java.lang.Object
- gaiasky.util.coord.Coordinates

```
public class Coordinates
extends java.lang.Object
```
Provides utility coordinate conversions between some astronomical coordinate systems and to Cartesian coordinates. All angles are in radians.

Field Summary

Fields
Modifier and Type	Field	Description
`static double`	`OBLIQUITY_ARCSEC_J2000`	Obliquity of ecliptic in J2000 in arcsec
`static double`	`OBLIQUITY_DEG_J2000`	Obliquity for low precision calculations in degrees and radians.
`static double`	`OBLIQUITY_RAD_J2000`

Constructor Summary

Constructors
Constructor Description

Coordinates()

Method Summary

All Methods Static Methods Concrete Methods
Modifier and Type	Method	Description
`static Vector3d`	`cartesianToSpherical(Vector3d vec, Vector3d out)`	Converts from Cartesian coordinates to spherical coordinates.
`static Matrix4d`	`eclipticToEquatorial()`
`static Matrix4d`	`eclipticToEquatorial(double jd)`
`static Vector2d`	`eclipticToEquatorial(double lambda, double beta, Vector2d out)`	Transforms from ecliptic to equatorial coordinates
`static Vector2d`	`eclipticToEquatorial(Vector2d vec, Vector2d out)`	Transforms from ecliptic to equatorial coordinates
`static com.badlogic.gdx.math.Matrix4`	`eclipticToEquatorialF()`
`static Matrix4d`	`eclipticToGalactic()`
`static com.badlogic.gdx.math.Matrix4`	`eclipticToGalacticF()`
`static Matrix4d`	`eclToEq()`	Gets the rotation matrix to transform equatorial to the ecliptic coordinates.
`static Matrix4d`	`eclToEq(double julianDate)`	Gets the rotation matrix to transform from the ecliptic system to the equatorial system.
`static com.badlogic.gdx.math.Matrix4`	`eclToEqF()`
`static Matrix4d`	`eqToEcl()`	Gets the rotation matrix to transform from the ecliptic system to the equatorial system.
`static Matrix4d`	`eqToEcl(double julianDate)`	Gets the rotation matrix to transform equatorial to the ecliptic coordinates.
`static com.badlogic.gdx.math.Matrix4`	`eqToEclF()`
`static Matrix4d`	`eqToGal()`	Gets the rotation matrix to transform equatorial to galactic coordinates.
`static com.badlogic.gdx.math.Matrix4`	`eqToGalF()`
`static Matrix4d`	`equatorialToEcliptic()`
`static Matrix4d`	`equatorialToEcliptic(double jd)`
`static com.badlogic.gdx.math.Matrix4`	`equatorialToEclipticF()`
`static Matrix4d`	`equatorialToGalactic()`
`static com.badlogic.gdx.math.Matrix4`	`equatorialToGalacticF()`
`static Matrix4d`	`galacticToEcliptic()`
`static com.badlogic.gdx.math.Matrix4`	`galacticToEclipticF()`
`static Matrix4d`	`galacticToEquatorial()`
`static com.badlogic.gdx.math.Matrix4`	`galacticToEquatorialF()`
`static Matrix4d`	`galToEq()`	Gets the rotation matrix to transform from the galactic system to the equatorial system.
`static com.badlogic.gdx.math.Matrix4`	`galToEqF()`
`static Matrix4d`	`getRotationMatrix(double alpha, double beta, double gamma)`	Gets the rotation matrix to apply for the given Euler angles α, β and γ.
`static Matrix4d`	`getTransformD(java.lang.String name)`
`static com.badlogic.gdx.math.Matrix4`	`getTransformF(java.lang.String name)`
`static Vector3d`	`sphericalToCartesian(double longitude, double latitude, double radius, Vector3d out)`	Converts from spherical to Cartesian coordinates, given a longitude (α), a latitude (δ) and the radius.
`static Vector3d`	`sphericalToCartesian(Vector3d vec, Vector3d out)`	Converts from spherical to Cartesian coordinates, given a longitude (α), a latitude (δ) and the radius.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Field Detail
  - OBLIQUITY_DEG_J2000
```
public static final double OBLIQUITY_DEG_J2000
```
    Obliquity for low precision calculations in degrees and radians. J2000 with T=0
    
    See Also:
    
    Constant Field Values
  - OBLIQUITY_RAD_J2000
```
public static final double OBLIQUITY_RAD_J2000
```
  - OBLIQUITY_ARCSEC_J2000
```
public static final double OBLIQUITY_ARCSEC_J2000
```
    Obliquity of ecliptic in J2000 in arcsec
    
    See Also:
    
    Constant Field Values
- Constructor Detail
  - Coordinates
```
public Coordinates()
```
- Method Detail
  - getRotationMatrix
```
public static Matrix4d getRotationMatrix(double alpha,
                                         double beta,
                                         double gamma)
```
    Gets the rotation matrix to apply for the given Euler angles α, β and γ. It applies Ry(γ)*Rz(β)*Ry(α), so that it rotates the fixed xyz system to make it coincide with the XYZ, where α is the angle between the axis z and the line of nodes N, β is the angle between the y axis and the Y axis, and γ is the angle between the Z axis and the line of nodes N.
    The assumed reference system is as follows:
    
    ZX is the fundamental plane.
    
