org.geotools.referencing.operation.projection
Class TransverseMercator

java.lang.Object
  org.geotools.referencing.wkt.Formattable
      org.geotools.referencing.operation.transform.AbstractMathTransform
          org.geotools.referencing.operation.projection.MapProjection
              org.geotools.referencing.operation.projection.TransverseMercator

All Implemented Interfaces:

org.opengis.referencing.operation.MathTransform, org.opengis.referencing.operation.MathTransform2D, java.io.Serializable

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 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

Version:

$Id: TransverseMercator.java 18517 2006-03-07 10:46:27Z desruisseaux $

Author:

Andr? Gosselin, Martin Desruisseaux, Rueben Schulz

See Also:

Transverse Mercator projection on MathWorld, "Transverse_Mercator" on Remote Sensing, Serialized Form

Nested Class Summary

static class	TransverseMercator.Provider The MathTransformProvider for a TransverseMercator projection.
static class	TransverseMercator.Provider_SouthOrientated The MathTransformProvider for a South Orientated TransverseMercator projection (EPSG code 9808).

Nested classes inherited from class org.geotools.referencing.operation.projection.MapProjection

MapProjection.AbstractProvider

Field Summary

Fields inherited from class org.geotools.referencing.operation.projection.MapProjection

centralMeridian, excentricity, excentricitySquared, falseEasting, falseNorthing, globalScale, isSpherical, latitudeOfOrigin, scaleFactor, semiMajor, semiMinor

Constructor Summary

protected

TransverseMercator(org.opengis.parameter.ParameterValueGroup parameters) Constructs a new map projection from the supplied parameters.

Method Summary

boolean	equals(java.lang.Object object) Compares the specified object with this map projection for equality.
double	getCentralMeridian() Convenience method returning the meridian in the middle of current zone.
org.opengis.parameter.ParameterDescriptorGroup	getParameterDescriptors() Returns the parameter descriptors for this map projection. This is used for a providing a default implementation of MapProjection.getParameterValues(), as well as arguments checking.
protected double	getToleranceForAssertions(double longitude, double latitude) Maximal error (in metres) tolerated for assertion, 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 AssertionError will be thrown. Subclasses should override this method if they need to relax the tolerance level.
int	getZone() Convenience method computing the zone code from the central meridian.
int	hashCode() Returns a hash value for this projection.
protected java.awt.geom.Point2D	inverseTransformNormalized(double x, double y, java.awt.geom.Point2D ptDst) Transforms the specified (x,y) coordinate and stores the result in .
protected java.awt.geom.Point2D	transformNormalized(double x, double y, java.awt.geom.Point2D ptDst) Transforms the specified (x,y) coordinate (units in radians) and stores the result in (linear distance on a unit sphere).

Methods inherited from class org.geotools.referencing.operation.projection.MapProjection

getParameterValues, getSourceDimensions, getTargetDimensions, inverse, transform, transform, transform

Methods inherited from class org.geotools.referencing.operation.transform.AbstractMathTransform

createTransformedShape, derivative, derivative, ensureNonNull, formatWKT, getDimSource, getDimTarget, isIdentity, needCopy, rollLongitude, transform

Methods inherited from class org.geotools.referencing.wkt.Formattable

toString, toWKT, toWKT, toWKT

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface org.opengis.referencing.operation.MathTransform2D

createTransformedShape, derivative

Methods inherited from interface org.opengis.referencing.operation.MathTransform

derivative, isIdentity, toWKT, transform

Constructor Detail

TransverseMercator

protected TransverseMercator(org.opengis.parameter.ParameterValueGroup parameters)
                      throws org.opengis.parameter.ParameterNotFoundException

Constructs a new map projection from the supplied parameters.

Parameters:

parameters - The parameter values in standard units.

Throws:

org.opengis.parameter.ParameterNotFoundException - if a mandatory parameter is missing.

Method Detail

getParameterDescriptors

public org.opengis.parameter.ParameterDescriptorGroup getParameterDescriptors()

Returns the parameter descriptors for this map projection. This is used for a providing a default implementation of MapProjection.getParameterValues(), as well as arguments checking.

Specified by:

getParameterDescriptors in class MapProjection

transformNormalized

protected java.awt.geom.Point2D transformNormalized(double x,
                                                    double y,
                                                    java.awt.geom.Point2D ptDst)
                                             throws ProjectionException

Transforms the specified (x,y) coordinate (units in radians) and stores the result in (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 , or . Ordinates will be in a dimensionless unit, as a linear distance on a unit sphere or ellipse.

Returns:

the coordinate point after transforming , and storing the result in .

Throws:

ProjectionException - if the point can't be transformed.

inverseTransformNormalized

protected java.awt.geom.Point2D inverseTransformNormalized(double x,
                                                           double y,
                                                           java.awt.geom.Point2D ptDst)
                                                    throws ProjectionException

Transforms the specified (x,y) coordinate and stores the result in .

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 , or . Ordinates will be in radians.

Returns:

the coordinate point after transforming , and storing the result in .

Throws:

ProjectionException - if the point can't be transformed.

getToleranceForAssertions

protected double getToleranceForAssertions(double longitude,
                                           double latitude)

Maximal error (in metres) tolerated for assertion, 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 AssertionError 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 degrees.

latitude - The latitude in 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(java.lang.Object object)

Compares the specified object with this map projection for equality.

Overrides:

equals in class MapProjection