org.cts.datum
Class Ellipsoid

java.lang.Object
  org.cts.IdentifiableComponent
      org.cts.datum.Ellipsoid

All Implemented Interfaces:

Identifiable

public class Ellipsoid
extends IdentifiableComponent

An ellipsoid is a mathematical surface used to describe the Earth surface.

It is only an approximation of the Earth surface, but it is used as a reference surface for the expression of coordinates as a latitude and a longitude.

The definition of an ellipsoid is based on two parameters :

• 1st parameter = semi-major axis
• 2nd parameter = inverse flattening, semi-minor axis or eccentricity. The parameter type is choosen among the values of SecondParameter enum.

Note on the precision of some algorithms :

• The calculation of semi-minor axis, inverse flattening and eccentricity are precise. For example, the construction of 10 successive ellipsoids using alternatively the 3 parameters keeps a precision of less than 0.01 micron for the semi-minor axis
• Default curvilinearAbscissa method or arcFromLat method using parameters computed from 4, 5 or 6 iteration (see initKCoeff) give consistant results at a precision of 1 micron (1E-6).

Author:

Michaël Michaud, Jules Party

Nested Class Summary

static class

Ellipsoid.SecondParameter The second parameter use to create the ellipsoid, this parameter can be the inverse flattening, the semi-minor axis or the eccentricity.

Field Summary

static Ellipsoid	AIRY Airy 1830.
static Ellipsoid	AIRYMOD Airy Modified 1849.
static Ellipsoid	AustSA GRS 1967 (SAD 1969) ellipsoid, used in Australian Geodetic Datum and in South American Datum 1969.
static Ellipsoid	BESSEL1841 Bessel 1841.
static Ellipsoid	BESSNAM Bessel Namibia (GLM).
static Ellipsoid	CLARKE1866 Clarke 1866.
static Ellipsoid	CLARKE1880ARC Clarke 1880 (Arc).
static Ellipsoid	CLARKE1880IGN Clarke 1880 (IGN).
static Ellipsoid	CLARKE1880RGS Clarke 1880 (RGS) or Clarke 1880 modified.
static Map<String,Ellipsoid>	ellipsoidFromName ellipsoidFromName associates each ellipsoid to a short string used to recognize it in CTS.
static Ellipsoid	EVERESTSS Everest 1830 (1967 definition).
static Ellipsoid	GRS67 GRS 1967 ellipsoid, used in Australian Geodetic Datum and in South American Datum 1969.
static Ellipsoid	GRS80 GRS 1980 ellipsoid, used in most recent spatial geodetic system (1990 and after).
static Ellipsoid	HELMERT Helmert 1906.
static Ellipsoid	INTERNATIONAL1924 International 1924.
static Ellipsoid	KRASSOWSKI Krassowski 1940.
static Ellipsoid	SPHERE Perfect SPHERE.
static Ellipsoid	WGS66 WGS 66.
static Ellipsoid	WGS72 WGS 72.
static Ellipsoid	WGS84 WGS84 ellipsoid, used with the WGS84 spatial geodetic datum.

