org.geotoolkit.referencing.operation.projection
Class TransverseMercator

Object
  FormattableObject
      AbstractMathTransform
          AbstractMathTransform2D
              UnitaryProjection
                  TransverseMercator

All Implemented Interfaces:

Serializable, Formattable, Parameterized, LenientComparable, MathTransform, MathTransform2D

@Immutable
public class TransverseMercator
extends UnitaryProjection

Transverse Mercator Projection (EPSG codes 9807, 9808). See the Mercator projection on MathWorld for an overview. See any of the following providers for a list of programmatic parameters:

• TransverseMercator
• TransverseMercator.SouthOrientated

Description
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 less than a millimetre ±10 degrees from the central meridian, a few millimetres ±15 degrees from the central meridian and a few centimetres ±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 500000 metres is used for all zones and a false northing of 10000000 metres is used for zones in the southern hemisphere.

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:

1.0

Version:

3.16

Author:

Gerald Evenden (USGS), André Gosselin (MPO), Martin Desruisseaux (MPO, IRD, Geomatys), Rueben Schulz (UBC)

See Also:

Mercator, ObliqueMercator, Serialized Form

Module:

referencing/geotk-referencing (download)

View source code for this class

Nested Class Summary

protected static class

TransverseMercator.Parameters Parameters of a Transverse Mercator projection.

Field Summary

Fields inherited from class UnitaryProjection

excentricity, excentricitySquared

Fields inherited from class FormattableObject

EPSG, GEOTIFF, INTERNAL, OGC, SINGLE_LINE

Constructor Summary

protected

TransverseMercator(TransverseMercator.Parameters parameters) Constructs a new map projection from the supplied parameters.

Method Summary

static MathTransform2D	create(ParameterDescriptorGroup descriptor, ParameterValueGroup values) Creates a Transverse Mercator projection from the given parameters.
Matrix	derivative(Point2D point) Gets the derivative of this transform at a point.
protected void	inverseTransform(double[] srcPts, int srcOff, double[] dstPts, int dstOff) Transforms the specified (x,y) coordinates and stores the result in dstPts (angles in radians).
protected void	transform(double[] srcPts, int srcOff, double[] dstPts, int dstOff) Transforms the specified (λ,φ) coordinates (units in radians) and stores the result in dstPts (linear distance on a unit sphere).

Methods inherited from class UnitaryProjection

computeHashCode, equals, finish, getParameterValues, getUnmarshalledParameters, inverse, resetWarnings, rollLongitude, transform, unrollLongitude

Methods inherited from class AbstractMathTransform2D

getParameterDescriptors, getSourceDimensions, getTargetDimensions, transform

Methods inherited from class AbstractMathTransform

createTransformedShape, derivative, ensureNonNull, equals, formatWKT, getName, hashCode, isIdentity, rollLongitude, transform, transform, transform, transform

Methods inherited from class FormattableObject

getDefaultIndentation, print, setDefaultIndentation, toString, toWKT, toWKT, toWKT

Methods inherited from class Object

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

Methods inherited from interface MathTransform2D

createTransformedShape

Methods inherited from interface MathTransform

derivative, isIdentity, toWKT, transform, transform, transform, transform

Constructor Detail

TransverseMercator

protected TransverseMercator(TransverseMercator.Parameters parameters)

Constructs a new map projection from the supplied parameters.

Parameters:

parameters - The parameters of the projection to be created.

Method Detail

create

public static MathTransform2D create(ParameterDescriptorGroup descriptor,
                                     ParameterValueGroup values)

Creates a Transverse Mercator projection from the given parameters. The descriptor argument is usually TransverseMercator.PARAMETERS, but is not restricted to. If a different descriptor is supplied, it is user's responsibility to ensure that it is suitable to a Transverse Mercator projection.

Parameters:

descriptor - Typically TransverseMercator.PARAMETERS.

values - The parameter values of the projection to create.

Returns:

The map projection.

Since:

3.00

transform

protected void transform(double[] srcPts,
                         int srcOff,
                         double[] dstPts,
                         int dstOff)
                  throws ProjectionException

Transforms the specified (λ,φ) coordinates (units in radians) and stores the result in dstPts (linear distance on a unit sphere).

Specified by:

transform in class UnitaryProjection

Parameters:

srcPts - The array containing the source point coordinate, as (longitude, latitude) angles in radians.

srcOff - The offset of the point to be converted in the source array.

dstPts - the array into which the converted point coordinate is returned (may be the same than srcPts). Ordinates will be in a dimensionless unit, as a linear distance on a unit sphere or ellipse.

dstOff - The offset of the location of the converted point that is stored in the destination array.

Throws:

ProjectionException - if the point can't be converted.

inverseTransform

protected void inverseTransform(double[] srcPts,
                                int srcOff,
                                double[] dstPts,
                                int dstOff)
                         throws ProjectionException

Transforms the specified (x,y) coordinates and stores the result in dstPts (angles in radians).

Specified by:

inverseTransform in class UnitaryProjection

Parameters:

srcPts - The array containing the source point coordinate, as linear distance on a unit sphere or ellipse.

srcOff - The offset of the point to be converted in the source array.

dstPts - the array into which the converted point coordinate is returned (may be the same than srcPts). Ordinates will be (longitude, latitude) angles in radians.

dstOff - The offset of the location of the converted point that is stored in the destination array.

Throws:

ProjectionException - if the point can't be converted.

derivative

public Matrix derivative(Point2D point)
                  throws ProjectionException

Gets the derivative of this transform at a point. The current implementation is derived from the spherical formulas.

Specified by:

derivative in interface MathTransform2D

Overrides:

derivative in class AbstractMathTransform

Parameters:

point - The coordinate point where to evaluate the derivative.

Returns:

The derivative at the specified point as a 2×2 matrix.

Throws:

ProjectionException - if the derivative can't be evaluated at the specified point.

Since:

3.16

See Also:

MathTransform2D.derivative(Point2D)