    Z points to the origin of the reference plane (the line of nodes N).
    
    Y points upwards.
    Parameters:
    
    alpha - The α angle in degrees, between z and N.
    
    beta - The β angle in degrees, between y and Y.
    
    gamma - The γ angle in degrees, Z and N.
    
    Returns:
    
    The rotation matrix.
  - eclToEq
```
public static Matrix4d eclToEq()
```
    Gets the rotation matrix to transform equatorial to the ecliptic coordinates. Since the zero point in both systems is the same (the vernal equinox, γ, defined as the intersection between the equator and the ecliptic), α and γ are zero. β, the angle between the up directions of both systems, is precisely the obliquity of the ecliptic, ε. So we have the Euler angles α=0°, β=ε;, γ=0°.
    
    Returns:
    
    The matrix to transform from equatorial coordinates to ecliptic coordinates.
  - eclipticToEquatorial
```
public static Matrix4d eclipticToEquatorial()
```
  - eclToEqF
```
public static com.badlogic.gdx.math.Matrix4 eclToEqF()
```
  - eclipticToEquatorialF
```
public static com.badlogic.gdx.math.Matrix4 eclipticToEquatorialF()
```
  - eclToEq
```
public static Matrix4d eclToEq(double julianDate)
```
    Gets the rotation matrix to transform from the ecliptic system to the equatorial system. See equatorialToEcliptic() for more information, for this is the inverse transformation.
    
    Returns:
    
    The transformation matrix.
  - eclipticToEquatorial
```
public static Matrix4d eclipticToEquatorial(double jd)
```
  - eqToEcl
```
public static Matrix4d eqToEcl()
```
    Gets the rotation matrix to transform from the ecliptic system to the equatorial system. See eclToEq() for more information, for this is the inverse transformation.
    
    Returns:
    
    The transformation matrix.
  - equatorialToEcliptic
```
public static Matrix4d equatorialToEcliptic()
```
  - eqToEclF
```
public static com.badlogic.gdx.math.Matrix4 eqToEclF()
```
  - equatorialToEclipticF
```
public static com.badlogic.gdx.math.Matrix4 equatorialToEclipticF()
```
  - eqToEcl
```
public static Matrix4d eqToEcl(double julianDate)
```
    Gets the rotation matrix to transform equatorial to the ecliptic coordinates. Since the zero point in both systems is the same (the vernal equinox, γ, defined as the intersection between the equator and the ecliptic), α and γ are zero. β, the angle between the up directions of both systems, is precisely the obliquity of the ecliptic, ε. So we have the Euler angles α=0°, β=ε;, γ=0°.
    
    Returns:
    
    The matrix to transform from equatorial coordinates to ecliptic coordinates.
  - equatorialToEcliptic
```
public static Matrix4d equatorialToEcliptic(double jd)
```
  - galToEq
```
public static Matrix4d galToEq()
```
    Gets the rotation matrix to transform from the galactic system to the equatorial system. See galToEq() for more information, since this is the inverse transformation. Use this matrix if you need to convert equatorial cartesian coordinates to galactic cartesian coordinates.
    
    Returns:
    
    The transformation matrix.
  - galacticToEquatorial
```
public static Matrix4d galacticToEquatorial()
```
  - galToEqF
```
public static com.badlogic.gdx.math.Matrix4 galToEqF()
```
  - galacticToEquatorialF
```
public static com.badlogic.gdx.math.Matrix4 galacticToEquatorialF()
```
  - eqToGal
```
public static Matrix4d eqToGal()
```
    Gets the rotation matrix to transform equatorial to galactic coordinates. The inclination of the galactic equator to the celestial equator is 62.9°. The intersection, or node line, of the two equators is at RA=282.25° DEC=0° and l=33° b=0°. So we have the Euler angles α=-33°, β=62.9°, γ=282.25°.
    
