Package org.geotools.referencing.operation.projection

Class TransverseMercator

  • All Implemented Interfaces:
    Serializable, MathTransform, MathTransform2D
    public class TransverseMercator
extends MapProjection
    Transverse Mercator Projection (EPSG code 9807). This is a cylindrical projection, in which the cylinder has been rotated 90°. Instead of being tangent to the equator (or to an other standard latitude), it is tangent to a central meridian. Deformation are more important as we are going futher from the central meridian. The Transverse Mercator projection is appropriate for region wich have a greater extent north-south than east-west.

    The elliptical equations used here are series approximations, and their accuracy decreases as points move farther from the central meridian of the projection. The forward equations here are accurate to a less than a mm ±10 degrees from the central meridian, a few mm ±15 degrees from the central meridian and a few cm ±20 degrees from the central meridian. The spherical equations are not approximations and should always give the correct values.

    There are a number of versions of the transverse mercator projection including the Universal (UTM) and Modified (MTM) Transverses Mercator projections. In these cases the earth is divided into zones. For the UTM the zones are 6 degrees wide, numbered from 1 to 60 proceeding east from 180 degrees longitude, and between lats 84 degrees North and 80 degrees South. The central meridian is taken as the center of the zone and the latitude of origin is the equator. A scale factor of 0.9996 and false easting of 500000m is used for all zones and a false northing of 10000000m is used for zones in the southern hemisphere.

    NOTE: formulas used below are not those of Snyder, but rather those from the proj4 package of the USGS survey, which have been reproduced verbatim. USGS work is acknowledged here.

    References:

    • Proj-4.4.6 available at www.remotesensing.org/proj
      Relevent files are: PJ_tmerc.c, pj_mlfn.c, pj_fwd.c and pj_inv.c.
    • John P. Snyder (Map Projections - A Working Manual, U.S. Geological Survey Professional Paper 1395, 1987).
    • "Coordinate Conversions and Transformations including Formulas", EPSG Guidence Note Number 7, Version 19.
    Since:
    2.1
    Author:
    André Gosselin, Martin Desruisseaux (PMO, IRD), Rueben Schulz
    See Also:
    Transverse Mercator projection on MathWorld, "Transverse_Mercator" on RemoteSensing.org, Serialized Form

    • Method Detail

      • transformNormalized

        protected Point2D transformNormalized​(double x,
                                      double y,
                                      Point2D ptDst)
                               throws ProjectionException
        Transforms the specified (λ,φ) coordinates (units in radians) and stores the result in ptDst (linear distance on a unit sphere).
        Specified by:
        transformNormalized in class MapProjection
        Parameters:
        x - The longitude of the coordinate, in radians.
        y - The latitude of the coordinate, in radians.
        ptDst - the specified coordinate point that stores the result of transforming ptSrc, or null. Ordinates will be in a dimensionless unit, as a linear distance on a unit sphere or ellipse.
        Returns:
        the coordinate point after transforming (lambda, phi) and storing the result in ptDst.
        Throws:
        ProjectionException - if the point can't be transformed.

      • inverseTransformNormalized

        protected Point2D inverseTransformNormalized​(double x,
                                             double y,
                                             Point2D ptDst)
                                      throws ProjectionException
        Transforms the specified (x,y) coordinates and stores the result in ptDst.
        Specified by:
        inverseTransformNormalized in class MapProjection
        Parameters:
        x - The easting of the coordinate, linear distance on a unit sphere or ellipse.
        y - The northing of the coordinate, linear distance on a unit sphere or ellipse.
        ptDst - the specified coordinate point that stores the result of transforming ptSrc, or null. Ordinates will be in radians.
        Returns:
        the coordinate point after transforming x, y and storing the result in ptDst.
        Throws:
        ProjectionException - if the point can't be transformed.

      • getToleranceForAssertions

        protected double getToleranceForAssertions​(double longitude,
                                           double latitude)
        Maximal error (in metres) tolerated for assertions, if enabled. When assertions are enabled, every direct projection is followed by an inverse projection, and the result is compared to the original coordinate. If a distance greater than the tolerance level is found, then an ProjectionException will be thrown. Subclasses should override this method if they need to relax the tolerance level.
        Overrides:
        getToleranceForAssertions in class MapProjection
        Parameters:
        longitude - The longitude in decimal degrees.
        latitude - The latitude in decimal degrees.
        Returns:
        The tolerance level for assertions, in meters.

      • getZone

        public int getZone()
        Convenience method computing the zone code from the central meridian.
        Returns:
        The zone number, using the scalefactor and false easting to decide if this is a UTM or MTM case. Returns 0 if the case of the projection cannot be determined.

      • getCentralMeridian

        public double getCentralMeridian()
        Convenience method returning the meridian in the middle of current zone. This meridian is typically the central meridian. This method may be invoked to make sure that the central meridian is correctly set.
        Returns:
        The central meridian, using the scalefactor and false easting to decide if this is a UTM or MTM case. Returns Double.NaN if the case of the projection cannot be determined.

      • hashCode

        public int hashCode()
        Returns a hash value for this projection.
        Overrides:
        hashCode in class MapProjection

      • equals

        public boolean equals​(Object o)
        Description copied from class: MapProjection
        Compares the specified object with this map projection for equality.
        Overrides:
        equals in class MapProjection
        Parameters:
        o - The object to compare with this transform.
        Returns:
        true if the given object is a transform of the same class and if, given identical source position, the transformed position would be the equals.