com.revolsys.gis.cs.projection

Class AlbersConicEqualArea

java.lang.Object

com.revolsys.gis.cs.projection.AbstractCoordinatesProjection

com.revolsys.gis.cs.projection.AlbersConicEqualArea

All Implemented Interfaces:

CoordinatesProjection

public class AlbersConicEqualArea
extends AbstractCoordinatesProjection

Albers Equal Area

(EPSG dataset coordinate operation method code 9822)

To derive the projected coordinates of a point, geodetic latitude (φ) is converted to authalic latitude (ß). The formulas to convert geodetic latitude and longitude (φ, λ) to Easting (E) and Northing (N) are:

 Easting (E) = EF + (ρ sin θ)
 Northing(N) = NF +ρO –(ρ cosθ)
 

where

 θ =n (λ–λO)
 ρ =[a (C–nα)0.5]/n ρO =[a (C–nαO)0.5]/n
 

and

 C = m12 + (n α1)
 n =(m12 –m22)/(α2 –α1)
 m1 = cos φ1 / (1 – e2sin2φ1)0.5
 m2 = cos φ2 / (1 – e2sin2φ2)0.5
 α = (1 – e2) {[sinφ / (1 – e2sin2φ)] – [1/(2e)] ln [(1 – esinφ) / (1 + esinφ)]}
 αO = (1 – e2) {[sinφO / (1 – e2sin2φO)] – [1/(2e)] ln [(1 – e sinφO) / (1 + e sinφO)]}
 α1 = (1 – e2) {[sinφ1 / (1 – e2sin2φ1)] – [1/(2e)] ln [(1 – e sinφ1) / (1 + e sinφ1)]}
 α2 = (1 – e2) {[sinφ2 / (1 – e2sin2φ2)] – [1/(2e)] ln [(1 – e sinφ2) / (1 + e sinφ2)]}
 

The reverse formulas to derive the geodetic latitude and longitude of a point from its Easting and Northing values are: φ = ß' + (e2/3 + 31e4/180 + 517e6/5040) sin 2ß'] + [(23e4/360 + 251e6/3780) sin 4ß'] + [(761e6/45360) sin 6ß']

 λ = λO + (θ / n)
 

where

 ß'= asin(α'/{1–[(1–e2)/(2 e)] ln[(1–e)/(1+e)] α'= [C–(ρ2 n2 /a2)]/n
 ρ= {(E–EF)2 +[ρO –(N–NF)]2 }0.5
 θ= atan[(E–EF)/[ρO –(N–NF)]
 

and C, n and ρO are as in the forward equations.

Author:

paustin

Constructor Summary

Constructors

Constructor and Description
AlbersConicEqualArea(ProjectedCoordinateSystem cs)

Method Summary

Methods

Modifier and Type	Method and Description
void	inverse(double x, double y, double[] targetCoordinates, int targetOffset, int targetAxisCount) n = sin(phi1) + sin (phi2)
void	project(double lambda, double phi, double[] targetCoordinates, int targetOffset, int targetAxisCount) a = semiMajorAxis lambda = lon; phi = lat; x = rho * sin(theta) y = rho0 - rho * sin(theta) rho = a * sqrt(C - n * q) / n

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, toString, wait, wait, wait

Constructor Detail

AlbersConicEqualArea

public AlbersConicEqualArea(ProjectedCoordinateSystem cs)

Method Detail

inverse

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

n = sin(phi1) + sin (phi2)

phi = sin-1( ( C - (rho ^ 2) * (n ^ 2) ) / 2 * n )

lambda =

project

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

 a = semiMajorAxis
 lambda = lon;
 phi = lat;

 x = rho * sin(theta)
 y = rho0 - rho * sin(theta)

 rho = a * sqrt(C - n * q) / n