Fields inherited from interface org.cts.Identifiable

DEFAULT, LOCAL, UNKNOWN

Method Summary

double	arcFromLat(double phi) Computes the meridian arc from equator to point with ellipsoidal latitude phi.
static Ellipsoid	createEllipsoidFromEccentricity(double semiMajorAxis, double eccentricity) Creates a new Ellipsoid whose definition is based on semi-major axis and eccentricity and initializes common parameters such as a, b, e, e2, f, 1/f, e'2 and coefficients for the meridian arc.
static Ellipsoid	createEllipsoidFromEccentricity(Identifier identifier, double semiMajorAxis, double eccentricity) Creates a new Ellipsoid whose definition is based on semi-major axis and eccentricity and initializes common parameters such as a, b, e, e2, f, 1/f, e'2 and coefficients for the meridian arc.
static Ellipsoid	createEllipsoidFromInverseFlattening(double semiMajorAxis, double invFlattening) Creates a new Ellipsoid whose definition is based on semi-major axis and inverse flattening and initializes common parameters such as a, b, e, e2, f, 1/f, e'2 and coefficients for the meridian arc.
static Ellipsoid	createEllipsoidFromInverseFlattening(Identifier identifier, double semiMajorAxis, double invFlattening) Creates a new Ellipsoid whose definition is based on semi-major axis and inverse flattening and initializes common parameters such as a, b, e, e2, f, 1/f, e'2 and coefficients for the meridian arc.
static Ellipsoid	createEllipsoidFromSemiMinorAxis(double semiMajorAxis, double semiMinorAxis) Creates a new Ellipsoid whose definition is based on semi-major axis and semi-minor axis and initializes common parameters such as a, b, e, e2, f, 1/f, e'2 and coefficients for the meridian arc.
static Ellipsoid	createEllipsoidFromSemiMinorAxis(Identifier identifier, double semiMajorAxis, double semiMinorAxis) Creates a new Ellipsoid whose definition is based on semi-major axis and semi-minor axis and initializes common parameters such as a, b, e, e2, f, 1/f, e'2 and coefficients for the meridian arc.
double	curvilinearAbscissa(double latitude) Returns the curvilinear abscissa of the meridian arc for this latitude on an ellipsoid with eccentricity = this.e and semi-major axis = 1.0.
boolean	equals(Object other) Returns true if this Ellipsoid can be considered as equals to another one.
double[]	getArcCoeff() Get coefficients for the meridian arc length.
double	getEccentricity() Return the eccentricity of this ellipsoid (fr : excentricit�).
double	getFlattening() Return the flattening of this ellipsoid (fr : aplatissement).
double	getInverseFlattening() Return the inverse flattening of this ellipsoid (fr : aplatissement inverse).
double[]	getKCoeff(int max) Get k coefficients computed with an iterative method.
double	getSecondEccentricitySquared() Return the second eccentricity ((a-b)/b) of this ellipsoid (fr : seconde excentricité).
double	getSemiMajorAxis() Return the semi-major axis of this ellipsoid (fr : demi grand axe).
double	getSemiMinorAxis() Return the semi-minor axis of this ellipsoid (fr : demi petit axe).
double	getSquareEccentricity() Return the square eccentricity of this ellipsoid (fr : carré de l'excentricité).
double	grandeNormale(double latitude)
int	hashCode() Returns the hash code for this Ellipsoid.
void	initKCoeff(int max) This second method to compute the meridian arc length is taken from .
double	isometricLatitude(double latitude) Computes isometric latitude from geographic (or geodetic) latitude.
double	latFromArc(double s) Computes the ellipsoidal latitude from meridian arc length.
double	latitude(double isoLatitude) Computes geographic latitude from isometric latitude.
double	latitude(double isoLatitude, double epsilon) Computes the geographic latitude from the isometric latitude (fr : calcul de la latitude géographique à partir de la latitude isometrique).
double	meridionalRadiusOfCurvature(double latitude) The Meridional Radius of Curvature is the radius of curvature, at a specific latitude, of the ellipse used to generate the ellipsoid.
String	toString() Return a string representtaion of this ellipsoid.
String	toWKT() Returns a WKT representation of the ellipsoid.
double	transverseRadiusOfCurvature(double latitude) The Transverse Radius of Curvature or radius of the first vertical section or prime vertical radius of curvature (fr : Grande Normale).

Methods inherited from class org.cts.IdentifiableComponent

addAlias, addRemark, getAliases, getAuthorityKey, getAuthorityName, getCode, getComponent, getIdentifier, getName, getRemarks, getShortName, setIdentifier, setRemarks, setShortName

Methods inherited from class java.lang.Object

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

Field Detail

SPHERE

public static final Ellipsoid SPHERE

Perfect SPHERE.

