com.revolsys.gis.cs.projection

Class TransverseMercator

java.lang.Object

com.revolsys.gis.cs.projection.AbstractCoordinatesProjection

com.revolsys.gis.cs.projection.TransverseMercator

All Implemented Interfaces:

CoordinatesProjection

public class TransverseMercator
extends AbstractCoordinatesProjection

An implementation of the Transverse Mercator projection. See section 1.3.5 of OGP Surveying and Positioning Guidance Note number 7, part 2.

Author:

Paul Austin

Constructor Summary

Constructors

Constructor and Description
TransverseMercator(ProjectedCoordinateSystem coordinateSystem) Construct a new TransverseMercator projection.

Method Summary

Methods

Modifier and Type	Method and Description
void	inverse(double x, double y, double[] targetCoordinates, int targetOffset, int targetAxisCount) Project the projected coordinates in metres to lon/lat ordinates in degrees.
void	project(double lambda, double phi, double[] targetCoordinates, int targetOffset, int targetAxisCount) Project the lon/lat ordinates in degrees to projected coordinates in metres.
String	toString() Return the string representation of the projection.

Methods inherited from class com.revolsys.gis.cs.projection.AbstractCoordinatesProjection

getInverseOperation, getProjectOperation

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

TransverseMercator

public TransverseMercator(ProjectedCoordinateSystem coordinateSystem)

Construct a new TransverseMercator projection.

Parameters:

coordinateSystem - The coordinate system.

Method Detail

inverse

public void inverse(double x,
           double y,
           double[] targetCoordinates,
           int targetOffset,
           int targetAxisCount)

Project the projected coordinates in metres to lon/lat ordinates in degrees.

 ϕ = ϕ1 – (ν1 * tanϕ1 / ρ1 ) * [
   D ˆ 2/2 –
   (5 + 3 * T1 + 10 * C1 – 4 * C1 ˆ 2 – 9 * e' ˆ 2) * D ˆ 4 / 24 +
   (61 + 90 * T1 + 298 * C1 + 45 * T1 ˆ 2 – 252 * e' ˆ 2 – 3 * C1 ˆ 2) * D ˆ 6 / 720
 ]
 λ = λO + [
   D –
   (1 + 2 * T1 + C1) * D ˆ 3 / 6 +
   (5 – 2 * C1 + 28 * T1 –
   3 * C1 ˆ 2 + 8 * e' ˆ 2 + 24 * T1 ˆ 2) * D ˆ 5 / 120
 ] / cosϕ1

 ν1 = a /(1 – e ˆ 2 * sinϕ1 ˆ 2) ˆ 0.5
 ρ1 = a * (1 – e ˆ 2) / (1 – e ˆ 2 * sinϕ1 ˆ 2) ˆ 1.5

 ϕ1 = μ1 +
   (3 * e1 / 2 – 27 * e1 ˆ 3 /32 + .....) * sin(2 * μ1) +
   (21 * e1 ˆ 2 / 16 – 55 * e1 ˆ 4 / 32 + ....) * sin(4 * μ1) +
   (151 * e1 ˆ 3 / 96 + .....) * sin(6 * μ1) +
   (1097 * e1 ˆ 4 / 512 – ....) * sin(8 * μ1) +
   ......

 e1 = [1 – (1 – e ˆ 2) ˆ 0.5] / [1 + (1 – e ˆ 2) ˆ 0.5]
 μ1 = M1 / [a * (1 – e ˆ 2 / 4 – 3 * e ˆ 4 / 64 – 5 * e ˆ 6 / 256 – ....)]
 M1 = MO + (y – y0) / k0
 T1 = tanϕ1 ˆ 2
 C1 = e' ˆ 2 * cosϕ1 ˆ 2
 e' ˆ 2 = e ˆ 2 / (1 – e ˆ 2)
 D = (x – x0) / (ν1 * kO)
 

Parameters:

from - The ordinates to convert.

to - The ordinates to write the converted ordinates to.

project

public void project(double lambda,
           double phi,
           double[] targetCoordinates,
           int targetOffset,
           int targetAxisCount)

Project the lon/lat ordinates in degrees to projected coordinates in metres.

 x = x0 + kO * ν * [
   A + (1 – T + C) * A ˆ 3 / 6 +
   (5 – 18 * T + T ˆ 2 + 72 *C – 58 *e' ˆ 2 ) * A ˆ 5 / 120
 ]
 y = y0 + kO * { M – MO + ν * tanϕ * [
   A ˆ 2 / 2 +
   (5 – T + 9 * C + 4 * C ˆ 2) * A ˆ 4 / 24 +
   (61 – 58 * T + T ˆ 2 + 600 * C – 330 * e' ˆ 2 ) * A ˆ 6 / 720
 ]}

 T = tanϕ * 2
 C = e ˆ 2 * cosϕ ˆ 2 / (1 – e ˆ 2)
 A = (λ – λO) * cosϕ
 ν = a / (1 – e ˆ 2 * sinϕ ˆ 2) ˆ 0.5
 

Parameters:

from - The ordinates to convert.

to - The ordinates to write the converted ordinates to.

toString

public String toString()

Return the string representation of the projection.

Overrides:

toString in class Object

Returns:

The string.