    Returns:
    
    The transformation matrix.
  - equatorialToGalactic
```
public static Matrix4d equatorialToGalactic()
```
  - eqToGalF
```
public static com.badlogic.gdx.math.Matrix4 eqToGalF()
```
  - equatorialToGalacticF
```
public static com.badlogic.gdx.math.Matrix4 equatorialToGalacticF()
```
  - eclipticToEquatorial
```
public static Vector2d eclipticToEquatorial(Vector2d vec,
                                            Vector2d out)
```
    Transforms from ecliptic to equatorial coordinates
    
    Parameters:
    
    vec - Vector with ecliptic longitude (λ) and ecliptic latitude (β) in radians.
    
    out - The output vector.
    
    Returns:
    
    The output vector with ra (α) and dec (δ) in radians, for chaining.
  - eclipticToEquatorial
```
public static Vector2d eclipticToEquatorial(double lambda,
                                            double beta,
                                            Vector2d out)
```
    Transforms from ecliptic to equatorial coordinates
    
    Parameters:
    
    lambda - Ecliptic longitude (λ) in radians.
    
    beta - Ecliptic latitude (β) in radians.
    
    out - The output vector.
    
    Returns:
    
    The output vector with ra (α) and dec (δ) in radians, for chaining.
  - eclipticToGalactic
```
public static Matrix4d eclipticToGalactic()
```
  - eclipticToGalacticF
```
public static com.badlogic.gdx.math.Matrix4 eclipticToGalacticF()
```
  - galacticToEcliptic
```
public static Matrix4d galacticToEcliptic()
```
  - galacticToEclipticF
```
public static com.badlogic.gdx.math.Matrix4 galacticToEclipticF()
```
  - sphericalToCartesian
```
public static Vector3d sphericalToCartesian(Vector3d vec,
                                            Vector3d out)
```
    Converts from spherical to Cartesian coordinates, given a longitude (α), a latitude (δ) and the radius. The result is in the XYZ space, where ZX is the fundamental plane, with Z pointing to the the origin of coordinates (equinox) and Y pointing to the north pole.
    Parameters:
    
    vec - Vector containing the spherical coordinates.
    
    The longitude or right ascension (α), from the Z direction to the X direction, in radians.
    
    The latitude or declination (δ), in radians.
    
    The radius or distance to the point.
    
    out - The output vector.
    
    Returns:
    
    Output vector in Cartesian coordinates where x and z are on the horizontal plane and y is in the up direction.
  - sphericalToCartesian
```
public static Vector3d sphericalToCartesian(double longitude,
                                            double latitude,
                                            double radius,
                                            Vector3d out)
```
    Converts from spherical to Cartesian coordinates, given a longitude (α), a latitude (δ) and the radius.
    
    Parameters:
    
    longitude - The longitude or right ascension angle, from the z direction to the x direction, in radians.
    
    latitude - The latitude or declination, in radians.
    
    radius - The radius or distance to the point.
    
    out - The output vector.
    
    Returns:
    
    Output vector with the Cartesian coordinates[x, y, z] where x and z are on the horizontal plane and y is in the up direction, for chaining.
  - cartesianToSpherical
```
public static Vector3d cartesianToSpherical(Vector3d vec,
                                            Vector3d out)
```
    Converts from Cartesian coordinates to spherical coordinates.
    Parameters:
    
    vec - Vector with the Cartesian coordinates[x, y, z] where x and z are on the horizontal plane and y is in the up direction.
    
    out - Output vector.
    
    Returns:
    
    Output vector containing the spherical coordinates.
    
    The longitude or right ascension (α), from the z direction to the x direction.
    
    The latitude or declination (δ).
    
    The radius or distance to the point.
  - getTransformD
```
public static Matrix4d getTransformD(java.lang.String name)
```
  - getTransformF
```
public static com.badlogic.gdx.math.Matrix4 getTransformF(java.lang.String name)
```

Class Coordinates

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

OBLIQUITY_DEG_J2000

OBLIQUITY_RAD_J2000

OBLIQUITY_ARCSEC_J2000

Constructor Detail

Coordinates

Method Detail

getRotationMatrix

eclToEq

eclipticToEquatorial

eclToEqF

eclipticToEquatorialF

eclToEq

eclipticToEquatorial

eqToEcl

equatorialToEcliptic

eqToEclF

equatorialToEclipticF

eqToEcl

equatorialToEcliptic

galToEq

galacticToEquatorial

galToEqF

galacticToEquatorialF

eqToGal

equatorialToGalactic

eqToGalF

equatorialToGalacticF

eclipticToEquatorial

eclipticToEquatorial

eclipticToGalactic

eclipticToGalacticF

galacticToEcliptic

galacticToEclipticF

sphericalToCartesian

sphericalToCartesian

cartesianToSpherical

getTransformD

getTransformF