org.openstreetmap.josm.data.projection.proj

Class AlbersEqualArea

java.lang.Object

org.openstreetmap.josm.data.projection.proj.AbstractProj

org.openstreetmap.josm.data.projection.proj.AlbersEqualArea

All Implemented Interfaces:

Proj

public class AlbersEqualArea
extends AbstractProj

Albers Equal Area Projection (EPSG code 9822). This is a conic projection with parallels being unequally spaced arcs of concentric circles, more closely spaced at north and south edges of the map. Merideans are equally spaced radii of the same circles and intersect parallels at right angles. As the name implies, this projection minimizes distortion in areas.

The "standard_parallel_2" parameter is optional and will be given the same value as "standard_parallel_1" if not set (creating a 1 standard parallel projection).

NOTE: formulae used below are from a port, to Java, of the proj4 package of the USGS survey. USGS work is acknowledged here.

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

References:

• Proj-4.4.7 available at www.remotesensing.org/proj
  Relevent files are: PJ_aea.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:

9419

See Also:

Albers Equal-Area Conic Projection on MathWorld, "Albers_Conic_Equal_Area" on RemoteSensing.org, British Columbia Albers Standard Projection

Field Summary

Fields

Modifier and Type	Field and Description
private double	c Constants used by the spherical and elliptical Albers projection.
private double	ec An error condition indicating iteration will not converge for the inverse ellipse.
private static double	EPSILON Maximum difference allowed when comparing real numbers.
private static double	ITERATION_TOLERANCE Difference allowed in iterative computations.
private static int	MAXIMUM_ITERATIONS Maximum number of iterations for iterative computations.
private double	n Constants used by the spherical and elliptical Albers projection.
private double	n2 Constants used by the spherical and elliptical Albers projection.
private double	rho0 Constants used by the spherical and elliptical Albers projection.

Fields inherited from class org.openstreetmap.josm.data.projection.proj.AbstractProj

e, e2, en0, en1, en2, en3, en4, spherical

Constructor Summary

Constructors

Constructor and Description
AlbersEqualArea()

Method Summary

Modifier and Type	Method and Description
Bounds	getAlgorithmBounds() Return the bounds where this projection is applicable.
java.lang.String	getName() Replies a human readable name of this projection.
java.lang.String	getProj4Id() Replies the Proj.4 identifier.
void	initialize(ProjParameters params) Initialize the projection using the provided parameters.
double[]	invproject(double x, double y) Convert east/north to lat/lon.
double	phi1(double qs) Iteratively solves equation (3-16) from Snyder.
double[]	project(double y, double x) Convert lat/lon to east/north.
private double	qsfn(double sinphi) Calculates q, Snyder equation (3-12)

Methods inherited from class org.openstreetmap.josm.data.projection.proj.AbstractProj

aasin, cphi2, invMlfn, isGeographic, mlfn, msfn, tsfn

Methods inherited from class java.lang.Object

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

Methods inherited from interface org.openstreetmap.josm.data.projection.proj.Proj

lonIsLinearToEast

Field Detail

MAXIMUM_ITERATIONS

private static final int MAXIMUM_ITERATIONS

Maximum number of iterations for iterative computations.

See Also:

Constant Field Values

ITERATION_TOLERANCE

private static final double ITERATION_TOLERANCE

Difference allowed in iterative computations.

See Also:

Constant Field Values

EPSILON

private static final double EPSILON

Maximum difference allowed when comparing real numbers.

See Also:

Constant Field Values

n

private double n

Constants used by the spherical and elliptical Albers projection.

n2

private double n2

Constants used by the spherical and elliptical Albers projection.

c

private double c

Constants used by the spherical and elliptical Albers projection.

rho0

private double rho0

Constants used by the spherical and elliptical Albers projection.

ec

private double ec

An error condition indicating iteration will not converge for the inverse ellipse. See Snyder (14-20)

Constructor Detail

AlbersEqualArea

public AlbersEqualArea()

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.

initialize

public void initialize(ProjParameters params)
                throws ProjectionConfigurationException

Description copied from interface: Proj

Initialize the projection using the provided parameters.

Specified by:

initialize in interface Proj

Overrides:

initialize in class AbstractProj

Parameters:

params - The projection parameters

Throws:

ProjectionConfigurationException - in case parameters are not suitable

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.

phi1

public double phi1(double qs)

Iteratively solves equation (3-16) from Snyder.

Parameters:

qs - arcsin(q/2), used in the first step of iteration

Returns:

the latitude

qsfn

private double qsfn(double sinphi)

Calculates q, Snyder equation (3-12)

Parameters:

sinphi - sin of the latitude q is calculated for

Returns:

q from Snyder equation (3-12)

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