Ellipsoid (cts 1.5.2 API)

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

Nested Classes
Modifier and Type	Class and Description
`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

Fields
Modifier and Type	Field and Description
`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

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`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 o)` 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 o)
```
    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:
    
    o - the object to compare this Ellipsoid against
  - hashCode
```
public int hashCode()
```
    Returns the hash code for this Ellipsoid.
    
    Overrides:
    
    hashCode in class IdentifiableComponent

Class Ellipsoid

Note on the precision of some algorithms :

Nested Class Summary

Field Summary

Fields inherited from interface org.cts.Identifiable

Method Summary

Methods inherited from class org.cts.IdentifiableComponent

Methods inherited from class java.lang.Object

Field Detail

SPHERE

GRS80

WGS84

INTERNATIONAL1924

BESSEL1841

CLARKE1866

CLARKE1880IGN

CLARKE1880RGS

CLARKE1880ARC

KRASSOWSKI

EVERESTSS

GRS67

AustSA

AIRY

BESSNAM

HELMERT

AIRYMOD

WGS66

WGS72

ellipsoidFromName

Method Detail

getSemiMajorAxis

getInverseFlattening

getSemiMinorAxis

getFlattening

getEccentricity

getSquareEccentricity

getSecondEccentricitySquared

getArcCoeff

getKCoeff

createEllipsoidFromInverseFlattening

createEllipsoidFromInverseFlattening

createEllipsoidFromSemiMinorAxis

createEllipsoidFromSemiMinorAxis

createEllipsoidFromEccentricity

createEllipsoidFromEccentricity

initKCoeff

arcFromLat

latFromArc

meridionalRadiusOfCurvature

transverseRadiusOfCurvature

grandeNormale

isometricLatitude

latitude

latitude

curvilinearAbscissa

toWKT

toString

equals

hashCode