Class Tilings

java.lang.Object
uk.ac.starlink.ttools.func.Tilings
public class Tilings extends Object
Pixel tiling functions for the celestial sphere.

The k parameter for the HEALPix functions is the HEALPix order, which can be in the range 0<=k<=29. This is the logarithm to base 2 of the HEALPix NSIDE parameter. At order k, there are 12*4^k pixels on the sphere.

Since:
6 Dec 2007
Author:
Mark Taylor
See Also:

  • Field Summary

    Fields
    Modifier and Type
    Field
    Description
    static final double
    SQDEG
    Solid angle in steradians corresponding to 1 square degree.

  • Method Summary

    Modifier and Type
    Method
    Description
    static int
    healpixK(double pixelsize)
    Gives the HEALPix resolution parameter suitable for a given pixel size.
    static long
    healpixNestIndex(int k, double lon, double lat)
    Gives the pixel index for a given sky position in the HEALPix NEST scheme.
    static double
    healpixNestLat(int k, long index)
    Returns the latitude of the approximate center of the tile with a given index in the HEALPix NEST scheme.
    static double
    healpixNestLon(int k, long index)
    Returns the longitude of the approximate center of the tile with a given index in the HEALPix NEST scheme.
    static long
    healpixNestToRing(int k, long nestIndex)
    Converts a healpix tile index from the NEST to the RING scheme at a given order.
    static double
    healpixResolution(int k)
    Gives the approximate resolution in degrees for a given HEALPix resolution parameter k This k value is the logarithm to base 2 of the Nside parameter.
    static long
    healpixRingIndex(int k, double lon, double lat)
    Gives the pixel index for a given sky position in the HEALPix RING scheme.
    static double
    healpixRingLat(int k, long index)
    Returns the latitude of the approximate center of the tile with a given index in the HEALPix RING scheme.
    static double
    healpixRingLon(int k, long index)
    Returns the longitude of the approximate center of the tile with a given index in the HEALPix RING scheme.
    static long
    healpixRingToNest(int k, long ringIndex)
    Converts a healpix tile index from the RING to the NEST scheme at a given order.
    static double
    healpixSqdeg(int k)
    Returns the solid angle in square degrees of each HEALPix pixel at a given order.
    static double
    healpixSteradians(int k)
    Returns the solid angle in steradians of each HEALPix pixel at a given order.
    static int
    htmLevel(double pixelsize)
    Gives the HTM level parameter suitable for a given pixel size.
    static double
    htmResolution(int level)
    Gives the approximate resolution in degrees for a given HTM depth level.
    static double
    sqdegToSteradians(double sqdeg)
    Converts a solid angle from square degrees to steradians.
    static double
    steradiansToSqdeg(double sr)
    Converts a solid angle from steradians to square degrees.

    Methods inherited from class Object

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

  • Field Details

    • SQDEG

      public static final double SQDEG
      Solid angle in steradians corresponding to 1 square degree.
      See Also:

  • Method Details

    • healpixNestIndex

      public static long healpixNestIndex(int k, double lon, double lat)
      Gives the pixel index for a given sky position in the HEALPix NEST scheme.
      Parameters:
      k - HEALPix order (0..29)
      lon - longitude in degrees
      lat - latitude in degrees
      Returns:
      pixel index
      See Also:

    • healpixRingIndex

      public static long healpixRingIndex(int k, double lon, double lat)
      Gives the pixel index for a given sky position in the HEALPix RING scheme.
      Parameters:
      k - HEALPix order (0..29)
      lon - longitude in degrees
      lat - latitude in degrees
      Returns:
      pixel index
      See Also:

    • healpixNestLon

      public static double healpixNestLon(int k, long index)
      Returns the longitude of the approximate center of the tile with a given index in the HEALPix NEST scheme.

      Note: the index parameter is 0-based, unlike the table row index special token $index (a.k.a. $0), which is 1-based. So if the HEALpix index is implicitly determined by the table row, the value $index-1 should be used.

      Parameters:
      k - HEALPix order (0..29)
      index - healpix index
      Returns:
      longitude in degrees
      See Also:

    • healpixNestLat

      public static double healpixNestLat(int k, long index)
      Returns the latitude of the approximate center of the tile with a given index in the HEALPix NEST scheme.

      Note: the index parameter is 0-based, unlike the table row index special token $index (a.k.a. $0), which is 1-based. So if the HEALpix index is implicitly determined by the table row, the value $index-1 should be used.