GRS80

public static final Ellipsoid GRS80

GRS 1980 ellipsoid, used in most recent spatial geodetic system (1990 and after).

WGS84

public static final Ellipsoid WGS84

WGS84 ellipsoid, used with the WGS84 spatial geodetic datum. This ellipsoid (and datum) is coherent with GRS80 and the ITRS.

INTERNATIONAL1924

public static final Ellipsoid INTERNATIONAL1924

International 1924.

BESSEL1841

public static final Ellipsoid BESSEL1841

Bessel 1841.

CLARKE1866

public static final Ellipsoid CLARKE1866

Clarke 1866.

CLARKE1880IGN

public static final Ellipsoid CLARKE1880IGN

Clarke 1880 (IGN).

CLARKE1880RGS

public static final Ellipsoid CLARKE1880RGS

Clarke 1880 (RGS) or Clarke 1880 modified.

CLARKE1880ARC

public static final Ellipsoid CLARKE1880ARC

Clarke 1880 (Arc). Note that the ellipsoid called clrk80 in the proj library is defined as the Clarke 1880 mod. (modified) which is refered as the Clarke 1880 (RGS) in the epsg database, with an inverse flattening parameter of 293.465 instead of 293.466

KRASSOWSKI

public static final Ellipsoid KRASSOWSKI

Krassowski 1940.

EVERESTSS

public static final Ellipsoid EVERESTSS

Everest 1830 (1967 definition).

GRS67

public static final Ellipsoid GRS67

GRS 1967 ellipsoid, used in Australian Geodetic Datum and in South American Datum 1969.

AustSA

public static final Ellipsoid AustSA

GRS 1967 (SAD 1969) ellipsoid, used in Australian Geodetic Datum and in South American Datum 1969.

AIRY

public static final Ellipsoid AIRY

Airy 1830.

BESSNAM

public static final Ellipsoid BESSNAM

Bessel Namibia (GLM).

HELMERT

public static final Ellipsoid HELMERT

Helmert 1906.

AIRYMOD

public static final Ellipsoid AIRYMOD

Airy Modified 1849.

WGS66

public static final Ellipsoid WGS66

WGS 66.

WGS72

public static final Ellipsoid WGS72

WGS 72.

ellipsoidFromName

public static final Map<String,Ellipsoid> ellipsoidFromName

ellipsoidFromName associates each ellipsoid to a short string used to recognize it in CTS.

Method Detail

getSemiMajorAxis

public double getSemiMajorAxis()

Return the semi-major axis of this ellipsoid (fr : demi grand axe).

getInverseFlattening

public double getInverseFlattening()

Return the inverse flattening of this ellipsoid (fr : aplatissement inverse).

getSemiMinorAxis

public double getSemiMinorAxis()

Return the semi-minor axis of this ellipsoid (fr : demi petit axe).

getFlattening

public double getFlattening()

Return the flattening of this ellipsoid (fr : aplatissement).

getEccentricity

public double getEccentricity()

Return the eccentricity of this ellipsoid (fr : excentricit�).

getSquareEccentricity

public double getSquareEccentricity()

Return the square eccentricity of this ellipsoid (fr : carré de l'excentricité).

getSecondEccentricitySquared

public double getSecondEccentricitySquared()

Return the second eccentricity ((a-b)/b) of this ellipsoid (fr : seconde excentricité).

getArcCoeff

public double[] getArcCoeff()

Get coefficients for the meridian arc length.

getKCoeff

public double[] getKCoeff(int max)

Get k coefficients computed with an iterative method.

createEllipsoidFromInverseFlattening

public static Ellipsoid createEllipsoidFromInverseFlattening(double semiMajorAxis,
                                                             double invFlattening)
                                                      throws IllegalArgumentException

Creates a new Ellipsoid whose definition is based on semi-major axis and inverse flattening and initializes common parameters such as a, b, e, e2, f, 1/f, e'2 and coefficients for the meridian arc.

