverseFlattening(
            6_378_137.0 * unit,
            298.257223563);

    const projection =
        TransverseMercator!double.fromParameters(
            ellipsoid,
            Latitude!double.fromDegrees(0.0),
            Longitude!double.fromDegrees(15.0),
            0.9996,
            500_000.0 * unit,
            0.0);

    foreach (i; 0 .. 2_000)
    {
        const latitudeDegrees =
            -80.0 + 160.0 * i / 2_000.0;

        const source =
            GeographicCoordinate!double.fromComponents(
                Latitude!double.fromDegrees(latitudeDegrees),
                Longitude!double.fromDegrees(75.0));

        const projected = projection.forward(source);

        GeographicCoordinate!double reversed;
        assert(projection.tryReverse(projected, reversed));
    }
}