      Parameters:
      k - HEALPix order (0..29)
      index - healpix index
      Returns:
      latitude in degrees
      See Also:

    • healpixRingLon

      public static double healpixRingLon(int k, long index)
      Returns the longitude of the approximate center of the tile with a given index in the HEALPix RING scheme.

      Note: the index parameter is 0-based, unlike the table row index special token $index (a.k.a. $0), which is 1-based. So if the HEALpix index is implicitly determined by the table row, the value $index-1 should be used.

      Parameters:
      k - HEALPix order (0..29)
      index - healpix index
      Returns:
      longitude in degrees
      See Also:

    • healpixRingLat

      public static double healpixRingLat(int k, long index)
      Returns the latitude of the approximate center of the tile with a given index in the HEALPix RING scheme.

      Note: the index parameter is 0-based, unlike the table row index special token $index (a.k.a. $0), which is 1-based. So if the HEALpix index is implicitly determined by the table row, the value $index-1 should be used.

      Parameters:
      k - HEALPix order (0..29)
      index - healpix index
      Returns:
      latitude in degrees
      See Also:

    • healpixNestToRing

      public static long healpixNestToRing(int k, long nestIndex)
      Converts a healpix tile index from the NEST to the RING scheme at a given order.

      Note: the nestIndex parameter is 0-based, unlike the table row index special token $index (a.k.a. $0), which is 1-based. So if the HEALpix index is implicitly determined by the table row, the value $index-1 should be used.

      Parameters:
      k - HEALPix order (0..29)
      nestIndex - pixel index in NEST scheme
      Returns:
      pixel index in RING scheme
      See Also:

    • healpixRingToNest

      public static long healpixRingToNest(int k, long ringIndex)
      Converts a healpix tile index from the RING to the NEST scheme at a given order.

      Note: the ringIndex parameter is 0-based, unlike the table row index special token $index (a.k.a. $0), which is 1-based. So if the HEALpix index is implicitly determined by the table row, the value $index-1 should be used.

      Parameters:
      k - HEALPix order (0..29)
      ringIndex - pixel index in RING scheme
      Returns:
      pixel index in NEST scheme
      See Also:

    • healpixK

      public static int healpixK(double pixelsize)
      Gives the HEALPix resolution parameter suitable for a given pixel size. This k value (also variously known as order, level, depth) is the logarithm to base 2 of the Nside parameter.
      Parameters:
      pixelsize - pixel size in degrees
      Returns:
      HEALPix order k
      See Also:

    • healpixResolution

      public static double healpixResolution(int k)
      Gives the approximate resolution in degrees for a given HEALPix resolution parameter k This k value is the logarithm to base 2 of the Nside parameter.
      Parameters:
      k - HEALPix order (0..29)
      Returns:
      approximate angular resolution in degrees

    • healpixSteradians

      public static double healpixSteradians(int k)
      Returns the solid angle in steradians of each HEALPix pixel at a given order.
      Parameters:
      k - HEALPix order (0..29)
      Returns:
      pixel size in steradians
      Examples:
      healpixSteradians(5) = 0.0010226538585904274, 4*PI/healpixSteradians(0) = 12.0

    • healpixSqdeg

      public static double healpixSqdeg(int k)
      Returns the solid angle in square degrees of each HEALPix pixel at a given order.
      Parameters:
      k - HEALPix order (0..29)
      Returns:
      pixel size in steradians
      Examples:
      healpixSqdeg(5) = 3.357174580844667, round(12 * healpixSqdeg(0)) = 41253

    • steradiansToSqdeg

      public static double steradiansToSqdeg(double sr)
      Converts a solid angle from steradians to square degrees.

      The unit sphere is 4*PI steradians = 360*360/PI square degrees.

      Parameters:
      sr - quantity in steradians
      Returns:
      quantity in sqare degrees
      Examples:
      round(steradiansToSqdeg(4*PI)) = 41253

    • sqdegToSteradians

      public static double sqdegToSteradians(double sqdeg)
      Converts a solid angle from square degrees to steradians.

      The unit sphere is 4*PI steradians = 360*360/PI square degrees.

      Parameters:
      sqdeg - quantity in square degrees
      Returns:
      quantity in steradians
      Examples:
      round(sqdegToSteradians(41253)/PI) = 4

    • htmLevel

      public static int htmLevel(double pixelsize)
      Gives the HTM level parameter suitable for a given pixel size.
      Parameters:
      pixelsize - required resolution in degrees
      Returns:
      HTM level parameter

    • htmResolution

      public static double htmResolution(int level)
      Gives the approximate resolution in degrees for a given HTM depth level.
      Parameters:
      level - HTM depth
      Returns:
      approximate angular resolution in degrees

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