Parameters:

semiMajorAxis - length of the semi-major axis in meters

invFlattening - inverse flattening of the ellipsoid

Throws:

IllegalArgumentException

createEllipsoidFromInverseFlattening

public static Ellipsoid createEllipsoidFromInverseFlattening(Identifier identifier,
                                                             double semiMajorAxis,
                                                             double invFlattening)
                                                      throws IllegalArgumentException

Creates a new Ellipsoid whose definition is based on semi-major axis and inverse flattening and initializes common parameters such as a, b, e, e2, f, 1/f, e'2 and coefficients for the meridian arc.

Parameters:

identifier - ellipsoid identifier

semiMajorAxis - length of the semi-major axis in meters

invFlattening - inverse flattening of the ellipsoid

Throws:

IllegalArgumentException

createEllipsoidFromSemiMinorAxis

public static Ellipsoid createEllipsoidFromSemiMinorAxis(double semiMajorAxis,
                                                         double semiMinorAxis)
                                                  throws IllegalArgumentException

Creates a new Ellipsoid whose definition is based on semi-major axis and semi-minor axis and initializes common parameters such as a, b, e, e2, f, 1/f, e'2 and coefficients for the meridian arc.

Parameters:

semiMajorAxis - length of the semi-major axis in meters

semiMinorAxis - semi-minor-axis of the ellipsoid

Throws:

IllegalArgumentException

createEllipsoidFromSemiMinorAxis

public static Ellipsoid createEllipsoidFromSemiMinorAxis(Identifier identifier,
                                                         double semiMajorAxis,
                                                         double semiMinorAxis)
                                                  throws IllegalArgumentException

Creates a new Ellipsoid whose definition is based on semi-major axis and semi-minor axis and initializes common parameters such as a, b, e, e2, f, 1/f, e'2 and coefficients for the meridian arc.

Parameters:

identifier - ellipsoid identifier

semiMajorAxis - length of the semi-major axis in meters

semiMinorAxis - semi-minor-axis of the ellipsoid

Throws:

IllegalArgumentException

createEllipsoidFromEccentricity

public static Ellipsoid createEllipsoidFromEccentricity(double semiMajorAxis,
                                                        double eccentricity)
                                                 throws IllegalArgumentException

Creates a new Ellipsoid whose definition is based on semi-major axis and eccentricity and initializes common parameters such as a, b, e, e2, f, 1/f, e'2 and coefficients for the meridian arc.

Parameters:

semiMajorAxis - length of the semi-major axis in meters

eccentricity - semi-minor-axis of the ellipsoid

Throws:

IllegalArgumentException

createEllipsoidFromEccentricity

public static Ellipsoid createEllipsoidFromEccentricity(Identifier identifier,
                                                        double semiMajorAxis,
                                                        double eccentricity)
                                                 throws IllegalArgumentException

Creates a new Ellipsoid whose definition is based on semi-major axis and eccentricity and initializes common parameters such as a, b, e, e2, f, 1/f, e'2 and coefficients for the meridian arc.

Parameters:

identifier - ellipsoid identifier

semiMajorAxis - length of the semi-major axis in meters

eccentricity - semi-minor-axis of the ellipsoid

Throws:

IllegalArgumentException

initKCoeff

public void initKCoeff(int max)

This second method to compute the meridian arc length is taken from . It is based upon an iterative method and the precision of the result will depend on the number of iterations. It is to be used with arcFromLat or from latFromArc.

arcFromLat

public double arcFromLat(double phi)

Computes the meridian arc from equator to point with ellipsoidal latitude phi.

Parameters:

phi - the ellipsoidal latitude

Returns:

the meridian arc in meters

latFromArc

public double latFromArc(double s)
                  throws ArithmeticException

Computes the ellipsoidal latitude from meridian arc length.

