Package org.openstreetmap.josm.data.projection.proj

Class TransverseMercator

  • All Implemented Interfaces:
    Proj
    public class TransverseMercator
extends AbstractProj
    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 further from the central meridian. The Transverse Mercator projection is appropriate for region which 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.

    This class has been derived from the implementation of the Geotools project; git 8cbf52d, org.geotools.referencing.operation.projection.TransverseMercator at the time of migration.

    The non-standard parameter gamma has been added as a method to rotate the projected coordinates by a certain angle (clockwise, see ObliqueMercator).

    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.
    See Also:
    Transverse Mercator projection on MathWorld, "Transverse_Mercator" on RemoteSensing.org

    • Field Summary

      Fields 
      Modifier and Type Field Description
      private double cosrot
      Sine and Cosine values for the coordinate system rotation angle
      private double eb2
      A derived quantity of excentricity, computed by e'² = (a²-b²)/b² = es/(1-es) where a is the semi-major axis length and b is the semi-minor axis length.
      private static double EPSILON
      Maximum difference allowed when comparing real numbers.
      private static double FC1
      Constants used for the forward and inverse transform for the elliptical case of the Transverse Mercator.
      private static double FC2  
      private static double FC3  
      private static double FC4  
      private static double FC5  
      private static double FC6  
      private static double FC7  
      private static double FC8  
      protected double latitudeOfOrigin
      Latitude of origin in radians.
      private double ml0
      Meridian distance at the latitudeOfOrigin.
      protected double rectifiedGridAngle
      The rectified bearing of the central line, in radians.
      private double sinrot
      Sine and Cosine values for the coordinate system rotation angle

    • Field Detail

      • FC1

        private static final double FC1
        Constants used for the forward and inverse transform for the elliptical case of the Transverse Mercator.
        See Also:
        Constant Field Values

      • eb2

        private double eb2
        A derived quantity of excentricity, computed by e'² = (a²-b²)/b² = es/(1-es) where a is the semi-major axis length and b is the semi-minor axis length.

      • latitudeOfOrigin

        protected double latitudeOfOrigin
        Latitude of origin in radians. Default value is 0, the equator. This is called 'phi0' in Snyder.

      • ml0

        private double ml0
        Meridian distance at the latitudeOfOrigin. Used for calculations for the ellipsoid.

      • rectifiedGridAngle

        protected double rectifiedGridAngle
        The rectified bearing of the central line, in radians.

      • sinrot

        private double sinrot
        Sine and Cosine values for the coordinate system rotation angle

      • cosrot

        private double cosrot
        Sine and Cosine values for the coordinate system rotation angle

    • Method Detail

      • getName

        public java.lang.String getName()
        Description copied from interface: Proj
        Replies a human readable name of this projection.
        Returns:
        The projection name. must not be null.

      • getProj4Id

        public java.lang.String getProj4Id()
        Description copied from interface: Proj
        Replies the Proj.4 identifier.
        Returns:
        The Proj.4 identifier (as reported by cs2cs -lp). If no id exists, return null.

      • project

        public double[] project​(double y,
                        double x)
        Description copied from interface: Proj
        Convert lat/lon to east/north.
        Parameters:
        y - the latitude in radians
        x - the longitude in radians
        Returns:
        array of length 2, containing east and north value in meters, divided by the semi major axis of the ellipsoid.

      • invproject

        public double[] invproject​(double x,
                           double y)
        Description copied from interface: Proj
        Convert east/north to lat/lon.
        Parameters:
        x - east value in meters, divided by the semi major axis of the ellipsoid
        y - north value in meters, divided by the semi major axis of the ellipsoid
        Returns:
        array of length 2, containing lat and lon in radians.

      • getAlgorithmBounds

        public Bounds getAlgorithmBounds()
        Description copied from interface: Proj
        Return the bounds where this projection is applicable. This is a fallback for when the projection bounds are not specified explicitly. In this area, the round trip lat/lon → east/north → lat/lon should return the starting value with small error. In addition, regions with extreme distortions should be excluded, if possible. It need not be the absolute maximum, but rather an area that is safe to display in JOSM and contain everything that one would expect to use.
        Returns:
        the bounds where this projection is applicable, null if unknown