Parameters:

s - the meridian arc length in meters

Returns:

the ellipsoidal latitude

Throws:

ArithmeticException

meridionalRadiusOfCurvature

public final double meridionalRadiusOfCurvature(double latitude)

The Meridional Radius of Curvature is the radius of curvature, at a specific latitude, of the ellipse used to generate the ellipsoid.

Parameters:

latitude - the geographic latitude

Returns:

the radius of curvature in meters

transverseRadiusOfCurvature

public final double transverseRadiusOfCurvature(double latitude)

The Transverse Radius of Curvature or radius of the first vertical section or prime vertical radius of curvature (fr : Grande Normale).

This is the radius of curvature in the plane which is normal to (i.e. perpendicular to) both the surface of the ellipsoid at, and the meridian passing through, the specific point of interest.

Parameters:

latitude - geographic latitude in radians

Returns:

a double value representing a length in meters

grandeNormale

public final double grandeNormale(double latitude)

isometricLatitude

public final double isometricLatitude(double latitude)

Computes isometric latitude from geographic (or geodetic) latitude.

Geographic latitude of a point P located on the surface of the ellipsoid is the angle between the perpendicular to the ellipsoid surface at P and the equatorial plan.

Isometric latitude is a function of geographic latitude L(lat) such as (lambda, L) is a symmetric parametric form of the ellipsoid surface.

Ref. IGN ALG0001

Parameters:

latitude - geographic latitude

Returns:

isometric latitude in radians

latitude

public final double latitude(double isoLatitude,
                             double epsilon)

Computes the geographic latitude from the isometric latitude (fr : calcul de la latitude géographique à partir de la latitude isometrique).

Geographic latitude of a point P located on the surface of the ellipsoid is the angle between the perpendicular to the ellipsoid surface at P and the equatorial plan.

Isometric latitude is a function of geographic latitude L(lat) such as (lambda, L) is a symmetric parametric form of the ellipsoid surface.

Geographic latitude is computed as the limit of a convergent suite. The loop is stopped when two consecutive terms of the suite is less than epsilon.

Ref. IGN ALG0002

Parameters:

isoLatitude - latitude isometrique

epsilon - value controlling the stop condition of this convergent sequence. Use 1E-10 for a precision of about 0.6 mm, 1E-11 for a precision of about 0.06 mm and 1E-12 for a preciison of about 0.006 mm

Returns:

the geographic latitude as a double

latitude

public final double latitude(double isoLatitude)

Computes geographic latitude from isometric latitude. The process stops as soon as the result reaches a pecision of 1.0E-11.

fr : Calcul la latitude géographique d'un point P à partir de sa latitude isométrique.

La latitude géographique est définie comme étant la limite d'une suite convergente. Le calcul de cette suite est interrompu lorsque la différence entre deux termes consécutifs est plus petit que 1E-11 (soit environ 0.006 mm).

Parameters:

isoLatitude - isometric latitude

Returns:

the geographic latitude in radians

curvilinearAbscissa

public double curvilinearAbscissa(double latitude)

Returns the curvilinear abscissa of the meridian arc for this latitude on an ellipsoid with eccentricity = this.e and semi-major axis = 1.0.

Usually noted beta, the meridian arc length is obtained by multiplying this result by the semi-major axis.

Parameters:

latitude - latitude.

Returns:

the curvilinear abscissa of this latitude on the meridian arc

toWKT

public String toWKT()

Returns a WKT representation of the ellipsoid.

toString

public String toString()

Return a string representtaion of this ellipsoid.

Overrides:

toString in class IdentifiableComponent

equals

public boolean equals(Object other)

Returns true if this Ellipsoid can be considered as equals to another one. Ellipsoid equals method is based on a comparison of the object dimensions with a sensibility of 0.1 mm.

Overrides:

equals in class IdentifiableComponent

Parameters:

other - the object to compare this Ellipsoid against

hashCode

public int hashCode()

Returns the hash code for this Ellipsoid.

Overrides:

hashCode in class IdentifiableComponent